Cord Algebra 1: Mathematics in Context

Section I - Organization and Features

The student text for Cord Algebra 1: Mathematics in Context contains 855 pages organized into 12 chapters. The chapters are arranged and identified by math topics, not by context topics. The student text appears to be available as a single volume or as a two-volume set.

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 a moderated number of 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.

There are also self-testing sections, although answers are not provided in all cases.

Section II - Major Topic Summaries

A) Linear equations in one variable

Much of this material is presented at a pre-algebra level. There are very few problems at all beyond the most basic level. Within this constraint the exposition is good, there are some nice elements of mathematical reasoning or justification, calculators are not over used and there is relatively little use of algebra tiles or blocks. Word problems are poorly presented and fall below an acceptable level in terms of presentation and challenge.

This topic is satisfactory for learning at a less-than-comprehensive level. The presentation is clear, and the technology is appropriate, but the book appears to be designed for non-advanced students only. Clever students, or students who want to go farther in math will be board to tears and not as prepared as they could and should be.

This is a less than satisfactory treatment of this topic. As good points, the pages are not nearly as "busy" as in some other books, some presentations are clear, and there is some logical development. On the other hand, some topics are essentially missing and others contain few challenging problems. Parallel and perpendicular lines, and their equations, are missing from the text and index. There are few, if any, medium or hard problems. Even after learning slope intercept form, students are asked to graph by making a table and plotting points. There are huge lessons on graphing calculators and math labs. These are much too long, tedious and take time away from doing algebra.

This is a poor treatment of this topic. The presentation is at a very elementary level with very elementary problems. There is little depth or complexity and few problems. The problems are so simple that it is not clear that mastery would occur even for low level at which this material is presented. There appear to be only 16 problems on factoring trinomials. On the positive side, in spite of using some algebra tiles, the expositions are usually clear given the constraints of their low level.

The presentation is generally clear but sticks to a low difficulty level. There are sometimes sufficient worked-out examples and sometimes not. The sequence is fine until the discussion of systems of linear inequalities, which is mixed in with the discussion of linear programming in a way that results in neither topic being addressed well.

The most positive feature is the section on problem solving in which many different contexts are presented and some moderate to difficult problems are encountered. But there is no direct exposition for this section. Instead, the student is "guided" through the solutions in many different contexts. It is unclear whether this is sufficient to allow the student to succeed independently without the guides.

The section on matrix solutions using determinants is nothing but a complex cookbook design. Even if students can learn the complex steps, the process has no meaning. What benefit there is to the problem solving section is not sufficient to outweigh the negative consequences of the treatment of inequalities. The matrix solution section should be ignored. The general picture is of a presentation that is not likely to be very effective in terms of student achievement.

While some preliminary material about the properties of exponents with numeric values appears in chapter 2 in connection with scientific notation, they are not really addressed until chapter 10. There, they are given a brief treatment that mostly consists of presenting each with a short introduction.

A notable error is that the book uses the quotient property to "explain" zero and negative exponents before the quotient property is introduced. The presentation for this major topic generally lacks sufficient explanation and examples, and keeps the focus at very simple levels.

The meager number of exercises likewise sticks to the lowest difficulty levels. Fractional exponents are not covered. This material is not sufficient to support later work with exponents that students should encounter.

This book treats this major topic in chapter 12, the last chapter of the text, although some discussion of square roots had appeared in chapter 6. In general, the treatment is very cursory. Explanations are short and not very informative and there are few examples that are worked out to illustrate the topic.

The problem sets are very limited, offering little hope of student mastery even at low levels of complexity. There are a few more exercises for the Pythagorean theorem than for the other subtopics. However, there is little hope that students in this program will succeed in working with radical expressions.

Section III - Overall Evaluation

Mathematical Depth and Breadth

Good coverage of math topics is in this text is limited to the most basic material, while coverage of more advanced material is fair to poor. Thus, the depth of coverage is generally inadequate, and the support that students need to achieve beyond the most basic levels is not generally provided. While the treatments of linear equations and inequalities are adequate, the coverage of functions is only fair and other major topics are poorly addressed.

Overall the quality of presentation is fair to poor in terms of the depth of student understanding supported. Terms, concepts, and procedures are sometimes addressed clearly, but other times the details are not addressed sufficiently or are missing entirely. Examples are not extensive enough or lack sufficient detail to support adequate depth of understanding.

The emphasis on properties, proof, and derivations is moderate, giving students at least some opportunity to comprehend the mathematical underpinnings of algebra. The use of technology is generally appropriate and not apt to interfere with student learning. The emphasis on analytical approaches is good.

The number of student exercises is dangerously low, placing consolidation of learning at risk.

The student work does not cover a sufficient range of depth and scope. Student work is almost always at only basic levels, especially in the more advanced major topic areas. Thus, the presentation provides poor support for moderate and high levels of achievement.

The book provides a poor opportunity for student learning, with support for only basic levels of achievement. The appropriateness of the use of technology and the emphasis on analytic methods are good, but the mathematics content coverage and depth are seriously insufficient. This is most clearly reflected in insufficient student work in exercises and the low expectations for student achievement that the problems seem to assume.

The presentation style is fair in terms of the mathematical underpinnings of algebra, but the text as a whole and the student work in particular lack sufficient breadth and depth.