The number of student exercises is very low, and this is the most blatant negative feature of this text. These exercises are most typically at basic achievement levels with a few moderately difficult problems presented in some instances. For example, the section on solving linear systems by substitution includes six symbolic problems giving very simple systems and three word problems giving very simple systems. The actual number of problems to be solved is less than it appears to be as many of the exercise items are procedure questions. The extent, range, and scope of student work is low enough to cause serious concerns about the consolidation of learning. (Section 3: Overall Evaluation—exercises–

One can see very different views of engagement in these varied comments, and hence, one would expect varied ratings based on one’s meaning for the term.

A persistent criticism found in certain content analyses, but not in others, involves their timeliness and support for diversity. We interpret this criterion to apply to meeting the needs of all students, in terms of the level of preparation (high, medium, and low), the diverse perspectives, the cultural resources and backgrounds of students, and the timeliness of the pace of instruction.

As one illustration of the issues subsumed in this criterion, material may be presented so late in the school program that it could jeopardize options for those students going to college or planning a technically oriented career. To support Askey’s remark that a “content analysis should consider the structure of the program, whether essential topics have been taught in a timely way,” in testimony to the committee, he provided an example where the tardiness in presentation could affect college options. “For Core-Plus, I illustrated how this has not been done by remarking that (a+b)2 = a2 + 2ab + b2 is only done in grade 11. This is far too late, for students need time to develop algebra skills, and plenty of problems using algebra to develop the needed skills.” Christian Hirsch, Western Michigan University and author of Core-Plus, responded in written testimony, “the topic is treated in CPMP Course 3, pages 212-214 for the beginning of the expansion/factorization development,” and that “students study Course 3 in grade 11 or grade 10, if accelerated.” Yet including timeliness raises the legitimate issue of whether such a delay in learning this material could put students at a disadvantage when compared with the growing number of students entering college with Advanced Placement calculus and more advanced training in mathematics.

Although absent from some studies, this timeliness theme is consistent through those content analyses that focused on the challenge of the mathematics. To illustrate how this issue can be studied in a content analysis, Adams and colleagues (2000, p. 11) point out, “we find that CMP students are not expected to compute fluently, flexibly and efficiently with fractions,

The National Academies of Sciences, Engineering, and Medicine
500 Fifth St. N.W. | Washington, D.C. 20001

Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement