Home > Math News Archive Detail

<< Prev 5/4/2014 Next >>

A Worry Solved Too Late

A mathematics test is to occur in a classroom. On the student's end, the "worry" elements include the expected math anxiety, time window to produce, and ample preparation for what exactly will be asked (and how). On the teacher's end, the "worry" elements include ample coverage of topics involved (but what about making extensions or making of connections), "do-able" length (based on which student type/ability), variable level of difficulty, and clarity.

For me, another concern was the ordering of the test questions. Though I told students to jump around and respond to the one's they felt most confident first, that rarely occurred as most worked from front to back.

So, I often wondered...should the questions on a math test be ordered easiest to hardest (to build confidence in teacher's view), hardest to easiest (to be sure student's ability is properly tested and measured), or randomly mixed?Compounding all of this was the problem of whose criteria determined the level of difficulty--students' or teacher?

Serendipity occurred a few days ago, when cleaning out a book shelf....I discovered the report of an old research study (1975) conducted by the Wisconsin Research and Development Center for Cognitive Learning. It's title: "The Effect of Test item Ordering on the Performance of Children of Different Test Anxiety Levels."

The mathematics computation component of the "olde" Metropolitan Achievement Test was given to 53 grade 5 students, separated into Low, Intermediate, and High levels of test anxiety. Also, using random assignments to students using an experimental design, the MAT was administered in three different question arrangements--Easy to Hard format (A), Hard to Easy format (D), and Randomly Mixed format (M).

Do you think they found significant differences between the different formats, especially via interactions across the different anxiety levels?

The research conclusions:

  • Students tended to score higher on questions in the Randomly Mixed format, even across all three test anxiety groups.
  • The Low Anxious students tended to score higher on all three test formats
  • And "It is surprising that there is little difference between the means obtained by students who took form A and those who took form D of the test. No explanation for this occurance is offered."
Now, I know this study is old and dealt with only computation, but the last result was surprising. A strong believer in constructing my own tests (and not using vendor-provided tests), I used to spend hours and hours writing questions, arranging them, deleting items, etc....basically worrying about how to best measure what students knew of what I felt was not only being learned (emphasized) but also important. A big worry was the ordering of the questions. And this study suggested that most of my worry was for naught, as the ordering did not matter.

But, I want to re-quote the authors of the study: "No explanation for this occurance is offered."

In fact, this last statement describes most of teaching career, working with students. Whatever I tried, expected, wished, or thought I knew, students (or all ability levels) would constantly surprise me! And I was ever lost with "no explanation."

Source: Technical Report No. 297, WRDCCL, July 1975