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
The student text contains:This book is organized differently from nearly every math book on the market (with the exception of other books from the same publisher) and is different in presentation and homework from so called traditional math programs. Given the difference between the style and philosophy of this book and the rather uniform style and philosophy of other books for use at the same level, it might be informative for anyone interested in this series to read the preface to the teachers edition. This book expressly states that it is a pre-pre-algebra book and is not the book to be used the year before algebra. The 135 lessons follow one to the next with no chapter divisions. This number of lessons can clearly be completed in a 180 day school year, with plenty of time for tests, enrichment activities and days lost to assemblies and so on. Each lesson has a clearly defined and limited topic, with a clear exposition, examples very closely linked to the exposition and a few practice problems to be worked in class. The homework, about 30 problems, contains a very small number of problems related to the lesson of the day, but problems related to the lesson will appear in at least the next 5 lessons and in many lessons after that. Thus, students do as many problems related to any particular lesson as in any other program, but the problems are spread out over an extended period of time. Those topics chosen for particular emphasis are closely related to skills needed for success in pre-algebra and are practiced essentially continually through the book. Every problem set begins with a series of word problems based upon material already covered.
The lack of a chapter format sometimes results in seemingly unusual juxtapositions of topics. In the middle of a set of obviously related lessons will be one, two or several lessons that are completely unrelated to the topic. It is unclear if this is a positive for student learning.
There are no extraneous illustrations or color pictures. Everything is directed at mathematics. Neither word problems nor examples use currently popular and soon to be outdated people, movies or other issues as subjects. There is no use of manipulatives, calculators or computers. The only tools a student needs are a pencil and paper.
Content Area Evaluations
Properties, Order of Operations [3.0]
Order of operations are mentioned briefly midway through the book, omitting parentheses and exponents. In a later section symbols of inclusion (parentheses, brackets) are discussed. In almost all cases the practice problems use numbers rather than variables. A few problems involving evaluating by numerical substitution of expressions with variables are sprinkled in early on with little formal discussion. A formal section evaluating variable expressions occurs toward the end but is brief. Signed numbers are included by the end. The commutative, associative and distributive properties are not discussed, but problems applying them are present in examples and problem sets. The properties of equality are mentioned but not named as such.
Exponents, squares, roots [2.5]
Powers, squares and roots of whole numbers are clearly introduced. Scientific notation is presented in two sections, one for large numbers and one for small. The unit on multiplying numbers in scientific notation is a nice addition. This skill is often lacking in pre-algebra texts. Aside from scientific notation, negative exponents are not used, nor are generalized multiplication and division involving exponents with a common base. Powers and roots of variable expressions are not considered, but there are some interesting multistep simplifications with whole number powers.
Fractions [3.0]
Fraction computations are clearly taught, and multistep computations involving parentheses are offered in exercises. The level of difficulty is only average. A student would not have to use division rules or prime factorization to simplify or add fractions in this course, although prime factorization is taught. Negative factions are introduced very briefly with few examples or practice problems.
Decimals [3.0]
Decimals are covered moderately but little attention is given to negatives. The book has excellent simplification problems, in which expressions involving fractions and decimals are simplified by converting all terms to one form or another. All conversions among fractions, decimals and percents (with the minor exception of repeating decimals to fractions) are drilled throughout the course in the form of tables. These are an excellent way to ensure that students retain such important skills.
Percents [3.0]
The content areas that need to be covered are covered and all the basic skills and problem types are present, but the level of difficulty is more appropriate for a pre-pre-algebra course than for a pre-algebra course. As noted in the section on decimals, there is relatively good coverage on inter-conversion of fractions, decimals and percents.
Proportions [3.0]
Nearly every necessary topic is covered with the exception of converting between unit systems. The author does a good job with ratio, proportion, time and customary measures. The problems are straightforward and provide an appropriate challenge for pre-pre-algebra, but are not of sufficient depth or difficulty to prepare students for algebra.
Expressions and Equations - Simplifying and Solving [3.0]
This book provides an excellent introduction to solving one and two step equations involving whole numbers, integers and simple fractions and decimals. There are no inequalities. The level of complexity, in general, is not sufficient for pre-algebra. For instance, there are no equations requiring simplification by the distributive property or with variables on both sides.
Expressions and Equations - Writing [2.0]
Since this is not a pre-algebra book there is very little emphasis on writing equations. The problems require lots of proportion writing, often using a "ratio box". There are equations involving percents, but there are no "let" statements (e.g. let A= the number of apples), nor are there examples in which several unknowns are all expressed in terms of one variable.
Graphing [2.0]
The graphing units are very basic. Students learn to plot linear equations based on a table of values, to relate a graph, its equation and a table of values, and to recognize direct variation and graphs of direct variation. Slope and plotting strategies based on slope are not covered. Although plotting inequalities on the number line is covered, plotting them on the coordinate plane is not. It is commendable that this book does not have an over-emphasis on less important graphing topics (e.g. scatter plots, etc.) but the introduction to functions graphing is not sufficient for a pre-algebra course.
Shapes, Objects, Angles, Similarity, Congruence [2.5]
This book gives an adequate coverage of some but not all topics that should be covered in pre-algebra. Construction is notably absent as are problems dealing with the interior angles and diagonals of polygons. The rating reflects these absences.
Area, Volume, Perimeter, Distance [4.0]
This book contains an above average coverage of this topic. All essential topics are covered. Lots of attention is paid to irregular two and three dimensional shapes which makes the problems more difficult and more interesting.
Program Quality Evaluations
Mathematical Depth [2.7]
This book admits to being a pre-pre-algebra book. As the preface notes, a pre-algebra text should present "upper-level topics in an upper-level manner," while this book "presents upper-level concepts but does so in a lower-level manner." Because of what this book tries to be, it tends to fall short of some of the content objectives for a grade 7 course preceding algebra. This is reflected in the relatively low rating. On the other hand, the content is perfectly acceptable for a pre-pre-algebra course.
Quality of Presentation [4.0]
The instructional design of the program is such that one might expect a high proportion of the prepared students entering the course to master the material. Within individual sections, the book received high ratings for clarity of objectives, explanations, examples and efficiency of learning, range of depth and scope and proof/mathematical logic. This is not a trivial consideration. A book that hides or dilutes the key elements with less important topics or confusing, jumbled expositions will not allow the high level success for many that we wish to see.
The book is strikingly free of any lessons that distract from the major topics of importance. There is no dilution of the key topics with less important lessons. Unlike most of the other books covered in this review, this book has little tendency toward the "inch deep and mile wide" presentation for which some have criticized American textbooks. A teacher starting at page 1 and progressing to the end is very likely to finish in a school year and give her or his students a high chance of learning the material. There is relatively little need for teachers to pick and choose among lessons and therefore much less possible variance in coverage between teachers. What variance there is will be relatively unimportant and will reflect whatever outside enrichment activities individual teachers choose to add.
The one area in which there is a perceived relative weakness is the sequence of presentation. As noted above, coverage of some major topics seems to be broken up by inclusion of pieces of other topics.
In contrast to most other books currently in use at this level, this book stresses the mental over the mechanical and eschews calculators, thus leading to both greater calculational competence and to development of a deeper "feel" for the concepts involved.
Quality of Student Work [4.5]
Within the constraints of the level at which the course is taught, the pedagogical evaluations within each topic, such as clarity of objectives, explanations, examples and efficiency of learning are relatively high. As such, there is a relatively high probability that students who do the work of the course as expected will do reasonably well in mastering the content at the level at which it is taught.
As noted above, the lack of a chapter format results in what sometimes seems a jumping around between and within topics.
Overall Program Evaluation
As noted in the preface, this is a "pre-pre-algebra" book, not a pre-algebra book. The preface also makes the important point that mastery of an appropriate pre-algebra course, no matter what the name, is important for success in algebra. Thus, this is not the book to use immediately before algebra, although it could reasonably be used with students, at any grade, who are not yet ready for pre-algebra but would be on course to take algebra in two years. The relatively low expected level of teacher to teacher variance and the clarity of the lessons might make this an excellent pre-pre-algebra choice for many districts.
| Prior | Contents | Next |