Teachers' role in facilitating students' strategic and metacognitive processes during the representational, solution, and evaluation phase of mathematics problem-solving
Description
The present study investigated the role of teachers in facilitating children's strategy use and metacognitive knowledge in mathematical problem solving. Second- and fifth-grade teachers were chosen for the study to describe differences in the kinds of cognitive processes teachers suggest to early versus late elementary school children Sixteen second-grade and 17 fifth-grade teachers participated in the study. A questionnaire was developed to describe teachers' expectations of their students' strategy use and metacognitive knowledge. As hypothesized, second- and fifth-grade teachers had different expectations for their students' use of strategies and metacognition. Generally, teachers of older children expected their students to possess greater metacognitive knowledge than second-grade teachers did of their students. Teachers expected higher achievers to be more strategic and to possess greater metacognitive knowledge than lower achievers. Teachers varied their expectations for certain types of processes In addition, classroom observations were conducted to describe teachers' cognitive suggestions to children. Different types of strategies were classified according to problem solving phase: the representational phase included those activities aimed at facilitating understanding of the math problem and planning of the solution; the solution phase involved activities used to solve a math equation; and the evaluative phase included activities aimed at assessing the correctness of an answer. Metacognitive suggestions were categorized into type: person, task, and strategy knowledge. Teachers devoted a relatively large amount of time to the instruction of cognitive processes, particularly strategy instruction. Teachers presented more representational strategies than solution or evaluative strategies; therefore, their instruction did focus heavily in teaching children to understand math processes. Teachers taught children strategies that were developmentally appropriate. Second-grade teachers more often presented strategies that facilitated understanding by representing numbers concretely than fifth-grade teachers did. Fifth-grade teachers, on the other hand, directed more planning and goal-formation strategies than second-grade teachers, which is consistent with research indicating that older elementary school children are capable of greater self-regulatory skills In conclusion, teachers appeared to have an important role in instructing children strategies that would enhance their understanding of math problem solving. The strategies that teachers suggested were appropriate to the developmental level of their students