Algebra 1: Integration - Applications - Connections

Section I - Organization and Features

The student text for Algebra 1: Integration - Applications - Connections contains 862 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 large number of entries. Index entries contain some context references, but most entries 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

This is a fair coverage of this topic. The order of subtopics is generally good, but extraneous subtopics tend to interfere with continuity. Terms are generally well defined and clear descriptions are present.

Unfortunately, much of the clarity may be lost amidst an over emphasis on manipulatives and calculators. Problem sets barely enter the middle level of difficulty. Most sections are introduced with a story that does not really lead well to the topic. One such introduction introduces a completely irrelevant topic.

Some problems are literally plug-and-chug with computers. Neither understanding of algebra nor of the logic of the computer is required.

This is at best a fair coverage of the topic. There are some good points. The problems generally cover at least the easy and medium levels and, in some cases, the hard levels. The expository and analytical parts are well presented. On the other hand, the pages are too busy, there is far too much space and time spent on manipulatives, the text is weak in word problems and the flow of topics is interrupted by extraneous topics.

Except for some inappropriate calculator use and insertion of irrelevant topics, this would be a very good presentation. The exposition in the absence of calculators is strong, in most cases the problems cover the full range of difficulties, and there is a good derivation and demonstration of why the slope-intercept form works. Word problems may not be of sufficient difficulty and some uses of technology are clearly without thought or understanding. For example, there is a plug and chug exercise with a spreadsheet to determine slope. There is neither understanding of slope nor understanding of the programming of a spreadsheet. Similarly, the first introduction into solving equations in two variables is mindless plug and chug with calculators.

There are also serious errors in related data analysis topics. On page 341 students are asked, as part of an example, to fit a line of "best fit" to a set of plotted data points. The book shows a potential such line and states, as a side note, "The best-fit line drawn in this example is arbitrary. You may draw another best-fit line that is equally as valid." This is completely wrong and encourages a lack of understanding of the meaning and concept of "line of best fit."

This is a very good coverage of this important topic. The organization is good, all topics are covered and there are some challenging problems.

Although the quality of the problems is high, there should be more of them. There is a reasonable representation of difficulty levels across the problem sets.

This major topic is presented with reasonably good exposition sections. Each develops a part of the topic in a context situation that is a little wordy, but only light reading and is clear. Examples are numerous. A reasonable number of problems appear in each section, with some moderate and very few hard problems. Word problems are scattered throughout.

There are sufficient student activities to consume several class days and at least one homework night without much benefit. There is an introductory section (8.1a) that is heavily based on the graphing calculator without much exposition or understanding being possible.

There are a smattering of graphic calculator instances throughout the rest of the chapter, but not excessive. There are, however, instances with manipulatives that are not an efficient use of time or lead to much benefit for understanding.

Elimination is covered in two separate sections, one for addition/subtraction and one for multiplication. This gives lots of coverage to this subtopic. The exposition and examples are good. No reference to properties is made, however.

The graphing solution and graphing of inequalities sections are fairly well done and clear, with sufficient and good examples and adequate problem counts.

Problem solving situations are not given a separate section, but are fairly well addressed throughout.

Systems of 3 equations in 3 unknowns are not addressed, although 6 problems of this sort appear without discussion. Linear programming is not covered, and matrix solutions are not covered.

Thus, the exposition is generally good and the examples are generally good and the problem count is generally sufficient. Efficient use of classroom and homework time would require the benefit of a skillful teacher.

More difficult subtopics are missing, and justifications by reference to principles, if not proofs, are missing. More difficult problems should be included.

The quality of exposition and examples make for the potential for a highly rated major topic. However, deficiencies in coverage, inefficiencies of some sections, and insufficient difficulty level obviate the potential for a high rating.

The product/power properties are given and illustrated for cases involving variables, not just numeric values. A "Power of a monomial" property is given and illustrated as being a consequence of the other properties listed. Criteria for simplest form are then listed, although the quotient property and zero and negative exponents have not been covered yet, so this is premature.

This is followed by a reasonable number of exercises involving the simplification of expressions containing variables, although these do not extend beyond the easy to moderate level of difficulty.

The next section introduces the quotient property and zero and negative exponents. Similar examples are given with references to properties in their explanations. A similar problem set appears, again of easy to moderate difficulty level. On-topic application problems in the two sections are very limited and involve plugging numeric values into a given formula. The great majority of the application problems presented actually involve content from prior lessons.

Fractional exponents are not addressed.

In general, the presentation of this major topic is moderately clear. Terms and procedures and concepts are generally adequately defined. Student exercises are marginally sufficient in quantity at an easy difficulty level, but moderate problems are not sufficient and difficult problems are not included. There is some attention to derivation in the zero power case. Thus, a fair opportunity for student learning is provided, but only to moderate levels of achievement.

This topic includes a mixture of good and bad features.

Most notable on the plus side are that examples almost always give justifications at each step, that variables are included when the properties are introduced, and that the number of problems is generally adequate. Also, the presentation is generally clear and terms are defined. There are some instances where medium and a few hard problems appear.

Negative features include the political correctness invades the introduction to this chapter. The definition of perfect squares is missed. Software-specific syntax appears. Rational roots are differentiated from irrational roots on the basis of the calculator display. The use of variables disappears in the simplification section. The geoboard is used in an ineffective application. This topic closes the book and risks getting skipped. Giving a corollary rather than the converse of the Pythagorean theorem is problematic.

These negative features combine to detract from an otherwise adequate presentation.

Section III - Overall Evaluation

Mathematical Depth and Breadth

The coverage of math topics is good. Nearly all specifics receive some attention with omissions typically only at the greatest difficulty levels.

The depth of coverage is generally adequate. The support and experience that students need to achieve beyond the most basic levels is provided, although the highest achievement levels are not well supported.

The treatment of factoring is very good, with the rest of the major topics receiving reasonably adequate coverage.

Overall the quality of presentation is good in terms of the depth of student learning supported.

Terms, concepts, and procedures are usually addressed clearly and stated explicitly.

Examples are sometimes very good, and often include explicit references to properties in their presentation. The justifications are sometimes complete for each step of the example, but at other times are not provided. Examples also go beyond the simplest cases in many instances.

The emphasis on properties is often very good. On the other hand, derivations and proof receive little attention.

The use of technology is sometimes excessive in application without underlying understanding. Fortunately, the most severe of these instances are rare and could be avoided. The emphasis on analytical approaches ranges from fair to good. Sections identified as "Modeling Mathematics" generally employ manipulatives in ways that are not likely to promote greater understanding and could easily be replaced with simple illustrations.

The number of student exercises is reasonably adequate in most topic areas.

The student work often extends into the moderate difficulty range to some extent, but the higher levels of difficulty are less apt to be provided. Thus, the presentation provides fair support for moderate levels of achievement.

The book provides a good opportunity for student learning, and should support student achievement at moderate levels.

The greatest strengths of the program lie in the clarity of definitions and explanations of concepts and procedures that are often coupled with informative examples.

The appropriateness of the use of technology and the emphasis on analytic methods are generally good. There are occasional uses of technology without understanding and activities that contribute little.

The greatest weakness of this text is that it does not provide support for high achievement levels. Difficult problems, including application problems, are rare and proof and derivation are not well addressed.