# Browsing by Subject "Middle school mathematics"

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Item The role of productive struggle in teaching and learning middle school mathematics(2011-12) Warshauer, Hiroko Kawaguchi; Empson, Susan B.; Barufaldi, James; Emmer, Edmund T.; Petrosino, Anthony; Treisman, Philip U.Show more Students’ struggle with learning mathematics is often cast in a negative light. Mathematics educators and researchers, however, suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. In order to investigate the possible connection between struggle and learning, this study examined students’ productive struggle as students worked on tasks of higher cognitive demand in middle school mathematics classrooms. Students’ productive struggle refers to students’ “effort to make sense of mathematics, to figure something out that is not immediately apparent” (Hiebert & Grouws, 2007, p. 287) as opposed to students’ effort made in despair or frustration. As an exploratory case study using embedded multiple cases, the study examined 186 episodes of student‐teacher interactions in order to identify the kinds and nature of student struggles that occurred in a naturalistic classroom setting as students engaged in mathematical tasks focused on proportional reasoning. The study identified the kinds of teacher responses used in the interaction with the students and the types of resolutions that occurred. The participants were 327 6th and 7th grade students and their six mathematics teachers from three middle schools located in mid‐size Texas cities. Findings from the study identified four basic types of student struggles: get started, carry out a process, give a mathematical explanation, and express misconception and errors. Four kinds of teacher responses to these struggles were identified as situated along a continuum: telling, directed guidance, probing guidance, and affordance. The outcomes of the student‐teacher interactions that resolved the students’ struggles were categorized as: productive, productive at a lower level, or unproductive. These categories were based on how the interactions maintained the cognitive level of the implemented task, addressed the externalized student struggle, and built on student thinking. Findings provide evidence that there are aspects of student‐teacher interactions that appear to be productive for student learning of mathematics. The struggle‐response framework developed in the study can be used to further examine the phenomenon of student struggle from initiation, interaction, to its resolution, and measure learning outcomes of students who experience struggle to make sense of mathematics.Show more Item A study on the use of history in middle school mathematics : the case of connected mathematics curriculum(2008-12) Haile, Tesfayohannes Kiflemariam; Treisman, Uri; Davis, O. L. (Ozro Luke), 1928-Show more This dissertation explores the use of history of mathematics in middle school mathematics. A rationale for the importance of the incorporation of historical dimensions (HD) of mathematics is provided through a review of the literature. The literature covers pedagogical, philosophical, psychological, and social issues and provides arguments for the use of history. The central argument is that history can help reveal significant aspects regarding the origins and evolutions of ideas that provide contexts for understanding the mathematical ideas. History can be used as a means to reflect on significant aspects—errors, contractions, challenges, breakthroughs, and changes—of mathematical developments. Noting recent NCTM (2000) calls for school math to include so-called process standards, I contend that incorporating the history of mathematics can be considered as part of this standard. This study examines how HD is addressed in a contemporary mathematics curriculum. Specifically, the study examines the Connected Mathematics Project (CMP) as a case. This curriculum has some historical references which triggered further exploration on how seriously the historical aspects are incorporated. The analysis and discussion focus on four CMP units and interviews with three curriculum experts, eight teachers, and 11 middle school students. The analysis of textbooks and interviews with the experts explore the nature and purpose of historical references in the curriculum. The interviews with teachers and students focus on their perspectives on the importance of HD in learning mathematics. This study examines specifically historical incorporations of the concepts of fractions, negative numbers, the Pythagorean Theorem, and irrational numbers. The analysis reveals that CMP exhibits some level of historical awareness, but the incorporation of HD was not systematically or seriously considered in the development of the curriculum. The interviews suggest that the teachers did not seriously use the limited historical aspects available in the textbooks. The experts’ and teachers’ interviews suggest skepticism about the relevance of HD for middle school mathematics. The teachers’ accounts indicate that students are most interested in topics that are related to their experience and to future applications. The students’ accounts do not fully support the teachers’ assessment of students’ interest in history. I contend that incorporating HD can complement instruction in ways that relate to students’ experiences and to applications besides adding an inquiry dimension to instruction.Show more