Constructed Response Tasks vs. Selected Response Tasks in Mathematics

 In Selected Response Assessment Tasks, the answer is visible and the student needs only to recognize it. This includes items such as multiple choice, matching, and true/false questions. Many standardized tests are based heavily on selected response items. Some students can depend on guessing. These type of items can easily be scored but take longer time in preparing the items. The selected response item might cover a broader range of curriculum in a shorter time.

In Constructed Response Assessment Tasks, the answer is not visible and students must recall the answer. This includes short answer items and essay items. These type of items take longer time to answer than selected response items. The constructed response items allows students to demonstrate complete understanding and it motivates students to learn in a way that stresses organization of information.

Since both have advantages and disadvantages, which type is better?

There is no consistent advantage of one over the other. Better items are items that provide direct measure of the intended learning outcome. It takes a lot of practice to develop good assessments items.

In a mathematics classroom, the selected response tasks may measure high cognitive demands. Teachers can construct items that require students to show some work to get to the correct answer.

Grading the constructed response items is harder than grading the selected response items. The selected response items is either a correct or incorrect answer. On the other hand, the constructed responses can vary from one student to another.

In the article “Constructed-Response Test Questions: Why We Use Them; How We Score Them”, Samuel Livingston does a great job explaining the constructed response items. He mentions that there are two basic approaches to the scoring of constructed response items. There is the analytic scoring and the holistic scoring. In both cases, there are guidelines set in a rubric. In the analytic response, the rubric lists the specific features of the responses and the specific points assigned to each feature. In the holistic scoring approach, the scorer reads the entire response and makes a single judgment of the quality of the response.
Some mathematics teachers assign a grade to each step of a problem. For example, a problem might be worth 5 points. Two points for writing the equation, two points for the solving strategy, and one point for the correct answer. Other mathematics teachers might use the holistic scoring by judging the response on the last step which is the answer. Although some students might write the equation correctly, use the accurate strategy of problem solving, but at the end have a simple mathematical error when finding the final answer. Either the student gets the entire grade assigned for the correct answer or gets zero points because the answer is wrong. In mathematics, I believe that a good assessment task will include a variety of selected response items and some constructed response items. I also believe that the holistic scoring approach, in mathematics, is unfair to students.