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Spatial Visualization, Visual Imagery, and Mathematical Problem Solving of Students with Varying Abilities

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Spatial Visualization, Visual Imagery, and Mathematical Problem Solving of Students with Varying Abilities

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This study investigated the relationship between the use of visual imagery and students’ ability to solve word problems. Gifted students performed better on visual imagery and visual-spatial representation than students with LD and average achievers. Visual representations increased students’ problem solving accuracy. Schematic images were more beneficial in solving word problems than pictoral images (Garderen, 2006).

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How Students “Unpack” the Structure of a Word Problem: Graphic Representations and Problem Solving

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How Students “Unpack” the Structure of a Word Problem: Graphic Representations and Problem Solving

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This study examined the relationship between how students solved word problems: graphic representations, spatial visualizations, drawing ability and their ability to solve word problems. The drawings that students created were rated based on if they were more pictorial or schematic in nature. Students who drew pictures more schematic in nature were more successful problem solvers, than students who drew pictorial representations (Edens & Potter, 2008).

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Teaching Students with LD to Use Diagrams to Solve Mathematical Word Problems

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Teaching Students with LD to Use Diagrams to Solve Mathematical Word Problems

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Three students with LD participated in the study.  Students learned how to draw diagrams to represent word problems. Students’ ability to problem solve improved (Garderen, 2007).

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The Effect of Cognitive Strategy Instruction on Knowledge of Math Problem-Solving Processes of Middle School Students with Learning Disabilities

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The Effect of Cognitive Strategy Instruction on Knowledge of Math Problem-Solving Processes of Middle School Students with Learning Disabilities

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Participants included students with learning disabilities (LD) and some students without LD. This study tested the effectiveness of a mathematics program called Solve It! Results showed that students with LD and without, who received Solve It! used more strategies to solve word problems than in the control group. Solve It! is cognitive strategy that involves reading a paraphrasing the word problem, visualizing through a representation,  hypothesizing and estimating, and computing and checking.  Solve It! was equally effective with students regardless of ability level (Krawec et al., 2012).

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The Effects of Using Drawings in Developing Young Children’s Mathematical Word Problem Solving

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The Effects of Using Drawings in Developing Young Children’s Mathematical Word Problem Solving

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This study sought to see if visual representations improved students’ ability to problem solve. Although there were significant gains in the both the ability of the control and the experimental group to problem solve, neither group improved more than the other (Csikos, Szitanyi, Kelemen, 2012).

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Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems

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Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems

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This study explored the effects of teaching model-based instruction on students’ ability to solve word problems.  Participating in the study were three 4th and 5th grade students who were at risk of mathematical disabilities. The intervention improved student performance on solving word problems (Xin & Zhang, 2009).

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The Effects of Mathematics Strategy Instruction for Children with Serious Problem-Solving Difficulties

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The Effects of Mathematics Strategy Instruction for Children with Serious Problem-Solving Difficulties

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This study examined the effects of mathematics strategy instruction on the problem solving skills of students with and without serious math difficulties (MD). Problem solving improved for students with MD who were in the verbal and visual group, as well as the materials only group (Swanson, Orosco & Lussier, 2014).

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Effect of Singapore’s Model Method on Elementary Student Problem Solving Performance

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Effect of Singapore’s Model Method on Elementary Student Problem Solving Performance

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This was a single-case study that researched the effect of Singapore’s model method on the word problem solving performance of four
third and fourth graders over the course of 8 weeks. This study showed
that model drawing raises understanding and performance in elementary students (Mahoney, 2012).

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Examining how Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

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Examining how Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

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Students at a variety of ability levels, gifted, typical-achieving and students with learning disabilities participated in this study.  It examined students’ understanding of diagrams and their use to solve mathematical problems. Schematic diagrams led to more success on word problems (Garderen, Scheuermann & Jackson, 2012).

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Effects of Mathematical Word Problem-Solving Instruction on Middle School Students

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Effects of Mathematical Word Problem-Solving Instruction on Middle School Students

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This study compared the efficacy of schema-based instruction (SBI) versus general strategy instruction (GSI) on students' ability to solve word problems. The SBI group performed significantly better than the GSI group on the posttests (Xin, Jitendra Deatline-Buchman, 2005).

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Schema-Based Instruction

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1. How does modeling word problems help students problem solve?

2. Are bar models and diagrams effective in teaching multi-step word problems?

3. Is schema-based instruction shown to be an effective way for students to solve problems?

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The Impact of Schema-Based Instruction on Students’ Ability to Problem Solve

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Strategies for Multi-step Problem Solving

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Strategies for Multi-step Problem Solving

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Schema-Based Instruction