Heath Algebra 1: An Integrated Approach

Section I - Organization and Features

The student text for Heath Algebra 1: An Integrated Approach contains 790 pages organized into 13 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 also contains a glossary with a moderate number of entries. The entries in the glossary do not 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, but the chapter assessments do not include answers.

Section II - Major Topic Summaries

A) Linear equations in one variable

This book does a well above average job of presenting linear equations and their solution and in coupling these to word problems. There is a strong emphasis on analytical methods and reasoning. There are somewhat fewer "hard" problems available than might be optimal for a comprehensive course. There is a tendency for certain worked out word problems to leave out units in the equations and in the answers.

The coverage of this topic is well above average. The presentation, although a bit "busy," is clear, subtopics are in a logical order, terms are explained and there are sufficient examples. There might be a few more problems, especially at the "hard" level. There is some use of calculators when algebraic solutions would be more appropriate.

This topic is covered in well above average manner. The presentation is clear and subtopics are in a logical order, although insertion of only semi-related topics does tend to break up the presentation. Definition of terms and explanation of procedures is particularly well done, as is the attention given to horizontal and vertical lines and quick graphing via intercepts.

A few more problems at the "hard" level would increase the usefulness of the text. There are places where a graphical calculator is used when analytical solution would be more appropriate.

This is only an average presentation of factoring and solution of quadratic equations. It is not bad on basic factoring, but is weak at the top end. Much of the exposition is based on algebra tiles and is far more confusing than need be.

Presentation of the quadratic formula prior to factoring makes it impossible to give a logical justification or proof of the formula. Removing a common monomial factor is insufficiently emphasized. There is no factoring by grouping. The word problems in this section are not challenging. Many have the equation given and those that don't are very simple.

Examples of poor problems:

Example 1

There is a problem involving finding the area of a disc with a hole in the middle, but the values of the radius of the disc and the radius of the hole are given, so the problem reduces to plug and chug. Worse yet, the disc is a specific object called a "jade pi." Imagine the confusion this could generate during discussion.

Example 2

One set of problems relates to a picture of "crop circles" and contains a description of how such circles have puzzled many people. This set of problems is not mathematically challenging, leads to a classroom discussion of UFOs, and lacks any note that such circles can be, and have been, generated as jokes by people using the simplest of technologies.

This major topic is addressed with generally clear presentations and adequate examples. There are detailed instructions for the steps of procedures. The emphasis on terminology could be stronger. There is a sufficient quantity of problems, but these tend to be at the easy level with some small number of medium difficulty problems. The section on problem-solving, together with word problems in other sections, combine to provide fairly good coverage of this subtopic.

There is a section on linear programming that gives moderate coverage, while the matrix solution and 3 equations in 3 unknowns is not covered. There is no emphasis on proof and derivation or the reliance on properties to justify procedures. Still, the coverage of topics in terms of student performance is good for promoting student success in general, but not close to approaching high levels of achievement.

This major topic is addressed with clear explanations, lots of detailed examples, and lots of student exercises. Terms, concepts, and procedures are clearly defined. However, the highest difficulty level and an emphasis on proof and derivation are not well supported in this text. Fractional exponents are not covered.

Thus, the major topic is addressed in a way that would support student achievement at moderate levels well, but would fall short of supporting higher levels or deeper understanding evidenced by derivation and proof.

This major topic is generally addressed with clear explanations and lots of examples and student exercises. Terms, concepts, and procedures are generally clearly defined. However, the level of difficulty level is generally low with a concentration on numeric solutions and without an emphasis on proof and derivation.

Preliminary material for this topic appears in connection with the earlier discussion of the Pythagorean theorem in chapter 9, while the bulk of the major topic comes very near to the end of the text. Even the sections on simplification and solutions have too much emphasis on numeric problems and not enough applications of variable expressions. Thus, the text provides a thorough presentation at basic levels of achievement, but high achievement levels would not be supported for this major topic.

Section III - Overall Evaluation

Math Content Coverage

The depth of math content covered in this text ranges from good to very good. Almost all content areas sampled were adequately addressed. Coverage of linear equations and inequalities is outstanding, while coverage of radicals is only fair. The content supplies solid support for moderate levels of achievement, but would fall short of supporting outstanding achievement.

Overall the quality of presentation and exposition is good. Terms, concepts, and procedures are addressed clearly and explained well. Topic arrangement is generally reasonable. Examples are usually extensive enough although occasionally could be expanded. The emphasis on principals, proof, and derivation is only fair. The use of technology is usually within reasonable limits and appropriate. There are a few instances of unnecessary cooperative activities. There is a clear focus on the analytic methods of algebra.

The number of student exercises is good. These exercises cover basic and moderate achievement levels well, but the most difficult applications are infrequent.

The book provides a good opportunity for student learning that should provide the support needed for student achievement at moderate levels. The greatest strengths of the program lie in the clarity of definitions and explanations of concepts and procedures, the quality of the explanations given in the examples, and the emphasis on analytic techniques.

The greatest weakness of this text is the insufficient support for high achievement levels. This is reflected in an insufficient emphasis on proof and derivation. Difficult problems, including application problems, are too rare, and coverage of radical expressions is only fair.

Overall, the text provides good support for student learning in algebra.