Theoretical portraits of mathematical understanding (2)

Posted: November 28, 2013 in The root of the matter

Today in class we watched a video where a psychologist (Varner) observed and asked students to attempt and explain various multiplication questions. This video highlighted a dismal fact about our teachings of mathematics: we teach rote memorization. While watching the video, I noticed that although many of the students could quickly solve 5 and 9 times table questions; questions involving 6, 7, or 8 left most students confused and unable to solve the answer-some were still unable to complete the problem even after Varner gave strategies and hints. I believe that students were able to solve 5 and 9 times table questions because teachers will often show students “tricks” for these number groups. I also believe that students were unable to solve other number groups due to lack of actual strategies and learning comprehension.

In order for conceptual understanding of multiplication to take place, teachers must utilise past experiences (including number sense strategies) and teach both paths of multiplication: grouping and repeated addition.  For this reason, I feel that it is extremely important to teach students a variety of algorithms in order to reinforce student’s number sense; and then encourage problem solving and personal connections in order to make the math more meaningful. As we saw from the video, when students do not have good number sense, they are unable to conceptualize numbers, cannot express their logic, and rely on rote memorization.


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