PRELIMINARY CONTENT REVIEW PANEL REPORT
Publisher: McDougal-Littell Title: Algebra: Structure and Method, Book 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 highly.  The book is well-organized, and topics are clearly and precisely explained.  We found no inaccuracies, terminological or otherwise.  Where possible, facts are proved/explained, not just asserted or conclude from a few examples.  There are many problems, including word problems, 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


Coverage is quite thorough.

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 quite accurate.

Content Criterion 3.  Mathematical terms are defined and used appropriately, precisely, and accurately.
x MEETS    _ DOES NOT MEET


Definitions were clear and concise.  We did not find any incorrect or imprecise use of terminology.

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


Of the algebra books we examined, this book did the best job of meeting this criterion.  For example, this book proves (pages 79 and 80) that 1/(-a) is -1/a and the reciprocal of a product is the product of the reciprocals.  On pages 152 and 155, the book proves that a^m a^n = a^(m+n) and that (a^m)^n = a^(mn).   (The proofs are appropriate to the grade level: a more rigorous proof would involve induction on exponents, but would confuse rather than clarify at this level.)  Of course the proof of the quadratic formula is presented (page 567).

One missed opportunity is the slope-intercept equation for a line: it is very easy to prove that if y=mx+b, then m is the slope, but this book does not do that: see page 366.  (It does try to make clear why b is the y-intercept.)

Similarly, the relationship (namely m_1m_2 = (-1)) between the slopes of perpendicular lines is simply asserted.  As indicated on pages 159-160 of the Framework, it is reasonable to defer the proof until the geometry course, but students should be told that it will be proved then.

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


This book is notable for the "extra" sections.  For example, on page 524, the square root of 2 is proved to be irrational.  On page 543, there is a worked example and then problems about proving the validity of the well-known divisibility tests for 3, 9, 4, etc.
On page 239, the book explains how to factor the sum and difference of two cubes.

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


This book is notable for the "extra" sections.  For example, on page 524, the square root of 2 is proved to be irrational.  On page 543, there is a worked example and then problems about proving the validity of the well-known divisibility tests for 3, 9, 4, etc.
On page 239, the book explains how to factor the sum and difference of two cubes.

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 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.
 


 

Corrections and Edits.