Constructing Open-Ended Math Problems

We communicate to students what we value through the questions we ask.  If we ask them questions always require them to memorize, then we are implicitly telling them, that mathematics is a science of procedures and formulas. On the other hand, if ask them challenging questions, we are telling them that mathematics is about problem solving.  In this post, we discuss these challenging questions — questions that are sometimes labeled as open-ended problems.

Open-ended math problems are problems with more than one correct solution and/or problems more than one correct answer. One of the benefits of asking this kind of questions is that it allows to explore more, even if they had already found the answer.  Giving open-ended math problems sometimes results to rich discussions in the classroom.

In the examples below, we revise ordinary textbook problems to produce open-ended math problems. The examples are closed ended problems, while the revised examples are open-ended math problems.

Example 1: Numbers

Which of the following symbols goes into the blank: \displaystyle\frac{7}{10}   ———-   \displaystyle\frac{5}{8}.

a. >
b. =
c. <
d. cannot be determined » Read more