The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions

C Kieran - ZDM–Mathematics Education, 2022 - Springer
Early algebraic thinking is the reasoning engaged in by 5-to 12-year-olds as they build
meaning for the objects and ways of thinking to be encountered within the later study of …

Methods of instructional improvement in algebra: A systematic review and meta-analysis

CR Rakes, JC Valentine… - Review of …, 2010 - journals.sagepub.com
This systematic review of algebra instructional improvement strategies identified 82 relevant
studies with 109 independent effect sizes representing a sample of 22,424 students. Five …

The development of children's algebraic thinking: The impact of a comprehensive early algebra intervention in third grade

M Blanton, A Stephens, E Knuth… - Journal for research in …, 2015 - pubs.nctm.org
This article reports results from a study investigating the impact of a sustained,
comprehensive early algebra intervention in third grade. Participants included 106 students; …

[图书][B] Early algebra: Research into its nature, its learning, its teaching

C Kieran, JS Pang, D Schifter, SF Ng - 2016 - library.oapen.org
This survey of the state of the art on research in early algebra traces the evolution of a
relatively new field of research and teaching practice. With its focus on the younger student …

The emergence of symbolic algebraic thinking in primary school

L Radford - Teaching and learning algebraic thinking with 5-to 12 …, 2018 - Springer
This chapter presents the results of a longitudinal investigation on the emergence of
symbolic algebraic thinking in young students in the context of sequence generalization. The …

A learning trajectory in 6-year-olds' thinking about generalizing functional relationships

M Blanton, BM Brizuela, AM Gardiner… - Journal for research in …, 2015 - pubs.nctm.org
The study of functions is a critical route into teaching and learning algebra in the elementary
grades, yet important questions remain regarding the nature of young children's …

Assessing the development of preschoolers' mathematical patterning

MM Papic, JT Mulligan… - Journal for Research in …, 2011 - pubs.nctm.org
The development of patterning strategies during the year prior to formal schooling was
studied in 53 children from 2 similar preschools. One preschool implemented a 6-month …

The progressive development of early embodied algebraic thinking

L Radford - Mathematics Education Research Journal, 2014 - Springer
In this article I present some results from a 5-year longitudinal investigation with young
students about the genesis of embodied, non-symbolic algebraic thinking and its …

[图书][B] Early algebraization: A global dialogue from multiple perspectives

J Cai, E Knuth - 2011 - books.google.com
In this volume, the authors address the development of students' algebraic thinking in the
elementary and middle school grades from curricular, cognitive, and instructional …

Early algebra and mathematical generalization

DW Carraher, MV Martinez, AD Schliemann - ZDM, 2008 - Springer
We examine issues that arise in students' making of generalizations about geometrical
figures as they are introduced to linear functions. We focus on the concepts of patterns …