Publisher: McDougal-Littell Title: Structure and Method, Course 2

Reviewer’s Name: CRP #4

__Conclusion__

A succinct statement summarizing the CRP’s evaluation.

x With regard to mathematics content only, this program sufficiently
addresses the content standards and applicable evaluation criteria to be
recommended for adoption as submitted.

_ With regard to mathematics content only, this program sufficiently addresses the content standards and applicable evaluation criteria to be recommended for adoption with corrections and edits as specified below.

_ With regard to mathematics content only, this program sufficiently addresses the content standards and applicable evaluation criteria to be recommended for adoption (with corrections and edits as specified below), but only for grades __________.

_ With regard to mathematics content only, this program does not sufficiently address the content standards and applicable evaluation criteria to be recommended for adoption.

We recommend this book strongly. The book is well-organized, and topics are clearly and precisely explained. We found no inaccuracies, terminological or otherwise. The book tends to explain/prove rather than just assert facts. There are many problems, including words problems throughout the text, of a range of difficulty.

A systematic review of determinations regarding the criteria in this section. Citations of standards not adequately addressed (if any) are of particular importance with regard to Content Criterion 1.

Content Criterion 1. The content supports teaching the mathematics
standards at each grade level (as detailed, discussed, and prioritized
in Chapters 2 and 3 of the framework).

x MEETS _ DOES NOT MEET

The main text covers most of the standards quite well. Because it was written before the standards were issued, some topics in the standards are missing from the text. The publisher has filled those gaps with supplementary materials, in particular the "California Standards Key Concepts Book Course 2: Concepts and Skills".

Content Criterion 2. A checklist of evidence accompanies the submission
and includes page numbers or other references and demonstrates alignment
with the mathematics content standards and, to the extent possible, the
framework.

x MEETS _ DOES NOT MEET

The citation map is on the whole quite accurate, with these exceptions:

For algebra and functions standard 1.4, there are 13 citations to the main text. However, only the first two and the last two do indeed address this standard.

References to the "California Standards Practice Workbook" are usually
off by 1 or 2 pages. For example, for algebra and functions standard
3.1, the reference to pages 52 and 97-98 should be to pages 54 and 99-100,
respectively. For measurement and geometry standard 2.3, the reference
to pages 101-102 should be to page 103.

Content Criterion 3. Mathematical terms are defined and used appropriately,
precisely, and accurately.

x MEETS _ DOES NOT MEET

In general, definitions were clear and concise and terminology was precise and correct.

However, the book defines irrational numbers in terms of their decimal
expansions (page 133). Although this is not incorrect, we would have
preferred the usual definition in terms of ratios of integers, especially
since rational numbers are defined as ratios of integers (page 108).

Content Criterion 4. Concepts and procedures are explained and
are accompanied by examples to reinforce the lessons.

x MEETS _ DOES NOT MEET

Typically explanations are followed by several worked examples.

Content Criterion 5. Opportunities for both mental and written
calculations are provided.

x MEETS _ DOES NOT MEET

Content Criterion 6. Many types of problems are provided: those that help develop a concept, those that provide practice in learning a skill, those that apply previously learned concepts and skills to new situations, those that are mathematically interesting and challenging, and those that require proofs.

x MEETS _ DOES NOT MEET

Content Criterion 7. Ample practice is provided with both routine
calculations and more involved multi-step procedures in order to foster
the automatic use of these procedures and to foster the development of
mathematical understanding, which is described in Chapters 1 and 4.

x MEETS _ DOES NOT MEET

Content Criterion 8. Applications of mathematics are given when
appropriate, both within mathematics and to problems arising from daily
life. Applications must not dictate the scope and sequence of the mathematics
program and the use of brand names and logos should be avoided. When the
mathematics is understood, one can teach students how to apply it.

x MEETS _ DOES NOT MEET

Content Criterion 9. Selected solved examples and strategies for
solving various classes of problems are provided.

x MEETS _ DOES NOT MEET

Content Criterion 10. Materials must be written for individual
study as well as for classroom instruction and for practice outside the
classroom.

x MEETS _ DOES NOT MEET

Content Criterion 11. Mathematical discussions are brought to
closure. Discussion of a mathematical concept, once initiated, should be
completed.

x MEETS _ DOES NOT MEET

Content Criterion 12. All formulas and theorems appropriate for
the grade level should be proved, and reasons should be given when an important
proof is not proved.

x MEETS _ DOES NOT MEET

On the whole, the book does a good job in this respect. For instance, it proves that vertical angles are congruent (p. 197) and that the sum of the angles in a triangle is 180 degrees (p. 204), it explains why the formulas for areas of triangles and parallelograms are true (pp. 306, 312), and it explains (using the distributive property) that the product of a positive and a negative number is negative and that the product of two negative numbers is positive (pp. 88, 89).

There is a nice explanation (p. 132) of why the decimal expansions of rational numbers either terminate or repeat. Unfortunately, it is certainly too terse for most students, but perhaps some will understand it.

We did find a few places where the text’s adherence to content criterion 12 could be improved:

The treatment of rational and irrational numbers is problematic.
In particular, on page 359, we find: "Because the square root of 55 is
a non-terminating, non-repeating decimal, we say that the square root of
55 is an irrational number." The text states this as though the non-termination
and non-repetition were obvious. We would not recommend proving the
statement, but the text should say something like:

"It can be proved that…". The same comment applies to the statement
about square roots of integers on page s23 of the "California Key Concepts
Book".

Measurement and geometry standard 2.3 includes: "Understand that when
the lengths of all dimensions are multiplied by a scale factor, the surface
area is multiplied by the square of the scale factor and the volume is
multiplied by the cube of the scale factor." This only appears on one page
(page 103 of the "California Standards Practice Workbook"), and it is just
stated as a fact, with no explanation. Although a proof is not appropriate,
an explanation is called for.

Content Criterion 13. Topics cover broad levels of difficulty.
Materials must address mathematical content from the standards well beyond
a minimal level of competence.

x MEETS _ DOES NOT MEET

.

Content Criterion 14. Attention and emphasis differ across the
standards in accordance with (1) the emphasis given to standards in Chap--ter
3; and (2) the inherent complexity and difficulty of a given standard.

x MEETS _ DOES NOT MEET

Content Criterion 15. Optional activities, advanced problems,
discretionary activities, enrichment activities, and supplemental activities
or examples are clearly identified and are easily accessible to teachers
and students alike.

x MEETS _ DOES NOT MEET

Throughout the text there are "enrichment" sections, "non-routine problem solving" sections, and "calculator investigation" and "computer investigation" sections. There is also a 24 page section of "explorations" at the beginning of the text.

For example, one of the "enrichment" sections (p. 264) explores Fibonacci
numbers. Another (p. 223) explores some ways of making ellipses.

Content Criterion 16. A substantial majority of the material relates
directly to the mathematics standards for each grade level, although standards
from earlier grades may be reinforced. The foundation for the mastery of
later standards should be built at each grade level.

x MEETS _ DOES NOT MEET

Content Criterion 17. An overwhelming majority of the submission
is devoted directly to mathematics. Extraneous topics that are not tied
to meeting or exceeding the standards, or to the goals of the framework,
are kept to a minimum; and extraneous material is not in conflict with
the standards. Any non-mathe-matical content must be clearly relevant to
mathematics. Mathematical content can include applications, worked problems,
problem sets, and line drawings that represent and clarify the process
of abstraction.

x MEETS _ DOES NOT MEET

Content Criterion 18. Factually accurate material is provided.

x MEETS _ DOES NOT MEET

The only factual inaccuracy we found was on page 265. The text states that "a pine cone is made up of 8 spirals swirling upward in one direction and 13 spirals swirling upward in the opposite direction," which is true for some, but not all, pine cones.

Content Criterion 19. Principles of instruction are reflective
of current and confirmed research.

_ MEETS _ DOES NOT MEET

The CRP members generally agreed that they would not comment on this criterion.

Content Criterion 20. Materials drawn from other subject-matter
areas are scholarly and accurate in relation to that other subject-matter
area. For example, if a mathematics program includes an example related
to science, the scientific references must be scholarly and accurate.

x MEETS _ DOES NOT MEET

The only factual inaccuracy we found was on page 265. The
text states that "a pine cone is made up of 8 spirals swirling upward in
one direction and 13 spirals swirling upward in the opposite direction,"
which is true for some, but not all, pine cones.

Content Criterion 21. Regular opportunities are provided for students
to demonstrate mathematical reasoning. Such demonstrations may take a variety
of forms, but they should always focus on logical reasoning, such as showing
steps in calculations or giving oral and written explanations of how to
solve a particular problem.

x MEETS _ DOES NOT MEET

Content Criterion 22. Homework assignments are provided beyond
grade three (they are optional prior to grade three).

x MEETS _ DOES NOT MEET

Additional Comments and Citations.

1. The book, written a number of years ago, includes a chapter about using a square root table. Of course this section could be skipped, or the teacher could indicate that the students could do the problems in the section with the aid of a calculator.

2. The margins of the "California Standards Key Concepts Book" contain in the margins references called "textbook links". However, they seem to be references to another McDougal-Little text. We recommend that the publisher either make a separate edition of the Key Concepts Book with references to the relevant chapters of the "Structure and Method" text, or else have a single edition that contains the relevant references in both texts.

3. In the current submission, citations in the standards map are spread out over the text plus two supplements. We would like the publisher for a future submission to incorporate more of the material into the main text.

Corrections and Edits.