Addison-Wesley Secondary Math: Focus on Algebra

Section I - Organization and Features

The student text for Addison-Wesley Secondary Math: Focus on Algebra contains 843 pages organized into 10 chapters. The chapters are arranged and identified by math topics, not by context topics.

The student text contains an index with a moderate number of entries. Index entries include some context references as opposed to references to math topics.

The student text contains a glossary with a moderate number of entries. The entries in the glossary include page number references. The breadth of coverage of mathematics terms in the glossary is moderate.

There are many answers to problems for students to check their own work.

There are many pictures within the text beyond those that clearly illustrate the material being presented.

The book includes self-testing sections.

Section II - Major Topic Summaries

A) Linear equations in one variable

This is a less than satisfactory treatment of this topic. The emphasis seems to be directed away from actually doing algebra. There are close to 20 pages dedicated to "guess and check" and graphical methods for solving linear equations before they actually teach an algebraic method.

The exposition is diluted with non-analytical techniques and there is no effort to emphasize efficient solution strategies over less efficient strategies. There are creative writing, computer programs, spreadsheets and lots of graphs and charts, all of which hide the algebra.

This topic has some strong points, but the near total lack of compound or absolute value inequalities brings the rating to the lower end of satisfactory. For what is present, the quality of exposition is occasionally above average. There is a good and relevant presentation of the triangle inequality and some interesting and challenging "think" problems in the problem sets. There are too few problems at each level, although the problems on transformation of inequalities do extend to the "hard" level.

The coverage of this topic is poor. This book seems to do everything possible to avoid algebra and number manipulation in general. Much time is spent on getting a feel for functions, but the focus is on graphing and graphical presentation, not on writing and solving equations. The pages are too busy, there are too many extra subjects crammed in, and it takes too long to move from plotting points to writing accurate equations and identifying families of lines as parallel or perpendicular based on the properties of their equations. There are too many projects drumming in the same old points and too much creative writing.

This is a less than satisfactory treatment of this topic. Factoring of trinomials never goes beyond factoring with lead coefficient of 1. Factoring by grouping is missing. Solving quadratic equations is introduced via graphing and calculators. Only later is solution by factoring introduced.

Among the word problems there are lots of charts and graphs, and situations in which the appropriate equation is just given, but little opportunity to analyze a problem, convert the information of the problem to an equation, and solve the equation. Only a few sections reach the lowest level of medium difficulty problems, the others stop at easy level problems.

The presentation is generally fairly clear and the subtopics reasonably well ordered. Terms are usually defined, but concepts and procedures are often not fully explained. There are a moderate number of easy problems, but more difficult problems are few. There are often worked out examples. There is no emphasis on proof or derivation. The use of manipulatives and technology is within reasonable limits (except for matrix inversion).

There is no specific section on problem solving. However, many of these occur throughout the other subtopics. This provides some of the exposition needed. Unfortunately, this organization fails to provide worked out word problems for the more difficult cases, with one exception.

The section on matrix solutions is highly unusual. The students are given the steps to compute the solution using matrix inversion completed by a calculator. While there is a very short piece attempting to explain this process, it is very unlikely that students will understand what and why. Therefore, this is a negative use of technology and very lacking in conceptual understanding. There are medium and hard problems included, only because students can follow the directions.

In general, most of the topics are adequate to promote student learning but only at modest levels. Comprehensive and rigorous learning is not well supported. The more advanced sub-topics are ineffective or missing.

This major topic is addressed in one contiguous but short portion of the text. There is some introduction to each set, but it is inadequate. For example, the quotient of a power is merely stated with a statement to subtract the exponents. The examples for each subtopic are not at all sufficient.

The problem sets are too brief. Although the work at least involves variables rather than merely addressing the topic with numeric values, the problems never go beyond the easy level. Fractional exponents are not addressed. Student learning for application to later problems at more difficult levels is not likely to result.

Coverage of the major topic is seriously deficient in this text. It is as though having to know something about square roots to use the quadratic formula, and an obligation to present the Pythagorean theorem and distance formula, are the only reasons the topic appears at all.

The introduction to square roots is fair, but problems are only easy. The product property is mentioned, almost in passing, and given only 7 easy problems.

The Pythagorean theorem is presented along with a correct statement of the converse and telling what a converse is. A modest problem count appears, with a few that might be medium level. The distance formula appears with insufficient and easy problems.

The remainder of the major topic is not really addressed, although it is alluded to in explorations and graphing of functions.

The section on simplification cannot be successful as students aren't even given the quotient property.

The section on solutions is grossly inadequate. It merely shows you can solve a quadratic equation that doesn't have a linear term by manipulating until you can take the root of both sides.

Section III - Overall Evaluation

Math Content Coverage

The coverage of the major topics and subtopics is often poor. There is a fair coverage of inequalities and of systems of equations, but most major topics are not covered sufficiently and provide material only at basic achievement levels.

Overall the quality of presentation and exposition is poor. Terms are usually defined, but concepts and procedures may not be fully explained. There are often worked out examples for the sections that do appear, but the depth of the mathematics involved is insufficient. There is typically no emphasis on proof or derivation. The use of manipulatives and technology is sometimes within reasonable limits, but too often students are asked to make inferences about methods based on calculator output. The major focus is often interrupted by other contents that may not be very related to the focus of the lesson.

The number of student exercises is low. These exercises are most typically at only basic achievement levels.

The book provides a poor opportunity for student learning, even at a less-than-comprehensive level. The sequence of presentation is reasonable for the material covered, but the mathematics content coverage and depth are insufficient. The treatment of functions, exponents, and radicals are especially poor. In general, both the presentation and the student work seriously lack sufficient breadth and depth needed for success at moderate levels.