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Purpose • The purpose of this study was to investigate how third

grade mathematics teachers choose manipulatives to teach concepts related to fraction size. This study aims to examine teachers’ perceptions about whether manipulatives are helpful in teaching students about fractions and which type of manipulative(s) is effective for teaching students this concept. In particular, the research questions are:• What manipulative(s) do teachers choose when

teaching concepts about fraction size?• What are teachers’ reasons for selecting that

particular manipulative(s)?

Procedures• Qualitative methods • Nine teacher participants• Eight to 15 minute semi-structured interviews• Participants were asked to read through the above lesson

and participate in a semi-structured interview regarding their manipulative selection.

• The participants were presented six manipulative options.• The interview questions were designed to elicit teachers’

preferences on manipulatives. • The interviews started by gauging the teachers’

experience and how they select manipulatives on a regular basis and then the researcher questioned the teacher on their preferred manipulative to teach equivalent fractions. Once the teachers selected a manipulative, the researcher asked the teacher about the benefits, drawbacks, misconceptions, reason for their preference, and any other information that they wanted to share with respect to their preferred manipulative.

• Data Analysis – first cycle descriptive coding, refined codes, second cycle descriptive coding with refined codes, organized codes into themes

Implications• All of the different reasons that teachers

shared about selecting manipulatives are subjective but in aggregate can be used as a guide for manipulative selection. Most manipulatives have strengths that align with certain mathematical concepts more than others while come may promote misconceptions. The combined findings from this research generated by a group of teachers are a resource indicating a comprehensive evaluation of strengths and drawbacks of manipulatives related to fraction equivalence.

Limitations• Sample size: the researcher only interviewed

nine teachers. Therefore, the themes that emerged from this study are from a small sub-group of teachers and may not represent all teachers’ perspectives towards the selection of manipulatives. The findings from this study would be further supported and potentially altered by a larger sample size.

Future Research • Future research should incorporate a larger

sample size, more grade bands, and additional mathematical concepts. While the study is still transferrable, additional research would result in more generalizable findings.

Lesson Plan

FindingsManipulatives chosen:• Five of the teachers selected pattern blocks and four selected fraction

strips as the manipulative that they would use to teach equivalent fractions.

The following themes emerged from the data:• Selection of manipulatives

• Teachers make choices based on what they believe displays the content best, what works best for their students, what their curriculum requires, what the standards require, and to what manipulatives they have immediate access.

• Benefits• The teachers identified benefits of concrete manipulatives,

pattern blocks, and fraction strips such as their ability to represent the concept and the specific qualities of the manipulative.

• Drawbacks• The teachers identified drawbacks of pattern blocks, fraction

strips, and virtual manipulatives. The drawbacks included lack of labels, ”not as concrete,” and difficulty understanding repeated copies of unit fraction.

• Exposing students to multiple methods and strategies• Teacher’s believe that students should have multiple experiences

with manipulatives and they should only be exposed to manipulatives at the beginning of instruction to avoid dependence on the manipulative.

Manipulative Choices

Pattern Blocks Virtual Pattern Blocks

Fraction Strips Virtual Fraction Strips

Cuisenaire Rods Fraction Circles

Finding the Right Manipulative: How Teachers Chose Tools for Learning Mathematics

Haley Fussell, M.Ed. Candidate Mathematics Education Research Advisor: Dr. Sarah Quebec Fuentes, Texas Christian University

References Kennedy, L. M. (1986). Selection criteria. The Arithmetic Teacher, 33(6).

11-13.

Moyer, P. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

Watanabe, T. (2002). Representations in teaching and learning fractions. Teaching Children Mathematics, 8(8). 457-463.

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Literature Representations:• The National Council for Teachers of Mathematics (NCTM,

2000) defines a representation as anything that “captures a mathematical concept or relationship” (p. 67). The NCTM believes that students should be able to represent mathematics in ways that make sense to them. They argue that one of the most important representations is a visual representation. Visuals enable students to cement ideas in their head, helping to advance the students’ understanding of different concepts and to make sense of a problem (NCTM, 2014).

Manipulatives: • Moyer (2001) defines manipulatives as “objects designed to

represent explicitly and concretely mathematical ideas that are abstract” (p. 176). Furthermore, Kennedy (1986) explains that a manipulative is an “object that appeal to several senses and that can be touched, moved about, rearranged, and otherwise handled by children” (p. 6). Research has documented the benefits of manipulatives. The main theme of this research is that students who use manipulatives in mathematics far surpass the students who do not use manipulatives, with respect to their understanding of the content and scores on assessments (Moyer, 2001).

Fraction Representations:• Different representations can be used for various aspects of

complex concepts. For example, fractions are represented differently depending on the nature of particular interpretations. “Students usually learn to represent fractions as sectors of a circle … Sometimes they use physical displays of pattern blocks or fraction strips that convey the part-whole interpretation of fractions. Such displays can help students see fraction equivalence” (NCTM, 2000, p. 69).

Fraction Manipulatives: • Manipulatives are a means to learn abstract ideas related to

fractions. Watanabe (2002) suggests that teachers can use fraction strips, pattern blocks, and Cuisenaire rods in fraction instruction.