South-Western Algebra 1: An Integrated Approach

Section I - Organization and Features

The student text for South-Western Algebra 1: An Integrated Approach contains 790 pages organized into 14 chapters. The chapters are arranged and identified by math topics, not by context topics, although each chapter also has a context theme.

The student text contains an index with a large number of entries. Index entries are not based on context references, they are references to math topics.

The student text also contains a glossary with a large 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 student text includes self-testing sections.

Section II - Major Topic Summaries

A) Linear equations in one variable

On balance, the coverage of this topic is barely satisfactory. It is possible that a teacher could do an excellent job with this material, but if the presentation is as in the book without substantial removal of superfluous material, the presentation will be poor. There is good material provided, but it is all too often hidden or diluted by extraneous material, manipulatives and inappropriate use of calculators.

For most topics, the problems cover the full range of difficulty. Some topics, such as percent problems, seem to come too soon. There are a number of good word problems, but the strategies for approaching different kinds of problems are poorly presented and the problems are scattered.

B) Linear inequalities in one variable

This section is satisfactory. Subtopics occur in a logical order, terms are generally well defined and concepts and procedures are clearly explained. Use of technology is appropriate. On the other hand, each section starts with a distracting exploration not clearly related to the topic at hand. The number and depth of problems at each stage is less than top level. Word problems are weak.

This topic is covered in a notably less-than-satisfactory manner. The exposition fails to stress analytical methods that are the key to algebra, instead emphasizing "graphing utilities" and manipulatives. Many sections begin by punching numbers into a calculator as part of an "exploration" followed by an assertion of what the students should have "discovered." There is little logical or proof-like development of the key points or why methods work. There is a lack of harder problems in most subtopics.

As example of inappropriate use of technology and out of order topics, 65 pages before the introduction of the techniques to graph linear functions, there is an introduction to solving simultaneous linear equations in two variables by graphing on a calculator.

There is a fair edging to moderately good coverage of this topic. Unfortunately, most of the material does not occur until chapter 12, making it likely that some classes will not get to this material. The general quality of the exposition is good and most subtopics occur in a reasonable order. Word problems cover the range of difficulties and there are a sufficient number.

Factoring of trinomials is weak, never going beyond easy problems or expressions with lead coefficient 2. There is a significant error in topic order -- the quadratic formula and discriminant are introduced two chapters before students learn the techniques that allow them to understand the derivation and meaning of these items.

There are many distractions in the text and a sufficient number of activities, both related and unrelated to the mathematical focus, to interfere with learning of the material. For example, a city planning context theme runs throughout chapter 7. There are two pages of reading/activities that don't have much relationship to the focus. For example, "Work in groups of four or five ... brainstorm a list of features that make a city attractive ... research the 'most livable' cities in the United States ..."

The section on linear combinations takes a focus on "elimination" and thus fails to communicate the ideas about combinations of equations as effectively. The discussion does not refer to the properties of equality. In addition, the "algeblocks" appear in a cooperative activity that is again not very enlightening. Worse yet, this section doesn't explain the whys of elimination. Instead, a more cook-book approach is taken.

The introduction to graphing and extensions to definitions combine to provide a moderate coverage. There are few problems beyond the easy level, and students would have to work all problems to get to these. The sections on substitution and elimination are a little worse. There is too much exploration and use of algeblocks and the exposition is unclear. Again there are a few problems at the moderate level.

The treatment of systems in word problems is given modest coverage. Some examples are worked out with explanations of steps given. These do not cover more complex cases. They also fail to provide sufficient focus on identifying what is being asked for in the problem statement and on checking results.

The section on linear inequalities is modest, and does contain one problem at the difficult level. The steps in the process are not clearly justified or explained beyond mechanics. It is not clear to the student that the solution area extends beyond the graphic display. The section on linear programming, often not addressed in many modern books, is actually one of the best in terms of clarity and completeness. Constraints and the feasible region are defined.

The section on matrix solutions is very weak. It uses determinants in a cook book approach that is unlikely to yield any understanding. The relationship between the matrix approach and the standard algebraic solutions is not clarified. The treatment of 3 equations in 3 unknowns is not addressed other than by two problems buried in an earlier section without introduction or explanation.

While the overall quality of the explanations is modest and the subtopics organized in a reasonable way, terms are not always defined or their definitions are deferred. There are a moderate number of easy problems, but medium problems are rare and hard problems are almost non-existent. Sometimes there are sufficient and clearly worked out examples and other times there are not. There is no emphasis on proof. Non-analytical methods, especially the use of algeblocks, occur too frequently. Overall, the prospects for comprehensive student learning are very low. Even learning at a modest level is at risk with this text and would require skillful selection and amplification by the teacher.

The text treats this major topic with very brief exposition. Each property is typically introduced with an example and then the property is stated. While this material is generally clear, it is less extensive than might be provided to promote better understanding.

The examples are primarily symbolic and don't provide much understanding in application. The number of exercises is low and restricted to low difficulty levels in most cases. Proof and derivation are not attended to, and fractional exponents are not addressed. Thus, the presentation is too weak overall to promote effective student learning.

This text touches on the major topic as needed in early chapters before the bulk of the topic appears in chapter 13. The introductory material on roots and the product and quotient properties are thus given twice.

The text generally defines terms well and the presentation is clear. There are typically sufficient examples, although only some include complete justifications of steps. There is typically a generalization from working just with numbers to expressions with variables, although the latter are typically very limited.

The number of problems is marginally adequate, but more would be preferred. In particular, the level of the problems is typically easy with very few at a medium level.

Sections typically begin with a short investigation or directions that attempt to lead students to infer a rule, but then the rule is given immediately afterward.

Section III - Overall Evaluation

Math Content Coverage

The range of math topics covered is limited, meaning several specific topics are not covered. For the topics covered, the depth of coverage is generally at basic achievement levels with some entry into more moderate levels. The treatments of linear inequalities and factoring are reasonably adequate, while the treatment of linear functions is notably weak.

Overall the quality of presentation and exposition is fair. Terms, concepts, and procedures are sometimes addressed clearly, but other times not addressed sufficiently. Topic arrangement is generally reasonable. Examples are not extensive enough or lack sufficient detail. The emphasis on principals, proof, and derivation is very low. The use of technology can be excessive enough to interfere with learning opportunities.

The number of student exercises is moderate to low. These exercises are most typically at basic achievement levels with some moderately difficult problems presented.

The book provides only a modest opportunity for student learning at a less-than-comprehensive level. The features of the book organization are reasonable and adequate, but the mathematics content coverage and depth are insufficient. The presentation style is moderate, and the presentation and the practice exercises lack sufficient breadth and depth.