The introduction, found only in the teacher guide, suggests a way for the teacher to introduce the context of the lesson, clarify directions, review old ideas and make clear the connection to prior work, and sometimes to introduce a new idea. It is during the introduction that the teacher also poses the central question for the first investigation. The successful MathScape teacher develops an important balance between helping students understand the question they will be exploring without specifying how they should think about it or telling them how to do it.
The first investigation provides a means for students to explore the main idea for the lesson. This usually involves students working in pairs or small groups, using some kind of manipulative or set of tools to explore the idea. First investigations are often structured enough to give students some guidance about how to explore the idea and how to record what they come up with. The teacher’s role is to move about the classroom, observing, clarifying misunderstandings and posing questions that provide guidance or suggest a particular direction to explore.
The discussion that follows is central to every MathScape lesson. It is here that the teacher focuses the class’s attention on collecting students’ results and making sense of those results. Many discussions begin by having a subset of students report their results or their thinking process. The teacher then helps students compare different approaches, synthesize the class’s results into a set of mathematical ideas and put mathematical language and/or symbols to their results.
Working through the introduction, first investigation and initial discussion often takes 1-2 class periods, depending on the task, the mathematics involved and the interest level of the class.
Many lessons have a second investigation that often provides an extension to the first investigation – it may be more complex or take the mathematics to a next higher level. Sometimes this investigation is key to the lesson; other times, it may be optional.
The final step for each lesson wraps up the lesson by suggesting a final class discussion or writing assignment in which students often summarize main points or understandings gained from the lesson. It is not always necessary to share these results as a whole class; the teacher may decide to collect written work from this step as a means of assessing students’ understanding.