Manipulatives can help students develop a conceptual understanding of mathematical topics.
These concrete, hands-on materials and objects-for example, an abacus or coins-help students to represent the mathematical idea they are trying to learn or the problem they are attempting to solve. Very young children and students who struggle with mathematics often require different types of visual representations known as manipulatives. Some students will not be able to grasp mathematics skills and concepts using only the types of visual representations noted in the table above.
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Without explicit, systematic instruction on how to create and use visual representations, these students often create visual representations that are disorganized or contain incorrect or partial information.
This is especially the case for students who struggle with mathematics and those with mathematics learning disabilities. Some students-specifically, high-achieving students, gifted students-do this automatically, whereas others need to be explicitly taught how. – opposite side of right angle is longest side (hypotenuse)īefore they can solve problems, however, students must first know what type of visual representation to create and use for a given mathematics problem. This was equally true for students who had LD, were low-achieving, or were average-achieving.ĭefinition: Visual that assists students in remembering and organizing information, as well as depicting the relationships between ideas (e.g., word webs, tables, Venn diagrams). Students who use visual representations to solve word problems are more likely to solve the problems accurately.(van Garderen, Scheuermann, & Jackson, 2012 van Garderen, Scheuermann, & Poch, 2014) Teaching students to systematically use a visual representation to solve word problems has led to substantial improvements in math achievement for students with learning disabilities. Students with a learning disability (LD) often do not create accurate visual representations or use them strategically to solve problems.(Boonen, van Wesel, Jolles, & van der Schoot, 2014) However, students who use inaccurate visual representations are less likely to correctly solve mathematics problems than those who do not use visual representations at all. Students who use accurate visual representations are six times more likely to correctly solve mathematics problems than are students who do not use them.