## 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

## Popularizing Lesson Study

The reason that I was away for two days was that I observed the lesson implementation in Nueva Ecija High School (NEHS). It was part of lesson study, one of the components of the 2-year project of our institute and NEHS.

Lesson study is a professional development program for teachers that originated in Japan.  In lesson study teachers collaborate with one another in developing and implementing a lesson. If you have not heard about this type of professional development program, it is now gaining popularity worldwide and is already practiced by elementary school and high school teachers in many countries.

The process in lesson comprises of the following steps:

1. Defining a teaching problem based upon student needs
2. Lesson Study planning, with the student and the teacher as the focus
3. Focusing the lesson on student thinking, learning, and misconception
4. Evaluating the lesson’s impact on student learning and reflecting on its effect
5. Revising the lesson based upon the data collected
6. Teaching the revised lesson to a new class of students
7. Evaluating and reflecting
8. Sharing the results.

The lesson developed in lesson study is called ‘research lesson.’ » Read more