Section I - Organization and Features

The student text for Algebra: Tools for a Changing World contains 672 pages organized into 11 chapters. The chapters are arranged and identified by math topics, not by context topics.

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

The student text also contains a glossary with a small 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

This book offers a fair coverage of this topic. Subtopics are generally in logical order and the analytic portions of the exposition are reasonably good. There are serious deficiencies in the numbers of word problems and a need for more challenging equations. There is an over emphasis on manipulatives and calculators.

There is fair coverage of this topic. Linear inequalities follow right after linear equalities and subtopics are presented in a logical order. Most topics are covered at a middle level. There are too few problems at each stage, word problems are generally lacking, there is too much emphasis on calculators, and, generally, not enough algebra.

There is solid basic coverage of this topic. No ratings are strikingly high or strikingly low. The analytical exposition is fine but is muddled by encouraging the use of calculators for basic material and by the inclusion of extraneous intervening topics. Most sections lack "hard" level problems.

This is a poor treatment of this important topic. Most subtopics are covered but the depth and complexity of problems rarely exceeds the lowest level. Almost all topics are introduced with algebra tiles before other presentations. There is an emphasis on using tiles in problem sets.

Calculators are emphasized, especially in earlier sections and in graphical/calculator solutions of quadratic functions. Most word problems just give the formula to be used, students are not asked to write their own equations from the terms of the problem and the situation.

The introduction to this major topic illustrates the style of coverage. It begins with a "Guess and Test" section that treats two equations in two unknowns in a simple case by guessing. Evidently, the point is to show the "advantages and disadvantages" of guessing. However, this appears before any other solution strategies have been presented, so students are not in a very good position to make such a judgment.

The graphic approach to systems of equations includes specific commands for the graphing calculator. The student is told to "Set an appropriate range" and without clarification. A section on "Special Types of Systems" gives the cases where "no solution" and "infinitely many solutions" are covered. Parallel lines are mentioned, but terms like "consistent" are not defined.

Next comes a "Critical Thinking" section, which in this text often means an important point is left to the student to discover. Next comes work with a partner to complete a table calling for the generation of systems to give various types of solutions. The exercises for this section require a time commitment that is excessive for the number of actual problems completed.

The next section begins with work with a partner using a given graph to estimate the solution of

a system. Pairs then use the graphing calculator to graph the given equations and press Calc or Table to find the intersection point. Pairs compare their estimate to the calculator exact answer.

Pairs are then asked choose to use paper and pencil or a calculator to solve 3 more systems, and explain why they chose a particular method. It seems odd that they would use paper and pencil since they have not been given the algebraic techniques. Again, the more powerful technique is being evaluated before it is given.

The next "think and discuss" section says, "Sometimes you won't have a graphing calculator to use. Another way to solve a system is to use substitution." This is an inadequate representation of the distinctions among methods.

The general form of the presentation for this major topic includes only very brief expositions. Examples tend to be very easy and give directions but not a lot for understanding. There are often questions after each example that try to get students to generate further understanding, but important aspects remain unstated. There are a lot of process type questions in the exercises so that although the number of exercises seems reasonable, the count is actually lower when you see how few require actual solutions.

The problems are almost entirely at the easy level. Thus, most presentations are weak. Three equations in three unknowns and matrix solutions are not covered.

The subtopics within this major topic are typically introduced with student work to lead up to the statement of the various laws. A typical number of examples are provided with notes to explain each step. The emphasis on discovery, cooperative activities of no particular benefit, and calculator use is a bit excessive.

On the other hand, the number of problems approaches an adequate level. While most problems are at an easy level, medium difficulty problems are included in some subtopics. Fractional exponents are not addressed. Opportunity for student learning at an easy level is good, with some opportunity for success at a moderate level.

The sequence of presentation is somewhat unusual, since both the Pythagorean Theorem and the distance formula appear early on and are followed by the introduction of trigonometric ratios before going on with the topic.

The greatest failing of this topic is that variables make scant appearance prior to the final topic on solving equations with radicals. The consistent failure to generalize from numbers to variables characterizes all other sections in this topic.

There are a reasonable number of problems, but they are mostly at the easiest levels since the use of variables is avoided until the end.

The section fails to teach how rational roots are differentiated from irrational roots, and it is likely that students will conclude that they should look for the answer on their calculator display.

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.

Overall the quality of presentation and exposition is fair. Terms, concepts, and procedures are sometimes addressed clearly, but other times not addressed sufficiently. There is too much of a reliance on a discovery approach that often means that important points are not formally addressed. 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 and cooperative activities 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 actual number of problems to be solved is less than it appears to be as many of the exercise items are procedure questions.

The book provides only a modest opportunity for student learning at a less-than-comprehensive level. The sequence of the book organization is generally reasonable, but there are too many distractions so that 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.