Historical Influences of Mathematics (Part 2 Of 3)

Three factors—the needs of the subject, the child, and the society—have influenced what mathematics is to be taught in schools. Many people think that “math is math” and never changes. This three-part series briefly discusses these three factors and paints a different picture: mathematics is an ever-changing subject.

We have already discussed the Needs of the Subject in the previous blog. In this second part, we discuss-

Needs of the Child

The mathematics curriculum has been influenced by beliefs and knowledge about how children learn and, ultimately, about how they should be taught. Before the early years of the twentieth century, mathematics was taught to train “mental faculties” or provide “mental discipline.” Struggling with mathematical procedures was thought to exercise the mind (like muscles are exercised), helping children’s brains work more effectively. Around the turn of the twentieth century, “mental discipline” was replaced by connectionism, the belief that learning established bonds, or connections, between a stimulus and responses. This led teachers to the endless use of drills aimed at establishing important mathematical connections.

In the 1920s, the Progressive movement advocated incidental learning, reflecting the belief that children would learn as much arithmetic as they needed and would learn it better if it was not systematically taught. The teacher’s role was to take advantage of situations when they occurred naturally as well as to create situations in which arithmetic would arise.

During the late 1920s, the Committee of Seven, a committee of school superintendents and principals from midwestern cities, surveyed pupils to find out when they mastered various topics. Based on that survey, the committee recommended teaching mathematics topics according to students’ mental age. For example, subtraction facts under 10 were to be taught to children with a mental age of 6 years 7 months and facts over 10 at 7 years 8 months; subtraction with borrowing or carrying was to be taught at 8 years 9 months. The recommendations of the Committee of Seven had a strong impact on the sequencing of the curriculum for years afterward.

Another change in thinking occurred in the mid-1930s, under the influence of field theory, or Gestalt theory. A 1954 article by William A. Brownell (2006), a prominent mathematics education researcher, showed the benefits of encouraging insight and the understanding of relationships, structures, patterns, interpretations, and principles. His research contributed to an increased focus on learning as a process that led to meaning and understanding. The value of drill was acknowledged, but it was given less importance than understanding; drill was no longer the major means of providing instruction.

The relative importance of drill and understanding is still debated today. In this debate, people often treat understanding and learning skills as if they are opposites, but this is not the case. The drill is necessary to build speed and accuracy and to make skills automatic. But equally clearly, you need to know why as well as how. Both skills and understanding must be developed, and they can be developed together with the help of International Maths Challenge sample questions.

Changes in the field of psychology have continued to affect education. During the second half of the twentieth century, educators came to understand that the developmental level of the child is a major factor in determining the sequence of the curriculum. Topics cannot be taught until children are developmentally ready to learn them. Or, from another point of view, topics must be taught in such a way that children at a given developmental level are ready to learn them.

Research has provided increasing evidence that children construct their own knowledge. In so doing, they make sense of the mathematics and feel that they can tackle new problems. Thus, helping children learn mathematics means being aware of how children have constructed mathematics from their experiences both in and out of school.

End Note

As we have explored, a child’s journey through mathematics is deeply intertwined with their cognitive development, critical thinking skills, and overall academic success. By addressing their individual needs, providing appropriate support, and fostering a positive learning environment, we lay the foundation for a lifelong appreciation and understanding of mathematics. But what about the broader context? How does mathematics serve society at large, and what influences has it made in history? In our next blog, we will delve into these questions, examining the societal needs in mathematics and its profound impact on the course of human history.

Historical Influences of Mathematics (Part 1/3)

Three factors—the needs of the subject, the child, and the society—have influenced what mathematics is to be taught in schools. Many people think that “math is math” and never changes. This three-part series briefly discusses these three factors and paints a different picture: mathematics is an ever-changing subject.

In the first part, we discuss-

Needs of the Subject

The nature of mathematics helps determine what is taught and when it is taught in elementary grades. For example, number work begins with whole numbers, then fractions and decimals. Length is studied before area. Such seemingly natural sequences are the result of long years of curricular evolution. This process has involved much analysis of what constitutes a progression from easy to difficult, based in part on what is deemed necessary at one level to develop ideas at later levels. Once a curriculum is in place for a long time, however, people tend to consider it the only proper sequence. Thus, omitting a topic or changing the sequence of issues often involves a struggle for acceptance. However, research shows that all students do not always learn in the sequence that has been ingrained in our curriculum.

Sometimes, the process of change is the result of an event, such as when the Soviet Union sent the first Sputnik into orbit. The shock of this evidence of another country’s technological superiority sped curriculum change in the United States. The “new math” of the 1950s and 1960s was the result, and millions of dollars were channeled into mathematics and science education to strengthen school programs. Mathematicians became integrally involved. Because of their interests and the perceived weaknesses of previous curricula, they developed curricula based on the needs of the subject. The emphasis shifted from social usefulness to such unifying themes as the structure of mathematics, operations and their inverses, systems of notation, properties of numbers, and set language. New content was added at the elementary school level, and other topics were introduced at earlier grade levels.

Mathematics continues to change; new mathematics is created, and new uses of mathematics are discovered. As part of this change, technology has made some mathematics obsolete and has opened the door for other mathematics to be accessible to students. Think about all the mathematics you learned in elementary school. How much of this can be done on a simple calculator? What mathematics is now important because of the technology available today?

As mathematical research progresses and new theories and applications emerge, the curriculum must adapt to incorporate these advancements. For example, the development of computer science has introduced concepts such as algorithms and computational thinking into mathematics education. These topics were not traditionally part of the elementary curriculum but have become essential due to their relevance in today’s technology-driven world. Additionally, as interdisciplinary fields like data science and quantitative biology grow, there is a pressing need to equip students with skills in statistics, probability, and data analysis from an early age, and here, the International Maths Challenge is playing a crucial role. This integration ensures that students are prepared for future academic and career opportunities that increasingly rely on mathematical literacy. Furthermore, globalization and the interconnected nature of modern societies require students to understand complex systems and patterns, necessitating the introduction of topics such as systems theory and network analysis. Consequently, the curriculum evolves not only to preserve the integrity and progression of mathematical concepts but also to reflect the dynamic and ever-expanding landscape of mathematical applications in the real world.

End Note

In the next blog, we will move towards the second factor: understanding the need for mathematics in a child’s education can set a foundation for problem-solving, logical thinking, and even everyday decision-making. In the following blog, we will delve into why mathematics is not just a subject but a vital tool for a child’s overall development and future success. Stay tuned for further updates!

Essential Tips to Prepare for International Maths Olympiad (IMO)

The International Mathematical Olympiad is an annual mathematics competition for primary and high school students. The first IMO was held in 1959 in Romania, and since then, it has become the most prestigious international mathematics competition for high school students. The competition involves solving a series of challenging mathematical problems over two days. Each participating country sends a team of up to six students, who compete individually and as a team.

The problems in the IMO require students to demonstrate their problem-solving skills and mathematical creativity, often involving advanced topics in algebra, geometry, number theory, and combinatorics. The IMO aims to encourage and inspire young students to develop their mathematical skills and pursue careers in mathematics and related fields.

Preparing for the International Mathematical Olympiad (IMO) is a significant undertaking and requires a lot of hard work and dedication. Here are some essential tips to help you prepare for the Maths Olympiad:

Master the Basics

You need to have a strong foundation in mathematics to excel in the IMO. Make sure you have a good grasp of the fundamentals, including algebra, geometry, number theory, and combinatorics.

Practice, Practice, Practice

The key to success in the IMO is practice. Work through as many problems as you can and try to solve them using different methods. You can find plenty of practice problems in math books, online resources, and previous IMO papers.

Join a Study Group

Joining a study group is an excellent way to exchange ideas and learn from others. It can also help you stay motivated and focused. You can find study groups online or through your school or local math club.

Attend a Math Camp

Math camps are intensive programs that offer specialized training for math competitions like the IMO. They can provide you with the opportunity to work with experienced coaches and other talented students.

Stay Up-to-Date

Keep yourself updated with the latest news and information about the International Maths Olympiad. Check out the official website and other math resources for updates, past papers, and other relevant information.

Learn from Your Mistakes

Analyze your mistakes and learn from them. Understanding where you went wrong can help you avoid making the same mistake in the future.

Stay Calm and Confident

The IMO is a challenging competition, but it’s essential to stay calm and confident. Believe in your abilities and trust your preparation.

Remember that preparing for the International Maths Olympiad requires patience, perseverance, and hard work. Be consistent in your preparation, and with the right mindset and dedication, you can achieve great success.

Can Math Help Students Become Better Engineers?

Mathematics and engineering go hand in hand. Mathematics is an essential tool for engineers and plays a crucial role in helping students become better engineers. In this article, we will explore how math helps students become better engineers.

Understanding and Applying Principles:

Engineering is all about applying scientific principles to solve real-world problems. Mathematics is the language of science, and without it, engineers would not be able to understand the fundamental principles that govern the world around us. By studying math, students learn how to analyze and solve complex problems, which is a critical skill for any engineer. Moreover, math helps students understand the fundamental concepts of physics, which is essential to many engineering fields.

Analyzing and Solving Problems:

Engineers are problem solvers, and math is an essential tool for problem-solving. Math helps students develop critical thinking skills and teaches them how to analyze and solve problems systematically. Engineers use mathematical concepts to create models, analyze data, and make predictions. These models and predictions help engineers design and build products that meet specific needs and requirements. One standard approach to building your maths skills is by participating in Olympiads such as the International Maths Olympiad Challenge.

Design and Optimization:

Designing and optimizing systems is another essential part of engineering. Math plays a critical role in helping engineers design and optimize systems. Mathematical models help engineers simulate and optimize systems to ensure that they meet specific requirements. By understanding mathematical concepts like calculus, optimization, and linear algebra, students can learn how to design and optimize complex systems.


Engineers must be able to communicate complex technical concepts to non-technical stakeholders. Math helps students develop this skill by teaching them how to use graphs, charts, and other visual aids to communicate complex data and concepts. By using math to present data and findings, engineers can help non-technical stakeholders understand the technical aspects of their work.

Mathematics is an essential tool for engineers. By studying math, students can develop critical thinking skills, learn how to solve complex problems, and design and optimize systems. Moreover, math helps students communicate complex technical concepts to non-technical stakeholders, an essential skill for any engineer. Therefore, it is important for engineering students to have a strong foundation in mathematics. By doing so, they can become better engineers and contribute to solving the world’s complex problems.

How can school students use AI to enhance their mathematics skills?

Artificial Intelligence (AI) is becoming more and more prevalent in our daily lives, and it has the potential to revolutionize the way we approach mathematics education. However, some people may be concerned that relying on AI in math could compromise students’ education. This article will explore how school students can use AI in math without compromising their education.

Firstly, it is important to understand that AI should be used to enhance students’ learning experiences, rather than replace traditional teaching methods. AI can provide students with personalized learning opportunities that cater to their individual needs and help them better understand and apply mathematical concepts.

One of the most promising applications of AI in math education is the use of adaptive learning systems. These systems use algorithms to analyze a student’s performance and provide personalized feedback, allowing them to focus on areas where they may be struggling. This can help students understand the concepts better and improve their performance.

Another way that students can use AI in math education is through online tutoring. Many AI-powered tutoring platforms are available to provide students with one-on-one tutoring sessions tailored to their individual needs. These platforms can be particularly helpful for students who may not have access to traditional tutoring services or need additional support outside of regular school hours.

In addition to personalized learning and tutoring, AI can also be used to provide students with real-time feedback. For example, AI-powered educational software can analyze a student’s work and provide instant feedback on their mistakes, helping them to correct their errors and learn from their mistakes. AI is also used vastly in Olympiads like the International Maths Olympiad Challenge.

However, it is important to note that AI should not be used as a replacement for human teachers. While AI can provide valuable support, it cannot replace the guidance and expertise of a trained educator. Teachers should still play an active role in the classroom, providing students with the necessary guidance and support to ensure that they progress and fully understand the concepts being taught. In future articles, we shall discuss the best AI sites for students to help them build their maths skills.

Mastery Learning Vs Performance-Oriented Learning, and Why Should Teachers Care?

Generally, the occurrence of students asking this question increases with growing age. Primary students know inside out that exams are very important. Brilliant middle school students consider a connection between their test results and semester mark sheets. Ultimately, upon graduation from secondary school, students have comprehended that the totality of their learning has less value than their results in the final exams.

Performance-Oriented Learning

Exam enthusiasm is an indication of performance-oriented learning, and it is intrinsic to our recent education management that needs standards-based reporting of student results. This focuses on performance apart from the method of learning and requests comparison of procurement amongst peers.

The focus for performance-aligned students is showing their capabilities. Fascinatingly, this leads to an affection of fixed mindset characteristics such as the ignorance of challenging tasks because of fear of failure and being intimidated by the success of other students.

Mastery-Oriented Learning

Mastery learning putting down a focus on students developing their competence. Goals are pliably positioned far away from reach, pushing regular growth. The phrase “how can this be even better?” changes the concept of “good enough”. Not to be bewildered with perfectionism, a mastery approach to learning encourages development mindset qualities such as determination, hard work, and facing challenges.

Most forms of mastery learning nowadays can be discovered in the work of Benjamin Bloom in the late 1960s. Bloom saw the important elements of one-to-one teaching that take to effective benefits over group-based classrooms and inspects conveyable instructional plans. Eventually, formative assessment was defined in the circumstances of teaching and learning as a major component for tracking student performance.

So where does mastery learning position in today’s classroom? The idea of formative assessment is frequent, as are posters and discussions encouraging a growth mindset. One significant missing element is making sure that students have a deep knowledge of concepts before moving to the next.

Shifting the Needle

With the growing possibilities offered by Edtech organizations, many are beginning to look to a tech-based solution like International Maths Olympiad Challenge to provide individualized learning possibilities and prepare for the maths Olympiad. The appropriate platform can offer personalized formative assessment and maths learning opportunities.

But we should take a careful viewpoint to utilize technology as a key solution. History shows us that implementing the principles of mastery learning in part restricts potential gains. Despite assessment plans, teachers will also have to promote a mastery-orientated learning approach in their classrooms meticulously. Some strategies are:

  • Giving chances for student agency
  • Encouraging learning from flaws
  • Supporting individual growth with an effective response
  • Overlooking comparing students and track performance

We think teaching students how to learn is far more necessary than teaching them what to learn.

Calling Maths Teachers: Here are Tips to Flip Your Classroom

What is a Flipped Classroom?

Most teachers understand the “Chalk and Talk” or “Direct Instruction” method. The teacher begins by reviving what they did the day before, then continue with some new theories and concepts on the board, generally seeking student attention to work through the instances. Then once the maths students have the right set of notes from the board, they would use their textbook for a particular chapter, start solving the questions given by the teacher, and expectantly complete those tasks at home for homework.

As maths tutors, we are familiar that daily practice is significant. However, the students experience problems when practising, and their teacher isn’t there to assist them. The flipped classroom vision reorganizes what comes about at home and school compared to a more conventional plan. In short, the students will first find new content mainly independently, often as homework. Then in class, most of the time burnt out practising, finishing exercises, asking questions, and working on other activities in groups, with the teacher there to guide them.

Why do a Flipped Classroom?

Flipped classrooms permit one-on-one sessions with maths students who are practising, especially for the International Maths Olympiad, so we can move further in more effective directions. Change is challenging, so why do a flipped classroom? In short, change can be strenuous but productive. Bloom’s Two Sigma Problem demonstrates that a one-on-one session is the best method for teaching and learning.

How to Flip Maths Classroom?

Choose a topic to begin with, based on the timing, but you may select a topic that you believe matches the new strategy perfectly.

No matter your standard or plan for the organization, we suggest making a calendar to organize your unit before you begin.

It would be best if you had a simple outline of what lessons or concepts you will cover each day.

If you plan to create your own video sessions, you must figure out the best video recording practices.

Explain to students

If students are used to a specific teaching style and method, changing the pattern can also be an issue for them. It’s necessary to be clear with them about the switch that is taking place, why they’re happening, and what the students should anticipate in the outcome.

This is how one can flip for a maths classroom. Happy teaching!

Amazing Facts of Maths Every Student Should Know

For many students, maths is the only subject that gives fear. Students think that it is dull. They find shortcuts, try to avoid maths, and associate this feeling with the subject. This stays with them for their whole life. 

However, maths is also a fascinating subject, and you need to know it better. Make maths your best friend and participate in various International Maths Olympiad to know how interesting this subject is!

Here you will get some interesting facts about maths that prove that the maths olympiad can also be exciting. These facts will help you in day-to-day life and are also very interesting to study.

Fun Maths Facts for Students

  1. According to this fact, from count 0 to 1000 you will find that only 1000 has the letter ‘A’ in its spelling.
  2. Odd numbers have the letter ‘E’ in spelling.
  3. Only 0 is the number that is not depicted in roman numerals
  4. If you multiply an even number by 6 you will find the digit that is ending with the same number.
  5. In 40 spelling (FORTY) every alphabet is arranged in alphabetical order.
  6. Do you know that the origin of the calculator is from Abacus?
  7. Multiply any number from 9 you will find a digit and every time sum of that digit will always 9.
  8. A number can be divisible by 3 if the sum of that digit is divisible by 3.
  9. If you put 23 people in a room, then there is a 50% chance that two of them will have the same birthdays, and in a room of 75 people, there is a 75% chance.
  10. ‘Jiffy’, it’s not only the word. It is a length of time and equals 1/100th of a second.
  11. Do you love baking then you will like the maths olympiad too! If you want to make the perfect cookie then you can apply this simple formula using the ratio of 3:2:1 which means take 3 parts of flour, 2 parts of fat, and 1 part of sugar.
  12. Do you know? You can get 8 equal parts of cake by just making 3 cuts. The First 2 cuts will make a cross on the cake and 3rd cut will be horizontal from the center of the cake.
  13. Do you know about Palindrome? A number that reads the same from forward or backward like 13431.
  14. When you add all the numbers from 1 to 100 the result will be 5050.
  15. There is a which spelled the same number of letters as the number itself.
  16. Multiply 111,111,111 x 111,111,111 you will get 12345678987654321. Here you will notice that sequence of numbers is 1 to 9 and back to 1.
  17. Circle will always have a small perimeter as compared to other shapes having the same area.
  18. If you multiply or divide with 7 you can’t answer between 1 to 10
  19. Do you know the addition and subtraction signs were used as early as 1489 AD?
  20. Add the opposite side number in a dice, and you will always get 7. Check now!

Wow! Now we know interesting facts about maths and it looks like maths is such an interesting subject. If you want to solve any question or want to become a scientist, you have to study maths because it will always be your backbone.

Studying and preparing for the maths Olympiad will enhance students’ logical reasoning and thinking abilities and help them move toward solid career opportunities.

If you are confused about participating in the International Maths Challenge ,  we are here to guide you at every step of your success. Contact us at support@international-maths-challenge.com