Materials must addressmathematical content from the standards well beyond a minimal level ofcompetence.ġ3. All formulas and theorems appropriate for the grade levelshould be proved, and reasons should be given when an important proof isnot proved.ġ2. Discussionof a mathematical concept, once initiated, should be completed.ġ1. Mathematical discussions are brought to closure. Materials must be written for individual study as well asfor classroom instruction and for practice outside the classroom.ġ0. Selected solved examples and strategies for solving variousclasses of problems are provided.ĩ. When the mathematicsis understood, one can teach students how to apply it.Ĩ. Applicationsmust not dictate the scope and sequence of the mathematics program andthe use of brand names and logos should be avoided. Applications of mathematics are given when appropriate, bothwithin mathematics and to problems arising from daily life. Ample practice is provided with both routine calculationsand more involved multi-step procedures in order to foster the automaticuse of these procedures and to foster the development of mathematical understanding,which is described in Chapters 1 and 4.ħ. Many types of problems are provided: those that help developa concept, those that provide practice in learning a skill, those thatapply previously learned concepts and skills to new situations, those thatare mathematically interesting and challenging, and those that requireproofs.Ħ. Opportunities for both mental and written calculations areprovided.ĥ. Concepts and procedures are explained and are accompaniedby examples to reinforce the lessons.Ĥ. Mathematical terms are defined and used appropriately, precisely,and accurately.ģ. The content supports teaching the mathematicsstandards at each grade level (as detailed, discussed, and prioritizedin Chapters 2 and 3 of the framework).Ģ. If a statement looks to be true, studentsare told to put it into their "Tool Kit", then to be available in all settingsof study and assessment thereafter.ġ. Finally, there is a systemic misconception as to what is meant bylogical argument in mathematics. In summary, most of the program is below the specified standards leveland there is too much of an assumption that work will be done in teams.Although the publisher claims that all standards are met, several are clearlynot met and several more identified herein as met are, in fact, not adequatelymet. Overall Summary With regard to mathematics content, this program doesnot sufficiently address the content standards and applicable evaluationcriteria to be recommended for adoption. He is, however,more than happy to testify informally, by legal deposition, or in person,as to the quality and consistency of this report in comparison with thosewhich he formally helped to prepare. Nonetheless, the criteria usedherein were developed from the state criteria that Professor Bishopused for the official reviews of the 2001 adoption cycle. Although Professor Bishop was a memberof both the 19 state adoption cycleContent Review Panels, any official role as a CRP member ended withthe conclusion of the 2001 cycle so this report is that of an experiencedprivate citizen, not an official CRP review. 6.0) and the California MathematicsStandards", hereafter, "Correlation". NOTE: CPM withdrew its application to California so this report isnot based on its formal submission but, instead, on the documentthat CPM supplies as part of the Teacher's Version entitled, "Correlationof CPM Mathematics 1, 2nd ed. Content Review of CPM Mathematics Content Review of CPM Mathematics Wayne Bishopĭepartment of Mathematics and Computer Sciences
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