Only the Evens

I can remember getting assigned work from the math textbook almost every day. We were only asked to do the even numbered problems. It didn’t seem strange that the teachers were assigning only half of the problems – everyone knows the answers to the odd numbered problems are in the back of the book. I understand why my teachers commonly did this, but it did not help me learn math.  It only reinforced the false idea that math is just about getting the right answer.   

 

Fortunately, math education has come a long way. Teachers recognize and value math as a process, not just a list of right answers. Providing students with access to the final answer is an easy way to put the focus back on the process. It is also a quick solution for teachers who have a hard time getting their students to show their thinking. The “answer” is no longer the answer. The thinking has become the answer. I tried this technique out in my own classroom one year. I would provide students with a math situation and a solution. Their focus became showing how to get from the situation to the solution. I was amazed with results. My students were able to represent, analyze and communicate mathematical ideas. Their thinking became more creative and flexible, since they were not so concerned with “the right answer.” They looked forward to working on these types of problems and would even ask for more. 

 

If we want our students to be mathematicians, we must give them opportunities to think like mathematicians. This requires a change in our instruction and our expectations. Unfortunately, thinking cannot be found in the back of the book.

 

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Training Spotlight

1st-3rd grade educators worked together to learn engaging ways to develop number sense. Students will develop fact fluency while playing games that use their number sense strategies. By learning their facts in this way, students are not merely memorizing, but rather learning to work with numbers flexibly.  “Low achievers are often low achievers not because they know less but because they don’t use numbers flexibly – they have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly.” Jo Boaler,  Stanford University, 2009

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