Mathematical manipulative materials (manipulatives) invite students to explore and represent abstract mathematical concepts in varied, concrete, tactile, and visually rich ways. Considering the prominence of the use of mathematical manipulatives in current K-12 curricula, pedagogical resources and professional development, research studies show that few secondary school teachers use them. While these studies do not examine this issue from the teachers’ perspective, they posit that some teachers lack the mathematical knowledge connected to manipulatives, are uncomfortable with or uncertain how to use them, or do not believe that manipulatives have value in the teaching of secondary school mathematics. As a result there is a great need for research that provides further detail as to why and how secondary school mathematics teachers use manipulatives in their classrooms. This study, guided by the research questions: ‘How do secondary school teachers view the use of manipulatives in teaching mathematics?’ and ‘How do secondary school teachers describe their use of manipulatives in teaching mathematics?’, sought to examine these issues through semi-structured interviews with six secondary school mathematics teachers. This study supports the notion that the use of manipulatives in secondary school mathematics classrooms is influenced by teachers' views and experience with manipulatives. It highlights some of the challenges that teachers face, and supports from which they gain confidence and competence in their efforts to integrate the use of mathematical manipulatives into their teaching practice.

Mathematical manipulative materials (manipulatives) invite students to explore and represent abstract mathematical concepts in varied, concrete, tactile, and visually rich ways. Considering the prominence of the use of mathematical manipulatives in current K-12 curricula, pedagogical resources and professional development, research studies show that few secondary school teachers use them. While these studies do not examine this issue from the teachers’ perspective, they posit that some teachers lack the mathematical knowledge connected to manipulatives, are uncomfortable with or uncertain how to use them, or do not believe that manipulatives have value in the teaching of secondary school mathematics. As a result there is a great need for research that provides further detail as to why and how secondary school mathematics teachers use manipulatives in their classrooms. This study, guided by the research questions: ‘How do secondary school teachers view the use of manipulatives in teaching mathematics?’ and ‘How do secondary school teachers describe their use of manipulatives in teaching mathematics?’, sought to examine these issues through semi-structured interviews with six secondary school mathematics teachers. This study supports the notion that the use of manipulatives in secondary school mathematics classrooms is influenced by teachers' views and experience with manipulatives. It highlights some of the challenges that teachers face, and supports from which they gain confidence and competence in their efforts to integrate the use of mathematical manipulatives into their teaching practice.

Mathematical manipulative materials (manipulatives) invite students to explore and represent abstract mathematical concepts in varied, concrete, tactile, and visually rich ways. Considering the prominence of the use of mathematical manipulatives in current K-12 curricula, pedagogical resources and professional development, research studies show that few secondary school teachers use them. While these studies do not examine this issue from the teachers’ perspective, they posit that some teachers lack the mathematical knowledge connected to manipulatives, are uncomfortable with or uncertain how to use them, or do not believe that manipulatives have value in the teaching of secondary school mathematics. As a result there is a great need for research that provides further detail as to why and how secondary school mathematics teachers use manipulatives in their classrooms. This study, guided by the research questions: ‘How do secondary school teachers view the use of manipulatives in teaching mathematics?’ and ‘How do secondary school teachers describe their use of manipulatives in teaching mathematics?’, sought to examine these issues through semi-structured interviews with six secondary school mathematics teachers. This study supports the notion that the use of manipulatives in secondary school mathematics classrooms is influenced by teachers' views and experience with manipulatives. It highlights some of the challenges that teachers face, and supports from which they gain confidence and competence in their efforts to integrate the use of mathematical manipulatives into their teaching practice.

Mathematical manipulative materials (manipulatives) invite students to explore and represent abstract mathematical concepts in varied, concrete, tactile, and visually rich ways. Considering the prominence of the use of mathematical manipulatives in current K-12 curricula, pedagogical resources and professional development, research studies show that few secondary school teachers use them. While these studies do not examine this issue from the teachers’ perspective, they posit that some teachers lack the mathematical knowledge connected to manipulatives, are uncomfortable with or uncertain how to use them, or do not believe that manipulatives have value in the teaching of secondary school mathematics. As a result there is a great need for research that provides further detail as to why and how secondary school mathematics teachers use manipulatives in their classrooms. This study, guided by the research questions: ‘How do secondary school teachers view the use of manipulatives in teaching mathematics?’ and ‘How do secondary school teachers describe their use of manipulatives in teaching mathematics?’, sought to examine these issues through semi-structured interviews with six secondary school mathematics teachers. This study supports the notion that the use of manipulatives in secondary school mathematics classrooms is influenced by teachers' views and experience with manipulatives. It highlights some of the challenges that teachers face, and supports from which they gain confidence and competence in their efforts to integrate the use of mathematical manipulatives into their teaching practice.

This qualitative case study examined the use of manipulatives in mathematics instruction by six first-year intermediate teachers in a north Texas school district. Their preparation for, access to, and perceptions about manipulatives were examined. Specific content associated with manipulative usage was identified.

Manipulatives of various kinds are used in elementary schools as part of the mathematics curriculum. They are recognized for their affordances for helping children understand abstract ideas by connecting them to concrete objects, but not all research about the use of manipulatives has been positive. It is sometimes difficult for children to make connections between what they are doing and the ideas the manipulatives embody. Constructionist research suggests that taking a design approach to learning that involves the learner in constructing not only ideas but also public artifacts facilitates learning particularly well. Further, it suggests that one should design a learning environment that will allow learners to leverage personal and epistemological connections rather than scripting everything that should happen. Additionally, previous research suggests that integrating math with craft and design helps learners engage with math in a personally meaningful manner. Manipulatives such as pattern tiles and quilt builder tiles are used for design in the classroom, but there is often little to no support for the analysis of designed patterns or other kinds of learning. On the other hand, computerized versions of manipulatives that provide feedback about fractions (or other math concepts) do not offer affordances for design. My goal has been to integrate the best of what computational manipulatives can offer with a design approach to help learners engage with math in a meaningful way. In this dissertation, I describe the use of a manipulative that combines affordances for design and also links and maintains connections between representations. This gave learners opportunities to see and make connections between symbolic and concrete representations while engaged in designing personally meaningful artifacts. I describe methods that made this constructionist educational experience accessible to a wide range of learners, including aspects of the socio-technical system that seemed to play greater or lesser roles at various times throughout the study. I emphasize roles of the DigiQuilt manipulative and highlight how this software builds on previous work, yet represents a new kind of manipulative one that simultaneously supports design and connecting targeted math concepts with concrete artifacts.

Thesis (M.S.) -- Central Connecticut State University, 2005. / Thesis advisor: Philip Halloran. "... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 23-24). Also available via the World Wide Web.

Thesis (M.S.)--Rowan University, 2005. / Typescript. Includes bibliographical references.

Thesis (M.Ed.)--University of Central Florida, 2008. / Adviser: Gina Gresham. Includes bibliographical references (p. 95-99).

Thesis (M. Ed.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.