# [Testing Testing] SBAC Grade 11 Practice Test #11

June 3, 2013 2 Comments

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.

The SBAC Practice Tests are available for public viewing, and we are grateful to have these problems available for public comment.

Agree with the interface issues on this question. I also think the language is quite confusing.

This question is at least as much a test of whether students get thrown off by the notation “y = f(x)” as it is of the relevant standards. That notation is extremely confusing for most students because they think of f(x) as meaning the same thing as y.

Alternate question:

The graphs of y1 = 2|x – 3| + 1 and y2 = root(x) are shown. Drag points to show a solution to y1 = 2|x-3| + 1, a solution to y2 = root(x), and a solution to 2|x-3| + 1 = root(x). This modification may be a slight abuse of notation, but is clearly testing the relevant standards.

It is true that the notation “y = f(x)” is used in describing some standards, but that does not mean that knowing this notation is part of the standard (I don’t think). The authors seem to be literally testing the actual written standard rather than using a specific example that addresses the standard.

They did not ask student to place a point that “is” a solution, they asked them to place points that “shows” a solution. So I think I am ok with choosing a point to “show” the solution to f(x) = g(x).

With two of the questions you have a 50% chance by guessing – not good. Maybe ask for a point that meets more than one condition? Also, how would they determine which point the student meant to go with which question?

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