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.


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!


Case Study: How a maths teacher makes his subject interesting

It’s first period, Monday morning, and I’ve written a math problem on the board. But in front of me is a room full of blank stares and lowered heads.

I’ve got to get this class motivated, so I look to one of the students in the last row. “Hey Sally,” I ask, “did you watch the Giants game yesterday?”

“No, I’m a Jets fan. They’re way better.”

Another student, Sam, pipes up, “The Patriots are the best. They have Tom Brady.”

A few other kids chime in, throwing out their favorite teams. This goes on for a minute or two. Then I turn back to Sally and ask, “What was the score of the Jets game?”

“27–14. They beat the Dolphins.”

“Was it a close game?”

I get puzzled looks, but at least the whole class is looking at me now.

“No way! They won by 13, it was a blowout,” scoffs Sally.

Another student raises his hand, “Two more touchdowns and the Dolphins would have won. The quarterback threw an interception that should’ve been a touchdown.”

“Well, what did the Dolphins need to do in order to tie the game? A few field goals?”

Heads pop up. Now I’ve got their attention.

I start by writing on the board all the ways to score in football, and how many points a team gets for each: 6 for a touchdown, 3 for a field goal, 2 for a safety, and 1 (extra point kick) or 2 (scoring on a run or pass) for a conversion after a touchdown.

Excited, the students start discussing how the game could have been tied by the Dolphins. After a bit of back and forth, they agree that a touchdown, an extra point and two field goals is the best solution to tie the game. (6 + 1 + 3 + 3 = 13 points.) Though a field goal and five safeties would have been cool to see. (3 + 2 + 2 + 2 + 2 + 2 = 13 points.)

If you have a child who struggles with math, one thing you can do is connect math to his everyday life and interests. That real-world connection can get your child excited and engaged in learning.

Football is one of my favorite ways to motivate kids because there’s literally a new, fun math problem on every play. If you watch a game with your child, you can use this to your advantage.

Ask questions about score changes, yards gained or lost, time remaining, and so on. You’re not solving problems on a worksheet. This is a chance to be the coach or the announcer and analyze the game, all while reinforcing math concepts.

Want to try it out? Here are a few of my favorite conversation starters to get the football math flowing:

Situation #1: The score is Giants 17, Dolphins 21. There’s only enough time for the Giants to run one more play. Should the Giants go for a touchdown or kick a field goal?


Five Ways to Reduce Math Anxiety in Kids: What Parents Can Do

Primary school is where it begins. This is when kids normally get introduced to math learning and when math uneasiness takes root repeatedly. Some children find math challenging yet exciting, while some find it extremely strenuous. They might feel distressed about not getting the answers correctly, or not keeping up with their levels of what the trainer or teacher is explaining.  

When kids don’t improve math learning skills at an early age, they tend to grow stress levels while doing math questions. This anxiety develops as they proceed through school and, due to the progressive structure of math, they go down further and further at the back. This generally results in hating the subject. Lack of skills and confidence in maths subjects can lead to self-hesitancy and not only below-par performance in math, but in other subjects as well.

Children who are anxious about math are expected to avoid it, which embellish a further barrier to studying math. Instead of being anxious, students should look for IMO sample papers and practice hard to participate in the International Maths Challenge and gain confidence.

Parents can play a key role in guiding to lessen their kids’ stress levels about math and develop their confidence and belief. It begins with encouraging children to learn and practice math and providing support at home. Moreover, by making Math playful and exciting at home, parents can remove negative discussions about math assignments and assure their kids to adopt a positive approach towards solving it, helping them recover their excitement and interest to learn more and grow their skills.

Some effective ways parents can reduce their kid’s math anxiety

Make math interesting at home by arranging math games and quizzes and engaging your child in math-related works around the house. 

Be up to date on your connection and viewpoint toward math. Did you know that math anxiety can be infectious? The study has shown that parents can transfer their burden and stress about math to their kids, which can lead to bad performance and marks for your kid at school. Remember that you’re not manifesting negative feelings in front of your kid. Try to develop a positive, cool attitude in front of your child. 

Reach out to your kid’s school and meet teachers to discuss how you can help your child’s math learning skills at home. There are many assets out there, including IMO sample papers by International Maths Challenge for kids to help them practice the maths concepts they’re learning at school. Ask the teacher to suggest an excellent productive resource where your kid is at in their learning. A resource that is too tough to understand can create anxiety and more hesitation!

Enhance your math skills before giving attention to your child. Use resources and IMO sample papers and practice doing math questions. Communicate with your child in a comforting, positive way about math and have daily discussions about their recent math challenges and small successes that can take them to greater heights. Help them realize that mistakes are not the end; learning opportunities are limitless.

IMC (International Maths Challenge) offers a curriculum-specific student assessment & practice resource that is created by International Maths Olympiad experts on how your children learn best and efficiently. Don’t get distracted by any usual black-and-white practice books. For more information about the maths practice, visit our website.