Analyzing Data

We are taking the District Benchmark test today.  We are on an A/B schedule … so half of my students took the test on Friday.  The answers are mostly multiple choice and can be scanned so I have the results of their tests to think about today while these students test.

The district created the test to address content from November, December, and January. I thought the questions were mostly fair but also challenging.  Only one question addressed a topic we have not yet taught.

We took the test “cold.”  Students knew about the test, and they knew the topics it covered.  I pointed them to some previous work we had done, a couple of test reviews, but I did not require a review.  They also know that our PLC typically records the Benchmark test as a quiz grade.

The class averages from Friday are OK but not as high as I had hoped they would be.  They range from 73 to 79.  For advanced students I expected class averages in the 80s. I am wondering what my colleagues’ averages are.

The scoring machine produces really nice reports.  I have an item analysis for the first group of students.  Interestingly enough the 4 most missed problems all share some strong similarities and connect geometry with algebra.  Here are problems like the ones on the test …

The owner of a ranch decides to enclose a rectangular region with 140 feet of fencing. To help the fencing

cover more land, he plans to use one side of his barn as part of the enclosed region. What is the maximum area the rancher can enclose?  Only on our test, students were given the equation and asked for the domain of the problem situation.  I’m surprised at these results.

The second most missed problem is similar in concept:  A rectangular garden is surrounded by a walk of uniform width. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find an equation to represent the area of the walkway.  Again it is clear from these results that students are confused.  In this problem the confusion may be more about simplifying the math, keeping negative signs straight, than about setting up the equation.  It’s difficult to tell since I don’t have their work to study.

The third most missed problem is similar yet again but not.  This one requires them to remember and apply

the Pythagorean Theorem as well as the target skill of squaring binomials.  Suppose a rectangle has a length of 3x – 4 and a width of x + 2.  Which expression best describes the length of the diagonal of the rectangle?  These results are more polarized … may be easier to correct the error in thinking on this one.

The last problem involves the area of a triangle.  The base of a triangle is 3 inches more than twice its height.  If the area of the triangle is 64 square inches, which of the following equations can be used to find h, the height of the triangle?  Again as in the previous problem the answers selected are polarized and I can see that students forgot to multiply “64” by 2 in finishing up the problem. 

I’ll use these problems on our next “My Favorite No” activity although I won’t have student work for students to examine.  I plan to use the graph though … and ask students to discover what mistakes were made that would cause their classmates to choose the incorrect answers that were chosen.

Taking the time to reflect on these four problems this morning while my students are testing has been a beneficial use of my time.  Now I need to finish up tomorrow’s lesson plans!