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Guiding Mathematical Discussions in High School Mathematics Classes
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GUIDING THE MATHEMATICS OF MATHEMATICAL DISCUSSIONS
Megan Staples
Purdue University
## email not listed ##
Despite calls for reform that support the enactment of collaborative learning environments in mathematics classrooms (NCTM, 1989, 2000), implementation of such environments is not widespread. There remains a pressing need for research that focuses closely on teachers’ successful enactment of reform pedagogies (Boaler, 2003). An assumption of this study is that one reason for the lack of implementation of reform ideals is that insufficient attention has been given to the mathematics and how teachers can productively guide the development of mathematical ideas during collaborative activities. Findings from an in-depth longitudinal case study of a collaborative high school mathematics classroom are presented. A conceptualization of the teacher’s role in guiding the mathematics is developed, and particular strategies that supported this student-centered collaborative environment are identified.
Introduction
In recent decades, there has been a multitude of reform efforts in mathematics education
aimed at generating more collaborative and student-centered learning environments. In the United States, the vision of reform has been guided by the National Council of Teachers of Mathematics (NCTM) Standards documents (NCTM, 1989, 2000). In classrooms that exemplify this vision, students actively engaged in mathematical sense making and communicating with one another (NCTM, 2000). There is mounting evidence demonstrating the value of these environments for students’ learning (Boaler, 1997; Stein et al., 2000; Wood & Sellers, 1997) and fostering a productive disposition towards mathematics (Boaler & Greeno, 2000). However, such classrooms remain relatively rare, particularly on the secondary level (Stigler & Hiebert, 1999).
One factor contributing to their lack of prevalence is our underdeveloped understanding of
the complex pedagogies required to support these more interactive, discussion-based learning environments (RAND, 2002). In particular, insufficient attention has been given to the mathematical ideas and how they are developed through collaborative activity. Too often “surface features” associated with reform practices, such as groupwork or high levels of interaction among students, are taken as evidence of successful realization of the reform ideals. Yet, classrooms supporting these features may not support the quality of mathematics instruction espoused by the Standards. As the most recent version of the Standards (2000) states:
As with any educational innovation … the ideas of the Standards have been interpreted in many different ways and have been implemented with varying degrees of fidelity. Sometimes the changes made in the name of standards have been superficial or incomplete. For example, some of the pedagogical ideas from the NCTM Standards—such as the emphases on discourse, worthwhile mathematical tasks, or learning through problem solving—have been enacted without sufficient attention to students' understanding of mathematics content. Efforts to move in the directions of the original NCTM Standards are by no means fully developed or firmly in place. (p. 5)
Thus there remains a pressing need for research that focuses closely on teachers’ successful enactment of reform pedagogies (Boaler, 2003), and specifically, how teachers guide students’ engagement with mathematical ideas and participation in mathematical practices.
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GUIDING THE MATHEMATICS OF MATHEMATICAL DISCUSSIONS
Megan Staples
Purdue University
## email not listed ##
Despite calls for reform that support the enactment of collaborative learning environments in
mathematics classrooms (NCTM, 1989, 2000), implementation of such environments is not
widespread. There remains a pressing need for research that focuses closely on teachers’
successful enactment of reform pedagogies (Boaler, 2003). An assumption of this study is that
one reason for the lack of implementation of reform ideals is that insufficient attention has been
given to the mathematics and how teachers can productively guide the development of
mathematical ideas during collaborative activities. Findings from an in-depth longitudinal case
study of a collaborative high school mathematics classroom are presented. A conceptualization
of the teacher’s role in guiding the mathematics is developed, and particular strategies that
supported this student-centered collaborative environment are identified.
Introduction
In recent decades, there has been a multitude of reform efforts in mathematics education
aimed at generating more collaborative and student-centered learning environments. In the
United States, the vision of reform has been guided by the National Council of Teachers of
Mathematics (NCTM) Standards documents (NCTM, 1989, 2000). In classrooms that exemplify
this vision, students actively engaged in mathematical sense making and communicating with
one another (NCTM, 2000). There is mounting evidence demonstrating the value of these
environments for students’ learning (Boaler, 1997; Stein et al., 2000; Wood & Sellers, 1997) and
fostering a productive disposition towards mathematics (Boaler & Greeno, 2000). However, such
classrooms remain relatively rare, particularly on the secondary level (Stigler & Hiebert, 1999).
One factor contributing to their lack of prevalence is our underdeveloped understanding of
the complex pedagogies required to support these more interactive, discussion-based learning
environments (RAND, 2002). In particular, insufficient attention has been given to the
mathematical ideas and how they are developed through collaborative activity. Too often
“surface features” associated with reform practices, such as groupwork or high levels of
interaction among students, are taken as evidence of successful realization of the reform ideals.
Yet, classrooms supporting these features may not support the quality of mathematics instruction
espoused by the Standards. As the most recent version of the Standards (2000) states:
As with any educational innovation … the ideas of the Standards have been
interpreted in many different ways and have been implemented with varying
degrees of fidelity. Sometimes the changes made in the name of standards have
been superficial or incomplete. For example, some of the pedagogical ideas from
the NCTM Standards—such as the emphases on discourse, worthwhile
mathematical tasks, or learning through problem solving—have been enacted
without sufficient attention to students' understanding of mathematics content.
Efforts to move in the directions of the original NCTM Standards are by no means
fully developed or firmly in place. (p. 5)
Thus there remains a pressing need for research that focuses closely on teachers’ successful
enactment of reform pedagogies (Boaler, 2003), and specifically, how teachers guide students’
engagement with mathematical ideas and participation in mathematical practices.
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