Recursive and explicit rules: How can we build student algebraic understanding?

Lannin, John K.; Barker, David; Townsend, Brian E.

doi:10.1016/j.jmathb.2006.11.004

Cited by 55 publications

(61 citation statements)

References 17 publications

(32 reference statements)

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“…This relates to research by Rivera and Becker (2006) who found that students who were able to use the figural clues in a geometric growing pattern rather than rely on numeric clues were more likely to be able to create an explicit generalisation. Lannin, Barker, and Townsend (2006) also found that students who moved too quickly to numeric strategies had difficulty making connections across different generalisation tasks. Another teacher also referred to "visual" patterns as benefiting her students who typically struggled in mathematics and additionally commented on the novelty of the learning tasks, that they were different to usual (Molly).…”

Section: Modifying Beliefs By Observing Their Studentsmentioning

confidence: 97%

Pathways to Professional Growth: Investigating Upper Primary School Teachers’ Perspectives on Learning to Teach Algebra

Wilkie¹,

Clarke

2015

AJTE

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Section: Modifying Beliefs By Observing Their Studentsmentioning

confidence: 97%

Pathways to Professional Growth: Investigating Upper Primary School Teachers’ Perspectives on Learning to Teach Algebra

Wilkie¹,

Clarke

2015

AJTE

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“…The kindergarten students aged 5-6 years reveal a unique fact. It was found that these children indicated early algebraic thinking [10]. These children already recognized the number more than 20 and could perform addition and subtraction with it.…”

Section: Introductionmentioning

confidence: 89%

Pattern Generalization by Elementary Students

Rusdiana¹,

Suriaty²,

Sutawidjaja³

et al. 2017

Proceedings of the 5th SEA-DR (South East Asia Development Research) International Conference 2017 (SEADRIC 2017)

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Abstract-This paper presents the strategies used by fifth and sixth grade elementary students when they faced problem on pattern generalization. The samples were 3 elementary school students from grade 5 and 6. Students were given a problem of pattern and asked to make generalizations on the given pattern. The data were analyzed to describe the strategies used by students in solving the problem of generalizing patterns. The results indicated that the students were able to generalize on a pattern and start using mathematical symbols in solving problem. The results also revealed that the students used effective strategies to solve the problem of generalizing patterns. Although pattern generalization is not a new concept for elementary school students, it is considered important because pattern generalization can help students learn arithmetic thinking to algebraic thinking so that students are able to produce rules that can be used to determine any value of the pattern.

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“…Given classroom research indicating how generic examples support students' progression from inductive to deductive reasoning (Lannin, Barker & Townsend, 2006;Pedemonte & Buchbinder, 2011), opportunities for teachers to develop this component of SCK seem particularly salient. As demonstrated in the second small group seminar discussion, leaders critically evaluated the array and area models presented in the Halving and Doubling videocase.…”

Section: Exploring Generic Examplesmentioning

confidence: 99%

Investigating Mathematical Knowledge for Teaching Proof in Professional Development

Lesseig

2016

IJRES

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Research documenting teachers' fragile understanding of proof and how it is advanced suggests that enhancing the role of proof in school mathematics will demand substantial teacher learning. To date, there is little research detailing what mathematical knowledge might support the teaching of proof or how professional development (PD) might afford such learning. This paper advances a framework for Mathematical Knowledge for Teaching Proof (MKT for Proof) that specifies proof knowledge across subject matter and pedagogical domains. To explore the utility of the framework, this paper examines data from four different PD settings in which teachers and leaders worked on the same proof-related task. Analysis of discussions across these four settings revealed similarities and differences in knowledge of proof made available in each setting. These findings provide a means to detail the MKT for Proof framework and demonstrate its usefulness as a tool for designing, analyzing and evaluating proof experiences in PD.

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Recursive and explicit rules: How can we build student algebraic understanding?

Cited by 55 publications

References 17 publications

Pathways to Professional Growth: Investigating Upper Primary School Teachers’ Perspectives on Learning to Teach Algebra

Pathways to Professional Growth: Investigating Upper Primary School Teachers’ Perspectives on Learning to Teach Algebra

Pattern Generalization by Elementary Students

Investigating Mathematical Knowledge for Teaching Proof in Professional Development

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