TCHERS' VOICE / Math

Math Journals as Formative Assessment

Getting Better Together

I'm a huge fan of writing in math class! While I was teaching, I had my 5th graders write in their math journals every single day. Whether they used the journals before the lesson to write down estimations, during class to show their reasoning through a problem, or at the end of class for an exit prompt, the journals were always a safe and not-graded place for students to jot down their thoughts. No matter the prompt, I always learned so much about what they understood by reading their entries each day.

This year, as a math specialist, I get to see student writing in math classes across many grade levels, and it's so incredibly interesting. I'm able to see where it all begins, in kindergarten, before students are even writing explanations in words, to 5th grade, where the writing becomes very articulate. In each lesson I plan with teachers, we incorporate a writing aspect that we use for reflection after the lesson. The students' written pieces, in addition to our classroom observations, help to ground our reflective conversation after the lesson.

When the 3rd grade team and I planned for the lesson seen in this video, Creating a Culture of Collaborative Learning, we created an exit prompt based on the Number Talk we did with the students during class. We gave students the same image we used during class, asked them to choose two mathematical expressions shared during the Number Talk, and show how they were the same. We then used the student responses as the basis for our conversation after the activity to see where students were in their thinking about multiplication. In each of the sample responses below, we learned something about how each student was thinking.

The Commutative Property

The majority of students chose two expressions demonstrating the commutative property of multiplication. Often students see that you can change the order of the numbers in a multiplication problem and the product remains the same, however in the journal entries, we were able to see student understanding of this property in a representation.

16 x 2 = 2 x 16

Commutative Property Worksheet 1

8 x 4 = 4 x 8

Commutative Property Worksheet 2

16 x 2 = 2 x 16 and 4 x 8 = 8 x 4

Commutative Property Worksheet 3

Changing the Number of Groups and Number in Each Group

A few students noticed that when they changed the number of groups and the number of dots in each group, the product remained the same. While these students are not yet articulating how the groups are changing, this work provides a great opportunity to plan future conversations around this idea.

Number Groups Worksheet 1

Rearranging the Groups

This response is very similar to the previous responses, however this student is beginning to articulate how the groups are changing from one to another. Instead of having 10 groups of 3, the student explains he takes some dots away and adds them to another group to make 16 groups of 2.

Number Groups Worksheet 2

Relating Operations

Some students related expressions based on what they understand about the operations and were able to represent these understandings in the dot image.

Number Groups Worksheet 3

While the team and I heard and observed so many interesting things during the Number Talk itself, the journal prompt served as a wonderful formative assessment to look deeper into each student's understanding and the connections they were making.

The use of math journals has transformed the way in which I listen to students' thinking and I'm so excited to see math journaling being used at all different grade levels. The journals offered my students who weren't comfortable sharing the space to do so, while at the same time gave me so much insight into their thinking. I encourage all math teachers to incorporate math journals in their classrooms to allow students not only to explain how they answered a problem, but also to express mathematical connections, understandings, and confusions. It truly informed all of the planning and decision making in my classroom.

Kristin Gray is a National Board Certified fifth grade math teacher at Richard A. Shields Elementary School in the Cape Henlopen School District in Lewes, Delaware and a Teaching Channel Laureate. During her 19 years in education, she has taught 5th–8th grade math, as well as spent two years as a K-5 Math Specialist. She feels fortunate to be involved with Illustrative Mathematics and Teaching Channel on projects developing math tasks, facilitating professional development, and blogging about these experiences. She is always excited to share her love of teaching at conferences such as NCTM, NCSM, ISTE, as well as on her blog. Follow Kristin on Twitter: @MathMinds.

2 Comments
I used journals across all my high school math classes for years. Every Friday had a time allocated to journal writing. I committed to respond to every student in writing by Monday. Thus many weekends were spent writing responses to up to 90 students, from Grade 9 through Grade 12 I learned so much about my students (but this was a huge time sucker for me). Each journal response had two parts. The first part was always "This week in math". I wasn't looking for a blow by blow summary, but a self assessment of what they knew, what they didn't know, and what questions they might have (and were reluctant to ask in front of a whole class). I then responded with things like "check the example on page x; look at this online resource; come see me next week; etc. The second part of the journal was more metacognitive, usually with a sentence stem or starter, like "my favourite subject is _____ because_____ ; when I see a math test, I ________; my study plan for this week's assessment is ________; convince me you understand _________. I loved that I learned a lot about my students, but the time commitment was huge. I used journals for a long time, and eventually was transitioning them to an on line platform when I was promoted to vice principal.
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Hi Jeff, I completely agree, my 5th grade journals took a TON of time! Like you, I couldn't stop putting in the time because I learned SO much about them each time I read them. I also found them to be a really safe place for students to explain their thinking without any fear of judgement of right or wrong. Through the journals, I learned I had to get so much better with my feedback because I was so used to grading things that this was such an amazing push to just enjoy them, write some feedback, and see them grow each week! Thank you so much for your comments, I love hearing your prompts!!
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