Variations in mathematics problem-solving support for lower and higher achieving elementary students: A study of the one-on-one instructional practices of teachers who use a reform-based curriculum.

摘要

This study was designed to investigate whether and how upper elementary grade teachers who use a reform-based mathematics curriculum adjust instruction for their lower achieving (LA) compared to higher achieving (HA) students during a one-on-one mathematics problem-solving lesson. Little is known about the individualized support teachers provide to students during mathematics problem solving even though such support may be especially important to the learning of the students who struggle most with mathematics.;Eleven teachers and one LA and one HA student from each teacher's classroom participated. Each teacher conducted a problem-solving lesson with each of their participating students. Teachers used a researcher-provided task that asked students to "Find where these fractions go on the number line. " The provided fractions varied in how challenging they were expected to be for students. Teachers were encouraged to use the fractions to conduct the lesson they thought most appropriate for each student.;Teacher-student interactions were analyzed using a four-dimension framework that investigated teachers' (a) adjustments to task content, (b) use of nonverbal external cognitive support, (c) types of verbalized instructions (e.g., whether focusing on procedures or understanding), and (d) levels of verbalized instructions (e.g., whether guiding or directive). It was found that the support teachers provided to their LA compared to HA students differed in relation to three of the dimensions: (a) Teachers assigned fewer fractions and an easier overall set of fractions to LA students; (b) they provided LA students more nonverbalized external cognitive support; and (c) their verbalized instructions were more directive with LA students.;Follow-up analyses tested two possible explanations of the group-related differences in teachers' verbalized instructions: (a) one hypothesis proposed that students' problem-solving difficulty explains the effect; (b) the second hypothesis proposed that teachers' mental models of students explain the effect. It was concluded that both mechanisms influence teachers' adjustments to levels of one-on-one math instruction support. Overall, teachers' support of students during individual math problem-solving work reflected desired reform practices in some respects but not others. Future research should investigate the effectiveness of instructional alterations teachers make for LA and HA math students.