Dylan's incredible way to solve two digit and three digit subtraction and his teacher understanding what a monumentous event this was,
Today we must differentiate instruction to every student, but to do that we must understand what the students know, understands, and how the student knows. The conversation with Dylan started because the teacher noticed he always got the right answer, but he never wrote the process. Because Dylan was at the time, the explanation had to be talked out. The teacher asked Dylan to go through his thought process. Through the interview, the teacher found out what Dylan did know (that you must start with the ones column). Dylan also knew that you must subtract the smaller number from the larger number in the one's column (Dylan did not understand regrouping). However, the rest of his thinking was logical. Yet this seven year old found out a different way to arrive at the correct answer, showing divergent thinking. I am old school, so I will not use his method because I find more complicated than the algorithm in which regrouping is used.
The teacher learned about how her student solved problems, the misconceptions he had (regrouping), and he had the correct answers. Even though Dylan discovered a new way to subtract, Dylan will need to learn how to solve two-digit and three-digit subtraction.
Students need to learn various ways to solve a mathematical problem because it encourages mental flexibility, and a thorough understanding of the math, and logic behind the problem.
If teachers are to individualize instruction, you must also listen to the thinking behind the computations that the students do.
I agree...It is important to understand the reasoning behind each student's decision making so you can guide them accordingly.
ReplyDeleteI agree...It is important to understand the reasoning behind each student's decision making so you can guide them accordingly.
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