Balancing Perspectives on Mathematics Instruction

Focus on Exceptional Children, May 2003 by Jones, Eric D, Southern, W Thomas

1. Math curricula vary but are dependent on commercially published programs (Carnine, 1992; Kameenui & Griffin, 1989; Tyson & Woodward, 1989).

2. Instruction tends to be teacher-led and didactic (Woodward & Montague, 2002), but

a. teachers, especially at the elementary levels, do not have extensive knowledge of the content of mathematics (Porter, Floden, Freeman, Sehmidt, & Schwule, 1988),

b. the commercially available curricula rarely provide instructions for teachers that will assure consistent implementations of the curricular programs (Carnine, Jones, & Dixon, 1994; Maccini, & Gagnon, 2002; Stein, Silbert, & Carnine, 1997),

c. teachers who provide instruction in basic mathematics knowledge and skills generally do not perceive themselves as having expertise in mathematics instruction (Porter et al., 1988), and

d. their decisions on how to present curricula are heavily influenced by introspections, perceptions, and impressions of how they were taught the same mathematical skills and concepts (Porter et al., 1988).

3. Most commercial curricula in elementary or basic mathematics do not provide adequate sequences of instruction or adequate indications of the amounts and types of practice (Carnine, 1989; Stein, Silbert, & Carnine, 1997).

4. Commercial curricula do not provide adequate articulations of the scope and sequence of the domains of mathematical knowledge and skills (Carnine, 1992; Kameenui & Griffin, 1989; Stein, Silbert, & Carnine, 1997).

5. Math curricula tend to disproportionately emphasize computational skills at the expense of problem-solving skills (Woodward & Montague, 2002).

6. Math curricula tend to provide for instruction thai involves a limited range of modes for presenting tasks and allowing for student responses (Cawley, Fitzmaurice, Lepore, Sedlak, & Althaus, 1979; Cawley, Filzmaurice, Shaw, Kahn, & Bates, 1978).

Generally speaking, mathematics instruction is directed by teachers who do not perceive that they have sufficient expertise in mathematics content or instruction. They are apt to rely on commercially available curricula that have substantial inadequacies in organization, content, and direction for implementation. Teachers are inclined to teach mathematics knowledge and skills as they perceive what they were taught. In short, mathematics instruction, especially at the level of basic skills, seems to be neither well organized nor rationally delivered.

Although direct instruction and constructivism are based on quite different notions about teaching and learning, they are not discussed often in direct opposition to each other within professional literature. Instead, critics most often characterize each as exemplifying the faults of traditional mathematics instruclion. The deficiencies of traditional mathematics are broad enough for proponents of direct instruction and constructivist instruction to use some aspect of traditional education as a basis for opposing the other. For example, proponents of direct instruction have criticized traditional or current state-of-the-art instruction for its lack of coherent teacher direction and explicit organization of curriculum content. Then, by extension, they have also criticized constructivist approaches because constructivists argue against explicit control of either presentation or content of instruction.