What Knowledge Do You Need to Plan a Unit?
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
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
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, firstname.lastname@example.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.