Wait, isn't this the opposite of what a math teacher is supposed to do?
Attention-grabbing headline aside, I wanted to explore a method for learning mathematics I never used in school. Ever.
As any proficient, self-righteous high school math student does, my years in secondary were spent whizzing through lessons and homework. From a young age, the abstractness of algebra and graphs and functions all made sense in my brain. Even though things became more difficult in my university math classes, I was generally still able to perform at a high level.
However, I recently attended a session on using manipulatives (toys, for lack of a better term) to help with math concepts and I felt so, so lost.
This understanding of mathematics is much more spatial and therefore something my algebraic mind was much less comfortable with. Here is a specific problem we were given in this session:
In a "normal" question using this information, I think I would have easily been able to acknowledge a linear pattern and create a formula for it. This question, however, forced me to make a 3x3 cube, then a 4x4 cube, then a 5x5 cube. Clearly I was not getting the picture.
I was reading in a textbook for another class about how English speakers and Chinese speakers actually activate different parts of their brain when performing math operations. The study they referenced (which you can find at the bottom if you so choose,or click here) stated that when English speakers perform math they more often use the language part of their brain, while Chinese speakers (possibly due to the use of an abacus when they learn math) more often activate the movement part of their brains.
This realization that people can actually have different brain pathways to arriving at a mathematical solution was a revelation. This allows me to see significant value in the use of manipulatives and hands-on activities to help ALL students gain a proper understanding of math.
It also helped to humble me as a mathematician.
To the person who says "I'm just not good at math, and that's that": maybe you simply needed a different approach to the problem?
-KJ
References
Tang, Y., Zhang, W., Chen, K., Feng, S., Ji, Y., Shen, J., ... & Liu, Y. (2006). Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences, 103(28), 10775-10780.
Attention-grabbing headline aside, I wanted to explore a method for learning mathematics I never used in school. Ever.
As any proficient, self-righteous high school math student does, my years in secondary were spent whizzing through lessons and homework. From a young age, the abstractness of algebra and graphs and functions all made sense in my brain. Even though things became more difficult in my university math classes, I was generally still able to perform at a high level.
However, I recently attended a session on using manipulatives (toys, for lack of a better term) to help with math concepts and I felt so, so lost.
This understanding of mathematics is much more spatial and therefore something my algebraic mind was much less comfortable with. Here is a specific problem we were given in this session:
The Problem of My Nightmares
My Solution (sort of)
I was reading in a textbook for another class about how English speakers and Chinese speakers actually activate different parts of their brain when performing math operations. The study they referenced (which you can find at the bottom if you so choose,or click here) stated that when English speakers perform math they more often use the language part of their brain, while Chinese speakers (possibly due to the use of an abacus when they learn math) more often activate the movement part of their brains.
This realization that people can actually have different brain pathways to arriving at a mathematical solution was a revelation. This allows me to see significant value in the use of manipulatives and hands-on activities to help ALL students gain a proper understanding of math.
It also helped to humble me as a mathematician.
To the person who says "I'm just not good at math, and that's that": maybe you simply needed a different approach to the problem?
-KJ
References
Tang, Y., Zhang, W., Chen, K., Feng, S., Ji, Y., Shen, J., ... & Liu, Y. (2006). Arithmetic processing in the brain shaped by cultures. Proceedings of the National Academy of Sciences, 103(28), 10775-10780.
Thanks for your thoughts Ken. I too have been humbled many times by people who can solve a mathematical problem in a much more elegant visual way than my algebra. While algebra definitely has a place a purpose, there is some beautiful mathematics that exists in other forms as well.
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