An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: triangular numbers

Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés

doi:10.1007/s11858-015-0749-5

Cited by 8 publications

(1 citation statement)

References 26 publications

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“…Algebraic thinking can be broadly defined as a process by which students are analysing relationships between quantities, noticing structures, studying changes, generalising, solving problems, modelling, justifying, proving, and predicting (Kieran, 2004). Similar descriptions treat algebraic thinking as working with unknown numbers when analysing relations between and structures within numbers when these unknowns can be named or symbolised, even in a non-symbolic way (Radford, 2013), or as an arithmetic-algebraic work space (Hitt et al, 2016). Another suggested definition of algebraic thinking entails identifying four component abilities (Blanton & Kaput, 2005): understanding patterns, relations, and functions; representing and analysing mathematical situations and structures using algebraic symbols; using mathematical models to represent and understand quantitative relationships; and analysing changes in various contexts.…”

Section: Algebraic Thinkingmentioning

confidence: 99%

Algebraic and fractional thinking in collective mathematical reasoning

Eriksson

Sumpter

2021

Educ Stud Math

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This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the El´konin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic thinking. Further analysis showed that these arguments were characterised by interplay between fractional and algebraic thinking except in the conclusion stage. In the conclusion and the evaluative arguments, these two types of thinking appeared to be intertwined. Another result is the discovery of a new type of argument, identifying arguments, which deals with the first step in task solving. Here, the different types of arguments, including the identifying arguments, were not initiated only by the teachers but also by the students. This in a multilingual classroom with a large proportion of students newly arrived. Compared to earlier research, this study offers a more detailed analysis of algebraic and fractional thinking including possible patterns within the collective mathematical reasoning. An implication of this is that algebraic and fractional thinking appear to be more intertwined than previous suggested.

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Section: Algebraic Thinkingmentioning

confidence: 99%