[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 …
called “the concept of function.” The phrase “concept of function,” regardless of its meaning …
Design research: An analysis and critique
Globalization and unprecedented levels of migration were partly responsible for the
expansion of research on mathematical learning in and out of school, including a focus on …
expansion of research on mathematical learning in and out of school, including a focus on …
Negative integer understanding: Characterizing first graders' mental models
L Bofferding - Journal for research in mathematics education, 2014 - pubs.nctm.org
This article presents results of a research study with a pretest, instruction, and posttest
design that aimed to identify students' mental models of integers and investigate how these …
design that aimed to identify students' mental models of integers and investigate how these …
Obstacles and affordances for integer reasoning: An analysis of children's thinking and the history of mathematics
We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of
integer understanding that can function as either an obstacle or affordance for learners while …
integer understanding that can function as either an obstacle or affordance for learners while …
An exponential growth learning trajectory: Students' emerging understanding of exponential growth through covariation
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory
identifying and characterizing middle grade students' initial and developing understanding …
identifying and characterizing middle grade students' initial and developing understanding …
A hypothetical learning trajectory for conceptualizing matrices as linear transformations
C Andrews-Larson, M Wawro… - International Journal of …, 2017 - Taylor & Francis
In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting
students in developing flexible ways of reasoning about matrices as linear transformations in …
students in developing flexible ways of reasoning about matrices as linear transformations in …
[PDF][PDF] Frameworks and principles for task design
The opening citation, drawn from The Sciences of the Artificial by HA Simon (1969), on
design being concerned with “how things might be,” evokes the idea that the field of …
design being concerned with “how things might be,” evokes the idea that the field of …
Examining individual and collective level mathematical progress
A challenge in mathematics education research is to coordinate different analyses to
develop a more comprehensive account of teaching and learning. We contribute to these …
develop a more comprehensive account of teaching and learning. We contribute to these …
Evidence for cognitive science principles that impact learning in mathematics
Numerous issues with mathematics education in the United States have led to repeated
calls for instruction to align more fully with evidence-based practices. The field of cognitive …
calls for instruction to align more fully with evidence-based practices. The field of cognitive …
Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers.
NF Fuadiah, D Suryadi - International Journal of Instruction, 2019 - ERIC
This study is a series of Didactical Design Research in prospective analysis stage to
comprehensively identify some obstacles in learning negative integer in order to capture …
comprehensively identify some obstacles in learning negative integer in order to capture …