Math Explanations

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This year I’ve been working with a group of 20-25 second grade math students.  I see them daily for about 20-30 minutes.  This group has been exploring a number of math concepts related to computation, place value and measurement.  At the beginning of each unit this group is given a pre-assessment and the class investigates a number of concepts for approximately a month.  During that month that class puts together and takes apart numbers, uses math tools, reflects on our math experiences and sharpens  different computation strategies.  The unit concludes with a post-assessment.  The class then reviews the assessment, looks for trends and analyzes possible errors before moving onto the next unit of study.

Every unit assessment has some type of open response which asks students to explain their mathematical thinking.  The performance on these questions has been rough. This isn’t a new experience and I wrote about this a while back here.  Students seem to have trouble creating complete math statements that answer the open response question.  Students have noticed this trend too.  Earlier in the week I ended up having a class discussion about math statements and written responses.  Through our discussion I also realized this is something that I need to learn more about.  This opportunity also had me wondering about past assignments and how often kids are really asked to explain their mathematical writing in written form.

To me, this issue looked like a professional need as well as a student need.  I looked online for additional resources related to helping students identify quality mathematical writing.  I found a few rubrics, but they were very generic and included words like “high-quality” or “fully understands the topic” that I think are valued, but not necessarily quantifiable.  So the class had another brief discussion about what math explanations should look like.  We came up with a list of what should be included:

  • Math vocabulary
  • Restating the question
  • Number models

A draft rubric was built and students completed a pre-assessment using the new expectations.  After writing a mathematical response to an estimation problem earlier in the week, students circled where they felt they were in relation to the expectation.

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I then went through the student responses and added my own thoughts in blue. Next week I’ll be passing these back to my students. This was the first time using this particular rubric and there may be changes to this as the year progresses.  I still need to hone in on helping students recognize what “restating the question” means as I think that’s a bit fuzzy.

The good news is that we’re making progress and students are becoming more aware of their mathematical writing skills.  I’m looking forward to seeing how this evolves over time.  I’ll also be sharing this with my second grade team before winter break.

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