Examining How Students With Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

Garderen, Delinda van; Scheuermann, Amy; Jackson, Christa

doi:10.1177/0731948712438558

Cited by 47 publications

(57 citation statements)

References 20 publications

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“…Additional studies have not gone so far as to determine a strategic order to the effectiveness of visual representation strategies, but they have studied the value of schematic and pictorial representations (Hegarty & Kozhevnikov, 1999;Jitendra et al, 2007;van Garderen & Montague, 2003;van Garderen et al, 2012). A general consensus has emerged from this research that would agree with van Garderen's (2008) findings.…”

Section: The Value Of Pictorial and Schematic Representationssupporting

confidence: 56%

“…688). Due to these pragmatic statistics many studies are calling for strategic diagram instruction in the classroom (Hegarty & Kozhevnikov, 1999;van Garderen & Montague, 2003;van Garderen et al, 2012). This instruction in schematic visual-spatial representations would provide some much needed structure, focused instruction, and support to the mathematics classroom.…”

Section: The Value Of Pictorial and Schematic Representationsmentioning

confidence: 99%

“…These subtle variances between pictorial and schematic strategies have intrigued many researchers (Hegarty & Kozhevnikov, 1999;Jitendra et al, 2002;Montague & Applegate;2000;van Garderen & Montague, 2003;van Garderen et al, 2012). In 2008, van Garderen administered a survey to 99 New York state special education teachers to determine their instructional practices when solving word problems (p. 141).…”

Section: The Value Of Pictorial and Schematic Representationsmentioning

confidence: 99%

“…Van Garderen and Montague (2003) found a significant positive correlation between the total number of visual-spatial representations and students' overall mathematical problem-solving ability. A significant portion of research on visual-spatial representations focuses on pictorial and schematic diagrams (Hegarty & Kozhevnikov, 1999;Jitendra et al, 2002;Montague & Applegate;2000;van Garderen & Montague, 2003;van Garderen et al, 2012). Hegarty and Kozhevnikov (1999) conducted seminal research on the effects of these visual and spatial images; in order to do so they specified what a diagram within each of these categories might contain (p. 685-686).…”

Section: Visual Spatial Representations As Word Problem-solving Stratmentioning

confidence: 99%

See 3 more Smart Citations

A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

Kribbs¹,

Rogowsky²

2015

IJRES

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Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or persons while neglecting the spatial relationships between those components (Hegarty & Kozhevnikov, p. 686). Research supports schematic diagrams that highlight spatial relationships and focus on related information within the problem (Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003). In addition to these strategies, educators have used heuristics (systematic scripted procedures to solve word problems) as a way to provide structure and routine to a variety of word problems. This review of the literature found varying results for the use of some heuristics being implemented in present-day classrooms. On the other hand, both visual-spatial diagrams and heuristics have demonstrated value in middle school special education classrooms. These findings support the further use and research of visual-spatial representations and problemsolving heuristics in order to solve mathematics word problems.

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Section: The Value Of Pictorial and Schematic Representationssupporting

confidence: 56%

Section: The Value Of Pictorial and Schematic Representationsmentioning

confidence: 99%

Section: The Value Of Pictorial and Schematic Representationsmentioning

confidence: 99%

Section: Visual Spatial Representations As Word Problem-solving Stratmentioning

confidence: 99%

See 2 more Smart Citations

A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

Kribbs¹,

Rogowsky²

2015

IJRES

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“…Diagrams are used in design studies and the cognitive sciences (Nickerson et al, 2013;Tversky, 2011;Tversky & Kessell, 2014;Tversky & Suwa, 2009). Diagrams are used in research to understand how exceptional children learn (Poch, van Garderen, & Scheuermann, 2015;van Garderen, Scheuermann, & Jackson, 2013). Diagrams are used in the health sciences field to collect data in qualitative research settings Umoquit, Tso, Burchett, & Dobrow, 2011;Umoquit, Tso, Vargas-Atkins, O'Brien, & Wheeldon 2013).…”

Section: Mediating Incoherence In the Classroommentioning

confidence: 99%

Diagramming prior knowledge in the classroom

Conroy

2016

ITLCP

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Engaging the student's prior knowledge is considered by educational researchers to be an important part of constructing a strong foundation for new learning. Diagrams are one technique used in the classroom. Jill Larkin and Herbert Simon described the computational advantages of diagrams over text when used to communicate information in their 1987 article entitled "Why a Diagram is (Sometimes) Worth Ten Thousand Words." This presentation describes a novel abstract diagramming technique designed to be facilitated in the classroom. Using paper and crayons, the participants create three diagrams that represent the externalization of their own prior knowledge of concepts in a domain of study. The presentation illustrates how differences in prior knowledge can be visualized using diagrams with greater speed in less time than the traditional use of textbased descriptions. The student diagrams were shown to contain a hidden conceptual topology, one that is described by Egenhofer in his 1991 article entitled "Reasoning About Binary Topological Relations." This topology is recommended as a framework for structuring and facilitating student collaboration and sharing of prior knowledge and new learning.Discovery of experiential backgrounds with students is often conducted with the use of a common spoken language that is shared by the students and instructor during classroom conversations. Natural spoken languages are rich in content and context. These modalities combine to enable students and instructors to quickly send and receive messages, assign meaning to the interchanges, and generate inferences from the experience. A conversation rarely evokes the need for a lengthy inquiry regarding the prior knowledge of either party. The challenge of exploring prior knowledge using a shared language such as English, limits the depth to which individuals may share their personal worldviews. The inspiration for this article was based on the experience of teaching a three-day technical course in six countries over a period of several weeks. Engineers and managers from the United States, Mexico, Great Britain, Columbia, Brazil, and Sweden were provided a simple rectangle as the over-arching mental model to be used in representing the complexity experienced when managing data warehouses. The use of geometric shapes as an ad hoc grammar to communicate complex topics led to research that formalized the technique in the form of a visual language referred to as Draw Aloud.To better understand how a visual language could be used to communicate the complex epistemologies found in classroom setting, research into the nature of visual language was conducted in the form of a case study at two universities. The students were observed creating diagrams of prior knowledge using a novel abstract diagram elicitation technique. The technique was facilitated in four different classroom settings. The

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