Challenges students identified with a learning disability and as high-achieving experience when using diagrams as a visualization tool to solve mathematics word problems

This article addresses a much understudied topic and concern regarding how students of varying ability levels employ visualization as a strategy in mathematics learning. The importance of this topic can be found in its connection to students’ ability to solve mathematical word problems. Many students, particularly students with learning disabilities, often struggle to use visualization as a strategy and this impacts their mathematics performance. The purpose of this article is to present findings from a study that examined the challenges that students—those identified as learning disabled and high-achieving—displayed when using one visualization form, a diagram, to solve mathematics problems. Overall, nine challenges related to the use of diagram proficiency to solve problems were identified. Further, students with learning disabilities were found to be more likely than their high achieving peers to experience these challenges. Implications for practice are provided.

[1]  Sean M. Hurley,et al.  Evidence for abstract, schematic knowledge of three spatial diagram representations , 1999, Memory & cognition.

[2]  M. Pressley,et al.  But good strategy instructors are constructivists! , 1992 .

[3]  Carmel M. Diezmann ASSESSING DIAGRAM QUALITY: MAKING A DIFFERENCE TO REPRESENTATION , 1999 .

[4]  Daniel L. Schwartz,et al.  Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction , 2004 .

[5]  Susan P. Miller,et al.  Fraction Instruction for Students with Mathematics Disabilities: Comparing Two Teaching Sequences , 2003 .

[6]  Brooks Applegate,et al.  Middle School Students' Mathematical Problem Solving: An Analysis of Think-Aloud Protocols , 1993 .

[7]  M. Hegarty,et al.  Types of visual–spatial representations and mathematical problem solving. , 1999 .

[8]  Richard Lesh,et al.  A Models and Modeling Perspective on Problem Solving , 2003 .

[9]  A. J. Connolly Keymath‐3 Diagnostic Assessment , 2014 .

[10]  R. Ashlock Error Patterns in Computation: Using Error Patterns to Improve Instruction , 2001 .

[11]  Bradley Witzel,et al.  Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools. NCEE 2009-4060. , 2009 .

[12]  Despina A. Stylianou,et al.  On the interaction of visualization and analysis: the negotiation of a visual representation in expert problem solving , 2002 .

[13]  J. Corter,et al.  The Process of Probability Problem Solving: Use of External Visual Representations , 2010 .

[14]  Herbert A. Simon,et al.  Why a Diagram is (Sometimes) Worth Ten Thousand Words , 1987 .

[15]  R. Mayer Systematic Thinking Fostered by Illustrations in Scientific Text , 1989 .

[16]  Cecil D. Mercer,et al.  Teaching Algebra to Students with Learning Difficulties: An Investigation of an Explicit Instruction Model , 2003 .

[17]  Richard Lesh,et al.  Rational number relations and proportions , 1987 .

[18]  Asha K. Jitendra,et al.  An Exploratory Study of Schema-Based Word-Problem—Solving Instruction for Middle School Students with Learning Disabilities , 2002 .

[19]  Despina A. Stylianou Teachers’ conceptions of representation in middle school mathematics , 2010 .

[20]  D. Schifter,et al.  A research companion to Principles and standards for school mathematics , 2003 .

[21]  D. Garderen Teaching Students With LD to Use Diagrams to Solve Mathematical Word Problems , 2007 .

[22]  Denisse R. Thompson,et al.  Reading Visual Representations. , 2012 .

[23]  Andrea A. diSessa,et al.  Students’ Criteria for Representational Adequacy , 2002 .

[24]  Joan K. Gallini,et al.  When Is an Illustration Worth Ten Thousand Words , 1990 .

[25]  Delinda van Garderen,et al.  Visual–Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities , 2003 .

[26]  Carmel M. Diezmann The difficulties students experience in generating diagrams for novel problems , 2000 .

[27]  K. Owens,et al.  Representations in Spatial Problem Solving in the Classroom , 1998 .

[28]  C. Fosnot,et al.  Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction , 2001 .

[29]  Michael C. Rodriguez,et al.  Impact of Small-Group Tutoring Interventions on the Mathematical Problem Solving and Achievement of Third-Grade Students With Mathematics Difficulties , 2013 .

[30]  Stephen J. Pape,et al.  The Role of Representation(s) in Developing Mathematical Understanding , 2001 .

[31]  Andrea A. diSessa,et al.  Meta-representation: an introduction , 2000 .

[32]  Delinda van Garderen,et al.  Spatial Visualization, Visual Imagery, and Mathematical Problem Solving of Students With Varying Abilities , 2006 .

[33]  Norma C. Presmeg,et al.  Visualisation in High School Mathematics. , 1986 .

[34]  A. Strauss Basics Of Qualitative Research , 1992 .

[35]  Lyn D. English,et al.  Handbook of International Research in Mathematics Education , 2002 .

[36]  Yuri Uesaka,et al.  What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving? , 2007 .

[37]  Elizabeth Fennema,et al.  Using Children’s Mathematical Knowledge in Instruction , 1993 .

[38]  Lyn D. English,et al.  Promoting the use of diagrams as tools for thinking , 2001 .

[39]  J. Hiebert Making Sense: Teaching and Learning Mathematics with Understanding , 1997 .

[40]  Claude Janvier Problems of representation in the teaching and learning of mathematics , 1987 .

[41]  B. Rittle-Johnson,et al.  Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process. , 2001 .

[42]  Christa Jackson,et al.  Examining How Students With Diverse Abilities Use Diagrams to Solve Mathematics Word Problems , 2013 .

[43]  D. Wechsler Wechsler Intelligence Scale for Children , 2020, Definitions.

[44]  Norma C. Presmeg,et al.  Visualisation and mathematical giftedness , 1986 .

[45]  Jeremy Kilpatrick,et al.  Adding It Up: Helping Children Learn Mathematics , 2013 .

[46]  Gerald Kulm,et al.  Mathematics Assessment: What Works in the Classroom , 1994 .

[47]  Charles A. Hughes,et al.  Effects of a Problem-Solving Strategy on the Introductory Algebra Performance of Secondary Students With Learning Disabilities , 2000 .

[48]  Brooks Applegate,et al.  Mathematical Problem-Solving Characteristics of Middle School Students With Learning Disabilities , 1993 .

[49]  Frances R. Curcio,et al.  The Roles of Representation in School Mathematics: 2001 Yearbook , 2001 .

[50]  Larry Sowder,et al.  Drawings for Story Problems: Practices in Japan and the United States. , 1994 .

[51]  Cheri A. Hoy,et al.  Graphic Organizers Applied to Higher–Level Secondary Mathematics , 2003 .

[52]  M. Patton,et al.  Qualitative evaluation and research methods , 1992 .