Mathematical Manipulation with Summation Notation: Techniques and Strategies

Summation notation is a helpful tool used to represent and denote the sum of a sequence of terms. Summation notation is often denoted by the Greek letter sigma (∑). It works as a bridge between sequence and series, allowing us to efficiently describe the accumulation of values in a compact and comprehensible manner.

Calculus, number theory, statistics, and physics are just a few of the areas of mathematics where summation notation is useful. It enables mathematicians and scientists to evaluate and resolve complicated issues more quickly. Also, it is used to simply convey complex mathematical notions.

In this article, we will discuss the topic of summation with the help of the concept and representation of summation notation. You’ll learn the writing method of summation notation and different rules used for solving summation notation with examples.

Summation Notation and Its Representation

The basic structure of summation notation consists of the sigma symbol (Σ) followed by an expression that defines the terms to be summed. This expression typically involves an index variable that takes on different values as it progresses through the sequence.

The index variable is accompanied by a lower limit that specifies the starting point of the summation and an upper limit that signifies the ending point. The general form of summation notation can be expressed as follows:

summation notation symbol

Writing Long Sum in Sigma Notation: Different way

If given the long term of sequence and we want to represent it in single notation or sigma notation. How do we achieve this?

We’ll discuss this with the help of two ways:

Let’s suppose the sum of

1+ 2+ 3+ 4+ 5 and 6

To write them in summation notation using k as the i-th term notice the following:

  • There are six (6) terms to be summed
  • The operation is summation

Therefore, we should rewrite as follow:

summation example 1

Above is a sequence of numbers summed together. Assuming we have the following numbers to add:

1+ 4+ 9+ 16+ 25+36+ 49

How do we use the summation notation on the above?

  • Notice that the above terms are in the square form.
  • We can thus write them in summation notation with the help of k2. Meaning that the k-th item is squared.
  • There is a total of 7 terms (n = 7) in all which each should be squared
  • The first item is 1, thus k = 1.

This implies that we have the following:

Mathematical Manipulation with Summation Notation: Techniques and Strategies 1

Summation Notation: Rules

Summation notation, represented by the Greek letter sigma (Σ), comes with several rules and properties that help streamline its usage and facilitate calculations involving sequences and series. These rules guide manipulating and evaluating expressions written in summation notation.

Here are some key rules to keep in mind when working with summation notation:

Index range and limits:

  • The lower limit of the index indicates the starting value of the index variable.
  • The upper limit of the index specifies the final value that the index variable takes.
  • The summation is performed over all values of the index within the specified range.

Constant factors:

A constant factor outside the summation symbol can be brought inside the summation and multiplied with each term.

Linearity property:

The summation of the sum of two or more sequences is equal to the sum of the individual summations.

 In mathematical terms:

∑ (ai+ bi) = ∑ai +∑bi

Changing the index:

It is possible to change the index variable without affecting the value of the summation, as long as the new index variable follows the same pattern as the old one.

Arithmetic progressions:

If the sequence being summed is an arithmetic progression, the sum can be expressed using formulas that involve the number of terms, the first term, and the common difference.

Geometric progressions:

For geometric progressions, the sum of the first (n) terms can be computed using a formula involving the first term, the common ratio, and the number of terms.

Reversing the order:

The order of the terms in a summation can be reversed without affecting the value of the sum.

Combining Summations:

Summations with the same index can be combined into a single summation, as long as the range remains consistent.

Special series:

Special series, such as arithmetic series, geometric series, and power series, have specific formulas for their sums that can be used to simplify calculations.

Convergence and divergence:

In infinite series, understanding the convergence or divergence of the series is crucial. To assess whether an infinite series diverges to infinity or converges to a finite value, many criteria and tests can be utilized.

How to Expand Summation Notation?

Expanding summation notation requires understanding the range of the index of summation and the general term of the series. Here is a step-by-step guide on how to expand summation notation:

  • Identify the index of summation and its range: The index of summation is the variable used in the summation, and its range is given by the limits of the summation, typically written below and above the sigma (Σ) symbol.
  • Write out the general term: The general term is the expression that contains the index of summation and shows how each term in the series is calculated.
  • Substitute the values of the index: Substitute the values within the range of the index of summation into the general term, and write out each term of the series.
  • Simplify if necessary: Simplify each term of the series if possible.
  • Add up the terms: If required, add up the terms to find the sum of the series.

You can try a summation notation calculator to expand the summation notation. Here is an example to understand how to expand summation manually.


Evaluate the given sum

Mathematical Manipulation with Summation Notation: Techniques and Strategies 2


We simplify the given summation by putting the value of n one by one in the given equation.

So, the value of n starts with 1 and ends with 4.

We find the required solution step-by-step simplification.

Step 1:

Given equation is

 3x2 + 4(x) + 1                                                  

Put value of x from 1 to 4

Put the value of x = 1

3(1)2 +4 (1) +1 = 8

Step 2: For x = 2

3(2)2 + 4(2) +1

3(4) + 8 + 1= 12 + 9 = 21

Step 3:

For x = 3

3(3)2 +4(3) +1

3(9) +12+1= 27+13 = 30

Step 4:

For x = 4

3(4)2 + 4(4) +1

3(16) +16+1= 48+17 = 65

Step 5:

Put all step answers in equation 1.

4n=1(3x2 + 4(x) + 1) = 8 + 21 + 30 + 65 = 124


Summation notation is a useful tool used in calculus, statistics, and physics. This article discussed the concept with the help of examples, including the basic principles.

Summation notation, though simple, it’s usually confusing for students to comprehend. I believe that this article would help you understand and apply the concept.

In case you still have questions, kindly share them with us using the comment box below.


Question number 1:

How can I assess a summary?


Evaluating a summation involves substituting values of the index variable into the expression and adding up the resulting terms. Techniques like finding arithmetic or geometric series formulas, telescoping sums, and using mathematical properties can simplify evaluations.

Question number 2:

How does summation notation relate to calculus?


 Summation notation forms the foundation for understanding integration, as integration involves summing infinitesimal quantities to find total quantities. The concept of limits in calculus is closely tied to the idea of an infinite summation.

Question number 3:

What is the significance of summation notation in computer science?


Summation notation is essential for analyzing the efficiency of algorithms and data structures. It’s used to analyze time complexity, count operations, and express the cost of iterative processes.

Demystifying the Fundamentals of the Rule of Law in Government

Rule of Law is the absolute supremacy or predominance of the law over everybody – both rulers and the ruled and all decisions taken in a country.

According to professor A.V. Dicey (a Briton), a professor of English law who developed and popularized the phrase “Rule of Law” in his book titled “Introduction to the Law of the Constitution” published in 1885, “those entrusted with the administration of a country should rule or exercise their authority in accordance with the established law of the land and such established law should be regarded as supreme”.

The phrase has other phrases like “that no citizen can be punished except as prescribed by the law; which means that no one can be punished without trial and that the law must be known to all citizens. In other words, the rule of law emphasizes the supremacy of the law over individuals and government, it guarantees peoples liberty and equality of all individuals before the laws of the land.

The major aim of the rule of law is to ensure that the government rules in accordance with the laws of the land.

The Main Principles and Features of the Rule of Law

Supremacy of the law:

It means that the law of a state is supreme or higher than anybody in the state. A citizen is deemed innocent until proven guilty by the law court. Anybody who is arbitrarily arrested and detained for more than twenty-four hours can apply to the law court for a writ of habeas corpus.

Equality before the Law:

It means that nobody is above the law. The law is no respecter of persons irrespective of their position. In Dicey’s view, all men are equal before the laws of the land. All citizens of a country should enjoy equal access to law facilities, equal rights to fair hearings, and legal advice in the court of law. This principle assumes the notion of legality, which means due process of law in dealing with offenders.

The Rights of the individual:

This principle states that citizens of a country should enjoy certain basic inalienable rights and liberties under the law, violation of which they have the right to seek redress in a law court that has the exclusive jurisdiction to handle such cases according to the constitution. The UN 1948 Universal Declaration of Human Rights is a good basis on which the protection of citizens’ rights is hinged.

More Features of the Rule of Law

Access to legal facilities is a fundamental aspect of the rule of law. It means that individuals should have the means and opportunity to seek legal remedies and redress in a fair and efficient manner. This includes access to courts, legal representation, and other legal resources. Without such access, the rule of law cannot be upheld, as individuals would be unable to assert their rights, seek justice, or challenge actions by the government or other entities that may infringe upon their rights.

Rule of law - lawyers posing for a photo
Photo by August de Richelieu on

Provision of the constitution

The rule of law emphasizes that a nation’s legal framework must be based on a written constitution that outlines the fundamental principles, structure of government, and protection of individual rights. The constitution acts as a supreme law that both citizens and government institutions must adhere to. It sets the rules and limits for the exercise of state power and ensures that government actions are consistent with the law. A well-defined constitution is crucial for ensuring that the government operates within the bounds of the law and respects individual liberties.

Fair hearing

The principle of a fair hearing is a crucial component of the rule of law. It entails that every individual is entitled to a fair and impartial process when their rights or interests are at stake. This means that individuals must be given the opportunity to present their case, confront evidence and witnesses against them, and have the proceedings conducted by an unbiased and independent tribunal. The right to a fair hearing ensures that justice is dispensed in a just and equitable manner, and it is essential for upholding the rule of law and protecting individual rights.

The law should be made public

Transparency and accessibility of the law are essential to the rule of law. It implies that laws and regulations should be made available to the public, and their application should be predictable and consistent. Citizens should be aware of the laws that govern them, and the legal system should not operate in secrecy. Publicly accessible laws promote accountability, enable citizens to know and exercise their rights and prevent arbitrary or discriminatory use of legal powers. It also ensures that individuals are not subjected to “secret laws” or unpredictable legal consequences.

Problems of Application of the Rule of Law

The rule of law has maximum liberty for all the individuals in society. However, the effect of the rule of law is frustrated by the following:

Immunity provision:

Certain categories of public office holders like the president, diplomats, judges, legislatures, etc. may not be sued in the law court while the tenure of their respective offices lasts. In international law, foreign diplomats are not tried under the laws of their host countries.

Customs and traditions:

The practice of some people in terms of customs and traditions may hinder the full enjoyment of peoples’ rights. This limits the working of the rule of law.

Delegated legislation:

The delegation of law-making power to some bodies other than the legislature often brings about the complexity of law and abuse of such power which may lead to the violation of fundamental human rights of the citizens even without the opportunity of seeking redress.

Administrative tribunals:

This are quasi judiciary which may not give room for fair judgment, fair hearing, protection of human rights, and the right to exercise appeal against erroneous judgment due to the fact that tribunals are not legal courts the members may not have full legal knowledge

Illiteracy, ignorance, and abject poverty:

Where there is a high level of illiteracy many will be ignorant of their rights or how to get redress when such rights are violated. The cost of litigation also discourages poverty-ridden citizens from pursuing justice.

Factors that Can Significantly Aid the Operation of the Rule of Law

Independent judiciary

 An independent judiciary is a cornerstone of the rule of law. It means that the judiciary is free from political influence, interference, or manipulation. The judges are impartial and make decisions based on the law and evidence, not on the instructions of the government or other powerful interests. This independence ensures that the judiciary can serve as a check on the other branches of government, safeguard individual rights, and provide a fair and unbiased interpretation and application of the law.

Press freedom

Press freedom is vital for the rule of law because it ensures that information is disseminated without censorship or undue government control. A free press can hold the government and other powerful entities accountable by investigating and reporting on issues of public interest. This transparency and accountability help prevent abuse of power, corruption, and violations of the law. It also allows citizens to stay informed and engaged, which is essential for a functioning democracy and the rule of law.

The law to be kept open

Keeping the law open means that laws and regulations should be easily accessible and understandable to the general public. This promotes transparency, accountability, and adherence to the rule of law. When the law is clear and accessible, individuals can know their rights and responsibilities, and they can hold the government accountable for following the law. Open laws prevent arbitrary or discriminatory enforcement, as everyone can understand and follow the legal framework.

Quick dispensation of justice

Swift and efficient justice is crucial for upholding the rule of law. Delays in legal proceedings can undermine the rule of law because justice delayed is often perceived as justice denied. Quick dispensation of justice ensures that disputes are resolved in a timely manner, preventing prolonged uncertainty and potential injustices. It also deters potential wrongdoers, as they know that they will face legal consequences without undue delay.

Period of detention

The period of detention refers to the duration for which an individual can be held in custody without trial or formal charges. Limiting the period of detention is important for upholding the rule of law and protecting individual rights. Excessive or indefinite detention without due process can violate the principle of a fair hearing and the presumption of innocence. The rule of law requires that individuals are promptly informed of the charges against them, provided with a fair trial, and not subjected to arbitrary or extended detention.


The principles are integral to the concept of the rule of law. They ensure that legal systems are just, predictable, and accessible and that individuals have the means to seek legal remedies and protect their rights. The rule of law is a foundational principle for maintaining a just and democratic society, where the government is accountable and individual rights are safeguarded.

Finally, a well-functioning rule of law needs to be enhanced. Thus, independent judiciary, press freedom, open laws, quick dispensation of justice, and limitations on the period of detention all contribute to a just and accountable legal system that respects individual rights and ensures the fair and equal application of the law.


  1. What are the limitations to the application of the Rule of Law?
  2. Discuss the factors that can ensure or aid the successful operation of the Rule of Law
  3. What do you understand by freedom of the press with respect to the operation of the rule of law?
  4. The principle of fair hearing implies that every person is entitled to a fair and impartial process when their rights or interests are at stake. Discuss.

Generations of Computer: 6th and 7th

Over time, there have been notable breakthroughs made in the field of computer processors, enabling quicker and more effective computing.

The idea of generations of computer offers a framework for comprehending the gradual advancement of computing technology over time.

Each generation, from the 1st generation’s vacuum tubes to the 13th generation’s U-series mobile processors, has resulted in considerable improvements in processing power, storage capacity, networking, and user experience.

We have covered the 1st to 5th generations of computer earlier. In this article, we shall explore each of the 6th and 7th generations of computer with real-world examples and how they affect many facets of our life.

Generations of Computer

Earlier, we discussed how the fifth-generation computers were the era of artificial intelligence (AI) and quantum computing. We also discussed that it brought about the era of parallel processing and computing technology which are not clearly defined.

After the 5th generation, advancement in technology has led to the invention of highly capacitated machines, especially in the area of microprocessors. As a result, we can differentiate between these 6th and 9th generations of computer.

Let’s look at how these machines differ from one another in the next sections.

6th Generation of computer – semiconductors

The sixth generation of computers represents the pinnacle of computer development. In terms of size, speed, and the jobs it can complete, it differs from previous generations of computer.

Intelligent computers based on artificial intelligence or artificial brains are the term used to describe the sixth generation of computers. The raw ingredient for its processors is semiconductors.

Due to Ultra-reliable low latency communication (URLLC) technology, which allowed microprocessor chips with up to ten million pieces, the sixth generation of computers claimed higher speeds, more power, and increased efficiency.

Period of invention

The 6th generation processors were invented between the periods of late 1990s till early 2000s. The periods vary depending on the advancement made on each processor.


There was a substantial boost in the processing capacity of 6th-generation computers. Using advanced integrated circuits, these computers could perform calculations and execute tasks at significantly faster rates compared to previous generations. The clock speeds of central processing units (CPUs) increased, up to 3.8 GHz leading to improved overall performance.

Key features

The following are the notable features of the 6th generations of computer, and how to identify them.

Microprocessors: The introduction of microprocessors revolutionized the 6th generation computers. These computers have a key feature called Ultra-reliable Extremely Low Quiescence Dispatches (URLLC) that makes data transport faster and more effective. Integrated circuits combined multiple electronic components onto a single chip, enabling faster processing and reduced power consumption.

Increased memory capacity: The memory capacity of computers in the sixth generation has increased. Larger amounts of data can now be stored and retrieved because of the increased capacity of storage devices like solid-state drives and hard disk drives.

Semiconductors: The sixth generation of CPUs make use of semiconductors. The latest 3D transistor technology and other improvements that boost performance and efficiency were incorporated into the 6th Gen Intel Core and Intel Xeon processors from the ground up. High clock speeds, improved instruction sets, cutting-edge semiconductor technology, and expanded multimedia capabilities are some of its features.

6th generation - semiconductors

Graphical User Interface (GUI): GUI became more common in computers of the sixth generation, improving user-interface interaction. GUIs made use of windows, menus, and icons to improve user experience and make navigating easier.

Networking capabilities: Users were able to link their computers to local area networks (LANs) and eventually the internet; thanks to the 6th generation PCs’ broad use of networking. Communication, data sharing, and access to internet resources have all been changed by connection.

Examples of Computers:

During the 6th generation, a number of important computers were developed, including:

IBM ThinkPad: Since its 1992 release, the line of excellent laptops known as the IBM ThinkPad series has enjoyed tremendous success. These devices were renowned for their dependable operation, sturdy construction, and cutting-edge functionality.

generations of computer - 6th gen IBM thinkpad

Dell Dimension: During the sixth generation of personal computers, Dell Dimension desktop PCs, which were first introduced in the late 1990s, were quite popular. They provided a harmony of price, performance, and expandability.

Dell dimension - 6th generation

Apple iMac G3: The eye-catching iMac G3, which was introduced in 1998, helped Apple re-enter the mainstream. It had a modern appearance, a compact form factor, and an easy-to-use user interface.

generations of computer - 6th gen

Impact on everyday life and business

Home computing: It made personal computing available to a wider audience. People could buy and own desktops /laptops for personal use. This enabled the performance of tasks such as word processing, web browsing, multimedia playback, and gaming.

Use of the Internet: The spread of the Internet during this era transformed communication and access to information. The 6th generation of computers enabled online activities such as emailing, web browsing, online shopping, and research.

Basic business applications: This generation of computer enhanced business operations in different organizations. Businesses could efficiently run complex software applications, manage large databases, and streamline business operations.

Multimedia and entertainment: The 6th generation computers brought about the creation and consumption of multimedia. Users could enjoy interactive multimedia content.

In summary, the 6th generation of computers, introduced semiconductors, compact designs, and increased processing power. We had computers that were smaller, faster, and more user-friendly. They made life easy at home and in offices, enabling the use of Internet, business applications, and multimedia. Notable examples include the IBM ThinkPad, Dell Dimension, and Apple iMac G3.

7th Generation of computer – advanced semiconductor

Advanced semiconductor technology was used in the design of the 7th generation of computer processors. Compared to its predecessors, it offers faster clock speeds, more energy-efficient operation, and better graphics processing.

The seventh generation of computers delivers better performance and productivity along with more effective online usage. The utilization of slimmer and lighter devices, LCD flat panels, and access to UHD 4K video are also features of the seventh generation of computers.

intel 7th generation processors

Performance and power efficiency were significantly improved with the 7th-generation processors. These CPUs, also known as Kaby Lake, have increased clock rates, improved integrated graphics, and compatibility with cutting-edge technologies including Thunderbolt 3 and USB-C.

They were constructed using a 14nm manufacturing technology. The Intel Celeron G3930TE, Core i3-7101TE, Core i5-7500T, and i7-7700T are examples of 7th-generation processors. They outperformed their predecessors significantly.

Period of invention

The seventh generation of computers first appeared in the late 2010s and has since developed and improved. The development of these potent computing systems has been aided by improvements in essential technologies and the introduction of new architectures.


Depending on their use and application, computers of the seventh generation can have a wide range of sizes. They range from small, lightweight gadgets like high-performance laptops and tablets to bigger, more complex systems like server clusters and supercomputers. These computers’ sizes are frequently designed to strike a compromise between performance and usability.


The high processing speed of 7th-generation computers is well known. They include cutting-edge multi-core processors, fast memory, and effective data transfer technologies. They can handle large datasets and intricate calculations in real time because to these technologies. These computers process billions or even trillions of calculations per second, or gigaflops or teraflops, respectively.

Key features

Advanced processors: 7th generation computers use potent processors built on cutting-edge architectures, like multi-core CPUs and GPUs (Graphics Processing Units). These processors are capable of parallel processing, which enables them to carry out several tasks at once and boost system performance.

Large amounts of high-speed memory, such as DDR3L or DDR4 RAM (Random Access Memory), are present in these systems. These memory units allow for rapid data retrieval and manipulation. For effective data access, they may also include quick solid-state drives (SSDs) or incredibly quick NVMe (Non-Volatile Memory Express) storage.

Connectivity: To enable smooth data transfer and networking, 7th generation PCs come with cutting-edge connectivity choices. They often support wireless technologies like Wi-Fi 6 or Wi-Fi 6E in addition to high-speed wired connections like Ethernet and Thunderbolt, enabling quick and dependable communication between devices.

Cutting-edge graphics: Thanks to dedicated GPUs or integrated graphics processors, these PCs frequently have cutting-edge graphics capabilities. Because of this, they can easily perform graphically demanding jobs like gaming, multimedia editing, and virtual reality applications.

Examples of computers

High-end desktop workstations, gaming PCs, supercomputers, server clusters, and even some mobile devices like potent laptops or tablets are some examples. The Dell Precision line, HP Z Workstations, Apple iMac Pro, and NVIDIA DGX computers are a few famous examples.

generations of computer - 7th generation

Impact on life and business

Scientific research: By enabling sophisticated simulations, data modeling, and analysis, 7th generation computers are essential to scientific research. They handle enormous volumes of data and execute complex simulations in disciplines like physics, chemistry, biology, and climate science, assisting in ground-breaking discoveries and developments.

Applications of artificial intelligence (AI) mainly rely on the processing capacity of 7th generation computers. They can do real-time picture and speech recognition, natural language processing, and autonomous decision-making. In addition, they help in training and deploying complex machine-learning models. Applications for these characteristics can be found in fields including robots, virtual assistants, and intelligent systems.

Big data analytics: 7th generation computers are highly suited for large data analysis due to their enormous processing and memory capacities. Large datasets may be processed and analyzed quickly, revealing insightful information and patterns that help businesses make data-driven choices, streamline processes, and enhance customer experiences.

High-performance computing (HPC): Environments for high-performance computing frequently make use of 7th generation machines. In disciplines including computational fluid dynamics, financial modeling, genome sequencing, and weather prediction, they are capable of handling challenging computer jobs. These technologies enable researchers to tackle issues of unprecedented magnitude and complexity using supercomputers.


The computing power and capabilities of the 6th and 7th generations of computer represent a major improvement. These cutting-edge solutions enable people, businesses, and sectors to take on difficult problems and open up fresh opportunities in a variety of fields.

With the key features of each generation, you can easily identify which computer belongs to each generation. Next, we’re going to explore the 8th and 9th generations. Stay glued to this site by subscribing to our newsletters.

Before I go, what do you have to say? What generation is your laptop or desktop computer? How would you identify the generation of your next computer system?

The comment box below is open for you.

Proportionality: What is Proportion of Two Numbers?

We use proportions to compare two numbers. For example, if the proportion of two numbers is increasing or decreasing in the same ratio, it is a direct proportionality.

Proportionality or proportion of two numbers is therefore a technique of comparing two numbers in order. The proportion calculator can be used to solve such equations.

The proportionality is denoted by the symbol “::” or by the  “=”. The proportionality number is used to represent the equality or the relation of the two quantities.

We have heard the word proportionality when we are solving various problems in math. The ratio or the proportionality are the alternatives to each other. Solving proportions can be an uphill task if you cannot identify the direct and indirect proportionality.

In the following article, we are discussing the use of proportionality and ratio in various applications. We shall solve the direct and indirect proportionality of two quantities.

The proportion calculator can be of aid, especially, when computing direct proportions. In the end, you will learn how to solve the proportions of the direct and the indirect quantities.

What is Proportion of two numbers?

Proportion can be defined as the ratio or comparative relationship between two numbers. When two sets of numbers are increasing or decreasing in the same ratio, we call it a direct proportion. Inversely, when one set is increasing and another is decreasing, we call it indirect proportion.

It is sometimes difficult to calculate the proportionality of two quantities manually. But through the help of the proportions calculator by it can be simplified.

The proportions calculator makes it simple to identify the direct or indirect relationship between the two quantities. Proportionality can be applied in various situations. Let’s take a look at the different scenarios.

Direct proportionality

If two quantities, X and Y are increasing or decreasing together, it is called direct proportion.

Symbolically, we can say that: X = Y

For example, in a production environment, it takes more raw materials to produce more quantities and vice versa. Typically, we have a scenario like this:

Bolderer and Son’s Industries used 5kg of flour to produce 50 loaves of bread. How many kg of flour will be used to produce 200 loaves of bread?

This is a typical example of a direct proportion because producing more loaves requires more flour. How do we solve the above proportionality equation?


5 kg = 50 loaves

Therefore, x kg = 200 loaves

Since X = Y, then

Let us cross-multiply the numbers to have:


Let’s now divide 1000 by 50 to get x:

Therefore, it requires 20 kg of flour to produce 200 loaves of bread.

direct proportionality

Another example of direct proportionality is speed and distance. Consider a vehicle that covered 200 km in one hour. If the speed of the vehicle is increased, then it will cover more kilometers in one hour.

When solving direct proportions always remember that a = b or x = y.

Indirect Proportionality

The difference between direct and indirect proportionality is the inverse relationship between two numbers. This is why it is also called inverse proportionality.

An inverse proportion of two numbers or quantities is such that one increases when the other decreases.

If quantity M is increasing, then quantity N decreasing.

Symbolically, we can say that: M = 1/N or M = c/N, where c = constant

When solving equations of this magnitude, you must be very careful not to make mistakes. But I will take you through some examples.

In a construction environment, for example, it takes more labor to complete a given task in fewer days and vice versa. E.g., if 20 laborers completed a task in 5 days, it should take fewer laborers to complete a similar task in 10 days.

Proportionality Examples

We have shown an example of direct proportion, which is quite easier to solve. In the following section, I will show you how to solve inverse proportions.

  1. The Setraco construction company discovered that it took 8 laborers 24 days to cast a 5km gutter in a waterway. They want to retain only 5 laborers to complete the remaining 5km. How many days will it take these 5 laborers to finish the same work?


This is a case of inverse proportion because it should take more labor to complete similar work in fewer days. Conversely, to complete similar work by 5 labor should take more days.

Since we have identified the type of proportionality, let’s solve the problem.

8 labor = 24 days

Therefore, 5 labor = x days

In inverse proportion, X = 1/Y,


(Where c is a constant)


Given x = 5 labor, to find the number of days, we solve as follows:

Then we have:


Let’s now divide 192 by 5 to get y:

Therefore, it should take 5 laborers 38.5 days to complete the remaining 5KM.

indirect proportionality
  • Consider a job that is completed by 10 men in 4 days, how many men will do the same work in 5 days?


This is a case of inverse proportion because it should take fewer men to complete similar work in 5 days.

10 men = 4 days

Therefore, x men = 5 days

In inverse proportion, X = 1/Y,


(Where c is a constant)


Given y = 5 days, to find the number of men, we solve as follows:

Then we have:


Therefore, it should take 8 men 5 days to complete the same job, all things being equal.

inverse proportionality

Most times, it is difficult to determine if a problem is a direct or indirect proportion. This is where technology comes in.

The online calculator can be used to identify the various proportionality. It can be used to solve the direct and indirect proportionality by the ratio method and by the proportion method.

Direct and indirect proportionality is usually used to find the increasing or decreasing trend in two terms.

Ratios and proportions are used in everyday life as well as by businesses. For example, a business may use proportions to determine the amount of sales that yields an equivalent profit.

Also, proportions can be used in factory task completions and operational management.


Proportionality is a simple way to identify the relationship between different quantities. You may be surprised to learn the relationship of the proportional ratios. It is quite essential to know all the variables in the proportionality as described in the above examples.

Because of its relevance, not just in solving mathematical problems, but in everyday life, it is essential you understand its calculations.

Now, it’s your turn to respond. What did you learn and how difficult do you see the proportionality calculations?

Let us know by using the comment box below.

Constructive Comparison Between the Education Systems of the UK and Nigeria

There are a number of similarities and differences between the UK education system and that of Nigeria. Moreso, the UK is their colonial master. I looked at both education systems with the view of extracting their basic similarities and differences.

The process by which learning is aided is referred to as education. It is a method for people to teach others new behaviors, facts, viewpoints, ideals, and abilities. Using techniques like talks, storytelling, teaching, research, or training, the transfer is accomplished.

The majority of the time, education is carried out by teachers, however, self-education is also a form of autodidactic learning.

A system of education is where education occurs. Public schools are referred to as part of the education system as opposed to private schools. It includes all of the activities that occur, starting with those in kindergarten and ending with those in high school. These educational systems are also available in a variety of configurations, with schools and school districts being the smallest and countries being the largest.

The educational systems in many nations vary. The disparities result from the multiple levels of government—community, federal, and state—invested in promoting public education. The laws, rules, and policies put in place by each nation are a few of the elements that make their educational systems unique.

Education Systems of the UK vs That of Nigeria

The followings are the similarities and differences between the education systems of Nigeria and that of the United Kingdom.

The similarities

The education system in Nigeria and the United Kingdom shares a number of similarities. However, only three of these similarities are emphasized in this section. According to Barclay (2006), n.p., “the curricula and syllabi are in British English” which is one of the similarities between the two systems.

In contrast to American English, the books used for the study are written in proper British English. The education systems are both “broken down,” which is another similarity. Depending on the age of the students, they are divided into three stages. The first stage in quite a while comprises understudies whose age lies somewhere in the range of five and eleven years.

The children in the second stage range in age from 11 to 12 years old. Last but not least, “any learner over the age of sixteen falls into the third stage” (Barclay, 2006, n.p.). These steps are important because they help teachers create a level-specific curriculum. The same material is taught to students at each level.

Age determines the level of difficulty of the content. It is generally accepted that students who are older comprehend information more quickly than students who are younger. The two systems share a third thing: they use almost identical names for the same school stages. Primary school, secondary school, and university are the names used.

They are determined by the student’s age. The schools are also broken up into sessions and terms. To advance to the next stage, one must attend a predetermined number of terms and classes. They also take tests, which they must pass to meet the requirements of the examination board.

The Differences

There are likewise exists various contrasts between the UK and Nigeria school systems. ” According to Barclay (2006)[1], the law in the United Kingdom prohibits children under the age of five from attending school. “Children in Nigeria are free to enter school at any age,” on the other hand. Some sign up prior to 5. The majority, however, begin school before the age of five.

Additionally, the education of students between the ages of 5 and 16 is supported by the UK government. Students only receive a subsidy in Nigeria (Ryan, n.d., p. 217). Consequently, the majority of parents choose private schools over public ones due to their superior quality.

Lastly, according to Ryan (n.d.), “the education system of the UK requires one to attain the age of 11 to be legible to join secondary education, and the age of 18 to enroll in university education.” p. 217). In contrast, Nigeria does not have such laws. Nigeria does not have any restrictions or laws of this kind.


The government provides funding for public schools in the United Kingdom. The state government has presented a procedure of per-student subsidizing. That implies that each school gets a sum compared to the number of understudies enlisted. ” In the fiscal years 2011-2012 and 2014-2015, the sum allotted to each student was increased” (Mortimore, 2010, p. 1)[2].

However, in order to make education more accessible to the majority of Nigerians, the Ministry of Education also provides subsidized tuition. It does not cover everything. Thus, the UK has countless students while Nigeria has a modest number. This is because education is not prohibitively expensive.


In the United Kingdom, children between the ages of 5 and 16 are required to attend school. There should be five stages of education for them. Early childhood, primary, secondary, further education, and higher education (HE) are the stages. It is expected of all children to attend at least secondary school. Higher education is not required.

In contrast, education in Nigeria is open to all ages (Johnson, 2008, p. 48)[3]. However, in contrast to the United Kingdom, it is optional from birth. The strategy has reduced poverty and ignorance in the UK while raising illiteracy rates in Nigeria.

Quality of the Education Systems

“The UK’s education system is ranked second in Europe and sixth worldwide.” There are a lot of good teachers in the country. On the other hand, “Nigeria’s education system is poor because it lacks high-quality teachers.” The majority of educational establishments in Nigeria lack the necessary and adequate educational facilities (Ryan, n.d., p. 215)[4].

The student’s performance has suffered as a result. Clearly, there are more differences than similarities between Nigeria’s and the UK’s educational systems. The Unified Realm has a superior schooling system since training is necessary and supported. Additionally, the nation has the necessary educational facilities. On the other hand, because education is not required, Nigeria has a high rate of illiteracy.

Additionally, it is only subsidized, rendering it out of reach for many locals. Due to a lack of the necessary facilities and resources, the country also has poor teaching quality. As a result, Nigeria’s educational system is inferior to that of the UK.

What Are the Agencies of Education?

Education organizations can be either active or inactive. Active organizations are those that deliver education through direct communication and group participation. With the educator and learner influencing one another, education becomes a two-way process in this situation.

Typically, education serves three different social roles. First and foremost, it passes over unique or cultural heritage from one generation to the next. It is made up of the diverse experiences, traditions, values, and customs of the people.

Second, education preserves this cultural heritage by using its curricula, textbooks, teaching aids, and other components.

Thirdly, in order to evolve and improve society in light of evolving conditions and demands, education produces new social institutions and patterns.

In order to carry out certain unique duties in conjunction with the aforementioned activities, society has gradually developed a variety of organizations and institutions. The agencies of education are the name given to these establishments and businesses.

They mold their people in a variety of ways. Their personality, knowledge, understanding, attitude, interests, values, and aspirations are all shaped by them. They range from fundamental institutions like the family to others like the school, playground, and clubs.

Formal agencies

Formal agencies are those organizations and groups that society consciously creates with the sole purpose of disseminating predetermined, ready-made knowledge in a predetermined amount of time in a structured setting.

In these agencies, there are clear goals and objectives, a detailed curriculum, identifiable teachers and students, and a set time and location. In other words, everything about education is pre-planned or thought out in advance. These organizations include schools, colleges, universities, libraries, places of worship, recreation clubs, museums, picture and art galleries, zoos, and others.

Informal agencies

Informal organizations are those organizations that have a significant educational impact on people in a continuous, indirect manner throughout their lives. They are known as indirect agencies because they indirectly affect people’s behavior. Individuals receive education informally and unintentionally. All formalities, regulations, systematization, pre-planning, premeditation, or training are absent from these entities.

There are no specific locations or locations for teaching. People naturally and inadvertently learn through their own initiatives and efforts. Family, community, state, social gatherings, playgrounds, associations, religious rituals, crowds, markets, movie theaters, newspapers, fairs, exhibitions, radio, television, public meetings, field trips, etc. are a few examples of informal education agencies.

Active agencies

Active agencies of education are those organizations that promote education through interpersonal engagement. There is a two-way exchange of information. The educand and the educator, or the person and the group, both have an impact on and respond to one another.

Because both the agency and the individual actively participate and partake in the educational process, the agency is referred to as being “active.” The family, the school, the church, youth organizations, associations, social welfare organizations, sports clubs, museums, art galleries, entertainment programs, etc. are a few examples of such organizations.

Inactive agencies

Agencies classified as passive have the ability to impact a person but are not at all affected by them. There is just one method to interact. Since the individual plays a passive role because he is unable to influence the agencies, these organizations are referred to as passive. Libraries, the press, movies, newspapers, radio, television, theaters, magazines, etc. are a few examples of these organizations.

Commercial agencies

Commercial organizations are those that disseminate a wide range of knowledge, discoveries, innovations, and human achievements. Youngster gains a variety of social experiences and interactions through these organizations, helping to shape their social attitudes. These organizations, which include the media, radio, television, theater, clubs, newspapers, magazines, and periodicals, all have commercial goals.

Non-commercial agencies

Non-commercial organizations are ones that are founded for social good. Their priority is social welfare, not financial gain. Sports clubs, educational excursions, discussions, scouts, youth forums, charity initiatives, adult education facilities, red cross units, and more are examples. These are intended to help kids develop excellent character and contribute to society.

What Is The Importance Of Teaching Practice In Education Training?

The undergraduate teacher training program includes a significant portion of teaching practice. During this time, the student teacher has the opportunity to put their newly acquired knowledge and abilities to use in the classroom. Teaching practice is an essential part of teacher education and training because it gives student teachers the chance to gain practical experience.

According to Atputhasamy (2005), student teachers believe that the most critical factors in their growth as teachers are the practical experience of observing expert teachers, receiving feedback, and practicing strategies.

However, there is a widespread outcry regarding the quality of the majority of teachers who have undergone this practice. Teachers’ training colleges, secondary schools, and stakeholders in the education system collaborate to train teachers.

The Importance of Teaching Practice in Teacher Education

  1. Teaching practice is an essential component of teacher education. It provides student teachers with real-world teaching and learning experiences. Before entering the real world of teaching, a student-teacher has the opportunity to practice the art of teaching during teaching practice.
  2. Teaching practice is seen by student-teachers as an essential component of their preparation for the teaching profession because it serves as a real bridge between studenthood and membership in the profession.
  3. Because they play such an important role in the provision of high-quality education, teachers are considered to be social change agents. Quality teachers have a greater impact on student achievement than any other social factor, including class size, parent education, income and language background, or the number of parents in the household.
  4. Teachers have a significant impact on the futures of individuals and entire generations. They can also have an impact on the country’s economic dynamism by teaching skills that lead to workplace innovation and productivity.
  5. Teachers should be given a variety of skills, knowledge, attitudes, and relevant educational experience to help them deal with the changing and challenging world. Education is expected to play a key role in improving the socioeconomic and cultural status of developing countries.
  6. However, it is impossible to envision a high-quality education without the presence of teachers who are qualified academically and professionally. Therefore, a well-designed and successfully implemented teaching practice program for student teachers that aims to produce teachers who are academically qualified, professionally skilled, and attitudinally and ethically committed to their profession is necessary for teachers to play their role effectively in schools.
  7. The most significant influences on education quality and its contribution to national development are the teacher’s character and quality competence. Even with the best curriculum and enough time to teach, a teacher will not succeed unless he or she is passionate about the work, knowledgeable about the subject and how to teach it, interested, well-informed, passionate about the subject, and believes in its values despite difficulties and hand carps.

What is the Importance of Women’s Education in our Society?

Every type of education that attempts to increase the knowledge and skills of women and girls is referred to as “women’s education.” It comprises general education in schools and colleges, technical and vocational training, career and health education, etc. Both literary and non-literary education are included in women’s education.

Women with education can shift the socioeconomic landscape. Equal rights are guaranteed by the constitutions of almost all democratic nations, including India. Today, access to basic education is a right. The sustainability of society as a whole is maintained when a woman (or a girl) is given access to her rights.

Being educated gives a woman the abilities, information, and self-assurance she needs to be a better mother, employee, and citizen. A lady with a good education will also work harder and earn more money. In fact, women frequently see larger returns on their educational investments than men.

In particular, in a developing nation, it is imperative to educate women for the reasons listed below:

Prosperity and development of the economy:

Women will be empowered by education to speak up and contribute to the country’s growth and prosperity.

Economic independence:

The helpless state of women cannot be changed as long as they remain economically disadvantaged and dependent on men. Women’s proper education and employment are the only paths to economic independence.

Better life:

A woman can lead a happy life thanks to her education. She would never lose her individual identity. She is able to read and understand her rights. Her rights wouldn’t be violated. The life or state of ladies would work a great deal, on the off chance that we take an expansive standpoint in the field of female training.

Better health:

Taught young ladies and ladies know about the significance of well-being and cleanliness. They are empowered to lead a healthy lifestyle through health education. Mothers with education are better able to look after themselves and their children.

Poise and honor:

Nowadays, educated women are regarded with respect and dignity. Millions of young girls look to them as role models and find that they inspire them.


Women with more education are more aware of their legal rights. The use of dowry, forced prostitution, child marriage, female genital mutilation, and other forms of violence against women would eventually decrease as a result.

The decision to pick a profession of her choice:

Women with education have a better chance of succeeding in life. A girl should have the same opportunities for education as a boy does so that she can plan to be a successful doctor, engineer, nurse, air hostess, cook, or do something else she wants.

Reduce poverty:

To eradicate poverty, women must be educated. Women must shoulder equal responsibility for the enormous task of eradicating poverty. This would request an enormous commitment from instructed ladies. Until girls and women are given the right to an education, there won’t be much change in society or the economy.

Women should receive an education to help them understand the world and learn how to handle challenges. It should be mandatory for all women to go to school and get knowledge. Indeed, the majority of women would flourish and perform well.

What Is The Importance Of Pre-Retirement Education?

The advantages of training prior to retirement cannot be overstated. For some, retiring means making significant adjustments to one’s daily routine, including how one spends money, their time, and other aspects of life.

Retirement is viewed with mixed feelings in this region of the world. Usually, even people who are looking forward to retirement feel a great deal of loss.

However, experts have repeatedly emphasized how important it is to prepare in advance, particularly through training. They argued that retirement will be more successful for all workers if they are better prepared for changes.

As part of a financial wellness program, providing employees with access to pre-retirement workshops has a number of advantages, including reducing stress and increasing productivity. Employees can benefit from these courses in the following ways:

Productivity In 2017, the Chartered Institute of Personnel and Development found that one in four workers agreed that worries about money affect their work productivity.

Employees’ perceptions of their employer shift when pre-retirement planning and other benefits are made available, allowing them to experience greater personal and professional support and value. With a higher rate of employee retention, the company’s appeal can rise.

Wellbeing Program While providing pre-retirement seminars and courses to your employees is a great way to equip them with the information, they need to make more informed decisions about their future, it is also possible to provide financial well-being assistance to employees before they reach this stage.


Issues of funding, organization, and quality of learning are usually determined by the government in both countries. The education system in both countries allows for formal and informal agencies of education.

Also, the importance of women’s education is prioritized. So far, it’s your turn to bother me with your comments. Kindly use the box below.

[1] Barclay, L. (2006). UK law and your rights for dummies. Chichester: John Wiley.

[2] Mortimore, P. (2010). Ten education issues the new government should address. The Guardian.  Available at:

[3] Johnson, D. (2008). The changing landscape of education in Africa. Oxford: Symposium Books.

[4] Ryan, J. (n.d.). Cross-cultural teaching and learning for home and international students.

Simple Steps of Educational Research for Students

Educational research focuses on empirical approaches to problem-solving in education. It uses systematic investigation to determine causes and effects in education. It employs clearly defined scientific methods to collect and analyze data for the purpose of problem-solving and advancement of knowledge.

When teaching educational research and learning in schools, different teaching methods are employed. Each method has its benefits for learners and teachers.

In this article, we shall evaluate educational research and the steps to carry out educational research in different institutions.

What is Research?

Research is defined as “creative and methodical activity done to improve the body of knowledge.” It entails gathering, organizing, and analyzing data to better understand a subject and is distinguished by a focus on minimizing bias and error causes. These tasks are distinguished by taking biases into account and adjusting for them.

A research project might build on prior contributions to the field. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole.

Using scientific methods, research is the careful consideration of a specific issue or concern. “Research is a systematic inquiry to describe, explain, predict, and control the observed phenomenon,” states American sociologist Earl Robert Babbie. Both inductive and deductive methods are used.

Using scientific methods, research is the careful consideration of a specific issue or concern. “Research is a systematic inquiry to describe, explain, predict, and control the observed phenomenon,” states American sociologist Earl Robert Babbie. Both inductive and deductive methods are used.

Deductive methods verify an observed event, whereas inductive methods analyze it. Deductive methods are more frequently associated with quantitative analysis, whereas inductive approaches are associated with qualitative research.

What is Sociology?

Sociology is a social science that focuses on society, human social behavior, social interaction patterns, and aspects of daily life-related culture.[1] It is the study of human social institutions and relationships.

The study of sociology covers a wide range of topics, from criminal behavior to religion, the family to the state, racial and social class divisions to common cultural beliefs, and social stability to radical change in entire societies. Understanding how human action and consciousness both shape and are shaped by surrounding cultural and social structures is the goal of sociology, which seeks to unify the study of these diverse subjects.

The study of sociology, which looks at and explains important issues in our communities, our personal lives, and the world, is an exciting and fascinating field of study. Sociology examines the social causes and effects of romantic love, racial and gender identity, family conflict, deviant behavior, aging, and religious faith on a personal level.

Sociology looks at and explains things like law and order, poverty and wealth, prejudice and discrimination, schools and education, businesses, urban communities, and social movements at the societal level.[2] Sociology studies global phenomena like population growth and migration, war and peace, economic development, and so on.

To improve and deepen our comprehension of important social processes, sociologists place a strong emphasis on the careful collection and evaluation of evidence regarding social life. Sociologists employ a wide range of research techniques.

Sociologists study group interactions captured on video, conduct large-scale surveys, interpret historical documents, examine census data, interview group members, and carry out laboratory experiments.[3] Sociology’s research methods and theories provide powerful insights into the social processes that shape human lives, as well as current social issues and prospects. We gain a deeper comprehension of these social processes as well as the forces that influence our own personal experiences and outcomes.

Sociology makes use of diverse techniques for empirical research and critical analysis.[4] While some sociologists perform studies that can be used to improve social welfare and policy, others place a greater emphasis on improving our theoretical understanding of social dynamics. The focus might range from macro-level assessments of society to micro-level investigations of individual interaction and agency.

The social world in which we live and the forces that shape our lives can be seen and understood uniquely and insightfully through sociology. To provide deeper, more illuminating, and more challenging understandings of social life, sociology looks beyond conventional, taken-for-granted views of reality.

Sociology is a discipline that broadens our awareness and analyzes the human social relationships, cultures, and institutions that profoundly shape our lives and human history through its particular analytical perspective, social theories, and research methods.

What do you understand by the sociology of education?

The sociology of education examines how social structures and personal circumstances impact education and its results. The majority of its focus is on the public education systems seen in contemporary industrial cultures, particularly the growth of higher, further, adult, and continuing education.

The topic or area of study known as the sociology of education is concerned with society’s educational institutions and all other elements associated with them. The academic discipline known as the sociology of education “examines how people’s experiences affect their educational success and results,” according to another definition (Williams, 2011)[5].

The topic is “primarily concerned with education, and particularly the mass schooling systems of modern industrial societies, including the extension of higher, further, adult, and continuing education,” according to Scott (2014)[6].

In layman’s terms, the field explores education as a social institution and investigates its duties, functions, and other behaviors in relation to a larger social environment, as well as how it both influences and is influenced by individuals. It emphasizes the value of education within various cultural and other social groups and evaluates personal circumstances (including economic, political, etc.) that may have an impact on an individual’s ability to receive an education. Modules or curricula, testing procedures (like standardized testing), etc. are some subjects that are covered in the field.

The study of the interaction between society and education is known as the sociology of education. The study of how individual experiences and governmental structures might impact education and its results is referred to as the sociology of education. It is about the public education system in contemporary, industrialized societies. It also covers the growth of adult, higher, and continuing education. Known as the “Father of Sociology,” Auguste Comte.

The sociology of education attempts to investigate the influences that social factors have on schools and people, to learn about democratic beliefs, to assist in developing a curriculum that best suit each student’s needs and promotes personality development, etc.

The hopes for improving and advancing learning are a crucial, positive, and essential goal of the sociology of education. It is a way to raise educational standards and therefore assist the younger generation in leading lives of higher quality.

What is educational research?

Education research is a broad field that focuses on many different areas of knowledge; thus, it draws from a variety of disciplines. As a result, the research’s conclusions are multi-dimensional and subject to limitations based on the traits of the participants and the research environment.

According to J. W. Best, educational research is any activity that aims to develop a science of behavior in educational settings. The ultimate goal of such a science is to provide the educator with the knowledge necessary to accomplish his objectives in the most efficient ways.

The systematic collection and analysis of educational-related data are referred to as educational research. Learning by students, teaching methods, teacher education, classroom dynamics, and a variety of other aspects of education are all possible topics for research.

Instructive scientists by and large concur that exploration ought to be thorough and efficient. In any case, there is less arrangement of unambiguous principles, models, and examination systems. As a result, educational research’s value and quality have been questioned.

The primary goal of educational research is to improve teaching and learning practices while also adding to the existing body of knowledge by finding solutions to a variety of pedagogical issues. Additionally, educational researchers are looking for answers to concerns regarding classroom management, learner motivation, and development.

What Steps Should Be Taken When Carrying Out Educational Research?

Before starting to acquire, master, and develop your skills in the numerous approaches for carrying out the activities that each phase is defined by, it is essential that you, as an educational researcher, have a firm understanding of the major steps involved in the research process.

steps of educational research

Step 1: Define the research problem

The procedure begins with identifying an issue or formulating a research topic. An educational research issue may have its roots in a research report, personal experience, textbooks, etc.

Step 2: Examine previous work in the area of your investigation.

The review of the literature is the next step in the research process. The researcher must now learn more about the subject under examination after identifying the issue.

To do this, you should survey the writing (compositions of perceived specialists) connected with the exploration issue. This involved looking over concepts and theories as well as the results of previous research. Additionally, the purpose of the literature review is to provide useful recommendations for significant investigations and to eliminate redundant work.

Step 3: Form your hypothesis and/or research questions

The statement of the hypotheses and/or research questions is what brings the research study to the data collection stage. By stating the study’s hypotheses, you can better understand the issue and the reasoning behind the investigation.

Step 4: Create your research design or plan

A research design is a plan for carrying out the research. It clarifies who, what, why, when, and how the investigation was conducted. To put it another way, the design describes the subjects, the methods for data analysis, the instruments used to collect the data, and the procedures for doing so. All the more critically, it ought to be adaptable to ingest changes achieved in research during the execution.

Step 5: Implement the research plan by collecting data

Data collection and organization are how the research plan can be carried out. To provide the data required to test the hypothesis or respond to the research question, this step is crucial. A questionnaire, observations, the use of the literature, and other methods can all be used to gather data.

Step 6: Analysis of the research data

To test the hypotheses inferentially or provide a descriptive response to the research question, analysis of the collected research data is required. In point of fact, this crucial aspect is the culmination of all of your research time, effort, and resources.

The consequences of your information examination are summed up in a way straightforwardly connected with speculations or exploration questions. Even if you don’t know much about statistics or math, this guide will teach you how to use SPSS to analyze statistical data, which is an important and useful skill.

Step 7: Interpret and present the findings in your thesis

After the data analysis is complete, the results are interpreted and generalizations are drawn based on research questions, hypotheses, and a review of the relevant literature. After that, you can draw the implications for practice and future research that acknowledge your research’s limitations.

In conclusion, if the research is carried out correctly and according to plan, the problem should be solved and the research questions should be answered.


Educational research is a systematic way of gathering and analyzing data and information to improve existing knowledge.

It is carried out by students and teachers. For students, it is usually required to gain an educational award, say, B.A., B.Sc., etc. For teachers (lecturers, etc), it is usually required to gain mastery of the subject matter.

Whether you are a teacher or student, there are steps to successfully carry out research. This article discussed these steps in detail. I will now leave you to share your views on research methodology using the comment box below.

[1] Ashley, David; Orenstein, David M. (2005). Sociological Theory: Classical Statements (6 ed.). Boston: Pearson Education.

[2] Floud, J., Halsey, A. H. and Martin, F. (1956) Social class and educational opportunity: Heinemann.

[3] Macy, Michael W.; Willer, Robert (2002). “From Factors to Actors: Computational Sociology and Agent-Based Modeling”. Annual Review of Sociology. 28: 143–66.

[4] Giddens, Anthony, Duneier, Mitchell, Applebaum, Richard. (2007). Introduction to Sociology. Sixth Edition. New York: W.W. Norton and Company.

[5] Williams, S. M. (2011). Sociology of education. Education.

[6] Scott, J. (2014). A dictionary of sociology (4th ed.). Oxford University Press.

Actionable Education Evaluation Methods in Educational Management

Education evaluation is an important component of educational management. It is used to assess and evaluate the impact of teaching and learning on students.

Education is the process of providing learning experiences together with knowledge, skills, values, beliefs, habits, and attitudes. The educational system is a network of experts working in organizations including schools, unions, statutory boards, and government departments.

Political leaders, principals, instructional staff, support staff, administrative staff, and other educational professionals collaborate to enrich and improve the educational system. Management, which entails an institution’s planning, organizing, implementation, review, evaluation, and integration, is necessary at all levels of the educational ecosystem.

In today’s article, I will discuss the different education evaluation methods used in educational management. Let’s begin with the meaning of educational management.

What is Educational Management?

Educational management is the administration of the education system in which a group combines people and material resources to supervise, organize, strategize, and implement structures to execute an education system.

Educational management, which is also sometimes referred to as educational administration, is frequently associated with elementary and secondary schools as well as higher education institutions like colleges and universities. Professionals in education management can also be found working in private businesses, not-for-profit organizations, and government agencies.

Educational managers might work on education policy, study, or consult to help evaluate and come up with ways to improve the educational system at every level. Most people who work in educational management have at least a master’s degree, and many of them are licensed teachers or principals.

The application of techniques, instruments, and knowledge is the goal of the field of educational management, which aims to improve the performance of educational institutions in a particular nation. In the sense that it tries to view the educational process as a systemic, organized whole, it is a type of educational administration.

As a result, educational management can be viewed simultaneously as a discipline, a procedure, and a strategy that intervenes in the educational system to enhance its various stages. It encourages the integration of the various components of the educational process—students, teachers, and the community.

An educational community that overcomes the obstacles traditionally associated with education, such as school dropout and poor academic performance, is formed. It also exchanges information and provides feedback.

Hence, educational management encompasses a wide range of activities with the goal of bringing together education and society:

  1. establishing, creating, and maintaining the fundamental educational infrastructure, including schools, colleges, universities, libraries, museums, hostels, etc.
  2. upkeep of academic records
  3. evaluating student performance and keeping an eye on student behavior
  4. Keeping track of supply inventories for items like office supplies, books, hardware, digital equipment, building infrastructure, lab equipment, etc.
  5. scheduling classes, training, exhibits, seminars, and presentations, among other things
  6. ensuring order, coordination of work across all departments, and cooperation with educational authorities
  7. Create the course materials for lectures, tests, internal assessments, final exams, etc.
  8. managing resources, spending, social services, and the general well-being of every system user

The management of education is a continuous process that involves numerous tasks and duties. So, a balanced mix of constancy and dynamism is the foundation of effective educational management.

Mention the Different Education Evaluation Methods you know

Formative Assessment

Formative assessment is a common method of school evaluation. To encourage students to learn more effectively, educators or teachers conduct formative assessments multiple times throughout an academic year. You can use this kind of evaluation to help students understand their weaknesses because it is done repeatedly. Formative assessment tests can be used to assess how well students understand a particular section of the curriculum. If you want to see how well the students understand something, this would be an excellent approach.

Summative Evaluation

At the conclusion of an academic year or course, summative evaluation tests are administered. The promotion of students to the next stage of their learning journey is determined by this evaluation, which plays a crucial role in a student’s academic career. After completing summative exams, students frequently receive certificates that include information about their summative exam scores.

Diagnostic Evaluation

Diagnostic evaluations and formative assessments are very similar. This evaluation is helpful in identifying the students’ learning shortcomings. This approach can be used to help students comprehend their weaknesses. They will be able to make adjustments to the learning process and succeed academically once they comprehend the weaknesses in their learning.

Prognostic assessment

The purpose of a prognostic evaluation is to estimate and foresee a person’s future. An analysis of talents and potentials in a prognostic evaluation adds a new dimension to the findings of an assessment: the individual in question’s future development, in addition to the necessary conditions, timeline, and constraints.

Normal referenced evaluation

This kind of assessment focuses on comparing students’ relative performance, either by comparing the results of individual students in the group being evaluated or by comparing their performance to that of others of a similar age, background, and experience. It affects how students are arranged in the group.

Criterion-referenced assessment

A criterion-referenced evaluation describes a person’s performance in relation to a predetermined performance standard. It describes the accuracy of a student’s performance, or how well the student performs in relation to a particular standard. To put it another way, it’s similar to comparing a student’s performance to a set standard.

What is Library?

A library is a collection of items, such as books or movies, that may be used instead of just being displayed. A library is a place where people can go to borrow books in person or online. It can also be both.

Printed materials and other tangible resources in a variety of formats, such as DVDs, CDs, and cassettes, as well as access to data, music, and other items stored in bibliographic databases, can all be found in a library’s collection.

Traditional definitions of a library include a collection of books used for reading or research as well as the structure or space where such a collection is stored. The word comes from the Latin word liber, which means “book,” whereas the words for a library in German, Russian, and Romance come from the Latinized Greek word bibliotheca.

What is expected from an up-to-date Librarian?

To ensure that patrons have the resources they need to learn about and investigate issues of interest, a librarian, also known as a curator, is in charge of managing the day-to-day operations of a library.

Their responsibilities also include managing a team of employees to do daily chores, maintaining library databases, and developing educational programs for various age groups.

To effectively administer a library, a competent librarian combines a love of books with great interpersonal and computer abilities. To stay current on library trends and materials, librarians need to be strong readers in addition to having a natural tendency to operate in a media-driven workplace.

To communicate with a wide range of people, librarians employ their interpersonal and communication abilities. They must connect with library users and present a positive image. Additionally, librarians communicate with personnel and academic researchers who are working on publications.

With the increased use of technology in libraries, having computer skills and technological knowledge has become crucial. The operation of computer search databases and the use of software for administrative activities are skills that librarians must possess. Additionally, the requirement to provide tools and services that people desire makes innovative thinking crucial.

Good librarians are also very good at addressing problems. These skills are put to use in order to define research problems and to perform or help with resource searches. Additionally, librarians must find solutions to issues that arise from maintaining an effective and efficient library within a community. Initiative and assertiveness are closely associated in that they both become necessary when a library requires updating and funds need to be raised.

An up-to-date librarian is also expected to:

  1. Love reading a lot. After all, it is the focus of their entire professional life. All genres of books for all age ranges are read by librarians. It is important for librarians to be aware of hot and trending books.
  2. Be really organized and focused on the details. The management of media collections makes up a significant portion of a librarian’s duties. This covers media like music, movies, and novels. They must be extremely organized and pay close attention to every little thing a result.
  3. Follow technological trends. Utilizing technology in libraries is a crucial part of a modern librarian’s profession, according to the U.S. Bureau of Labor Statistics. Card catalogs on paper are a thing of the past. Librarians are responsible for using and maintaining the enormous amount of technology used in modern libraries, including computers used by users, services for borrowing digital content, systems and software used by library employees, and more.
  4. Excel as a researcher. To assist them in deciding which items should and should not be added to their collections, librarians conduct extensive research on what is popular. Additionally, they must determine which items are no longer popular enough to warrant keeping in the collection and removing them.
  5. Be devoted and self-controlled. Bookkeepers much of the time are compelled to work with little financing on the grounds that either the assets aren’t accessible or are decided to be more required somewhere else. Passion and a strong commitment to their careers and the work they do are therefore major characteristics of a librarian. The best librarians are disciplined and keep up with a variety of tasks, like reshelving books and updating catalogs.

An examination is not the true test of knowledge, Discuss

According to Google’s definition, an examination is a formal test taken to demonstrate knowledge or ability in a particular field or to earn a certification.

A test, according to the Oxford Advanced Learner’s Dictionary, is an examination of a person’s knowledge or ability that consists of activities or questions that they must complete.

The definition of knowledge in the Cambridge Dictionary is “the understanding of or the information about a subject that you get from experience or study, either known by one individual or by people generally.”

Exams and tests are closely related, but they are not the same thing, as the above definition shows. While tests are meant to test your knowledge of a specific lesson, examinations are meant to test one’s knowledge of several lessons.

In general, it is possible to make a convincing case, supported by solid facts, that examination is not a genuine test of knowledge.

Exams typically assess a student’s capacity to memorize information rather than their ability to fully comprehend what was taught. Because they have the ability to memorize for the exams, which were supposed to be carried out in order to ensure students understood what was taught, a student with a very good memory would not fully know what was taught in class to be able to pass the exams.

However, they would still be able to pass the exams. Consequently, this tends to render the examination’s ultimate objective meaningless; and this implies that only memory retention is tested.

Second, intelligence can’t be measured by looking at it. Edward de Bono asserts, “Many extremely intelligent people are poor thinkers.” A lot of people with average intelligence can think well. A car’s driving style separates its power from its power. The purpose of exams was to distinguish intelligent people from inept ones.

It is beyond the realm of possibility to expect to decide somebody’s insight by making them take tests in light of the fact that as prior pointed out, a few understudies have great retaining abilities. They have such excellent memory that they could simply record everything they saw in their notes and receive higher grades than students who actually engaged in creative thinking.

Thirdly, tests do not tell a person if they will succeed in life. They simply serve as a skill-testing exercise, which is not always accurate. Students are taught a variety of formulas that they will not use in life rather than money-making and life skills that are taught in schools. As a result, even if a student passes the A-level exams they took, they will not succeed in life.

The fact that students have different abilities is the fourth point. An understudy who is great in music or writing probably won’t be great in Math and Material science however similar tests are given in spite of the various capacities of the understudies.

This means that students’ grades cannot be considered an objective indicator of their intelligence. Students grades shouldn’t matter because the examiner has a greater impact on the exam’s outcome.

The fact that a student receives low grades does not imply that they are not intelligent or that they are not committed to their studies and work. It simply indicates that their learning capacities differ. While some grasp at a relatively faster rate than others, others might do so more slowly.

In conclusion, examinations should not be used as a true test of knowledge or intelligence, even though they are important tools for evaluation and assessment.


The concept of education management is important to students, parents, teachers, education administrators, and the government. To assess the impact of learning, education evaluation techniques are employed.

This article effectively discussed these concepts as a reference for researchers and educationists. As the case is, vital information may have been omitted in the article, hence, it’s your turn to respond. You are required to suggest possible additions to the concepts or ask questions in relation to the concepts discussed. Please, use the comment box below for your feedback.

The Importance of Adult Education in the Nigerian Education System

Adult education is a teaching and learning process specifically targeted at people who are considered adults by society. Adult education, though not integrated into the Nigerian education system, is approved by the government.

It helps to improve their technical and professional qualifications. It also helps to develop their abilities, and enrich their knowledge with the goal of completing a given level of formal education. This is part of the objective of Nigerian educational policies.

Adult education can be employed to acquire knowledge, skills, and competencies in a new field. Adults can also refresh or update their knowledge in a particular field.

The concept of adult learning can also be termed continuing education, recurrent education, and second chance education.

Recent years have seen different adults rising to obtain different educational qualifications in different fields. Due to the importance of adult education to society, we shall be dedicating this article to the subject matter.

Meanwhile, we shall first take a look at Nigerian educational policies. Its goals and objectives. We shall also discuss briefly, what is special education.

If you are a student, an adult, or an educationist that wants to learn more, keep scrolling for the detail.

What are the Educational Policies in Nigeria?

The goal of Nigeria’s National Policy on Education is to ensure proper management, administration, and execution of the educational system across the board. It gives instructional efforts direction.

The National Policy on Education in Nigeria is a declaration of the government’s objectives, rules, anticipations, expectations, requirements, and standards to guarantee the country’s education system is delivered to a high standard.

Nigeria has changed throughout the years, and the educational system appears to have undergone a technological makeover. There is currently a discernible electronic education system in Nigeria as a result of technical development and national policy reforms.

One essential component of Nigeria’s present national education policy is making education a top priority. Education is the most powerful tool for change, and it is the only way to achieve any significant shift in the social and intellectual orientation of a society.

The National Policy on Education in Nigeria calls for effective reform in all areas of the nation’s development, including education standards.

Even though the National Policy on Education in Nigeria places a lot of emphasis on the educational system of the nation, it is rather depressing to state that it has failed miserably and hasn’t achieved any of the criteria set forth in the policy for significant transformation.

Nigeria’s national education policy aims to create a more wealthy and cohesive country through a well-organized educational system.

Goals of Nigeria’s National Education Policy

The followings are the goals and aims of Nigeria’s national education policy:

  1. Nigeria’s educational policy aims to establish a democratic and free society.
  2. Additionally, it aims to establish a united, powerful, and self-sufficient nation.
  3. It likewise assists with building an extraordinary and dynamic economy for the country.
  4. The goal of the national education policy is to create a nation with numerous exciting opportunities for all citizens.
  5. It aims to create a society that is fair and equal.

Objectives of Nigeria’s National Education Policy

The following are the objectives of Nigeria’s national education policy:

  1. Present-day instruction methods will be progressively used to work on every one of the levels of the school system.
  2. All citizens of the nation will be entitled to a variety of forms of universal basic education.
  3. The country’s national development plan should continue to place a high value on education.
  4. Lifelong education will serve as the national educational policy’s foundation.
  5. In order to provide a more varied and adaptable selection, educational facilities must continue to be expanded in response to social needs and made more and more accessible to all individuals.
  6. For maximum self-development and fulfillment, educational activities would be centered on the student.
  7. Health and physical education should be emphasized at all educational levels.
  8. By relying in part on ongoing evaluation of the student’s or individual’s progress, the educational evaluation shall be liberalized.
  9. All citizens of the nation would have access to and be able to afford education.
  10. The public schooling system will be organized to foster the act of self-learning. In this regard, the government will continue to support the establishment of Young Readers Clubs in schools.
  11. Religious instruction will continue to be offered opportunities; No child will be compelled to accept religious instruction that goes against their parent’s wishes.
  12. After graduating from junior high school, students will have the option of continuing their education on a full-time basis, combining their work with their studies or beginning full-time employment without excluding the possibility of returning to school in the future.
  13. Education should be linked to the needs of the community as a whole.

What is Adult Education?

Adult education refers to the process by which individuals actively pursue new knowledge, abilities, attitudes, or values through prolonged and organized self-educational activities.[1] It can refer to any type of learning that people do that goes beyond traditional schooling, from fundamental literacy to ensuring one’s fulfillment as a lifelong learner.

Adult education and its importance
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Adult education, in particular, is a particular way of teaching and learning that is based on the idea that adults can and want to learn, that they can and want to take responsibility for their own learning, and that learning should meet their needs.

What is the importance of adult education in the Nigerian education system?

Adult education plays a crucial role in assisting older students in developing new skills and expanding their career options.

Adult education is an important tool for making sure people can keep up with the rapidly evolving technological world of today.

importance of adult education

Obviously, adult education is important for more than just that reason. Adults must continue their own education for a variety of reasons, in one way or another. Some of the most significant ones are listed below.

Boosts career

Adult education can assist individuals in establishing successful careers. Organizations these days need more from their workers. A single degree is no longer sufficient. It is essential for employees to be familiar with some aspects of their work. That can be done in a great way through adult education. Classes that are quick and simple help employees grow, achieve better results and become more employable.

Consistent with technological advancement

Adult education helps people keep up with the times. Older people might not be able to keep up with the rapid development of new technologies. They will most likely fall behind unless they begin their own education. That is no longer a major issue after a certain age. However, enhancing your educational background is not in question if you are still employed and intend to remain so for at least ten more years before retiring.

Retraining to remain relevant

When trying to build a successful career, sometimes retraining is not an option but an obligation. It’s important to recognize that as technology advances, some jobs will become obsolete or have already become obsolete. Adults who do those jobs must now concentrate on something else.

Active mindset

For those who want to keep their minds active, adult education is a must. The majority of people hold the belief that as we get older, our minds begin to become less sharp. It is incorrect. A person’s mind will begin to lose its sharpness if they have been working the same job from the age of 25 to the age of 35 without challenging themselves with new knowledge and topics. Learning a new language or perfecting new skills is a great way to keep your mind active, according to research. After all, it’s just as important to exercise your mind as your body.

Boosts creativity

Adults become more creative. Being active and creative can, without a doubt, have a significant impact on your life. The more information a person has, the more creative they can be. Education encourages creative thinking. You become more outgoing and creative as a result.

The Nigerian educational system must include adult education. This approach gives adults the chance to continue learning things that will enhance their lives, whether it’s honing their language abilities or learning how to use new technologies.

What is special education?

Special education is the practice of educating pupils in a way that fits their specific characteristics, impairments, and special needs. This entails the individually planned and consistently reviewed arrangement of instructional practices, specialized tools and resources, and accessible environments.

These interventions are intended to assist people with special needs in reaching higher levels of personal self-sufficiency and success in learning and in their communities, which may not be possible if the student only had access to conventional classroom education.

Special education
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Students who have been identified as having a disability that hinders their ability to learn and necessitates additional support in order to fully participate in school are eligible for special education services. Those with the following disabilities typically qualify for special education services:

Special education aims to ensure that students with any of these disabilities can participate in education alongside students without disabilities and can access the curriculum whenever and as much as possible.

Children who typically qualify for special education services include those with the following disabilities:

  1. Intellectual disability
  2. Hearing impairments (including deafness)
  3. Speech or language impairments
  4. Visual impairments (including blindness)
  5. Serious emotional disturbance
  6. Orthopedic impairments
  7. Autism spectrum disorder
  8. Traumatic brain injury
  9. Other health impairments
  10. Specific learning disabilities
  11. Developmental delay

In an ideal world, everyone would have equal access to education to fulfill their potential.

What makes for good interpersonal relationships in a school?

Successful classroom management depends on teachers and students having mutual trust, respect, compassion, and care. We can do this by developing relationships with our pupils.

The following justifications support the significance of the teacher-student relationship:

The majority of disruptive behaviors can be prevented if students and teachers have strong relationships.

Due to the absence of care and attention from their families, most pupils in today’s environment require the attention of their teachers.

Building trusting ties with students enables them to form solid friendships with classmates.

To support their healthy development, children with exceptional needs such as those with ADHD and autism—typically need the attention of numerous stakeholders. Building trusting relationships with these children is essential to controlling their behavior.

In light of the above, the following makes for good interpersonal relationships in a school.

A thriving classroom community

The most effective method for cultivating genuine relationships with your students is to establish a collaborative network with their parents and families. Even though doing that isn’t easy, you still have to work hard and succeed.

Make use of routines and traditions

Routines and traditions can help you connect well with your students and their families in the classroom. The teacher’s relationship with the students and their families is strengthened through daily, weekly, and monthly practices.

Making a good first impression

The teacher’s personality plays a big role in helping them build better relationships with their students. Take a genuine interest in your students’ lives and success. This will cause understudies to feel you care for them.

Utilization of both high-quality verbal and nonverbal behaviors

Utilizing both high-quality verbal and nonverbal behaviors has the potential to enhance the relationship that exists between students and teachers. It enhances healthier social and interpersonal interactions between teachers, students, and other students as well as conveys a strong message of acceptance.

Be an active and great listener

Being able to listen well helps you communicate well with your students. This helps you build a good relationship with them. Students will sense how genuine and respectful you are toward them if you pay close attention to them.

Be mindful of how you react to students and their actions

Instead of reacting negatively, react positively. Regardless of whether you agree or disagree with a student’s actions or words, it is essential to respond positively. If you don’t like the behavior or opinions of your students, disagree gently and politely. Otherwise, it will be difficult for you and your students to communicate effectively.


Adult education helps boost careers and keep the mind of the learner active, no matter the age. This article discussed relevant concepts that relate to adult learning including:

  • Nigerian educational policies
  • Importance of adult education in the Nigerian education system, and
  • Special education

You can now differentiate between adult and special education and are required to suggest and contribute to the concepts. Please, use the comment box below for your feedback.


 Merriam, Sharan B. & Brockett, Ralph G. (2007). The Profession and Practice of Adult Education: An Introduction. Jossey-Bass, p. 7.

Educational Psychology: Unlock Your Child’s Learning Potential

Educational psychology is a concept that helps teachers understand their learners so they can help them effectively.

It is a concept that encompasses the understanding of the cognitive, developmental, aptitude, and interests of learners. It can help a teacher understand efficiently the learning process of a child.

In this article, we shall be covering basic concepts in educational psychology and how it helps the learning process of children.

What Is the Subject Matter of Educational Psychology?

The subject matter of educational psychology revolves around the learner. It is the learner who needs to be studied well at all stages of development. Educational Psychology, thus, provides knowledge by which we can understand our learners.

It aids in our comprehension of the learners’ developmental traits, individual variances in intelligence, capacity for adjustment, and personality.

Educational psychology also looks into learners’ thought processes, attitudes, aptitudes, interests, creativity, and self-concept.

Therefore, educational psychology encompasses and is concerned with understanding learners and equipping them with the resources they require to learn.

Educational psychology is the study of how people learn, as well as individual learning differences and instructional processes. It looks at how the learning process is affected by cognitive, behavioral, emotional, and social factors. This understanding of how people learn is used by educational psychologists to create instructional strategies and assist students in succeeding in school.

The early childhood and adolescent learning processes are the primary focus of this subfield of psychology. However, it also investigates the social, emotional, and cognitive processes involved in learning across the lifespan.

The field of educational psychology is devoted to the study and enhancement of human learning across all stages of life and in any setting.

Schools are just one example, but there are also workplaces, organized sports, government agencies, retirement communities, and other places where people are learning and teach.

The importance of educational psychology lies in its emphasis on comprehending and enhancing the essential capacity of humans to learn.

What is the Psychology of Adult Education?

The study of how people learn, including teaching strategies, learning processes, and individual learning characteristics, is known as educational psychology. It investigates the influences of cognition, behavior, emotion, and society on learning. This comprehension of how people learn is used by educational psychologists to create instructional strategies and support student’s academic success.

Adult educational challenges are addressed by adult psychology. The scientific aspect of an individual’s growth inside educational settings is called adult education psychology. Adult education should continue when they leave school and should last the rest of their lives.

For people taking psychology in adult education courses and those with an interest in the psychology of adult development, adult educational psychology is helpful. Teachers in higher education, instructors in technical and further education, staff development and human resource professionals, as well as educators in the community, can all benefit directly from it.

It offers a thorough introduction to educational psychology from an adult perspective and is the first significant text of its kind. Human development, social psychology, social learning, emotion, motivation, interest, intelligence, cognition, retention, and learning are just a few of the core subjects it covers.

What do you Understand by Child Psychology?

Child psychology is the study of a child’s development from conception to adolescence. It is one of the many subfields of psychology. It focuses on the mind and behavior of children from prenatal development through adolescence. In addition to the physical growth of children, mental, emotional, and social development are all aspects of child psychology.

A kid therapist is a specialist in youth improvement who works with youngsters and teenagers to analyze and assist with settling issues that cause profound or conduct issues. The psychology of children is important because it can help us learn more about how kids work and how to help them become well-rounded people. As a result, it helps teachers and parents better understand and assist the children in their care.

The study of children’s psychological processes, also known as child development, focuses on how these processes differ from those of adults, how they develop from birth through adolescence, and how and why they differ from one child to another. The field of developmental psychology sometimes includes the subjects of childhood, adulthood, and aging.

What factors affect the learning process of children in nursery schools?

All of the internal and external agents that influence a child’s potential in a positive or negative way are factors that influence their learning. They affect academic achievement.

There are four socio-educational factors that affect learning: the application of study methods, intellectual abilities, prior knowledge, and motivation.

These aspects ought to be promoted, first within the family unit and then at school.

It should be understood that children’s learning relies on motivation. It is regarded as the factor that empowers an individual to make a decision and carry it out (in this instance: keep your interest in learning high).

  1. These things have to do with where the child grows up and lives. It is believed that their learning can be affected by everything around them. Skills can be developed based on a child’s habits thanks to the environment.
  2. : Each child has distinct characteristics that make him or her a special human being. In that regard, it is important to understand how far they can be demanded given their skills, aptitudes, and capacities. Parents, representatives, and teachers must be aware of each child’s limitations and potential.
  3. This aspect is about how parents and representatives raise their children. Ideally, the principles and study routines. In order to make learning more enjoyable in the future, the format will differ for each person.
  4. : The term “hereditary factors” refers to conditions that are present at birth that prevents a child from fully developing their intellectual capacities.
  5. : In addition to affecting children’s physical and psychological well-being, violence against children has an impact on learning. The child experiences feelings of fear, vengeance, and rage as a result of this act, and he or she stops thinking about school.

Why are teaching aids very important in teaching nursery pupils?

The use of teaching aids is essential in nursery settings. Among the many advantages of teaching aids are their ability to assist pupils to develop their reading abilities, illustrate or reinforce a skill or concept, differentiate training, as well as reduce anxiety or boredom by presenting information in a fresh and engaging way.

Since there are no restrictions on the kind of teaching aids that can be used to enhance a lesson, they also stimulate the pupil’s other senses.

  1. Teaching aids are helps teachers to close the reading gap and improve the reading comprehension skills of pupils.
  2. When teachers need to reinforce a skill or concept, teaching aids prove to be a powerful addition. They not only give pupils more time to practice, but they also present the information in a different way, giving pupils a new way to interact with it.
  3. Using visual aids gives pupils a new perspective on the topic and provides them with visual stimulation.
  4. The learning environment is made more interesting and interesting by teaching aids.
  5. Exciting presentations about a particular topic keep pupil’s attention rather than requiring them to concentrate on lengthy teachings.
  6. A teaching aid makes class examples come to life to the pupils and, as a result, clears up any confusion.

What are the stages of moral development in a child?

Moral advancement in youth might be viewed as one of the focal parts of socialization. Based on social and cultural norms, it is a process by which children learn to distinguish between right and wrong. Children’s morals are taught in large part by their parents and teachers.

educational psychology - child's moral development

The capacity to discern between right and wrong in one’s intentions, thoughts, actions, and behavior is morality. The primary objective of parenting is to impart this idea to children. The concepts of morality that a child acquires from birth through adulthood are referred to as moral development.

Stage 1: Infancy

Children’s moral development begins in infancy. Other than having a sense of rightness or wrongness as those feelings apply to himself, an infant cannot moralize. A baby is brought into the world expecting to be cared for for the next nine months in the womb. Baby concludes that hunger is incorrect despite never being hungry; It aches. Baby, who has never been left alone, finds it wrong to be alone; It scares me. Baby is always in touch and knows that being unresponsive is wrong. It feels right to be held in arms and responded to! Baby develops a sense of rightness that becomes her “norm,” and she believes she is the center of the universe.

Stage 2: Toddlers (ages 2 to 3 years old)

At this age, your child understands that other people also have rights and needs. He hasn’t yet figured out the difference between right and wrong, though. A toddler between the ages of two and three may exhibit moral and empathy-based guilt. The toddler learns that obedience is expected based on the parents’ actions.

Stage 3: Preschoolers: (ages 3 – 5)

Your child learns to internalize family values at this age. Rules and norms become important for your child as well because they are necessary for maintaining discipline in the family.

Your child anticipates that parents or other elders will take charge. They are aware of the distinction between “child” and “adult” and anticipate that maturity will be directed toward them. The child understands that what he or she does has repercussions: “If I do this, this will happen.”

The child connects with his parents and exhibits good behavior. Until he is not caught, the disconnected child will do whatever he wants.

Stage 4: Kids (Ages 7 – 10)

Children between the ages of seven and ten begin to question the infallibility of their parents and teachers. It’s possible that those in charge do not know everything. They hold the most respect for mature adults who are unbiased and able to exercise authority. Authority isn’t threatening to the youngster yet is important for social living.

They hold that children ought to follow their parents’ orders. Additionally, school-age children believe that they should be corrected if they break a rule. Some children are more likely to tattle due to this strong sense of “should do” and “should not do.”

Stage 5: Teens aged 11 to 16:

Children begin to develop their own moral principles as they approach adulthood, as well as question and evaluate the ones that their parents instill in them. Your adolescent will see rules as a set of social guidelines that benefit everyone, broadening his moral perspective.

While they respect rules, they also negotiate. As they improve their abstract reasoning skills, they develop an interest in what is beneficial to society as a whole. Your teen will begin to realize that the actions he takes have an impact on those around him. Your teen may alter or change his morals and values in order to be accepted by peers.

What Are the Qualities of a Good Leader?

The following are the qualities of a good leader.

  1. : Honesty and virtue are valued by leaders. They are supported by people who share their vision.
  2. : Leaders are great influencers because they are self-motivating. Their followers are encouraged by them. They assist others in comprehending their roles within a broader context.
  3. : Leaders are excellent communicators. They are open with their team and share both their successes and failures.
  4. : Visionaries are at the top. They know exactly what they want and how to get it. Leaders can effectively convey their vision to their team by communicating well.
  5. : The status quo is challenged by leaders. As a result, they never lose hope. They also have unique approaches to problem-solving.
  6. : Hortense le Gentil, a leadership coach, is of the opinion that hard decisions should be made by leaders using their intuition. Especially, because intuition relies heavily on a person’s previous knowledge and life experiences, making it more useful in complicated situations.
  7. : A leader’s ability to empathize with others and feel their emotions will help them build a strong bond with their team. A leader will also be able to better address the issues, concerns, and aspirations of his team members with the assistance of these characteristics.
  8. : Even though a leader needs to have empathy, it’s not a good idea to be overly emotional when making a big business decision. As a result, an objective leader is essential.
  9. : A good leader must be able to think creatively and find business solutions to difficult issues. A leader should also be analytical and weigh the advantages and disadvantages before making a choice. An all-inclusive leadership training program can improve this quality.
  10. : Someone who is open to new concepts, possibilities, and perspectives is a good leader. Understanding that there is no right or wrong way to do things is essential to being a good leader. As a result, a successful leader is always prepared to listen, observe, and adapt. They also think outside the box, which inspires their teams to do the same. All of these aspects will be covered in depth when you enroll in a leadership program.
  11. : A successful leader is aware that implementing a business strategy requires time. They also hold the belief that success can be achieved through “continuous improvement and patience.”
  12. : Because leaders are familiar with the idea of “continuous improvement,” they are also aware that being adaptable will ensure their success. Nothing goes according to plan. Therefore, being adaptable and intuitive enables a manager to maintain his composure in complex circumstances.

What is the place of communication skills in education management?

The process of exchanging ideas, thoughts, opinions, knowledge, and data in such a way that the message is received and understood with clarity and purpose is called effective communication. The sender and the receiver are content when we communicate effectively.

In education management, communication is important to both teachers and students.

  1. Communication and its composition are both integral to a foundational educational experience.
  2. The significance of providing students with proper communication instruction begins in the formative years.
  3. Throughout their early education, students are required to develop speaking and listening skills in accordance with the Common Core standards. This is to lay a central comprehension to plan understudies for school and their future professions.
  4. Good communication skills enable teachers to effectively assess the effectiveness of learning on students. The most efficient method for assessing a communication course’s effectiveness is to measure how students have progressed over time. A digital media platform that tracks students’ progress over time is used to measure progress.
  5. Through good communication, students are able to understand their assignments when it is communicated and what is expected of them.
  6. With good communication skills, student and teacher evaluation is made simple across school borders and curriculum assessment.
  7. Good communication skills enable the principal, teachers, as well as students to use the right communication medium to divulge the right information at the right time.

What do you understand by bureaucracy in schools?

Max Weber, a German sociologist, and political economist developed what is now referred to as bureaucracy as a theory to manage companies rationally and effectively. According to Weber, bureaucracies not only boost productivity and guarantee equality in the private sector but also in the public sector, which includes governmental institutions, educational institutions, and other businesses.

Although bureaucracy is a practical technique for organizing education, it contains intrinsic flaws that indiscriminately perpetuate both desired and undesirable societal problems.

A bureaucracy is a large, formal secondary organization with clear rules, a hierarchy of authority, and impersonal interactions among its members.

Theoretically, bureaucracies are meritocracies that boost productivity, guarantee equality of opportunity, and ensure efficiency. In fact, some people benefit from social and structural advantages, such as a dominant race, language, or culture, to which others may not have access.

The Industrial Revolution laid the groundwork for the current educational system. Standardization, specialization, and hierarchy came to define the school environment. It is difficult to bring about appropriate and immediate change in schools when it is required by society’s shifting needs.

Nonetheless, reorganizing bureaucracy is a necessary step toward resolving today’s pressing school issues. Issues in the present educational systems have established the innate meaning of organization. The extreme centralization of schools is one example of this kind of issue.

A centralized school system is run by professional administrators. The bureaucracy is under their control. They are authorized to oversee education. The administrators favor a centralized educational system for these reasons. A system like this keeps the administrators in charge.

However, these people do not make the effort to live within their schools’ communities. They are not a part of community life on a daily basis. The student’s education suffers as a result of this. As a result, the convergence of education and education would greatly benefit from a methodical approach to decentralization.

The staff of a decentralized school district would be made up of members of the community. These chairmen would incorporate the director. The community’s teaching staff would be warm and welcoming to the student. In school, the student would feel “at home.” The school would no longer be a place where people could talk about nothing personal. In a decentralized system, the quality of teachers would remain constant.

How do you Administrate School Laws in Nigeria?

Education Law is part of the law of Nigeria that purposefully governs educational institutions operating within her borders.

Because the average Nigerian teacher does not consider the notion of the education law to be significant for his or her duties as a teacher, an administrator, or for the welfare of the pupils, it is not widely accepted.

A state’s, a city’s, an area’s, or a nation’s education legislation is the section of the law that deals specifically with the administration of educational institutions such as public and private primary and secondary schools, and tertiary and non-tertiary educational institutions.

It is crucial to note that in order to comprehend education legislation, one needs to look at a number of pertinent problems, such as;

  1. The institution’s financing sources
  2. Staff requirements for teachers and support staff
  3. Requirements for hiring teaching and non-teaching employees
  4. Hiring and firing of teaching personnel as well as non-teaching staff
  5. Staff training and retraining
  6. Staff roles and responsibilities, including those of students
  7. Meetings, quorums, and punishment

To administer the education law, the principal and teachers in different schools, public and private, should know the various sources and content of the law. For example, the constitutional source of education law states:

  1. Government shall direct its policy toward ensuring that there are equal and adequate educational opportunities at all levels.
  2. Government shall promote science and technology
  3. Government shall strive to eradicate illiteracy and to this end, government shall as and when practicable provide:
    • Free, compulsory, and universal primary education.
    • Free secondary education.
    • Free university education and
    • Free adult literacy program.

In addition to the constitutional sources, there are federal and state statutes, case laws decided by courts, etc. With the knowledge of education law, both public and private schools can implement things like.

  1. Buying properties for the purpose of erecting an academic structure.
  2. Recruiting teachers and school administrators. All necessary skills and terms should be carefully considered.
  3. Seeking funding for the school for various reasons. Whether loans, grants, or donations, the laws guiding such funding must be considered.

How Would You Apply a Selected Motivational Theory in A School Setting?

We can accomplish a specific objective thanks to motivation. It is a crucial component of learning since it is crucial to both teaching and learning. It makes lessons more enjoyable for kids in the classroom, which improves learning. Maslow’s hierarchy of needs, Herzberg’s two-factor theory, incentive theory, and other motivational theories can all be used in the classroom.

The incentive theory

The incentive theory is predicated on the idea that every action has a favorable outcome, sometimes known as a reward. This paradigm, in which a student is guaranteed some kind of reward if they work hard and do well, can drive students into the classroom. According to this belief, any achievement or success should be followed with some sort of incentive (Beck, 2008)[1].

What Do You Understand By Micros-Teaching?

Micro-teaching is a teacher training and faculty development strategy in which the teacher analyzes a recording of a teaching session in order to receive constructive feedback from peers and/or students on what worked and how to improve their teaching technique.

Dwight W. Allen created micro-teaching at Stanford University in 1963, and it has since been applied to train teachers across many subject areas.

When a teacher gives feedback to their students and colleagues after seeing the recording of their own lesson, this is known as micro-teaching.

Micro-teaching is a unique teaching practice model or teaching development technique. There are numerous behaviors that take place in this educational context, including the application of methods, the use of media, learning guides, motivation, classroom management, assessment, analysis, and so forth.

Fundamental principles of micro-teaching:

To broaden its impact on teachers’ overall development, microteaching is based on a set of fundamentals.

Fundamental principles of micro teaching - Education psychology
One skill at a time:

In microteaching, each skill is worked on individually. Particular skills are taught until they are mastered. After mastering one skill, another one is targeted. As a result, microteaching concentrates on one skill at a time.

Substantial content:

The trainees have more freedom and ease when the content is limited. As a result, limited content is the foundation of micro-teaching. Since teachers are expected to prepare their lessons around the given content, it will be easier for them to teach.

Practice makes perfect:

Practice is required to master skills. The micro-teaching program not only focuses on one skill at a time but also gives students the chance to practice those skills. A lot of practice can help you develop your teaching skills and boost your self-confidence.


Any concept relies heavily on experiments. Numerous experiments are carried out in microteaching to evaluate teachers’ abilities.

Momentary input:

Microteaching uses students as teachers and supervisors. The teacher-student and supervisors provide feedback at the conclusion of each session. After the lesson plan is finished, this feedback is given right away. As a result, it aids in overcoming its shortcomings.

Possibilities for self-evaluation:

Every task relies heavily on evaluation. In micro-teaching, supervisors administer multiple tests, providing numerous opportunities for error analysis. Evaluation provides an opportunity to comprehend and rectify the error. There is a session in this program where shortcomings and solutions are discussed. As a result, achieving overall improvement becomes easier.

Constant efforts:

Skills development is a slow and ongoing process. One should always strive for improvement, even after mastering a previous skill. Making consistent efforts makes overall development simpler.


The knowledge of educational psychology will make you a better teacher. It is also a great and effective way to impart relevant knowledge to learners. This article discussed education psychology in addition to microteaching. You can now use the comment box to give us your feedback.

[1] Beck, R. C. (2008). Motivation: theories and principles. Englewood Cliffs, N.J.: Prentice-Hall.

Rounding Numbers: A Comprehensive Guide to Understanding the Basics

Rounding is a systematic way of simplifying a number while keeping its value close to the original. It is a mathematical operation that is used to write a number in its simpler form.

To round a number means to rewrite the original number in a simple form with a slight deviation.

The number rounded has a nearby value to the original and is easy to understand.

The round number is used in many fields like engineering, science, finance, the stock market, etc.

This article will introduce rounding numbers and the methods. If you are in any way confused about how to round numbers, continue reading.

What are Rounding Numbers?

Rounding a number is a systematic way of approximating the value of a such number. It is a way of rewriting the number so that the value stays close to the original value.

When you round a number, the final result is usually less accurate, but easier to use in computations.

For example, the final weights of 5 loaves of bread recorded by the quality control officer in grams are:

87.95, 90.24, 89.7, 88.05, and 90.35.

To easily calculate the average weight, we can convert the weights to the nearest whole number as follow:

88, 90, 90, 88, and 90.

Looking at the above round numbers you see that they deviate from the original value but are easy to compute.

Thus, rounding numbers are the simplest approximates of very large and small numbers. The process of approximating a number to its nearest number is known as rounding.

In the real world, we can perform rounding for those numbers for which the exact values do not hold much importance. But when dealing with financial values, it’s not always the best option to round numbers except with large decimals.

For example, we can round the value of 2.0125861 to 2.0126 instead of just 2. This is because multiplying the 0.012586 by 1000000 will result in 12,586. So, rounding to 2 means that you are losing 12,586 per 1 million.

There are usually two ways to round a number: round up, and round down.

Round up

When rounding a number, we approximate a number depending on the value next to it. Values are on a scale of 0, 1, 2, to 9, and the value halfway is 5. When the value next to the round number is 5 and above, we can round up the number.

Thus, round-up means increasing the value of the round number if the next value is equal to or greater than 5. This is not a rule, it depends on the situation on the ground. But it is what people generally do.

Round down

On the other hand, round down is decreasing the value of the round number if the next value is less than 5.

In our examples, we shall be rounding up or down depending on the value next to the round number.

Please, note that rounding up or down is at your discretion. You can choose to round up or down to ensure that your data does not deviate completely from an actual value.

For example, look at the table of data below.

rounding numbers examples

The sum of the first round-up deviated significantly from the actual value. But with the value in the green cell rounded down to 91, the sum became closer. So, choose whether to round up or down depending on the data accuracy you expect.

General rules for rounding numbers

There are acceptable rules that students should follow when rounding numbers. But an independent worker can choose his/her rules based on his/her discretion.

The general rules to be followed are as follows:

  • Determine the round number calculation. Is it to the nearest ten or tenth, whole number or hundred, etc.
  • Based on the above, locate the rounding digit in the number to be rounded. For example, to round the number 752 to the nearest ten, the rounding digit is 5. To the nearest hundred, the rounding digit is 7.
  • Haven identified the rounding digit, look at the value next (to the right) to the rounding digit. This value will determine whether you should round up or down
  • If the value next to the rounding digit is equal to or greater than 5, round up. This implies that the rounding digit will increase by 1. If the value is less than 5, round down. This means the rounding digit will remain the same.
  • Finally, whether you are rounding up or down, the values after the rounding digit will become zero (0).

How to Round Numbers

Rounding numbers is easy if you understand the basics. In this section, you will learn the basics of rounding numbers.

In number counting we begin from 1 and count to 10, then 100, 1000, and continuously. Thus, we have ones, tens, hundreds, thousands, ten thousand, hundred thousand, million, billion, and trillion.

Likewise, in places where decimals are represented, we have tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, billionths, and trillionths. Where the tenth is the inverse of ten, etc.

Naturally, Ones, tens, etc, and tenths, hundredths, etc are represented in the table below. Where the tenths, and hundredths represent the decimal or fractional part of a number.

How to round numbers

Consider the following example. The total sales of Ucheson & Sons for the month of January 2023 were 12,355,468.6523.

Let us represent the above in a table for clarity.

Rounding numbers placeholder chart

The above table shows a typical way to represent a number for onward rounding.

Values to the left of the decimal are ones, tens, etc, and values to the right are tenths, hundredths, etc.

Based on the above, you can round whole numbers to the nearest ten, hundred, thousand, etc. However, decimals are rounded to the nearest tenth, hundredth, etc.

Though you can easily round numbers using a rounding numbers calculator, you should know how to round numbers. In this section, you’ll learn some of the methods of rounding numbers.

How to round off decimals

A decimal number is made up of two parts. The whole number part and the fractional part. The decimal point separates these two parts.

Rounding off decimal numbers

The decimal part is the numbers to the right of the decimal point. They are usually rounded off in tenths, hundredths, thousandths, etc.

To round off decimals, the same rules explained above apply. For example, round off 78.257 to the nearest hundredth.

The answer is 78.26. (Since 7 is greater than 5, we increase the rounding digit by 1).

Rounding numbers to the nearest whole number

To round a number to the nearest whole number means eliminating the fractional part of a decimal number.

To do this, abide by the rules explained above. That is, determine the rounding digit and check whether to round up or down.

For example, rounding 78.257 to the nearest whole number will give you 78.

Rounding numbers to the nearest 10

When you think of the nearest ten, remember the chart displayed above to determine the rounding digit.

The nearest ten is a whole number with a single zero at the end. E.g. 10, 40, 7510, etc. Hence, the ones placeholder will be converted to zero. It then means that the fractional part of a decimal number will be converted to zeros.

For example, to convert the number 78.257 to the nearest 10, you’ll have 80.

Round numbers to the nearest 100

Just like the nearest 10, the nearest 100 leaves two zeros at the end. So, using the placeholder chart above, you can determine the rounding digit and either round up or down,

For example, to round the number 652410.25 to the nearest 100, we have the following result: 652400.00.

Rounding numbers to the nearest 1000

Using the idea of rounding numbers to the nearest 10 and 100, we can round numbers to the nearest thousand.

You’ll need to understand the placeholder chart to determine the rounding unit. Also, you should know how many zeros should be left at the end. Your guess is right, 1000, that is 3 zeros.

 For example, to round the number 652410.25 to the nearest 1000, you should have 652000.

Rounding Numbers Examples

Let us discuss how to round numbers with a simple example so that you can have clearer knowledge.


Oxlade Proclo LLC posted its financial report on its website. When comparing the results, the group managing director identified deviations between the hardcopy and the electronic reports. The table below is an excerpt of their sales for 6 months. Use it to answer the questions that follow.

MonthSales in $
January    58,764.25
February    78,654.45
March  105,423.05
April  95,015.00
May  152,470.55
June  87,265.10
  1. Convert the monthly sales to the nearest tenths
  2. Convert the monthly sales to the nearest thousand
  3. Total the original values and that of the nearest 1000. What is the difference?


  1. Let’s first place the numbers in a placeholder chart as follow:
Rounding to the nearest 10

To convert to the nearest tenth, the table below shows the rounding digit in the yellow column.

Rounding to the nearest 100

The numbers to the right of the rounding digits in rows 1, 2, 3, and 5 are 5 and above. Thus, we add 1 to the rounding digits (that is, round up).

But the number to the right of the rounding digits in rows 4 and 6 are less than 5. Thus, we leave the value of the rounding digits the same.

Therefore, the table below shows the result of rounding to the nearest tenth.

Rounding up or down

The new sales report will become as follow:

MonthSales in $
January    58,764.30
February    78,654.50
March  105,423.10
April  95,015.00
May  152,470.60
June  87,265.10
  1. Here, we’ll convert to the nearest 1000. Like in the above solution, let’s place the numbers in a placeholder chart and identify the rounding digit. The table below shows the placeholders and rounding digits with a red border line.
Determining the rounding digit in rounding numbers

The numbers to the right of the rounding digits in rows 1, and 2 are 5 and above. Thus, we add 1 to the rounding digits (that is, round up).

But the number to the right of the rounding digits in rows 3, 4, 5, and 6 are less than 5. Thus, we leave the value of the rounding digits the same (round down). We then convert all values to the right of the rounding digits to zero.

Therefore, the table below shows the result of rounding to the nearest thousand.

Rounding numbers example

The new sales report will become as follow:

MonthSales in $
January    59,000.00
February    79,000.00
March  105,000.00
April  95,000.00
May  152,000.00
June  87,000.00
  1. Here, we sum up the two sales and subtract the results. The table below shows the result.
Rounding numbers to the nearest 1000

From the result obtained above, you’ll notice a deviation of $592.40 from the original sales report. However, rounded numbers are easier and simpler to calculate.

I believe that the above example has given you a clearer understanding of how to calculate round numbers.


Rounding numbers is a common mathematical operation that is used to approximate numbers in order to understand them easily. It is mostly used in scientific calculations where you’ll need to approximate experimental data to easily compare their values.

Students in primary and secondary schools should learn and understand them. Also, applicants, employees, and business owners should learn them.

Though it makes computations easy, its results deviate from the original. However, you can randomly round up and down values to arrive at a very close result.

The rounding numbers calculator makes these computations easy, but it’ll be great if you understand their calculations.

This tutorial discussed how to round whole numbers and decimal numbers; it is now your turn to respond.

I will want you to ask questions and make contributions with regard to rounding whole numbers and decimals. Have you used round numbers before, and in what circumstances? Please, use the comment box below and respond, and do not forget to share your experiences.

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