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Questions for Math Students after Finishing a Problem

We’ve had some difficulties with math lately, with basic addition, areas and perimeters, estimation, and advanced algebra.  It’s frustrating for the children and for me, and I’m still struggling to find solutions.  I’ve briefly mentioned two of our approaches in my weekly wrap ups:  the need for basic fact drill and the importance of neatness and organization.  Joann had the brilliant suggestion to use graph paper to help little ones line up the numbers.

Another important approach is from our grade 7-10 math book series, Singapore’s New Elementary Mathematics.

Here’s what this high level math program tells students:

In learning to solve problems it is important to take time to think about what you have done.  At the end of each practice session, ask yourself some of the following questions.

  1. What do I like most about the problem?
  2. What strategies did I use?  Why?
  3. What did I do when I got stuck?  Which strategy helped me to get started?
  4. Did I check my work carefully?
  5. What kind of mistakes did I make?
  6. What were the hardest and easiest problems I solved?  Why were they easy or hard?
  7. Did I feel frustrated, bored or scared concerning these problems?  What did I do to overcome these bad feelings?
  8. Did I feel satisfied, happy and excited after doing these problems?

Now, obviously no one could, would, or should do this every day, but asking these questions once a week would benefit every student and help the teacher understand the source of difficulties as well.  It would lead to a level of understanding that blindly hurrying on to the next problem could never give.

Note: As a physicist and a homeschool mom, I’ve spent most of my life involved with math.

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3 Comments

  1. JoAnn says:

    Such good questions. I’ll definitely have to remember them.

  2. I always try to guess (well, really, estimate) the answer before I start, and encourage my students to do the same, so one of my questions is always “How could I have made a better estimate?”

    I also got a great suggestion from, well, I forget who, which is that at the end of a tough problem you should ask yourself “What one sentence would I want to send back in time to myself when I was starting this problem?” That makes you encapsulate your learning and point out to yourself where the real sticking point was.

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