ticing learned skills. We believe problem solving is vital because it calls on all strands of proficiency, thus increasing the chances of students integrating them. Problem solving also provides opportunities for teachers to assess students’ performance on all of the strands. Other activities, such as listening to an explanation or practicing solution methods, can help develop specific strands of proficiency, but too much emphasis on them, to the exclusion of solving problems, may give a one-sided character to learning and inhibit the formation of connections among the strands. We see problem solving as central to school mathematics:
We see problem solving as central to school mathematics.
Problem solving should be the site in which all of the strands of math ematics proficiency converge. It should provide opportunities for students to weave together the strands of proficiency and for teachers to assess students’ performance on all of the strands.
Analyses of the U.S. curriculum reveal much repetition from grade to grade and many topics, few of which are treated in much depth. Further, instructional materials in pre-K to grade 8 mathematics seldom provide the guidance and assistance that teachers in other countries find helpful, such as discussions of children’s typical misconceptions or alternative solution methods. How teachers might understand and use instructional materials to help students develop mathematical proficiency is not well understood. On the basis of our reasoned judgment, we offer the following recommendations for improving instructional materials in school mathematics:
Textbooks and other instructional materials should develop the core content of school mathematics in a focused way, in depth, and with continu ity in and across grades, supporting all strands of mathematical proficiency.
Textbooks and other instructional materials should support teacher understanding of mathematical concepts, of student thinking and student errors, and of effective pedagogical supports and techniques.
Activities and strategies should be developed and incorporated into instructional materials to assist teachers in helping all students become proficient in mathematics, including students low in socio-economic status, English language learners, special education students, and students with a special interest or talent in mathematics.