PRELIMINARY CONTENT REVIEW PANEL REPORT
Publisher: McDougal-Littell Title: Structure and Method, Course 1
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. It 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.

Mathematics Content/Alignment with Standards

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 1: Concepts and Skills".

A few topics seem to have fallen between the cracks:

Measurement and geometry standard 2.1: Identify angles as vertical, adjacent, …
The only mention of "vertical angles" is on page 46 of the "California Standards Practice Workbook"; it occurs in one worked example, but in that example the student is assumed to already know the concept. (The other topics ?adjacent, complementary, and supplementary- are covered.)

Topics involving statistics, data analysis, and probability are spread in a somewhat fragmented way over three books (the main text, the "California Standards Key Concepts Book", and the "California Standards Practice Workbook".

Statistics, Data Analysis, and Probability Standard 3.4 includes understanding the probability of two independent events both occurring is the product of the probabilities.  Dependent and independent events are not covered in the main text, but are clearly explained in the "Key Concepts Book" (S92-S94.)  In certain examples (in S92-S94), such probabilities are worked out, but not by multiplying the two probabilities.  The only occurrence of the "product rule" is in a worked example on page 61 of the "California Standards Practice Workbook", but there the student is expected to know the fact already.


 

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.

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.

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


Many word problems, involving a variety of applications, are given throughout the text.

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).

The text shows (on page 231) why one "cross multiply" when ratios are equal.  (Some other texts tell students to cross multiply, but do not explain what’s going on.)

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.

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


We found no factual inaccuracies.

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

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 margins of the "California Standards Key Concepts Book" contain 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.
2. 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.
3. Probabilities of independent events are not treated adequately in this submission.  On the other hand, this topic is treated adequately, if a little tersely, on pages 420 and 421 of the Course 2 book.  Perhaps the publisher could incorporate this section as is into either the course 1 text or into the "California Standards Key Concepts Book."

Corrections and Edits.