Visual–Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities

By Delinda van Garderen, M. Montague. 2003

260 citations recorded by the source corpus.

Subfields: Automotive Engineering, Experimental and Cognitive Psychology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7a04c85ca1081e9861ae410e68e5be3d43f203be

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In Automotive Engineering

In Experimental and Cognitive Psychology

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Citations in the corpus

Is Mathematical Representation of Problems an Evidence-Based Strategy for Students With Mathematics Difficulties? (2016, background): “Similarly, encouraging these students to merely visualize the problem or draw a diagram to solve a problem may not be effective (see van Garderen, 2006; van Garderen & Montague, 2003).”
Word Problem-Solving Instruction in Inclusive Third-Grade Mathematics Classrooms (2009, background): “Does word problem-solving instruction affect mathematics computation learning? Given the role that word problems play in the development of number operations ( Van de Walle, 2007 ), we also designed the present study to examine the influence of word problem-solving”
Word Problem Strategy for Latino English Language Learners at Risk for Math Disabilities (2014, background): “…a connection from verbal information to symbolic understanding by creating a mental model (e.g., Jitendra et al., 2007; Jitendra & Xin, 1997; Van Garderen & Montague, 2003), (c) using instructional feedback with peer-assisted learning strategies during instruction (e.g., Fuchs, Compton, et al.,…”
Computer-Assisted Intervention for Children with Low Numeracy Skills (2009, background): “…Xin, Jitendra, & Deatline-Buchman, 2005) and an ability to create and interpret visual representations of mathematical concepts (Booth & Thomas, 2000; Brown & Presmeg, 1993; Geary, 1995; Geary, Hamson, & Hoard, 2000; Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003) have been recorded.”
The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children (2014, methodology): “…) , they probably took the problem solvers ' attention away from constructing a coherent model of the word problem , including the appropriate relations between the solution - relevant elements contained in it ( Hegarty & Kozhevnikov , 1999 ; Van Garderen , 2006 ; Van Garderen & Montague , 2003 ) .”
Schema-Based Instruction for Mathematical Word Problem Solving: An Evidence-Based Review for Students With Learning Disabilities (2020, background): “…are similar in concept (e.g., adding) but different in content (e.g., word problems that require adding money as opposed to those adding other objects). van Garderen and Montague (2003) investigated the extent and efficacy of students’ use of pictorial and schematic diagrams during problem solving.”
The Effect of Visual–Chunking–Representation Accommodation on Geometry Testing for Students with Math Disabilities (2012, background): “…difﬁculties often have difﬁculties with spatially representing mathematics information and relationships and then manipulating the visual spatial relations (Geary, 2003; van Garderen & Montague, 2003); in addition, students with math difﬁculties are under-represented in geometry-related ﬁelds.”
Teaching with Concrete and Abstract Visual Representations: Effects on Students' Problem Solving, Problem Representations, and Learning Perceptions. (2011, background): “…of schematic (abstract) representations is associated with mathematical problem-solving success, whereas the use of pictorial (concrete) representations is negatively correlated with problem-solving success (Edens & Potter, 2007, 2008; Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003).”
Meeting the Curricular Needs of Academically Low-Achieving Students in Middle Grade Mathematics (2006, unknown): “…of visual models or manipulatives (Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Cass, Cates, & Smith, 2003; Jitendra, Hoff, & Beck, 1999; van Garderen & Montague, 2003; Witzel, Mercer, & Miller, 2003; Woodward, Baxter, & Robinson, 1999), carefully distributing practice on key concepts and…”
Designing Cognitive Complexity in Mathematical Problem-Solving Items (2010, background): “Other research suggests that equations may be represented in more concrete or idiosyncratic forms, such as visual–spatial representations (van Garderen & Montague, 2003) or text-based representations (e.g., Kintsch & Greeno, 1985; Lane, 1991).”
Changing representation in contextual mathematical problems from descriptive to depictive: The effect on students’ performance (2018, background): “…also considered research investigating specifically the solving of (word) problems by students, for instance, students of mixed ability, and their use of pictorial elements in the problem-solving process (Boonen, 2015; Hegarty, 2004; Krawec, 2014; Van Garderen & Montague, 2003; Van Garderen, 2006).”
A case study on the investigation of reasoning skills in geometry (2014, background): “The relationships between visualisation and mathematical problem solving (Moses, 1977; Van Garderen & Montague, 2003), as well as between visualization and mathematics achievement (Fennema & Sherman, 1977; Ünal, Jakubowski & Corey, 2009), have been shown in many studies.”
The Process of Probability Problem Solving: Use of External Visual Representations (2010, result): “This outcome, although not significant, is consistent with the results of studies by van Garderen and Montague (2003) and Hegarty and Kozhevnikov (1999), who found that the use of schematic diagrams was correlated with solution success whereas use of non-schematic or pictorial diagrams was…”