General Discussion
In reply to the discussion: Why Would a Math Teacher Punish a Child for Saying 5 x 3 = 15? [View all]Ms. Toad
(34,423 posts)How they use that language is where the creative process comes in. But the foundation is a common language.
And - it isn't just that it will be easier later on, it is that it will be understandable later on - without them having to teach themselves the basics (as I had to, because of teachers who did not have a clue what they were teaching me in elementary school).
I introduced a problem solving exercise to my math classes, with subject matter ranging from about 4th grade arithemetic skills to precalculus, back in the early 80s, before it was popular. The problems they were given each week ranged from simple to ones that had stumped graduate students. The point was not to get the answer, but to play with the problems. To fail, and learn from their failure. To wander down paths that were uncharted. There were no rules beyond a requirement that they describe their problem solving experience. I get that that thinking outside the box is essential.
I have never insisted students solve a problem a particular way. When the goal was problem solving, students were free to come up with all sorts of creative paths, get stuck, and I would pick up where they were and help them figure out the next step towards a solution.
BUT - it is a different story when the point is to develop problem solving tools - the common language being one of them. In that case, there is a very specific correct answer. That problem was testing two things: whether the student understood the concept that multiplication is just repeated addition, and how to translate a product into a sum. 5 x 3 means 5 addends, each having a value of 3. It doesn't mean 3 addends, each having a value of 5. The student got the first concept, but didn't get which number in the expression represented the number of addends, and which represented the value of the addend. S/he wasn't thinking outside the box, s/he just hadn't learned what each term in a product meant when multiplication is converted to addition. It is a simple translation exercise - not an exercise in creative problem solving.
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