Closing the gap on the map: Davydov’s contribution to current early algebra discourse in light of the 1960s Soviet debates over word-problem solving

Freiman, Viktor; Fellus, Olga

doi:10.1007/s10649-020-09989-6

Cited by 10 publications

(6 citation statements)

References 18 publications

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“…The American Measure Up (MU) project by Dougherty (2008) supported Davydov's claims: the exploration of quantitative reasoning offered evidence that young children were able to build meaningful, sophisticated and complex mathematics. Moreover, a recent study by Freiman and Fellus (2021) suggested that Davydov's approach could potentially bridge the gap between arithmetic and algebraic thinking by allowing pupils to build on various semiotic systems, including letters, in exploring relationships between quantities.…”

Section: Quantitative Relationship In Early Algebramentioning

confidence: 99%

Exploring quantitative relationship through area conservation activity

Sari

2022

j. math. educ.

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Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in early algebra can be explored through area conservation activities. Understanding area conservation is said to be fundamental in developing the concept of area measurement. In this study, a ten-year old pupil was observed during her involvement while comparing area of two polygons that can be decomposed into equivalent triangles. Data for this study include the pupil’s written artefacts, and video recordings of the activities and interviews. Findings from this study show that the area conservation activity has the potential to build the notion of quantitative relationships in early algebra. The quantitative relationship between the unit of measurement and the result of measurement of a shape can also be explored, that is, the smaller the unit of measurement, the larger the result of measurement. Hence, this study can provide a groundwork for further studies in the relation between quantitative relationship in algebra and area conservation in geometry at the elementary school level.

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Section: Quantitative Relationship In Early Algebramentioning

confidence: 99%

Exploring quantitative relationship through area conservation activity

Sari

2022

j. math. educ.

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“…This implies that teachers whose problem-solving skills and problem-solving PCK are high, are likely to train secondary school students to improve their problem-solving abilities. Teachers' PCK should include good selection of problem posing tasks for their students (Freiman & Fellus, 2021). The use of teaching models has been found to enhance high order problem-solving skills among students and overall mathematical cognitive development (Son, 2020).…”

Section: Problem Solving Approach In Mathematics Teaching and Learningmentioning

confidence: 99%

Gender Differences in High School Students’ Beliefs about Mathematical Problem Solving

Sintema

Jita²

2022

IJLTER

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This study investigated high school students’ mathematical problem- solving beliefs based on their gender. A mathematical problem-solving beliefs questionnaire comprising 36 items across six beliefs scales was administered to a sample of 490 students (288 boys and 202 girls) from three schools: a mixed-sex school (106 boys and 103 girls), a single-sex boys’ school with 182 students, and a single-sex girls’ school with 99 students. The independent samples t-test was used to analyse the effect of gender on high school students’ mathematical problem-solving beliefs. Results revealed that there was a significant difference in students’ beliefs that some word problems cannot be solved with simple, step-by-step procedures, with girls exhibiting higher beliefs than boys. However, when the entire sample was analysed, gender did not have an overall effect on students’ mathematical problem-solving beliefs. It was further revealed that gender did not have a significant effect on students’ mathematical problem-solving beliefs at a mixed-sex (boys and girls) school. Results are important for the implementation of a problem-solving approach in a new mathematics curriculum. In addition, the results contribute to the literature in mathematics education by highlighting the importance of gender when considering debates about students’ problem-solving beliefs in mathematics.

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“…Two articles in this special issue explicitly address the issue of early algebra, with which Davydov's work is often associated. Freiman and Fellus (2020) provide highly relevant historical context to Davydov's thinking (a form of deconstruction work called for by Mellone et al, 2020) in order to relate the curriculum proposals to wider issues in the teaching and learning of algebra. Their article provides a detailed analysis of what is meant by the ascent from the abstract to the concrete-a phrase that is perhaps one of the best known of Davydov's-and perhaps also one that is easily misunderstood.…”

Section: Transposing a Curriculummentioning

confidence: 99%

Commentary on a special issue: Davydov’s approach in the XXI century

Coles

2021

Educ Stud Math

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The articles in this special issue, collectively, provide overwhelming evidence that a curriculum which has as its primary basis the counting of discrete objects (and hence which introduces numbers as discrete) is not an effective or rational organisation. In this commentary, I discuss the contribution of each article to an understanding of Davydov’s ontology and epistemology, issues around the transposition of a pedagogy or curriculum from one country to another, early algebra and proportional or multiplicative reasoning. From Davydov’s own research and the writing in these articles, we know children are able to understand abstract structures from an early age. The thinking in this special issue provides tools to investigate and question any context in which such understanding is not routinely taking hold.

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Closing the gap on the map: Davydov’s contribution to current early algebra discourse in light of the 1960s Soviet debates over word-problem solving

Cited by 10 publications

References 18 publications

Exploring quantitative relationship through area conservation activity

Exploring quantitative relationship through area conservation activity

Gender Differences in High School Students’ Beliefs about Mathematical Problem Solving

Commentary on a special issue: Davydov’s approach in the XXI century

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