Production Design

Traditionally, mathematics teachers have instructed by explaining algorithms, theorems, and sample problems to large groups of students who are presumably interested in the topic at hand. Lectures may be an efficient means of transmitting information and facts from one mind to another. However, lectures may not effectively create opportunities for students to make the mathematical thought their own or allow teachers to evaluate understanding. By comparison, collaborative group work requires students to verbalize their ideas, hear the ideas of their peers, and challenge one another. The main benefit from instituting group work, therefore, is that within that framework students have a chance to think for themselves and share their developing thoughts. This process could be as simple as a teacher posing a series of questions about the properties of polygons that students discuss in small groups and report on in a large group discussion. Alternatively, groups might be involved in a more elaborate investigation that guides students in setting key criteria for classifying plane shapes. In these exchanges, teachers can more easily assess student progress and identify individual strengths and weaknesses.