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 …

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

C Kieran - 2016 - cdn.supo.vn
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 …

STEM education in the primary years to support mathematical thinking: Using coding to identify mathematical structures and patterns

J Miller - Zdm, 2019 - Springer
Cross-curricula opportunities afforded by STEM education (Science, Technology,
Engineering and Mathematics education), supports an environment where students can …

Towards a methodology for the characterization of teachers' didactic-mathematical knowledge

LR Pino-Fan, A Assis, WF Castro - EURASIA Journal of Mathematics …, 2015 - ejmste.com
Background: This research study aims at exploring the use of some dimensions and
theoretical-methodological tools suggested by the model of Didactic-Mathematical …

Research on the learning and teaching of algebra: A broadening of sources of meaning

C Kieran - Handbook of research on the psychology of …, 2006 - brill.com
The learning and teaching of algebra has always been a fundamental and vibrant stream of
the research carried out within the PME community–from the 1st PME conference in 1977 to …

An analytic framework of reasoning-and-proving

GJ Stylianides - For the learning of mathematics, 2008 - JSTOR
In the discipline of mathematics, the development of new knowledge often passes through
several stages, of which the development of proofs is typically the last. Earlier stages …

Patterning strategies in early childhood: A mixed methods study examining 3-to 5-year-old children's patterning competencies

MM Lüken, O Sauzet - Mathematical Thinking and Learning, 2021 - Taylor & Francis
Despite increasing data on young children's patterning skills and evidence of a link between
early pattern knowledge and later mathematics performance, little is known about the …

“Rising to the challenge”: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students

M Amit, D Neria - ZDM, 2008 - Springer
This study focuses on the generalization methods used by talented pre-algebra students in
solving linear and non-linear pattern problems. A qualitative analysis of the solutions of …

Four-year olds' understanding of repeating and growing patterns and its association with early numerical ability

N Wijns, J Torbeyns, M Bakker, B De Smedt… - Early Childhood …, 2019 - Elsevier
In this study, we aimed to address two gaps in research on early mathematical patterning,
namely the lack of attention (1) to growing patterns and (2) to the association between …

Knowledge building in mathematics: Supporting collaborative learning in pattern problems

J Moss, R Beatty - … Journal of Computer-Supported Collaborative Learning, 2006 - Springer
While it has been suggested that patterning activities support early algebra learning, it is
widely acknowledged that the shift from perceiving patterns to understanding algebraic …