Ideas foundational to calculus learning and their links to students' difficulties

PW Thompson, G Harel - ZDM–Mathematics Education, 2021 - Springer
Existing literature reviews of calculus learning made an important contribution to our
understanding of the development of mathematics education research in this area …

[PDF][PDF] Variation, covariation, and functions: Foundational ways of thinking mathematically

PW Thompson, MP Carlson - Compendium for research in …, 2017 - researchgate.net
In beginning this chapter we immediately faced a dilemma. There is nothing that can be
called “the concept of function.” The phrase “concept of function,” regardless of its meaning …

Learning is moving in new ways: The ecological dynamics of mathematics education

D Abrahamson, R Sánchez-García - Journal of the Learning …, 2016 - Taylor & Francis
Whereas emerging technologies, such as touchscreen tablets, are bringing sensorimotor
interaction back into mathematics learning activities, existing educational theory is not …

Teaching with embodied learning technologies for mathematics: Responsive teaching for embodied learning

VJ Flood, A Shvarts, D Abrahamson - ZDM, 2020 - Springer
As technologies that put the body at the center of mathematics learning enter formal and
informal learning spaces, we still know little about the teaching methods educators can use …

Secondary mathematics teachers' meanings for measure, slope, and rate of change

C Byerley, PW Thompson - The Journal of Mathematical Behavior, 2017 - Elsevier
This article reports an investigation of 251 high school mathematics teachers' meanings for
slope, measurement, and rate of change. The data was collected with a validated written …

Quantitative reasoning and the sine function: The case of Zac

KC Moore - Journal for Research in Mathematics Education, 2014 - pubs.nctm.org
A growing body of literature has identified quantitative and covariational reasoning as critical
for secondary and undergraduate student learning, particularly for topics that require …

An exponential growth learning trajectory: Students' emerging understanding of exponential growth through covariation

AB Ellis, Z Ozgur, T Kulow, MF Dogan… - … thinking and learning, 2016 - Taylor & Francis
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory
identifying and characterizing middle grade students' initial and developing understanding …

Covariational reasoning and invariance among coordinate systems

KC Moore, T Paoletti, S Musgrave - The Journal of Mathematical Behavior, 2013 - Elsevier
Researchers continue to emphasize the importance of covariational reasoning in the context
of students' function concept, particularly when graphing in the Cartesian coordinate system …

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

G Greefrath, HS Siller, K Vorhölter, G Kaiser - ZDM–Mathematics …, 2022 - Springer
Discrete mathematics and mathematical modelling, along with the educational discourse
surrounding these, have many connections. However, ways that the educational discourse …

Secondary students' quantification of ratio and rate: A framework for reasoning about change in covarying quantities

HL Johnson - Mathematical Thinking and Learning, 2015 - Taylor & Francis
Contributing to a growing body of research addressing secondary students' quantitative and
covariational reasoning, the multiple case study reported in this article investigated …