How well does Math Advantage address the content in the selected benchmarks?

This In Brief chart provides profiles showing how this textbook scored on content and instructional quality. For the content profile, the coverage of each specific mathematical idea in the selected benchmark was rated on a 0 to 3 scale (no coverage to substantive coverage). These ratings were then averaged to obtain an overall rating for each benchmark (Most content 2.6-3.0, Partial content 1.6-2.5, Minimal content 0-1.5). For the instruction profile, the score for each instructional category was computed by averaging the criterion ratings for the category. This was repeated for each benchmark, to produce ratings of instructional quality on a 0 to 3 scale (High potential for learning to take place 2.6-3.0, Some potential for learning to take place 1.6-2.5, Little potential for learning to take place 0.1-1.5, Not present 0).

 Benchmarks Number Concepts Number Skills Geometry Concepts Geometry Skills Algebra Graph Concepts Algebra Equation Concepts Content Instructional Categories Identifying a Sense of Purpose Building on Student Ideas about Mathematics Engaging Students in Mathematics Developing Mathematical Ideas Promoting Student Thinking about Mathematics Assessing Student Progress in Mathematics Enhancing the Mathematics Learning Environment
 Content Scale Instructional Categories Scale Most content Partial content Minimal content High potential for learning to take place Some potential for learning to take place Little potential for learning to take place Not present

The content ratings are estimates of what the textbook series attempts to present on only these benchmarks and are not an indication of overall content coverage or accuracy. The ratings also do not indicate whether or not the content will be learned. The instructional analysis provides information on the potential the series has for helping students actually learn the concepts and skills it attempts to present.

The following indicates how well Math Advantage attempts to address the substance, breadth, and sophistication of the ideas contained in each of the six mathematics benchmarks that were selected for the analysis.

Number Concepts — Minimal Content

 The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b. (Chapter 9A, grades 6-8, benchmark 5, pg. 213.)

Only one of the three parts of the benchmark is covered substantively in this material. The ideas "a parts of size 1/b" and "a divided by b" are reviewed briefly in grades 6 and 7 in preparation for skill development. The material addresses the meaning "a compared to b" across the grades with appropriate opportunities for application and practice.

Number Skills — Most Content

 Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents. (Chapter 12B, grades 6-8, benchmark 2, pg. 291.)

This benchmark receives ample treatment in the material. The skills are given the greatest attention at grades 6 and 7, with appropriately less coverage at grade 8. Across all three levels, students have numerous opportunities to compare and interpret equivalent forms of many different types of numbers. Emphasis is on drill and practice of interpreting and comparing equivalent forms. There is little explicit direction as to when one equivalent form would be more appropriate than another.

Geometry Concepts — Minimal Content

 Some shapes have special properties: Triangular shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes. (Chapter 9C, grades 6-8, benchmark 1, pg. 224.)

Parts of the benchmark, such as special properties of round shapes and congruence, receive minimal coverage in this material. Triangles receive the most attention in terms of special properties of shapes. There is ample coverage of similarity throughout all three books, but many of the lessons are near repetitions of those found at earlier levels. While there are some lessons and labs that stand out as challenging extensions, the sophistication of the mathematical ideas is low for the grade level at which they are presented. This benchmark is covered primarily in grade 7, with some references in grades 6 and 8.

Geometry Skills — Partial Content

 Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids. (Chapter 12B, grades 6-8, benchmark 3, pg. 291.)

There are few lessons or activities in this material on measurement of perimeter of triangles and rectangles and circumference of circles. Calculations of areas of rectangles, triangles, and circles receive more coverage, primarily in grades 6 and 7. Volume of rectangular solids is addressed at all levels, with a few lessons in grade 6, and progressively more at each higher level. The benchmark is distributed appropriately across grade levels, and the tasks help develop the skills from the concrete to the symbolic.

Algebra Graph Concepts — Partial Content

 Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these. (Chapter 9B, grades 6-8, benchmark 3, pg. 219.)

The study of graphs is distributed across all three grade levels. A grade 6 unit sets the stage and builds a case for using graphs. In grades 7 and 8, students examine the ways graphs can show relationships between two variables. Although reference is made to each part of the benchmark somewhere in the material, some types of graphs are presented only once. Primary emphasis is given to variables that increase or decrease steadily, step-wise, or alternately, with minimal attention to other relationships.

Algebra Equation Concepts — Minimal Content

 Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes. (Chapter 11C, grades 6-8, benchmark 4, pg. 274.)

When algebraic expressions are introduced in grade 6, neither the teacher commentary nor the student text makes the connection for students that a variable in an expression or equation represents something that changes. The concept that symbolic equations can summarize how something changes over time is not addressed in the material. Most of the applications of algebraic equations meet the sophistication of benchmarks for an earlier grade level.