the Math Toolkit
Student materials include student texts which provide the investigative
and summarizing questions and homework, and Reference and Practice (RAP)
books which provide summaries of concepts and skills, practice sets,
and tips for taking tests such as the ACT and SAT. These are the backbone
of the program, but the single most useful item is not one that is provided
but 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 checkpoints, but 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, 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.
- Have readily available a graphing calculator, graph and notebook
paper, ruler, compass, and protractor.
is it Used?
The toolkit becomes a very useful device when students are doing homework
or reviewing for a test or quiz. In a traditional 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.