The Effect of External Representations on Compare Word Problems: Supporting Mental Model Construction

Múñez, David; Orrantia, Josetxu; Rosales, Javier

doi:10.1080/00220973.2012.715095

Cited by 26 publications

(7 citation statements)

References 58 publications

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“…Representations are powerful tools to elicit and interpret students' mathematical thinking when they solve word problems because learners need to communicate and express mathematical ideas via representations (Goldin, 1998;Leikin, Leikin, Waisman, & Shaul, 2013;Lesh et al, 1987;Múñez, Orrantia, & Rosales, 2013). At this point, -what is a representation?‖ is an important question to put our perspective in the current study.…”

Section: Theoretical Background Word Problems and Multiple Representamentioning

confidence: 95%

Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews

Ulusoy¹,

Argün²

2017

International Journal of Education in Mathematics, Science and Technology

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Section: Theoretical Background Word Problems and Multiple Representamentioning

confidence: 95%

Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews

Ulusoy¹,

Argün²

2017

International Journal of Education in Mathematics, Science and Technology

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“…The field of mathematics education will continue to defer research involving students with disabilities to another field (e.g., special education), not make explicit disability issues in research, and/or explicitly exclude disability. In one article from the sample, Múñez et al [67] (p. 341) describe their participants as follows, "Participants were 50 students from a public secondary school in a middle-class suburb. We excluded from the analyses 1 student who was diagnosed with language/learning problems."…”

Section: Discussionmentioning

confidence: 99%

Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review

Lambert

Tan

2017

Education Sciences

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Students with disabilities are often framed as "the problem" and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

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“…Similarly, the study of Huang et al (2019) indicated that lessons that were based on a combination of an assumed learning trajectory and variation pedagogy (which focused on using multiple representations amongst other things) had high value for students' ability to solve QC. Múñez et al (2013) studied students at secondary schools; the other studies considered students from Grades 1-3.…”

Section: Quantitative Comparisonsmentioning

confidence: 99%

“…These criteria take into account former research on the development of strategies to solve QC (Carpenter et al, 2015), on the importance of linguistic flexibility (Schumacher & Fuchs, 2012;Stern, 1993), and on the meaning of multiple representations and their integration (Huang et al, 2019;Múñez et al, 2013;Mwangi & Sweller, 1998). For each of the subcategories, introduction, practice, and repetition, we assigned 0-5 points.…”

Section: Category 'Decomposed Of Numbers With a Missing Part'mentioning

confidence: 99%

The role of textbook quality in first graders’ ability to solve quantitative comparisons: a multilevel analysis

Sievert

Ham

Heinze

2021

ZDM Mathematics Education

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Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school year. Textbooks represent the most important learning resource for elementary school mathematics teachers. However, research on their impact on students’ knowledge is limited. Hence, we examined textbooks’ role in students’ ability to model quantitative comparisons by analyzing the learning opportunities presented by four German textbooks for Grade 1 and by conducting a secondary analysis of a dataset based on 1513 students from 84 classes that used one of these textbooks. The results revealed differences in the textbooks’ topic-specific instructional quality as well as a significant relation between this quality and student achievement in quantitative comparisons.

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The Effect of External Representations on Compare Word Problems: Supporting Mental Model Construction

Cited by 26 publications

References 58 publications

Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews

Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews

Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review

The role of textbook quality in first graders’ ability to solve quantitative comparisons: a multilevel analysis

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