A Mathematically Correct Review of

The University of Chicago School Mathematics Project (UCSMP) Algebra (2nd Edition)

Authors: John W. McConnell, Susan Brown, Zalman Usiskin, et. al.
Published by Scott Foresman/Addison-Wesley, 1998


Section I - Organization and Features

The student text for UCSMP Algebra contains 885 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 include many context references as opposed to 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

There are some very good points and some very weak points in the coverage of this topic, leading to an overall rating of only satisfactory. There is an excellent emphasis on proof and justification, technology is appropriate, terms are defined, concepts and procedures are explained clearly.

On the other hand, there are far too few problems for each subtopic and they fail to cover the upper difficulty levels. The coverage of word problems is especially weak as there is no good introduction to writing equations with variables for unknowns, far too little practice on this, and no word problems beyond the easy level.

Although equation solving is presented well, the organization of the book spreads this out over multiple chapters, possibly making it difficult to keep track of the material and consolidate it.

Rating

Category

3.6

Overall evaluation

3.0

Quality of presentation

4.0

Definitions of terms and explanations of concepts and procedures

1.0

Quality and sufficiency of student work

3.0

Range of depth and scope in student work

3.0

Quality and sufficiency of examples

4.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

B) Linear inequalities in one variable

This topic is fair at best. The coverage of the presented topics is reasonable but important points are spread over multiple chapters and some elements (e.g. compound inequalities and absolute value inequalities) are absent or barely covered. As with other topics in this book, the material is spread across multiple chapters, which may not be optimal.

Rating

Category

3.4

Overall evaluation

3.0

Quality of presentation

4.0

Definitions of terms and explanations of concepts and procedures

2.0

Quality and sufficiency of student work

3.0

Range of depth and scope in student work

3.0

Quality and sufficiency of examples

4.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

C) Linear functions

Except for appropriate use of technology and emphasis on analytical methods, this topic is merely satisfactory. If is unlikely that students will progress beyond a less-than-comprehensive level. The exposition feels both too slow and flitting about at the same time. There aren't enough problems and the problems don't get hard enough.

There is little on the slope of lines, writing equations when given various information about a line, or converting between representations.

Rating

Category

3.3

Overall evaluation

3.0

Quality of presentation

3.5

Definitions of terms and explanations of concepts and procedures

2.0

Quality and sufficiency of student work

2.0

Range of depth and scope in student work

4.0

Quality and sufficiency of examples

5.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

D) Factoring and applications

The coverage of this topic is less-than-fair. On top of this, most of the topic occurs in chapter 12, late enough that some classes may not reach it. There are notably too few problems; factoring by grouping is missing; factoring trinomials, solving equations by factoring and word problems never get beyond the easy level; and the word problems that do appear are spread out in a way that skills are hard to build.

Graphical and computer solutions are emphasized at the expense of analytical methods. The quadratic formula and discriminant are introduced two chapters before factoring, precluding any understanding or proof of the formula or why it works. Early use of the quadratic formula and calculator/graphing solutions of quadratic equations can make students dependent on these plug-and-chug techniques for solving quadratic equations.

Rating

Category

2.6

Overall evaluation

3.0

Quality of presentation

3.0

Definitions of terms and explanations of concepts and procedures

1.0

Quality and sufficiency of student work

2.0

Range of depth and scope in student work

2.0

Quality and sufficiency of examples

3.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

E) Systems of equations and inequalities

The presentations in the text are quite clear and understandable. The presentation is to be commended for devoting two sections to substitution and two sections to linear combinations.

Unfortunately, the three more difficult subtopics are missing, the number of exercises is very low and almost all are at the easiest level. As a consequence, there is a cap placed on student achievement with this program that is unnecessarily low. Furthermore, due to the small number of practice exercises, the risk of poor consolidation of learning is great. These negative aspects combined force a low overall rating for this major topic.

Rating

Category

2.9

Overall evaluation

4.0

Quality of presentation

3.5

Definitions of terms and explanations of concepts and procedures

1.5

Quality and sufficiency of student work

2.0

Range of depth and scope in student work

3.5

Quality and sufficiency of examples

4.5

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

F) Laws of exponents

The text treats this major topic with generally good exposition and examples with sufficient detail. Some attention to derivation is included as, for example, the zero power is derived from other laws. However, too much of the student work is based on numeric problems rather than those with variables and calculator use rather than analytic methods is too frequent.

The most serious problem with this major topic, however, is that the number of exercises is very low and too easy. Fractional exponents are not addressed.

The limited student experience and the easy level of these exercises threaten effective learning.

Rating

Category

3.0

Overall evaluation

4.0

Quality of presentation

4.0

Definitions of terms and explanations of concepts and procedures

2.0

Quality and sufficiency of student work

2.0

Range of depth and scope in student work

3.0

Quality and sufficiency of examples

3.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

G) Radicals and radical expressions

The organization of this major topic within the text is highly unusual.

Square roots and even the Pythagorean theorem are introduced in chapter 1. Rational and irrational roots are not dealt with for 700 pages. The Pythagorean theorem seems to have been selected for introduction in chapter one as it illustrates the contribution of historical mathematicians, the fact that people from many countries worked on this, and the fact that theorems are important. The topic appears briefly in a few other places in the book.

The book returns to the major topic in chapter 9 of 13, which is the quadratics chapter. Here, the product property of radicals is introduced as it seems a convenient place. The only material on simplification is given with the product property. Problems are mostly easy with a few medium problems related to the product property.

The quotient property is not addressed. Thus, a full treatment (or even a decent partial treatment) of simplification and solutions is not given. The distance formula is covered with modest problem count, nearly all easy.

The efficacy for this major topic is a disaster. The material is largely missing, and the little that is included is scattered in a way that isn't helpful to learning.

This text does not support even modest student learning for this major topic.

Rating

Category

1.5

Overall evaluation

2.0

Quality of presentation

3.0

Definitions of terms and explanations of concepts and procedures

2.0

Quality and sufficiency of student work

2.0

Range of depth and scope in student work

3.0

Quality and sufficiency of examples

4.0

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

Section III - Overall Evaluation

Math Content Coverage

The range of math topics covered is fair, but some specific topics are not covered. The depth of coverage is generally at basic achievement levels with some rare entry into more moderate levels. The treatment of factoring is marginal, while the treatment of radical expressions is very inadequate.

Presentation Style

Overall the quality of presentation and exposition is fair. The definition of terms and the explanations of concepts and procedures are generally good, and the presentation sequence is reasonable. Examples are fair in both number and detail. The emphasis on principals, proof, and derivation is also fair. The use of technology does not generally interfere with learning, and there is a decided emphasis on the analytic approach.

Exercises

The number of student exercises is very low, and this is the most blatant negative feature of this text. These exercises are most typically at basic achievement levels with a few moderately difficult problems presented in some instances. For example, the section on solving linear systems by substitution includes 6 symbolic problems giving very simple systems and 3 word problems giving very simple systems. 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 extent, range and scope of student work is low enough to cause serious concerns about the consolidation of learning.

Overall Summary

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, as are the presentations. Unfortunately, the mathematics content coverage and depth are insufficient. The presentation style is moderate, but the presentation and the practice exercises lack sufficient breadth and depth. The lack of greater depth and the weak prescriptions for student work are serious concerns.

Mean Ratings for Entire Text

Rating

Category

2.9

Overall evaluation

2.8

Quality of presentation

3.3

Logic and usefulness of presentation sequence

3.6

Definitions of terms and explanations of concepts and procedures

1.6

Quality and sufficiency of student work

2.3

Range of depth and scope in student work

3.1

Quality and sufficiency of examples

3.0

Emphasis on proof, derivation, and mathematical justification

4.2

Appropriateness of technology

3.9

Emphasis on analytic methods

[Scale: 1 (poor) to 5 (outstanding)]

Overall Ratings for Sampled Major Topic Areas

Rating

Major Topic Area

3.6

Linear equations in one variable

3.4

Linear inequalities in one variable

3.3

Linear functions

2.6

Factoring and applications

2.9

Systems of linear equations and inequalities

3.0

Laws of exponents

1.5

Radicals and radical expressions

[Scale: 1 (poor) to 5 (outstanding)]


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