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The chapter begins with a practical, step-by-step guide to planning a lesson based on the three-part lesson structure described in Chapter 4. If your students are involved in any type of field experience, are about to student teach, or even if they are inservice teachers, this guide is important. Other topics in the chapter are also practical and worth having students read.

Planning a Problem-Based Lesson

Chapter 4 of this book explains what a problem-based lesson looks like. However, I have found that this does not translate into good planning, even on the part of experienced teachers. As a result, I have developed these steps for planning a lesson. They are really thought steps or things to consider in order to create an effective lesson. I have used these steps with inservice teachers and have found them to be effective at getting them to think about the mathematics and about their students before they select a task. Two expanded lessons that reflect this process of lesson planning are found at the end of the chapter.

Diversity in the Classroom

Dealing with the wide range of abilities that frequently present themselves in today's classrooms may be one of the most difficult issues that teachers must confront. The main point to be made is that in a teacher-directed or traditional approach to instruction, there is only one method or idea offered, everyone must possess the same ideas to understand this method, and any other approaches - either sophisticated or less mature - are never considered. In a problem-based approach, every student in the room can approach tasks with his or her own ideas and strategies. This is absolutely the best if not the only way to effectively deal with a diverse class. Included in this discussion is the distinction between accommodation and modification with special consideration given to ELLs. It is important to point out that separating a class into ability groups effectively tells those in the lower groups, "You are not smart enough to get what everyone else is learning."

Planning for ELL

The table on p. 68 lists planning considerations for each of the 9 steps of the planning guide. In the right-hand column are additional considerations for English language learners. It is possible to get bogged down in a lengthy discussion of each of these suggestions. Many of these same ideas may have been covered in your students' general methods class. However, it is useful to point this table out to your students, especially if the schools they are or will be working in have a large ELL population.

Drill and Practice

With the emphasis on conceptual development and teaching through problem solving, many teachers ask about drill. To facilitate this discussion, I have offered definitions of both drill and practice that are designed to distinguish the two. (T-49) Practice is repeated opportunities to confront new ideas through problem-based tasks. The point is that students rarely develop the big ideas in a single lesson. Drill is repetitive, non-problem-based activities that are aimed at the improvement of skills already possessed. The discussion focuses on what is potentially gained from each. The important thing to stress is that nothing new is ever learned through drill. Students can only get better at what they already know. Yes drill has a place but only when students have an efficient strategy to practice and when speed and automaticity is desired. It is interesting to ponder what skills in the K-8 curriculum actually demand automaticity in this modern world.


I am offering the idea that homework can be a problem-based activity just the same as a lesson. Although homework may also be used for drill, I suggest some ideas you may find startling: provide an answer key, let students self assess their skills, never grade drill homework. Even if you disagree with what I suggest, this short section can be the basis for a useful discussion.

The Traditional Textbook

As a member of an author team for a major traditional textbook series, I believe that I can offer teachers some perspective on these books. My main agenda is that teachers not be bound to books with the belief that if they don't teach every page as is suggested something may happen. The nature of traditional textbook development makes it difficult for a page-at-a-time teacher to stand back and see the big ideas of a unit. Without a unit perspective, teachers will not well be able to implement the main ideas suggested in this text. It is also useful for teachers to understand why the books that are so popular in the U.S. are not very representative of the approach offered in this book.

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