Teaching math as language

One of the biggest misconceptions when it comes to math is that there are "math people" and not "math people." I have found this not to be the case. Some of the personality types stereotypically cast as "not math people" such as artists or musicians are types who are very proficient at math. The idea that someone is not a "math person" I believe is rooted in a language barrier, not a math one.

I gave my 5 year old son 12 jellybeans. I told him that he had to split the jelly beans up evenly with his brother. My 5 year old diligently put 6 jelly beans in 2 piles, counting them several times to make sure his brother did not get more than he did. I then asked him to split the 12 jellybeans between himself and 2 other friends. He proceeded to make 3 equal piles of 4 jelly beans each. I repeated this process with all the factors of 12; 6,4,3,2. What is interesting here is that a 5 year old has the capability to divide evenly and factor the number 12. This is something many middle school students struggle with. What this shows us is that early on in our upbringing we learn computation. We develop the idea of equal parts and dividing evenly. We seem to master the idea that 2 groups of 6 and 3 groups of 4 are different ways of splitting up 12 things. However, it is when we are introduce to the language of math where our confusion sets in. If I asked my 5 year old to answer the following math problem 12÷2 (twelve divided by two), he would have no idea. There is a missing link between 12÷2 and 12 jellybeans being split between him and his brother. This link is not intuitive or natural and must be taught.

The problem I see in math education in young people is that too quickly one moves from jelly beans to symbols. The symbols we use like '+' '=' '-' '÷' are very abstract and need to be concretely understood. The power of math is its ability to abstract and solve mathematical problems well beyond the intuitive. For example, once a child learns 12÷2 = 6 the jump to more complex numbers like 126÷ 7=18 is just a process of understanding how to perform longer division. But the concept that you have 126 things and you are dividing them into 7 equal parts is not lost. However, what I see is imbalance where the students are working more on the process of understanding longer division than what division really even means. As math becomes more abstract, the need to reconnect to the concrete is essential. If a student has not fully mastered the language, then the student can become confused or even lost when trying to figure math problems out.

We learn language by repeatedly going back to words and associating them to objects and ideas. we write things down, we read books, we interact with language constantly. Math is no different. The more the symbols on paper represent real ideas, objects and computations, the more we solidify our understanding of math as language. Often when a student is confused I have them re read the definition or property that concept comes from. I have them rewrite it. I am always surprised how often I need to do this. What I have learned is that it is not that the student is incapable of understanding it is simply that it takes practice, exposure and revisiting the same basic concept from different perspectives to really achieve understanding and mastery.