30 Oct Backwards Designing Curriculum from the SAT
At my school, students can get A’s in all our classes, yet score relatively low on the SAT. A plausible explanation for this discrepancy is a misalignment between what we test in our classrooms and the content of the SAT. Troubled by this possibility, I endeavored to reengineer our Algebra 2 curriculum around the SAT. We can deride it as “teaching to the test,” but backwards design is a well-respected approach to building curriculum.
SAT Practice Tests and Unit Planning
First, I had to figure out what the hell is really on this test. The best evidence is the eight official practice tests released by the SAT. Assigning myself the type of card sort activity I love giving my students, I chopped up all the questions from these eight practice tests and sorted them into categories.
The result was this document. It’s certainly not perfect, but it’s the best I could do before going insane by moving these four hundred sixty-four little pieces of paper around! This document can be used for at least two purposes: (1) developing a pacing guide to make sure all topics are covered before the big day, and (2) deciding what to cover within a particular unit.
I will focus mainly on how we can use the SAT questions to drive a particular unit.
As an example, consider the unit I began the year with: Linear and Exponential Functions. This unit only came about from studying SAT questions. Typically, I pair exponential functions with logarithms and study them both closer to the end of Algebra 2. However, there are no logarithms on the SAT. Plus, the questions with linear equations pretty much divide into two types: applied linear functions and abstract lines in the xy-plane. Thus, it makes sense to exploit the initial value / rate of change connection between linear functions and exponential functions in modeling contexts and teach both function types together. Lo and behold, there are several Common Core standards dealing with linear and exponential functions together (HSF.LE.A.1-3, B.5).
Now consider a particular SAT question like this one:
Following the principles of backwards design, we ask ourselves: if this is a problem we want our students to be able to solve on a quiz, what learning experiences would prepare them?
Let’s see how we can transform this SAT problem into a rich activity. I modified the problem slightly and scaffolded it thus:
I do not want my students to solve problems this way on the SAT, but as Tom Reardon emphasized at a recent workshop, we want our students to be able to shift fluently between verbal, numerical, graphical, and algebraic representations. Next, I enriched the problem with these further questions:
I hope this simple example illustrates how easy it is to turn SAT problems into quality learning materials. As one last example of how the SAT can drive our instruction, consider this type of problem:
There are enough problems like this one in the practice tests that we might like our students to be familiar with them. So, we could make a Desmos activity in which students can “slide” the value of k and see the effect on the graph:
If you feel inspired to transform any SAT problems into rich learning materials, please don’t hesitate to share them! Happy learning to you and your students!
Christopher Klerkx teaches Algebra 2 and Precalculus at Old Redford Academy Preparatory High School in Detroit, MI. A Woodrow Wilson Teaching Fellow, he received the M.A. in teaching and curriculum and the B.A. in philosophy and mathematics from Michigan State University. He runs the school chess club and serves as treasurer of his school’s union.