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Algebra Learning

The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform

Kenneth R Koedinger – 1st expert on this subject based on the ideXlab platform

  • Handwriting Interaction for Math Tutors: Lessons for HCI in Education
    , 2020
    Co-Authors: Lisa Anthony, Jie Yang, Kenneth R Koedinger

    Abstract:

    We discuss our position on key issues in HCI in education based on lessons learned during our work on incorporating handwriting interaction into intellig ent tutoring systems (ITS) for Algebra Learning. Pen-ba sed computing offers opportunities to support more natu ral and transparent (invisible) interactions, such as handwriting and sketch, for students in the math domain, allowing them to focus on the Learning task . We describe the technical and research challenges w e encountered in making an ITS-embedded handwriting recognition system usable by middle and high school Algebra students. Our efforts can be informative in designing usable and pedagogically-effective educational technology systems in the future.

  • Moving beyond Teachers’ Intuitive Beliefs about Algebra Learning.
    Mathematics Teacher: Learning and Teaching PK–12, 2020
    Co-Authors: Mitchell J. Nathan, Kenneth R Koedinger

    Abstract:

    Beliefs that teachers hold about students9 abilities most influence instructional practices hink about this question: Why are Algebra story problems considered to be the most difficult tasks facing Algebra students? Teachers generally regard them as difficult (Nathan and Koedinger forthcom ing), textbooks typically place these problems at the ends of chapters (Nathan and Long 1999), students find them least favorable, and even comic-strip folk lore presents story problems as the bane of formal education. (See fig. 1). Are these perceptions held by teachers and textbook authors justified? This article examines teachers’judgments of the difficul ty of Algebra problems. Our findings may surprise readers, and we hope that they will motivate read ers to reexamine some long-standing assumptions about mathematics Learning and instruction.

  • adapting handwriting recognition for applications in Algebra Learning
    ACM Multimedia, 2007
    Co-Authors: Lisa Anthony, Jie Yang, Kenneth R Koedinger

    Abstract:

    In this paper we report the progress of our ongoing project exploring the adaptation of handwriting recognition-based interfaces for applications in intelligent tutoring systems for students Learning Algebra equation-solving. The research is motivated by the hypothesis that handwriting as an input modality may be able to provide significant advantages over typing in the mathematics Learning domain. We review the literature of existing handwriting systems for mathematic applications and evaluations of handwriting recognition accuracy. We describe our approach and report results to date in exploring the use of handwriting recognition in interfaces for math Learning, from both a technical and a pedagogical perspective. We have found that handwriting input can provide benefits to students Learning math, and continue to pursue further technical and pedagogical enhancements.

Carolyn Kieran – 2nd expert on this subject based on the ideXlab platform

  • Task Design Frameworks in Mathematics Education Research: An Example of a Domain-Specific Frame for Algebra Learning with Technological Tools
    ICME-13 Monographs, 2019
    Co-Authors: Carolyn Kieran

    Abstract:

    Theorizing about task design is a fairly recent area of attention within the educational research community, emerging in the late ‚0s and continuing with growing interest to the present day. To reflect the evolution in task design theorization, this chapter focuses first on historical aspects and highlights the main theorizing initiatives of the past half-century. The second part offers a conceptualization of current theoretical frameworks and principles for task design within mathematics education research—a conceptualization that distinguishes among the three levels of grand, intermediate, and domain-specific frames. The third part of the chapter elaborates on the notion of domain-specific frames by presenting an example of the design features underpinning a study on the CAS-supported co-emergence of technique and theory within the activity of Algebraic factorization and describes how the classroom implementation of the proving phase of the designed task-sequence was supported by the instructional practice of the teacher and by the role played by the technology as a tool to spark thinking.

  • Cognitive Neuroscience and Algebra: Challenging Some Traditional Beliefs
    And the Rest is Just Algebra, 2016
    Co-Authors: Carolyn Kieran

    Abstract:

    Recent studies using neuroimaging technology with tasks touching on various areas of mathematics are raising a great deal of excitement with their findings. This chapter presents some key work related to higher level mathematical reasoning and a few insights arising from these studies with respect to our current understanding of Algebra Learning. After a general introduction on cognitive neuroscience and its recent advances relevant to mathematics education, the chapter focuses on two studies in particular, one on the Algebraic solving method and the other on representing functions. The chapter concludes with a discussion of the ways in which these results from the newly emerging field, which is at times referred to as mathematics educational neuroscience, offer the potential of casting a quite different light on how we think about students’ processing of Algebra-related material.

  • The False Dichotomy in Mathematics Education Between Conceptual Understanding and Procedural Skills: An Example from Algebra
    Vital Directions for Mathematics Education Research, 2013
    Co-Authors: Carolyn Kieran

    Abstract:

    The history of mathematics education provides ample evidence of the dichotomous distinction that has been made over the years between concepts and procedures, between concepts and skills, and between “knowing that” and “knowing how.” In no field of school mathematics Learning has this dichotomy been so damaging as in Algebra. While reform efforts of the past decade have attempted to imbue Algebra Learning with meaning by focusing on “real-life” problems and their various representations, these efforts have missed the main point with respect to the literal-symbolic: that is, that conceptual aspects of Algebra abound within the literal-­symbolic and that these are integral to most of the so-called procedures of Algebra. Both theoretical and empirical arguments will be used to make the point for adopting a different vision of the literal-symbolic domain, in which the procedural is so permeated with the conceptual as to render obsolete a primarily procedure-based view of Algebra in school mathematics.

Lisa Anthony – 3rd expert on this subject based on the ideXlab platform

  • Handwriting Interaction for Math Tutors: Lessons for HCI in Education
    , 2020
    Co-Authors: Lisa Anthony, Jie Yang, Kenneth R Koedinger

    Abstract:

    We discuss our position on key issues in HCI in education based on lessons learned during our work on incorporating handwriting interaction into intellig ent tutoring systems (ITS) for Algebra Learning. Pen-ba sed computing offers opportunities to support more natu ral and transparent (invisible) interactions, such as handwriting and sketch, for students in the math domain, allowing them to focus on the Learning task . We describe the technical and research challenges w e encountered in making an ITS-embedded handwriting recognition system usable by middle and high school Algebra students. Our efforts can be informative in designing usable and pedagogically-effective educational technology systems in the future.

  • adapting handwriting recognition for applications in Algebra Learning
    ACM Multimedia, 2007
    Co-Authors: Lisa Anthony, Jie Yang, Kenneth R Koedinger

    Abstract:

    In this paper we report the progress of our ongoing project exploring the adaptation of handwriting recognition-based interfaces for applications in intelligent tutoring systems for students Learning Algebra equation-solving. The research is motivated by the hypothesis that handwriting as an input modality may be able to provide significant advantages over typing in the mathematics Learning domain. We review the literature of existing handwriting systems for mathematic applications and evaluations of handwriting recognition accuracy. We describe our approach and report results to date in exploring the use of handwriting recognition in interfaces for math Learning, from both a technical and a pedagogical perspective. We have found that handwriting input can provide benefits to students Learning math, and continue to pursue further technical and pedagogical enhancements.

  • ACM Multimedia EMME Workshop – Adapting handwriting recognition for applications in Algebra Learning
    Proceedings of the international workshop on Educational multimedia and multimedia education – Emme '07, 2007
    Co-Authors: Lisa Anthony, Jie Yang, Kenneth R Koedinger

    Abstract:

    In this paper we report the progress of our ongoing project exploring the adaptation of handwriting recognition-based interfaces for applications in intelligent tutoring systems for students Learning Algebra equation-solving. The research is motivated by the hypothesis that handwriting as an input modality may be able to provide significant advantages over typing in the mathematics Learning domain. We review the literature of existing handwriting systems for mathematic applications and evaluations of handwriting recognition accuracy. We describe our approach and report results to date in exploring the use of handwriting recognition in interfaces for math Learning, from both a technical and a pedagogical perspective. We have found that handwriting input can provide benefits to students Learning math, and continue to pursue further technical and pedagogical enhancements.