Models for Initial Decimal Ideas

Cramer, Kathleen A.; Monson, Debra; Wyberg, Terry; Leavitt, Seth; Whitney, Stephanie

doi:10.5951/tcm.16.2.0106

Cited by 8 publications

(3 citation statements)

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“…The Lesh Translation Model (LTM) is a theoretical model widely used to explore students' representations of mathematical ideas and their translations among and within the representations (Cramer, 2003;Cramer, Monson, Wyberg, Leavitt, & Whitney, 2009;Moore et al, 2013). LTM identifies five modes of representation: (a) Realistic, (b) Concrete, (c) Pictorial, (d) Language, and (e) Symbolic as shown in Figure 1.…”

Section: The Lesh Translation Model In Mathematics Educationmentioning

confidence: 99%

“…The straight arrows between the ovals indicate that students make translations between different representations and the curved arrows on top of each oval indicate that students make transitions within the same representations (i.e., symbolic to symbolic, pictorial to pictorial). For example, if students represent decimal 0.34 using 10 × 10 grid, they are translating from written symbols to the pictorial mode of representation and if students model the same decimal using a 10 × 10 grid and also using a number line, they are translating within the pictorial mode (Cramer et al, 2009). If students represent 0.20 using fraction ⅕, they are translating from written symbols (i.e., symbolic) to the symbolic mode within the same mode of representations.…”

Section: The Lesh Translation Model In Mathematics Educationmentioning

confidence: 99%

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Preservice Teachers' Understanding of Decimals using Standard Algorithm and Alternative Strategies

Joung¹,

Lin²,

Kim³

2021

IJMTL

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The purpose of this study is to explore preservice teachers’ (PTs’) ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher Education Program at a mid-western university. These participants were asked to solve the Decimal Knowledge Test (DKT) in multiple ways. A qualitative approach was used to analyze PTs’ responses to the problems on the DKT. The results indicated that using standard algorithms, PTs demonstrated higher ability in solving decimal addition, subtraction, and multiplication involving a whole number. Alternative strategies posed difficulties in solving decimal multiplication problems involving two decimals, and division problems. Similarly, when examining operations, showing smooth or difficult translations between the representations, PTs found it difficult to translate representational modes in operations with multiplication involving two decimals, two division problems. The same results were seen when examining PTs’ conceptual understanding based on the Lesh Translation Model. The results provide teacher education programs with opportunities to create various instructional approaches involving translations among multiple representations in mathematics methods and content courses.

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Section: The Lesh Translation Model In Mathematics Educationmentioning

confidence: 99%

Section: The Lesh Translation Model In Mathematics Educationmentioning

confidence: 99%

Preservice Teachers' Understanding of Decimals using Standard Algorithm and Alternative Strategies

Joung¹,

Lin²,

Kim³

2021

IJMTL

View full text Add to dashboard Cite

show abstract

“…The Lesh translation model asserts that the understanding of concepts lies in the skills of learners to represent mathematical concepts through five different sets of representation and to translate within and between multiple modes of representation (Cramer, 2003;. A translation in this model is the reinterpretation of a mathematical concept within the same representation or between different representations (Cramer et al, 2009). It is important that students learn mathematics through representations.…”

Section: Lesh Translation Model With Technology Based Representational Media Layermentioning

confidence: 99%

Pre-Service Teachers’ Cognitive and Metacognitive Processes in Integrated STEM Modeling Activity

KANDEMİR¹,

KARADENİZ²

2020

Journal of Education in Science, Environment and Health

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This study was conducted during two educational technology courses in spring term of 2016-2017 academic years. The participants of the study were preservice teachers who were in mathematics teaching program in a university located at the west part of Turkey. Pre-service teachers were asked to solve a complex problem that requires mathematical model eliciting activities and report their solution. While pre-service teachers were solving the problem and writing their report, they were audio recorded. Additionally, their solutions and reports for problem were collected as data sources. All three various data sources used for triangulation to make the data collection process more reliable. The problemsolving behavior from the study conducted by Kim et al. (2013) was used as the theoretical framework. First, the behavior is classified as cognitive or metacognitive. Then the behavior (either cognitive or metacognitive) is also classified as at individual, social, or environmental levels. Additionally, Lesh Translation Model was used to decide the representations of mathematical content knowledge codes for metacognitive activities. The implications of this study are the developed metacognitive activities for pre-service teachers. Additionally, there is potential usage of technology for the role of metacognition in mathematics education.

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A Research-Validated Program for Improving At-Risk Students’ Fraction Magnitude Understanding, Word-Problem Solving, and Explanations

Malone

Fuchs

2016

Literacy Studies

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Models for Initial Decimal Ideas

Abstract: Put a twist on the familiar 10 × 10 grid model to build your students' understanding of effective decimal models.

Cited by 8 publications

References 0 publications

Preservice Teachers' Understanding of Decimals using Standard Algorithm and Alternative Strategies

Preservice Teachers' Understanding of Decimals using Standard Algorithm and Alternative Strategies

Pre-Service Teachers’ Cognitive and Metacognitive Processes in Integrated STEM Modeling Activity

A Research-Validated Program for Improving At-Risk Students’ Fraction Magnitude Understanding, Word-Problem Solving, and Explanations

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