Mathematically Correct congratulates the California State Board of Education on approving a new Mathematics Program Advisory. This Program Advisory is a significant move, at the highest levels of the California educational establishment, away from the controversial 1992 California Mathematics Framework and the classroom practices derived from it.
The Advisory repeats the Call for Balance of the Mathematics Task Force Report, but contains key descriptions of some of the components of a balanced program. Much of the document deals with two main points related to balance -- a balance of learning objectives among basic skills, conceptual understanding and problem solving, and a balance among instructional strategies. Unlike the Task Force Report, this document contains specific language that clarifies what should happen in a classroom, much of which is counter to the practices that have been implemented in textbooks and classrooms in response to the 1992 California Mathematics Framework.
This document largely represents the consensus opinion of a committee jointly convened by Superintendent Delaine Eastin and the State Board. The majority of the committee was composed of supporters of math reform, although there were a few notable exceptions. The supporters of math reform included the current and future presidents of the California Math Council, and at least one author of the 1992 Mathematics Framework. Those who have been critical of various aspects of math reform included a former President of the Mathematical Association of America and one member of Mathematically Correct. The Board was represented by Kathryn Dronenburg and Janet Nicholas.
Mathematically Correct commends Superintendent Eastin and the State Board for working together on this document and for presenting it to the districts, schools, teachers, parents and students of California.
The Program Advisory notes that basic skills should be used routinely and automatically, should be practiced regularly, and many should be committed to memory. The document makes it clear that many aspects of mathematics, above and beyond addition and multiplication, need to become automatic and routine. This allows basic skills at all levels to become goals in and of themselves, and encourages students to practice these skills directly. No longer is it necessary to address basic skills only within the context of open-ended problems as is common in the Framework-aligned texts.
The Program Advisory makes it clear that one of the goals of problem solving is to allow children to practice various kinds of problems until they become routine. It also stresses that students need computation skills, skills related to solving equations or inequalities, graphing skills, knowledge of geometric relationships and measurement concepts, and the analysis of graphical information and data. A mathematics program should include a substantial number of ready-to-solve exercises that are designed specifically to develop and reinforce these basic technical skills. These statements are critical as they indicate that a balanced mathematics program can and should include use of repeated exercises representing the kinds of problems that recur in a number of different situations, and that a good education in problem solving is not achieved by programs in which problem solving is taught exclusively via a small number of perplexing or open-ended problems.
Within the section on Instructional Strategies the Program Advisory makes it clear that no single instructional strategy is best or appropriate in all situations. It then lists a representative set of strategies, including expository or direct instruction, hands-on learning, classroom discussion, discovery, individual work, and group work. It further notes that choosing among these strategies is the responsibility of the teacher, who should consider the students and lessons involved. This is a drastic break with the current Framework. Programs designed under the current Framework have been strongly committed to an instructional strategy based on discovery learning and group activities. This statement makes it clear that teachers can choose the strategies, including direct instruction, that best suit the needs of their students.