decimals, and percents as late as eighth grade. Standard algorithms for computations with fractions…. are often not used…. [While] CMP does a good job of helping students discover the mathematical connections and patterns in the algebra strand, [it] falls short in a follow-through with more substantial statements, generalizations, formulas, or algorithms.” In an 8th-grade unit, “CMP misses the opportunity to discuss the quadratic formula or the process of completing the square.”
Other examples (AAAS, 1999b, Part 1 Conclusions [in box]—http://www.project2061.org/matheval/part1c.htm; Adams et al., 2000, p. 12) could be offered, but the critique permits one to see why the issue of balance is crucial in content analyses, as one examines whether emphasis on discovery approaches and new levels of understanding can carry the cost of a lack of basic knowledge of facts and standard mathematical algorithms at an early age. In addition to timeliness for all students, in many content analyses, there is expressed concern for the most mathematically inclined students to receive enough challenges. For example, Adams et al. (2000, p. 13) wrote that in Mathematics in Context:
Alongside each lesson are comments about the underlying mathematical concepts in the lesson (“About the Mathematics”) as well as how to plan and to actually teach the lesson. A nice feature is that these comments occur in the margins of the Teachers’ Guides…. On the other hand, these comments often contain some useful mathematical facts and language that could be, but most likely wouldn’t be, communicated to the students; in particular high-end students could benefit from these insights if they were available to them. In addition, the lack of a glossary hides mathematical terminology from the students, a language which they should be beginning to negotiate by the middle grades. Exposure to the precise terminology of mathematics is crucial for students at this stage, not only as a means of exemplifying the rigor of mathematics, but as a way to communicate their discoveries and hypotheses in a common language, rather than the idiosyncratic terms that a particular student or class may develop.
As a result of comments such as these, the authors summarize by stating, “high-end students may not find this curriculum very challenging or stimulating” (p. 14).
In the content analyses, support for diversity was typically addressed only in terms of performance levels, and even then, high performers were identified as needing the most attention (Howe testimony). In contrast, other researchers focused on the importance of providing activities that can be used successfully to meet the needs of a variety of student levels of preparation, scaffolding those needing more assistance and including extensions for those ready for more challenge (Schifter testimony). Furthermore, there are other aspects of support for diversity to be considered, such as language use or cultural experiences. More attention in these content analy-