We Got A Problem #13: Deal or No Deal






[Testing Testing] SBAC Grade 11 Practice Test #4


Here’s Problem 4 from the SBAC Grade 11 Math Practice Test.















[Testing Testing] SBAC Grade 11 Practice Test #11

Each “Testing Testing” post will analyze a released test item, focusing on both the mathematics and interface involved in the new breed of SBAC and PARCC exams. Interfaces can have huge effects on how problems are posed, read, answered, and scored. Posts will also provide suggestions on how to improve these exams, in terms of the mathematics presented, and also in terms of the interface students will use when taking exams.

Here’s Problem 11 from the SBAC Grade 11 Math Practice Test.  (A colleague suggests I have chosen Problems 7 and 11 as the first examples primarily because I love Slurpees.)


This problem targets HSA-REI-D.10 and HSA-REI.D.11, knowing that the points on a graph are the solutions to the corresponding equation, and that the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).

There is one mathematical error in the problem. When asking for “a solution for f(x) = g(x)”, the answer is an x-coordinate, not a point — something HSA-REI.D.11 states explicitly. This placement of points should be correct:


The problem interface will not allow the third point to be placed here. A placed point “snaps” to the nearest marked point on the grid. These interface behaviors need to be described in the problem, or the results can be surprising or frustrating. For example, a student might want to place their solution to y = g(x) at (0,0). The problem doesn’t exclude them from doing this, but the interface does.

The interface also causes trouble when points are placed atop one another. It looks like this:


Note that the newly placed point is not in the same position as the original. I can’t tell whether or not this solution would be accepted on the exam, and fixing the problem requires moving away the new point, then the old point, then replacing the new point. It’s a mess. If the exam requires all three points to be different from one another, this needs to be part of the problem statement, and the interface should “push” old points back to the gray area at the bottom if a new point is placed in the same location.

These interface issues can be fixed. Eliminate the dragging, label each target point in the grid, and ask the questions about the specific points. This also allows more explicit asking about HSA-REI.D.11 rather than the previous “solution for f(x) = g(x)”.


This new version keeps alive what makes the original question better than multiple-choice: there are several correct answers to each part. One might consider changing this version (or the original) to require the student to provide points that are on the graph of one function and not the other: “Name a point that is a solution to y = f(x) but not y = g(x)”.  Otherwise, a student can answer all three questions correctly with “C” without assurance that they have mastered the standard.
