I found interesting the information regarding systematic mistakes in thinking and reasoning, known as buggy algorithms. The chapter states that these mathematical bugs develop when students incorrectly generalize productions when they encounter new problems. The example used in the chapter is that students when working on regrouping tend to subtract the smaller number from larger no matter in which column the numbers are. I think it's important for teachers to keep this in mind and immediately correct the student because students instead of stopping when they don't know what to do, apply their own rules and can make themselves believe that they are doing the work correctly since their computations are producing answers.

You point out a part of the chapter that I also found very interesting. I had this same thing happen to me when I was a younger student. I was taught how to complete a specific math skill but somehow in the mix, I understood how to complete the problem incorrectly. I taught myself how I thought the math problem should be done and unfortunately the mistake in my learning was not caught until my 8th grade year of Pre-Algebra. By that time, I had already gotten to the point where I disliked Math because I never got the high grades in the subject that I thought I should. This dislike of Mathematics continues to this day. I was taught the correct way to solve those types of problems but by that time I already had a negative attitude towards Math and have never performed well in the subject. It’s amazing to me that this issue is also one that other students face and one that could have been prevented if a teacher had paid attention to my work in earlier grades.

ReplyDeleteOne of the examples in the book is the math problem fifty-three minus twenty-seven. Students that are ready for regrouping problems already understand that you subtract a big number from a small number. Therefore, students may generalize this skill to the regrouping problem by subtracting seven from three instead of borrowing from fifty. Students who make this “buggy algorithm” mistake need to practice using concrete objects such as ten and ones units until they internalize the need to borrow. This student will also need to work with smaller numbers until this skill is established. For example, the student will need to work with a problem like the following: thirteen minus seven. When the student sees this with the tens and ones units they will see that they can’t take seven from three. They will be stuck and then realize they will need to trade the ten in for ten ones. Once the student has mastered regrouping with problems with the larger number having two digits and the smaller number having one digit, then they can move on to problems with having both the larger and the smaller number having two digits. This practice will correct the “buggy algorithm” and move the student closer to truly understanding the concept behind regrouping.

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