Using the Math Toolkit

What Is It?
The Core-Plus Mathematics student texts provide investigative and summarizing questions and homework to engage students in building mathematical knowledge. The student books are the backbone of the program, but the single most useful item is student-generated: the Math Toolkit. Teachers may simply refer to this as notes, but the intention is not just to have students copy from something provided by the teacher. In keeping with current Research on Learning, the texts provide prompts at appropriate places so that students can reflect on concepts and skills, summarize them in their own words. Usually students make notes in their toolkits following major Summarize the Mathematics discussions. As students progress through the course, the decision about what to put in the toolkit and when to add to this should become a student responsibility. This summarizing activity is crucial to the learning process.

Students' toolkits should include concepts, properties, theorems, procedures, important formulas, summaries, and sample problems. Because they are chosen by students and individually annotated with hints, reminders, warnings, not only do they give an overview of the curriculum, but they function as study guides. The more individual it is, and the better it is organized, the more useful the Math Toolkit will be. Some ideas for organizing the toolkit are:

• Put titles and dates on all notes.

• Add personal notes to help recall what was tricky about an idea.

• Stay caught up.

• Highlight important ideas.

• Add examples.

• Include technology tips as needed.

How Is It Used?
The toolkit becomes a very useful device when students are doing homework or reviewing for a test or quiz. In a conventional text, there would be worked examples as reference. In CPMP, the same function is performed more meaningfully by using student class notes and the Math Toolkit. At a minimum, students should use this to review for quizzes and tests. At the teacher's discretion, the Math Toolkit may be used on in-class assessments. The philosophy of the program is to focus on conceptual development. However, there are cases where a teacher may decide that memorization of a procedure or a skill is essential. In those cases, the teacher will not permit use of the toolkit on a test or quiz. Obviously, whether as assistance on homework, or as a study guide for tests, the toolkit is only useful if it is complete, up to date, and well organized.

Some students think that if they can use a toolkit they do not have to study. But they then find that locating important information and reviewing how to use it become impossible in the context of the limited time that is available in class for assessments. The toolkit reflects the student's current thinking and understanding, but cannot replace study.