Representations in the mathematics classroom: Reflections and constructions

Seeger, Falk

doi:10.1017/cbo9780511720406.013

Cited by 21 publications

(10 citation statements)

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“…The third major purpose of the study was to test whether provision of visual representations of numerical magnitudes exerts a causal influence on learning of answers to addition problems. External representations, including pictorial, graphic, and diagrammatic forms, are an important part of mathematics education (Seeger, 1998). They are thought to increase understanding of mathematical concepts by helping children build relations among mathematical ideas (Hiebert & Carpenter, 1992).…”

Section: The Current Studymentioning

confidence: 99%

Numerical Magnitude Representations Influence Arithmetic Learning

2008

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This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.

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Section: The Current Studymentioning

confidence: 99%

Numerical Magnitude Representations Influence Arithmetic Learning

2008

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“…In translating among representations, students are not only interact with the basic concepts contained in the information, but also they must be able to connect parts of these basic concepts with different things related to the intended representation. This is because the process of making representations involves identifying, selecting and conveying ideas through something else [25]. This is in line with the opinion of Bosse et al [26] that someone who translates has to not only know or recognize the concept contained in the source by identifying and coding, but also can connect the concept into different forms according to the intended representation or target representation.…”

Section: Introductionmentioning

confidence: 53%

Profile of Student's Mathematical Representation Translation on the Verbal Problem

Nizaruddin¹,

Waluyo²,

Rochmad³

et al. 2020

ujer

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Translation among forms of representation defines as changing process one form of representation to other representations. Translation activities from one representation (source) to another (target) are very important in expressing mathematical ideas. In translating among representations, students are not only interacting with the basic concepts contained in the information, but also they must be able to connect parts of these basic concepts with different things related to the intended representation. The purpose of this qualitative research is: 1) to analyze the tendency of mathematical representations to be used in solving mathematical problems given in verbal representations, and 2) to analyze the translational structure of the target representations made. The research subjects were 3 rd year students of Mathematics Education at Universitas PGRI Semarang. The research data were taken by means of tests and interviews immediately after solving the math problems given in the form of verbal representations. The results showed that the group students who were solving the verbal questions indicated that they tended to translate from the verbal representations to symbolic representations in presenting definitions and in proof. However, this symbolic representation still contained verbal representations such as in the source problems. The stages of representation in this research followed the translation stages: unpacking the source, preliminary coordination, constructing the target, but left for determinant of equivalence. High-ability group of students in solving the questions tend to translate from verbal representation to symbolic representation. Further, some of them translate verbal to visual representation to increase understanding. The translation stages are unpacking the source, preliminary coordination, constructing symbol representation, constructing visual representation, determining the equivalence of the visual representation to verbal representation, and determining the equivalence of the symbol representation form to verbal representation.

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“…Representation is a kind of configuration process to present something in a different situation which involves identification, selection and the delivery of ideas (Goldin & Kaput, 1996;Romberg & Kaput, 1999;Seeger et al, 1998). Everything that students do to externalize and show their work is called representation (Kalathil & Sherin, 2013).…”

Section: Introductionmentioning

confidence: 99%

Exploring of Multi Mathematical Representation Capability in Problem Solving on Senior High School Students

Nizaruddin

Muhtarom

Murtianto

2017

PEC

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The students’ multi-mathematical representation capability in problem solving is very important and interesting to discuss, specifically for problems in the two-variable linear equation system. Data was collected from 48 students using written tests and in-depth interviews with selected participants. The research findings showed that few students are using three representations namely symbolic - verbal - table representation, and symbolic representation, however most of the students are using three representations namely symbolic - verbal - images representation, and two representations namely symbolic – verbal representations, and the rest used symbolic representation. In the use of verbal representation, some students had difficulty composing words and all students encountered difficulties in the translational process from symbolic representation and verbal representation to other types of representation. The ability to understand concepts and relationships between mathematical concepts was found to be a necessary condition for the achievement of multi-mathematical representation capability. It is therefore recommended that teachers use a variety of different types of representation, such as verbal, tables and images, to enhance students' understanding of the material. Keywords: multiple representations, problem solving, two-variable linear equation system.

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Representations in the mathematics classroom: Reflections and constructions

Cited by 21 publications

References 0 publications

Numerical Magnitude Representations Influence Arithmetic Learning

Numerical Magnitude Representations Influence Arithmetic Learning

Profile of Student's Mathematical Representation Translation on the Verbal Problem

Exploring of Multi Mathematical Representation Capability in Problem Solving on Senior High School Students

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