Sunday, June 10, 2007

Math textbook reviews

It is quite difficult to navigate around the Mathematically Correct site when looking for specific math textbook reviews. There is no search function. Updating is also sporadic and it is not possible to tell at a glance which entries are new or the date of other entries. Important articles like Barry Garelick's Miracle Math and An A-Maze-ing Approach To Math are not linked (at least I haven't been able to find links).

I did find a page that puts together reviews of second, fifth and seventh grade math textbooks in a handy fashion.

Glencoe/McGraw-Hill Pre-Algebra, an Integrated Transition to Algebra and Geometry comes out on top for seventh grade in these reviews. On the other hand, amazon reviewers panned this textbook. Where is the truth?

I use Scott Foresman/Addison Wesley Middle School Math and am quite happy with it.

Dale Seymour Publications Connected Mathematics Program gets an F from mathematically correct. CMP is a cult item in many districts, including here in Chicago.

It's worth citing the review for fun. I particularly like phrases like these: "If this topic is covered, it is extremely difficult to find." Also this: "Fractions [1.0] This topic is missing or cryptic."

Mathematically Correct Seventh Grade Mathematics Review
Dale Seymour Publications
Connected Mathematics Program
Lappan, Fey, Fitzgerald, Friel and Phillips
Menlo Park


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Introduction

This is part of a series of second, fifth, and seventh grade Mathematics Program Reviews. This review includes a summary of the structure of the program, evaluations of a selected set of content areas, and evaluations of program quality. Ratings in these areas were made on a scale from 1 (poor) to 5 (outstanding). The overall evaluation was made using the traditional system of letter grades. For details of the methods used in this evaluation see Methods for Seventh Grade Program Reviews.

Student Text Structure

This course is composed of 8 "books" of about 70-90 pages each.

Each book is arranged around a mathematical topic

1. Variables and patterns
2. Stretching and shrinking
3. Comparing and scaling
4. Accentuate the negative
5. Moving straight ahead
6. Filling and wrapping
7. What do you expect?
8. Data around us

Content Area Evaluations

Properties, Order of Operations [1.0]

If this topic is covered, it is extremely difficult to find. In any case, the coverage is insufficient.

Exponents, squares, roots [1.0]

This topic is very weak. Positive integers are raised to whole number powers only in the context of prime factorization. The small coverage of scientific notation includes only positive integer exponents and heavily emphasizes the use of calculators. All other topics are completely absent.

Fractions [1.0]

This topic is missing or cryptic.

Decimals [1.0]

None of these topics are presented in this book. Expressing decimals as percents is assumed. Perhaps students were taught to make this conversion on their calculators in an earlier grade.

Percents [1.2]

There is no evidence of development of this topic in this book. At the start of book 3 "percent" is described as one of the "terms developed in previous units." Perhaps so, but if so, the level of development was low. There is certainly no teaching of percent. Some percent problems are intermixed with ratio problems in the various exercises, but there is no instruction on interconverting fractions, decimals and percents. There are almost no word problems on discount, markups, commissions, increase or decrease. Some "scale factors" for similarity are expressed as percents.

Proportions [3.5]

This is an adequate treatment of this topic. Most of the grade 7 topics are covered at some level. It is interesting that although proportions are used relatively often, by the standards of this book, they are not referred to as such as the authors have decided to put "proportion" in the list of nonessential terms at the front of the book.

Expressions and Equations - Simplifying and Solving [1.1]

This book is devoid of algebraic manipulation. The only solving of equations is graphical, and that is limited to problems involving direct variation. It is difficult to see how a student can become prepared for any mathematics-based profession with this little instruction in the key skills leading to algebra.

Expressions and Equations - Writing [2.1]

This book has a heavy emphasis on using proportions to find the lengths of similar parts of similar figures. On the other hand, there is very little practice or instruction in writing equations from a verbal description. The problems related to this topic are stretched over an excessive period of time as students answer endless questions about the situation. Essentially all of these problems are dealt with via tables and then in a graphical context.

Graphing [4.0]

The one advantage of the heavy emphasis that this book places on graphical over analytic solutions is that graphing is covered moderately well. Nearly all topics that should be covered are covered.

Shapes, Objects, Angles, Similarity, Congruence [2.5]

Formulas and derivations, or even "discoveries" of area of two dimensional figures are not given. They may be assumed to have been mastered at an earlier year. Surface area and volume are "discovered" in a long series of construction projects, many of which look doomed to failure. At the end of this formulas that have been discovered are not explicitly stated in the text. The teacher's manual suggests that the appropriate formulae will "come out" in discussion. If the student discovered the wrong formula, or forgot to write it down, good luck, since there is no way to look back and remember a formula.

The exercises on finding volumes of irregular objects using displacement are interesting extensions. On the other hand, much of the teaching is absurd and again abjures analysis for experiment. For example, students spend who-knows-how-much-time filling cylinders and cones with beans to discover, approximately, the relationship between the volume of cylinders and the volume of cones. This is a waste of time and inaccurate. Unfortunately, this could describe many of the activities in this book.

Area, Volume, Perimeter, Distance [1.0]

Essentially none of the grade 7 level topics are covered. They may be assumed from previous years, but one cannot assume that from the presentation.

Program Quality Evaluations

Mathematical Depth [1.7]

There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills.

Quality of Presentation [1.4]

This book is completely dedicated to a constructivist philosophy of learning, with heavy emphasis on discovery exercises and rejection of whole class teacher directed instruction. The introduction to Part 1 says "Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them." In one of the great understatements, the Guide to the Connected Mathematics Curriculum states, "Students may not do as well on standardized tests assessing computational skills as students in classes that spend" time practicing these skills.

Quality of Student Work [1.5]

Students are busy, but they are not productively busy. Most of their time is directed away from true understanding and useful skills.

Overall Program Evaluation

F
Overall Evaluation [1.7]

This rating is perhaps deceivingly high, as 7 of the 11 topics rate no higher than 1.2. The rating is as high as it is based largely on two high subscores, proportions and graphing. It is impossible to recommend a book with as little content as this and an inefficient, if philosophically attractive, instructional method.

4 comments:

Dickey45 said...

Connecting Math Concepts F is coming out this summer by SRA. It will be worth a review. I'll be purchasing as soon as I can and am willing to lend it to someone who can do a review on it. It is a $300 set because it includes scripted teaching material, workbook, textbook and other supplements.

Rodrigo said...

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Anonymous said...

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Barry Garelick said...

Mathematically Correct is essentially non-existent at this point. Best to look at NYC HOLD, at www.nychold.com, which contains reviews of texts plus timely articles pertaining to math education.