Teaching Math and the Plasticity of the Brain
Jo Boaler and her student, Tanya Lamar, recently made the following statement on Time magazine: "A number of different studies have shown that when students are given the freedom to think in ways that make sense to them, learning disabilities are no longer a barrier to mathematical achievement. Yet many teachers have not been trained to teach in this way." This is quite a lofty statement and yet, it is difficult to find research supporting this generalization. Accepting this statement actually means that the only reason why students with disabilities are not doing well in math is the teacher. There are correct and wrong answers in mathematics and in the sciences, there are fruitful and unproductive approaches to understanding nature. For this reason, both math and science require a combination of procedural fluency and conceptual understanding.
Take for instance the addition of fractions. Without the correct procedure and an understanding of fractions, one may simply add the numerators and denominators. This, of course, leads to the wrong answer. With just a basic understanding of fractions and addition, one should easily spot that the sum cannot be less than the two that are being added.
What one must do first is to put both fractions on the same footing.
Here, one can clearly see a combination of fluency and understanding. What is amazing is that a student can in fact learn how to do the above even without conceptual understanding by simply following blindly a series of steps:
We often learn by doing. We just have to look at the things we do like cooking, sports, music and games, to name a few. Math and science are no exceptions. And in time, we develop a deeper understanding of what we are doing.
Teaching requires a lot of patience. It is indeed important to provide learning opportunities to all. This, however, also means teaching students the right way. Effective teaching does not mean disabilities will miraculously disappear. And when students do not do well in mathematics, it is not correct to blame immediately bad teaching. Bad teaching does occur but it is not as frequent and as directed toward students with special needs that the poor performance of students with disabilities in math can be entirely placed on the shoulders of teachers. Some students will always struggle in math. This comes with any discipline. A good teacher finds ways to accommodate a child's strength and weakness and we have had good teachers before neuroscientists have even discovered the "brains’ continual potential to change".
Take for instance the addition of fractions. Without the correct procedure and an understanding of fractions, one may simply add the numerators and denominators. This, of course, leads to the wrong answer. With just a basic understanding of fractions and addition, one should easily spot that the sum cannot be less than the two that are being added.
What one must do first is to put both fractions on the same footing.
Here, one can clearly see a combination of fluency and understanding. What is amazing is that a student can in fact learn how to do the above even without conceptual understanding by simply following blindly a series of steps:
We often learn by doing. We just have to look at the things we do like cooking, sports, music and games, to name a few. Math and science are no exceptions. And in time, we develop a deeper understanding of what we are doing.
Teaching requires a lot of patience. It is indeed important to provide learning opportunities to all. This, however, also means teaching students the right way. Effective teaching does not mean disabilities will miraculously disappear. And when students do not do well in mathematics, it is not correct to blame immediately bad teaching. Bad teaching does occur but it is not as frequent and as directed toward students with special needs that the poor performance of students with disabilities in math can be entirely placed on the shoulders of teachers. Some students will always struggle in math. This comes with any discipline. A good teacher finds ways to accommodate a child's strength and weakness and we have had good teachers before neuroscientists have even discovered the "brains’ continual potential to change".
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