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 …

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 …

Young students' functional thinking modes: The relation between recursive patterning, covariational thinking, and correspondence relations

M Pittalis, D Pitta-Pantazi, C Christou - Journal for Research in …, 2020 - pubs.nctm.org
A theoretical model describing young students'(Grades 1–3) functional-thinking modes was
formulated and validated empirically (n= 345), hypothesizing that young students' functional …

Students' use of variables and multiple representations in generalizing functional relationships prior to secondary school

KJ Wilkie - Educational Studies in Mathematics, 2016 - Springer
Abstract Algebra has been explicit in many school curriculum programs from the early years
but there are competing views on what content and approaches are appropriate for different …

The Position and Causes of Students Errors in Algebraic Thinking Based on Cognitive Style.

A Agoestanto, YL Sukestiyarno, MD Lestari - International Journal of …, 2019 - ERIC
The purpose of this research was to describe the positions and causes of students' errors in
algebraic thinking based on the cognitive style. This study was qualitative research with …

Generalization: strategies and representations used by sixth to eighth graders in a functional context

J Ureña, R Ramírez, M Molina, MC Cañadas - … Education Research Journal, 2024 - Springer
We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth
grade students' answers to a word problem, accompanied by diagrams, involving …

Functional thinking: A study with 10th-grade students

R Martins, F Viseu, H Rocha - Education Sciences, 2023 - mdpi.com
This study aims to understand the functional thinking of 10th-grade students while studying
functions. Specifically, we intend to answer the following research questions: what are the …

Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations

A Tondorf, S Prediger - Educational Studies in Mathematics, 2022 - Springer
One typical challenge in algebra education is that many students justify the equivalence of
expressions only by referring to transformation rules that they perceive as arbitrary without …

Metacognitive knowledge and mathematical intelligence—Two significant factors influencing school performance

V Chytrý, J Říčan, P Eisenmann, J Medová - Mathematics, 2020 - mdpi.com
Metacognitive knowledge and mathematical intelligence were tested in a group of 280
pupils of grade 7 age 12–13 years in the Czech Republic. Metacognitive knowledge was …

Early childhood mathematical development: the association between patterning and proportional reasoning

E Vanluydt, N Wijns, J Torbeyns… - Educational Studies in …, 2021 - Springer
Insight into early precursors of proportional reasoning is necessary to further our theoretical
understanding of mathematical development and to guide early interventions. Although …