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...regression model. The model was composed variables related to classroom practices from the student questionnaire. Separate analyses were conducted for the overall achievement score, and achievement scores for each of the five content areas, and differentiated by gender. The results were mixed. The more often a student worked on projects the lower the achievement score. There was a negative relationship between asking to explain their thinking in front of the class at the board and at the overhead and achievement. The more frequently a calculator was used the greater the achievement levels. The use of the calculator correlates strongly with achievement in the Geometry content area. Female students had a stronger negative correlation than males when the teacher asks what they know related to a new mathematics topic in Geometry.
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Introduction
The way mathematics is taught has recently gained the attention of policy makers, parents, and other stake-holders as the result of recent reports of low performance in an international comparison of United States students to students in other nations. The National Council of Teachers of Mathematics [NCTM] (2000) has taken the position that, "students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge" (p. 11). This position implies that students should receive mathematics instruction that builds on their prior knowledge and should be related to what they know and to real-life situations. Moreover, teachers are encouraged to establish and nurture a classroom climate where students collaborate and are comfortable in discussing their ideas, strategies, and solutions (NCTM, 2000).
Former Secretary of Education Riley (1998) recognized the debate between reform-oriented instruction and the back-to-basic movement. The debate centers on teaching strategies, where the back-to-basic traditionalists argue that mathematics should be taught by encouraging students to memorize and practice basic facts and skills (Starr, 1998), whereas, reform oriented instruction focuses on developing mathematical understanding through communicative strategies, dialogue among students and between the students and the teacher. The debate continues.
The Third International Mathematics and Science Study (TIMSS)-R database offers a wealth of information concerning the mathematics teaching practices, achievement, and curriculum of several countries and is the largest and most comprehensive international comparison to date of mathematics and science achievement (Martin, 1996). However, this paper focuses on United States eighth-grade students. As part of the study, data were collected regarding student achievement and factors related to mathematics performance (Schmidt & Logan, 1996). This database offers the opportunity to examine relationships between selected student characteristics and mathematics achievement. The research question was "How do mathematics classroom strategies that involve communication relate to United States eighth grade students' mathematics achievement?"
Teaching for understanding in mathematics involves incorporating various reform-oriented strategies. The strategies include building on students' prior understanding, building from informal to formal knowledge, the use of calculators, having students work cooperatively, involving students with projects, relating mathematics to real-life, and communication of ideas (NCTM, 2000). In a reform-oriented classroom, communication plays a crucial role. Communication in a classroom can occur in various ways. Students may be called upon to share ideas at the board, the overhead, or within a group. A traditional activity that occurs in many mathematics classes is discussing or going over homework. All of these various communication avenues can assist in developing mathematical understanding (Fennema & Romberg, 1999).
Moreover, social constructivism as a theory of how people arrive at "knowing" describes knowledge as being in flux, where an individual internally constructs knowledge through social and cultural mediation where communication has an important role (Ernest, 1998; Steffe & Gale, 1995; Fosnot, 1996). The construction of knowledge occurs through one's perceptions and experiences, which are judged, or assessed by previous experiences and currently held briefs (Ernest, 1991). Social activity and discourse play important roles for understanding to occur. Thus, the classroom is viewed as a mini society--a community of learners engaged in activity, discourse, and reflection. The teacher provides contextually meaningful experiences where students are permitted to raise their own questions, construct models, concepts, and strategies (Fosnot, 1996).
Steffe and D'Ambrosio (1995) argue for reflection from a constructivist perspective. It is through reflection that one critiques and/or compares and contrasts one's own thoughts with those of others in a dialogic format. In...
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