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View article: An embodied approach to covariational reasoning: a hand-tracking study
An embodied approach to covariational reasoning: a hand-tracking study Open
Covariational reasoning is critical for understanding functional relationships in mathematics. Yet, many students struggle to understand varying quantities and to conceptualize covariation. This study explores the research question of how …
View article: Chapter 11 Students' interaction with and appreciation of automated informative tutoring feedback
Chapter 11 Students' interaction with and appreciation of automated informative tutoring feedback Open
Computer aided formative assessment can be used to enhance a learning process, for instance by providing feedback. There are many design choices for delivering feedback, that lead to a feedback strategy. In an informative feedback strategy…
View article: Combining model tracing and constraint-based modeling for multistep strategy diagnoses
Combining model tracing and constraint-based modeling for multistep strategy diagnoses Open
Model tracing and constraint-based modeling are two approaches to diagnose student input in stepwise tasks. Model tracing supports identifying consecutive problem-solving steps taken by a student, whereas constraint-based modeling supports…
View article: Buggy rule diagnosis for combined steps through final answer evaluation in stepwise tasks
Buggy rule diagnosis for combined steps through final answer evaluation in stepwise tasks Open
Many intelligent tutoring systems can support a student in solving a stepwise task. When a student combines several steps in one step, the number of possible paths connecting consecutive inputs may be very large. This combinatorial explosi…
View article: Mathematics teachers’ professional experimentation with mathematical origami in secondary education
Mathematics teachers’ professional experimentation with mathematical origami in secondary education Open
Mathematical origami can be a valuable tool for teaching mathematics. This study explores mathematical origami teaching practices in secondary education. The addressed research question is: What do mathematics teachers report about their p…
View article: Reifying actions into artifacts: process–object duality from an embodied perspective on mathematics learning
Reifying actions into artifacts: process–object duality from an embodied perspective on mathematics learning Open
Grasping mathematical objects as related to processes is often considered critical for mathematics understanding. Yet, the ontology of mathematical objects remains under debate. In this paper, we theoretically oppose internalist approaches…
View article: Developing Functional Thinking: from Concrete to Abstract Through an Embodied Design
Developing Functional Thinking: from Concrete to Abstract Through an Embodied Design Open
In addressing the challenge of fostering functional thinking (FT) in secondary school students, our research centered on the question of how an embodied design can enhance FT’s different aspects, including input–output, covariation, and co…
View article: A taxonomy of didactic roles of dynamic visualization in animated mathematics videos
A taxonomy of didactic roles of dynamic visualization in animated mathematics videos Open
In recent years, a multitude of innovative educational videos focusing on mathematics and employing dynamic visualization techniques have been published on YouTube. From a sample of videos, we develop a taxonomy of didactical roles of dyna…
View article: Developing Functional Thinking: From concrete to abstract through an embodied design
Developing Functional Thinking: From concrete to abstract through an embodied design Open
In addressing the challenge of fostering functional thinking (FT) among secondary school students, our research centered on the question of how an embodied design can enhance FT's different aspects, including input-output, covariation and …
View article: Dynamic visualization in animated mathematics videos I: a classification of didactic roles
Dynamic visualization in animated mathematics videos I: a classification of didactic roles Open
In recent years, a multitude of innovative educational videos focusing on mathematics and employing dynamic visualization techniques have emerged on YouTube. This study investigates how creators of such videos aim to teach through dynamic …
View article: Activate students? Let them fold! Mathematical paper folding in secondary education in France and Germany
Activate students? Let them fold! Mathematical paper folding in secondary education in France and Germany Open
Though the potential of mathematical paper folding for learning mathematics is known, this practice is still rare in mathematics classes. To inform the design of mathematics lessons enriched with folding, we investigated via a literature r…
View article: Heuristic Trees as a Digital Tool to Foster Compression and Decompression in Problem-Solving
Heuristic Trees as a Digital Tool to Foster Compression and Decompression in Problem-Solving Open
This design-based study addresses the issue of how to digitally support students’ problem-solving by providing heuristics, in the absence of the teacher. The problem is that, so far, digital tutoring systems lack the ability to diagnose st…
View article: Embodied approaches to functional thinking using digital technology: A bibliometrics-guided review
Embodied approaches to functional thinking using digital technology: A bibliometrics-guided review Open
Digital technology offers many opportunities for embodied approaches to mathematics education. To investigate what is known from literature about such approaches for the case of Functional Thinking, we carried out a systematic literature r…
View article: Action-property duality in embodied design
Action-property duality in embodied design Open
For those working on embodied design it is a challenge to create tasks that enable students to develop abstract mathematical concepts. We approach this issue from the perspective of Sfard's notions of saming, encapsulation, and reification…
View article: Embodied design using augmented reality: the case of the gradient
Embodied design using augmented reality: the case of the gradient Open
We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of…
View article: Body checking, body avoidance and social behavior: The factorial structure of the Dutch translation of the Body Checking and Avoiding Questionnaire in a healthy female college sample
Body checking, body avoidance and social behavior: The factorial structure of the Dutch translation of the Body Checking and Avoiding Questionnaire in a healthy female college sample Open
Body checking and body avoidance are the two main components of the behavioral aspect of body image disturbances (BID), which is a core feature of multiple eating disorders (ED). The behavioral component of BID has not gotten as much atten…
View article: Supporting the reinvention of the slope of a curve in a point: A smooth slope to slide is a smooth slide to slope
Supporting the reinvention of the slope of a curve in a point: A smooth slope to slide is a smooth slide to slope Open
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View article: Structuring hints and heuristics in intelligent tutoring systems
Structuring hints and heuristics in intelligent tutoring systems Open
In this article we address how to teach the use of heuristics in problem solving. We present an approach using a new support model within an online tutoring system. The outcomes of a pilot study conducted in the Netherlands are discussed. …