Mathematical Problem

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Marjorie Montague - One of the best experts on this subject based on the ideXlab platform.

  • evaluating the evidence base for cognitive strategy instruction and Mathematical Problem solving
    Exceptional Children, 2009
    Co-Authors: Marjorie Montague, Samantha Dietz
    Abstract:

    This review considers both the content and methodologies of 5 single-subject and 2 group experimental design studies investigating the effects of cognitive strategy instruction on the Mathematical Problem solving of students with disabilities, using quality indicators proposed by Horner et al. (2005) and Gersten et al. (2005). Findings indicated that the research base of both single-subject and group experimental studies did not meet the methodological criteria to support cognitive strategy instruction as an evidence-based practice for improving Mathematical Problem solving of students with disabilities. The shortcomings identified in the empirical literature supporting cognitive strategy instruction, however, can be addressed in future intervention studies bearing in mind the quality indicators and standards for determining evidence-based practices.

  • self regulation strategies to improve Mathematical Problem solving for students with learning disabilities
    Learning Disability Quarterly, 2008
    Co-Authors: Marjorie Montague
    Abstract:

    This article provides a review of research in cognitive strategy instruction for improving Mathematical Problem solving for students with learning disabilities (LD). The particular focus is on one of the salient components of this instructional approach — self-regulation. Seven studies utilizing this approach for teaching Problem solving to students with LD were previously evaluated to determine its status as evidence-based practice. The results of this evaluation are described, and the self-regulation component embedded in the cognitive routine for each of the studies is presented. The article concludes with a discussion of several principles associated with research and practice in strategy instruction and some practical considerations for implementation in schools.

  • visual spatial representation Mathematical Problem solving and students of varying abilities
    Learning Disabilities Research and Practice, 2003
    Co-Authors: Delinda Van Garderen, Marjorie Montague
    Abstract:

    The purpose of this study was to investigate students' use of visual imagery while solving Mathematical Problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N= 66) participated in this study. Students were assessed on measures of Mathematical Problem solving and visual-spatial representation. Visual-spatial representations were coded as either primarily schematic representations that encode the spatial relations described in the Problem or primarily pictorial representations that encode persons, places, or things described in the Problem. Results indicated that gifted students used significantly more visual-spatial representations than the other two groups. Students with LD used significantly more pictorial representations than their peers. Successful Mathematical Problem solving was positively correlated with use of schematic representations; conversely, it was negatively correlated with use of pictorial representations.

  • Student Perception, Mathematical Problem Solving, and Learning Disabilities
    Remedial and Special Education, 1997
    Co-Authors: Marjorie Montague
    Abstract:

    The purpose of this article is to discuss student perception of Mathematical Problem solving. Findings from five studies measuring attitude toward mathematics, perception of performance, perception of the importance of Mathematical Problem solving, and perception of Problem difficulty are presented and discussed. Additionally, the interaction of affect and cognition and the implications of this interaction for assessing and teaching Mathematical Problem solving to students with learning disabilities are discussed.

Maria Kozhevnikov - One of the best experts on this subject based on the ideXlab platform.

  • types of visual spatial representations and Mathematical Problem solving
    Journal of Educational Psychology, 1999
    Co-Authors: Mary Hegarty, Maria Kozhevnikov
    Abstract:

    Although visual-spatial representations are used extensively in mathematics and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in Mathematical Problem solving. The authors distinguished 2 types of visual-spatial representations: schematic representations that encode the spatial relations described in a Problem and pictorial representations that encode the visual appearance of the objects described in the Problem. Participants solved Mathematical Problems and reported on their solution strategies. The authors were able to reliably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in Mathematical Problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic representations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and Mathematical Problem solving.

  • Types of visual–spatial representations and Mathematical Problem solving.
    Journal of Educational Psychology, 1999
    Co-Authors: Mary Hegarty, Maria Kozhevnikov
    Abstract:

    Although visual-spatial representations are used extensively in mathematics and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in Mathematical Problem solving. The authors distinguished 2 types of visual-spatial representations: schematic representations that encode the spatial relations described in a Problem and pictorial representations that encode the visual appearance of the objects described in the Problem. Participants solved Mathematical Problems and reported on their solution strategies. The authors were able to reliably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in Mathematical Problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic representations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and Mathematical Problem solving.

Delinda Van Garderen - One of the best experts on this subject based on the ideXlab platform.

  • spatial visualization visual imagery and Mathematical Problem solving of students with varying abilities
    Journal of Learning Disabilities, 2006
    Co-Authors: Delinda Van Garderen
    Abstract:

    The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving Mathematical word Problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of Mathematical Problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher Mathematical word-Problem-solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images.

  • visual spatial representation Mathematical Problem solving and students of varying abilities
    Learning Disabilities Research and Practice, 2003
    Co-Authors: Delinda Van Garderen, Marjorie Montague
    Abstract:

    The purpose of this study was to investigate students' use of visual imagery while solving Mathematical Problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N= 66) participated in this study. Students were assessed on measures of Mathematical Problem solving and visual-spatial representation. Visual-spatial representations were coded as either primarily schematic representations that encode the spatial relations described in the Problem or primarily pictorial representations that encode persons, places, or things described in the Problem. Results indicated that gifted students used significantly more visual-spatial representations than the other two groups. Students with LD used significantly more pictorial representations than their peers. Successful Mathematical Problem solving was positively correlated with use of schematic representations; conversely, it was negatively correlated with use of pictorial representations.

Mary Hegarty - One of the best experts on this subject based on the ideXlab platform.

  • types of visual spatial representations and Mathematical Problem solving
    Journal of Educational Psychology, 1999
    Co-Authors: Mary Hegarty, Maria Kozhevnikov
    Abstract:

    Although visual-spatial representations are used extensively in mathematics and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in Mathematical Problem solving. The authors distinguished 2 types of visual-spatial representations: schematic representations that encode the spatial relations described in a Problem and pictorial representations that encode the visual appearance of the objects described in the Problem. Participants solved Mathematical Problems and reported on their solution strategies. The authors were able to reliably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in Mathematical Problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic representations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and Mathematical Problem solving.

  • Types of visual–spatial representations and Mathematical Problem solving.
    Journal of Educational Psychology, 1999
    Co-Authors: Mary Hegarty, Maria Kozhevnikov
    Abstract:

    Although visual-spatial representations are used extensively in mathematics and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in Mathematical Problem solving. The authors distinguished 2 types of visual-spatial representations: schematic representations that encode the spatial relations described in a Problem and pictorial representations that encode the visual appearance of the objects described in the Problem. Participants solved Mathematical Problems and reported on their solution strategies. The authors were able to reliably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in Mathematical Problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic representations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and Mathematical Problem solving.

Asha K Jitendra - One of the best experts on this subject based on the ideXlab platform.

  • meeting the needs of students with learning disabilities in inclusive mathematics classrooms the role of schema based instruction on Mathematical Problem solving
    Theory Into Practice, 2011
    Co-Authors: Asha K Jitendra, Jon R Star
    Abstract:

    This article discusses schema-based instruction (SBI) as an alternative to traditional instruction for enhancing the Mathematical Problem solving performance of students with learning disabilities (LD). In the authors' most recent research and developmental efforts, they designed SBI to meet the needs of middle school students with LD in inclusive mathematics classrooms by addressing the research literatures in special education, cognitive psychology, and mathematics education. This innovative instructional approach encourages students to look beyond surface features of word Problems to grasp the underlying Mathematical structure of ratio and proportion Problems. In addition, SBI introduces students to multiple strategies for solving ratio and proportion Problems and encourages the selection of appropriate strategies.

  • a comparison of single and multiple strategy instruction on third grade students Mathematical Problem solving
    Journal of Educational Psychology, 2007
    Co-Authors: Asha K Jitendra, Cynthia C Griffin, Priti Haria, Jayne Melissa Leh, Aimee Adams, Anju Kaduvettoor
    Abstract:

    The purposes of this study were to assess the differential effects of a single strategy (schema-based instruction; SBI) versus multiple strategies (general strategy instruction, GSI) in promoting Mathematical Problem solving and mathematics achievement as well as to examine the influence of word Problem-solving instruction on the development of computational skills. Eighty-eight 3rd graders and their teachers were assigned randomly to conditions (SBI and GSI). Students were pre- and posttested on Mathematical Problem-solving and computation tests and were posttested on the Pennsylvania System of School Assessment Mathematics test, a criterion-referenced test that measures student attainment of academic standards. Results revealed SBI to be more effective than GSI in enhancing students' Mathematical word Problem-solving skills at posttest and maintenance. Further, results indicate that the SBI groups' performance exceeded that of the GSI group on the Pennsylvania System of School Assessment measure. On the computation test, both groups made gains over time.