By David Wees, Posted May 25, 2015 –

What knowledge about students’ understanding of mathematics helps teachers plan a unit? Is it a spreadsheet of scores on a diagnostic task? Is it a list of topics that students learned about last year? Spreadsheets of scores and lists of topics corresponding to student performance do not tell you enough about an individual student’s understanding. In this and the next three posts, I'm going to outline a procedure that you, as a teacher, can use to systematically gather evidence of student performance. Additionally, I will offer some suggestions to make your teaching more responsive to student needs.

The table below lists four students’ scores on a mathematical task called Patchwork Quilt. Here is a rubric for scoring this task so that the four scores below make more sense. The overall objective of this task was for students to determine and use a linear function given a context, which is aligned to the Common Core Standard 8.F.B.4.

Student 1:  Score 8

Student 2:  Score 8

Student 3:  Score 4

Student 4:  Score 4

Which students need to learn more about the topic? What do they need to learn? Do these four scores give you enough information to determine whether these students are able to create and use linear functions that are based on a visual pattern?

Let’s look at the student work from the task for student 1 and student 2.

Both of these students understood what they were asked to do in the task. Both students found the correct answer to the problem. Do they have the same mathematical understanding?

Now look at the work completed by student 3 and student 4.

These two students were both unsuccessful on this portion of this task, and both had different solution attempts. How can the answers help you determine what kind of support and how much support each student needs?

Although students 1 and 2 had perfect scores according to the rubric, they had clear differences in how they approached the last question. Students 3 and 4 met the cut score for the task, but they were clearly not ready to solve this problem on their own. The scores by themselves hide important differences in how these four students approached this task. To some degree, for every problem given to students, information is compressed when the task is scored. The rich thinking that is evident in the student work (see the left side of the image below) is hidden in the numbers produced by scoring (in the center), which makes instructional decision making much more difficult (see at right).

In the next post, I will outline a procedure that you can use to sort student work into categories and systematically record much more information about what students understand, can do, and where they need support. After that, I will share some strategies for using that student work to inform your lesson planning.

David Wees, dwees@newvisions.org, is a Formative Assessment Specialist for New Visions for Public Schools in New York. He tweets at @davidwees and blogs at http://davidwees.com.