Research on the Learning and Teaching of Algebra

Warren, Elizabeth; Trigueros, María; Ursini, Sonia

doi:10.1007/978-94-6300-561-6_3

Cited by 36 publications

(24 citation statements)

References 32 publications

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“…At the same time, understanding the general nature of properties may allow students to delve more deeply into the meaning of operations and connect arithmetic with algebraic reasoning ( Schifter, 2009). Further research is needed, however, to fully understand the relationship between arithmetic and algebraic reasoning in the early grades and its effect on older students' ability to learn algebra (Warren, Trigueros, & Ursini, 2016).…”

mentioning

confidence: 99%

Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties

Uclés

Brizuela

Blanton

2020

Early Childhood Educ J

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We present a study that explores Kindergarten and first-grade students' understandings and representations of arithmetic properties. Sixteen students participated in a classroom teaching experiment designed to explore children's algebraic understandings, including their understandings and symbolic representations of three arithmetic properties: additive identity, additive inverse, and commutativity. We characterized students' understandings in terms of Skemp's framework of understandings: rules without reason (instrumental) and knowing what to do and why (relational). Then, following Vergnaud, we analyzed the types of additive relationships (transformation, comparison, or combination) and representations used by students. Our findings show that students' understandings developed in sophistication over time. We observed the least sophisticated understandings for the commutative property, particularly among Kindergarten students who exhibited instrumental understandings even after instruction.

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mentioning

confidence: 99%

Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties

Uclés

Brizuela

Blanton

2020

Early Childhood Educ J

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“…Research over the past three decades has shown that each use of variables is linked to specific epistemological and didactic barriers (Warren, Trigueros, & Ursini, 2016). The starting point of algebra needs to be the use of only a specific type of variable.…”

Section: Discussionmentioning

confidence: 99%

A Learning Trajectory Study on How the Concept of Variable Is Constructed by Students

Gürbüz

Özdemi̇r

2020

WJE

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The aim of this study was to examine 6th-grade students’ mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations, interviews, and the Diagnostic Algebra Test were used as data collection instruments to reveal the students’ abstraction processes and determine their learning trajectories. Qualitative data were analyzed through content analysis, and qualitative data were analyzed through paired-samples t-test. The learning trajectories showed that only the students with good performance exhibited the “construction” action when using “variables as changing quantities,” but the “building-with” action when using the other types of variables. Mediocre students, however, needed teacher support to perform the building-with action in the process of abstraction of variables. The students’ written tips such as drawing arrows or deleting the variable show that it helps to learn how to replace a variable with a known value. This study shows that the development of thought on variables is embedded in the progression of the concept of variable as a changing quantity. Similar studies can be conducted for the use of variables in equations and for the understanding and interpretation of variables when solving equations.

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“…Construction of the algebraic function formula involved a student to think algebraically within processing object of though mentally and product of thought that contained the functional relationship graphically [20]. Its construction process was explained Chimoni & Pitta-Pantazi [24] and Warren et al [25] as an algebraic thinking ability. Furthermore, generalization has done by NI, AN, and PR in determining process the function formula of the graph.…”

Section: Algebraic Level Of Student Thinkingmentioning

confidence: 99%

Student Thinking Levels in Solving Open-Ended Geometric-Function Problem by Algebraic Representation Approach

Yuni¹,

Alghadari²,

Wulandari³

et al. 2021

Advances in Social Science, Education and Humanities Research

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The mathematical problem mostly has been involved in the measurement of student ability according to study objectives and data needs. In this study, geometric-function problem has been used to data collection, analyzed problem type, and students thinking levels based on their completion. The sample of this study was three student high school in a science programme in the region of West Jakarta who selected purposively. Based on data analyzed, the result was found that students view the problem as the task constructed algebraic function formula. The completion and solution that have been shown by students, categorized the problem in open-ended type. The finding of mathematical thinking levels analysis there was a different complexity of thinking process between students because the number of concepts applicate. According to van Hiele theory, student's geometry thinking levels was on abstraction level minimally, and the problem is not relevant for deduction thinking level criterion. For the analysis result about algebraic thinking levels, by the structure of the observed learning outcome (SOLO) taxonomy, students at the levels between relational and extended abstract. Students in these levels was a student high ability so it is appropriate with the background of the sample selected.

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Research on the Learning and Teaching of Algebra

Cited by 36 publications

References 32 publications

Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties

Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties

A Learning Trajectory Study on How the Concept of Variable Is Constructed by Students

Student Thinking Levels in Solving Open-Ended Geometric-Function Problem by Algebraic Representation Approach

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