I am of the opinion that many of the students who profess to hate math do not, in fact, hate math. They just dislike computation (the rote skills of addition, subtraction, etc.). This view of math stems from two main problems: 1) lack of understanding, and 2) lack of support for the subject (e.g., parents telling children who have trouble with school math, “Math is hard,” or, “I’m not good at math”).

From an early grade students relate mathematics to procedure. To solve the area of a trapezoid I have to add the lengths of the bases, divide the sum by two, then multiply by the height. To calculate the missing value in this polynomial I must apply the quadratic formula.

Students learn *how* the formulas work. They collect them through the years, stashing them away in their mathematics tool kits and, when the need arises, rummaging through the lot to find the appropriate tool. While this method works when pressed for time during a standardized test and faced with a question about 30-60-90 triangles for which two lengths are known and the student has to find the length of side *b*, it fails when it comes to really understanding mathematics.

Mathematics is not about the *how* so much as the *why*. Oftentimes mathematicians consider the proof for a mathematical finding more important than the mathematical finding itself.

Now, I’m not suggesting that teachers introduce elementary school students to the tedious though satisfying process of working through the proofs of 1+1 or the area of a circle, , but rather that students intuitively recognize *why* the computation works.

Some amount of memorization does help, but that is not the goal. The misconception begun in elementary mathematics instruction – that it is a manner of number and sign manipulation – creates an early atmosphere of dislike. Given a solid grounding in the concepts, one can skip down the halls of mathematics without a head full of disconnected equations, formulas, and other mathematical constructs.

In learning about area, a student doesn’t need the whole kit and caboodle for area formulas. With just the area of a rectangle/square, all other polygonal areas could be derived. For example, take a -inch square. Drawing a grid of square inches in the square’s borders, as below,

shows that its area is 16 square inches, the product of multiplying the height and the length. Cutting the square in half, you have a triangle. What does that suggest about the area of a triangle? Once you have the area of the triangle, you can determine the area of a trapezoid, which looks like a quadrilateral with a triangle attached on either side.

Eventually, by cutting pentagons, hexagons, and other “greater” polygons into triangles, you could see and explain yourself why the area of any polygon is x perimeter x apothem.

Of course, at some point in mathematics visual explanations are not sufficient. As students move into the realm of calculus, differential equations, linear algebra, and others, math focuses more on functions, variables, and algebraic constructs. Nevertheless, even at these levels – or, perhaps, especially at these levels – understanding the concepts is more important than knowing the “methods.”

The way that schools teach mathematics puts students at a disadvantage when they enter college and enroll in college-level math courses. They arrive unprepared for what mathematics really embodies – exploration, discovery, understanding – because twelve years of elementary and high school left the impression that mathematics is about manipulation, computation, and memorization.

Mathematics is, dare I say it, creative. Alas, it is also sadly misunderstood.

You’re spot on as to why I grew up hating math. I failed my first year of algebra because I couldn’t understand how adding two letters of the alphabet could result in a number. It took a special teacher to explain what a+b=4 really meant. It wasn’t until much later in life that I began to see the meaning of mathematics – beyond the memorization, computation, and confusion.

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As a lover of math and prospective math college major, I think it a most unfortunate circumstance that school math classes often misrepresent the subject. I think a growing emphasis on grades and test scores has contributed to that memorization/computation teaching method. Pressed to boost test scores for the school board, teachers stress method over matter.

I’m glad to hear that math is no longer such a hated subject for you. What a blessing it is to have special teachers like the one you met!

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It is an interesting read though I am not so into maths as you obviously do. My impression is maths also has a poor reputation in Norwegian schools. It is perceived as a dull and difficult subject. You mentioned the insuffiency of maths teaching in particular. I wrote a post about how maths were taught in China and why Chinese pupils proved to generally have higher maths skills compared to pupils from other countries. You may have a look at it if you are interested, but it is absolutely not necessary. Here is the link:

https://isabellepan.wordpress.com/2017/04/26/why-are-shanghai-pupils-so-good-at-maths/#more-542

Hope the link works.

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Thank you, Isabelle! While math isn’t everyone’s cup of tea, I think it’s a subject that deserves a little appreciation from everyone. America, in its pursuit of improving test scores, often compares its student performance with Asian countries like China and Japan. I’ll be sure to give your post a look.

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It is an old post from April last year which I shared my experience of studying maths in Norway. Not surprisingly, the method adopted by Norwegian teachers is different from the one employed by Chinese teachers. And I referred to the research conducted by BBC as part of the explanation of Chinese pupils’ excellent result of maths.

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If teachers did as you suggest (put emphasis on concepts for true understanding rather than on memorization for test scores), I may have actually liked math a lot sooner. Still not a huge fan (you of all people would know), but I’m gaining appreciation for how neat and logical it is.

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Thank you for stopping by and commenting, Emma! I read a post once that compared computation in math to fence-painting in art. If one had spent their childhood just painting fences – no creativity, no room for exploration – they might leave the experience with the conviction that they don’t like art when, in fact, they just don’t like painting fences. Students who leave mathematics classes calling curses

upon the subject don’t see the whole world of discovery that is true mathematics. They just see the years of computation – no creativity, no room for exploration.

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This is akin to chess. Knowing only the formulas is like knowing only the moves of the pieces in the game of chess. In chess, you won’t win if you are just aware of the moves but not the meanings behind them. There are many possibilities, tactics and strategies to explore if you are willing to invest some time and energy to think about them. In other words, you have to play the game in order to learn.

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That’s a great analogy, Edmark. I started to learn how to play chess in ninth grade, but haven’t had anyone with whom to play, so I’m in the “only know how the pieces move” boat.

I do admire the game, but I don’t play it very well. Thank you for sharing.

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Well written.. I think more focus should be placed on students loving maths than it becoming a stressful subject to just pass…also chess is a brilliant game for young starting minds

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Yes, I complete agree, both about the direction mathematics instruction should take and the value of chess. I don’t play chess much myself, but I do know the basics, and I watch the chess club at the local library where I volunteer. At first, only adults participated, but in the past few months more children have joined. It is amazing to watch their progress. They have such a maturity when playing the game.

I’m curious about your user name “Actuary just a student.” Are you studying to be an actuary? I’ve considered in the past year pursuing that career and have tried to learn what I can about it from articles/resources online, but nothing beats an anecdotal experience.

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Hi…. I am so inspired by your volunteer work! I am studying to become an actuary yes. I would recommend pursing this career if you have a burning passion for challenges (in the mathematical and statistical realm especially) also if you have a great sense of perseverance. It is definitely tough and I cannot tell you how many nights I’ve cried on considered changing but at the end of the day, the work is interesting and somewhat rewarding. It’s not for everyone but you will never know until you try it yourself 🙂

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Well, I do like a challenge. The combination of mathematics, economics, finance, and business in actuarial work has especially attracted me, as I don’t intend to work with math in isolation (i.e. development of theories), though I do like learning about that aspect. Thank you for sharing your experience and for the encouragement. I’ll continue to play with the idea.

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