Mathematically Correct
Mathematics Program Reviews

Comparative Summary for Seventh Grade

The books under study break down easily into 5 groups. The top (A) group consists of true pre-Algebra texts. The next (B) group consists of books at a lower level of content that might work as pre-Algebra texts under certain situations, but which would better serve as pre-pre-Algebra texts. Given the quality of these books, a true pre-Algebra book in the same series might well score in the same range as other pre-Algebra books. The third (C) group contains books that are not suited for pre-Algebra relative to any of the books above them, but which, under certain circumstances, might work for pre-pre-Algebra. The final two groups (D, F) are unlikely to allow any significant number of students to meet our criteria for even pre-pre-Algebra.

Overall Ratings

Please read the individual reviews to determine if a particular book is likely to meet the needs of a particular school or district. As noted below, not all books with the same grade are equivalent in presentation or organization.

A - Well suited to pre-Algebra. These books may be considered 8th grade texts in some areas, but should be considered for seventh grade students where possible, and were evaluated based on seventh grade criteria.

B - Possibly suited to pre-Algebra. Definitely suited to pre-pre-Algebra. A true pre-Algebra book in the same series would probably rate at the A level

C - Not suited to pre-Algebra. May do well in certain pre-pre-algebra situations

D - Not suitable

F - Not suitable

Content Area Evaluations

The content area evaluations for each program are summarized in the figure below. The pattern of strengths and weaknesses varies from program to program. This means that careful attention to weak areas should be given in evaluating programs and in implementing them. The two content areas for expressions and equations (simplifying/solving and writing) were among the content areas with the lowest average across all programs. Work with algebraic equations was found to be more pronounced in the TIMSS countries that did well in eighth grade. In any case, all but the highest-rated programs have areas of weakness that require attention.

Content Area Ratings - Part 1
Program Property Expon Fract Decimal Percent Proport
Glencoe ** Pre-algebra
McD/L ** Alg/Geo
Saxon ** Alg 1/2
Scott Foresman/AW
Glencoe
Harcourt Brace
Prentice Hall
Saxon Math 87
McD/L Passport
McD/L Math Thematics
Dale Seymour

** These books may be considered 8th grade texts in some areas, but
should be considered for seventh grade students where possible,
and were evaluated based on seventh grade criteria.

Content Area Ratings - Part 2
Program Solve Write Graph Shape Area
Glencoe ** Pre-algebra
McD/L ** Alg/Geo
Saxon ** Alg 1/2
Scott Foresman/AW
Glencoe
Harcourt Brace
Prentice Hall
Saxon Math 87
McD/L Passport
McD/L Math Thematics
Dale Seymour

** These books may be considered 8th grade texts in some areas, but
should be considered for seventh grade students where possible,
and were evaluated based on seventh grade criteria.

Program Quality Evaluations

The ratings of program quality for the seventh grade programs are summarized in the figure below. Although the overall ratings generally follow the ratings for mathematical depth, the presentation quality and student work ratings reflect the fact that there are some substantial differences among these programs, some of which will be discussed in the next section.

Program Quality Ratings

Program Math
Depth		 Presen-
tation		 Student
Work		 Overall
Eval.
Glencoe ** Pre-algebra
McD/L ** Alg/Geo
Saxon ** Alg 1/2
Scott Foresman/AW
Glencoe
Harcourt Brace
Prentice Hall
Saxon Math 87
McD/L Passport
McD/L Math Thematics
Dale Seymour

** These books may be considered 8th grade texts in some areas, but
should be considered for seventh grade students where possible,
and were evaluated based on seventh grade criteria.

Other Considerations

Among all the books, there are clear stylistic classes. In deciding what program to use, it is important to consider how these differences will mesh with the particular needs of individual districts or schools.

The bulk of the books are very similar in style, in terms of presentation of the lessons and organization of student work. Indeed, given a single lesson in isolation, it would be difficult to determine which of these books was the source. These books are similar beyond the structure of individual lessons, in that they are, in some ways, fusions of two very different kinds of instruction. On the one hand, there are relatively clear, teacher-directed lessons with well structured problems sets and reviews. On the other hand, there are whole sets of activities that are based on discovery learning and the constructivist theory of knowledge. This fusion has a number of negative consequences. First, it makes the books very long and engenders fear that important material will not be covered in real classrooms. This concern is expressed in many reviews. Second, because picking and choosing will be necessary to use these books, there will be substantial variation from teacher to teacher and class to class in terms of both content and presentation. Finally, it makes the reviews somewhat unreliable relative to what could happen in classrooms. In general, the material in the bulk of the lessons would receive moderately high marks for presentation and student work, but many of the activities and the heavy use of calculators lead to serious concerns and a lowering of both presentation and student work subscores. In general, but not always, nearly everyone of the books in this category would be improved substantially with removal of most discovery lessons and the over use of calculators.

Reviewed books in this class include:

A second class of books are those from Saxon Publishers. The style of these books is sometimes referred to, incorrectly, as traditional. The books are what might be called traditional in terms of the particular material that is covered, in the stress on analytical methods over guess and check or graphical methods, as well as a general rejection of the need for calculators to learn seventh grade math. The books are free of any extraneous material and are short enough that a teacher starting at lesson 1 on day 1 is likely to finish the last lesson before the end of the year. The books also focus on key and important topics at teach level, without a lot of coverage of less central topics. Presentations are terse but clear, although not necessarily drastically different from individual presentations in other books. On the other hand, the homework stresses repeated, distributed practice in a way that far exceeds any spiral or cumulative reviews in any other book. Important topics are practiced regularly throughout the course and have a very high probability of being learned. The clarity of focus and the fact that choices as to what material to skip need not be made, make these books less subject to teacher to teacher variation, even as some of the material that is covered in less depth slightly lowers the mathematical depth portions of the reviews.

Reviewed books in this class include:

Finally, there are the books that commit significantly to discovery learning and a constructivist theory of knowledge. These books fall notably short in content, have ill defined goals for each lesson, as least in the eyes of the reviewers, and have insufficient or poorly designed student work. The two books in this category have the lowest ratings.

Reviewed books in this class include:

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