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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One of my primary classes just finished up a math pre-assessment. One of the questions on this assessment asked students to explain their mathematical reasoning. Specifically, they were given a prompt, a student example, and then asked to explain in their own words what happened. Students had a lot of questions about this problem. Since it was a pre-assessment, I basically kept quiet and asked them to persevere. Some did, others didn’t.

A few students dropped their faces when they saw their pre-assessment results. Many, and I mean over half of the kids didn’t meet the expectations on the written response. Instead of putting together sentences, the majority of students created number models and that was that. Some students even wrote that the character was wrong and didn’t explain anything further. I was a bit disappointed, but no worries though – this is a pre-assessment. The actual assessment won’t happen for another couple weeks.

I noticed that I needed to look more closely at how to address the math writing issue. I also needed to clarify the expectations for written responses. This was new territory for kids. Most students are able to tell me (with prodding) their thinking and how it relates to the problem solving process. It’s a different story when it comes to writing it down. In the next few week I want to ensure that students are explaining their mathematical thinking clearly and in a way that answers the question.

So this Wednesday students were asked to start looking for specific details in their writing. We began by having the entire class analyze one math response from another “student” from a couple years ago (ok … maybe I created this). Students went into teams and analyzed the exemplar and looked for key components in the response. Students looked for an answer statement, math vocabulary and important numbers. They then coded the response with circles, rectangles and underlining. The student teams explained to the class what they thought qualified as an answer statement. This was a great discussion as students came to a consensus to what qualifies as a statement that answers the question. Students also discussed the numbers that were important and the math vocabulary that was used.

Later in the day students answered a similar prompt and then switched papers with a peer. The other student coded the paper and then the pairs discussed what they wrote and why.

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The class will be meeting next week to review more examples. Afterwards we plan on responding to a different math prompt and code our own writing. I’m looking forward to seeing how this emphasis on mathematical writing transfers throughout the year.