Mitchell J Nathan
Biographic Data
| ID | 315305 |
|---|---|
| NAME | Mitchell J Nathan |
| GIVEN NAMES | Mitchell J |
| FAMILY NAME | Nathan |
| SIGNATURE | NATHAN M J |
| AFFILIATIONS | University of Wisconsin–Madison |
| ORCID | 0000-0003-2058-7016 |
| VERIFIED | Yes |
| TOTAL WORKS | 19 |
| TOTAL CITATIONS | 57 |
| WORKS AS AUTHOR | 19 |
| WORKS AS EDITOR | 0 |
| FIRST PUBLICATION YEAR | 2002 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 3 |
The impact of different collaboration formats on mathematical problem-solving in augmented reality
Augmented reality (AR), where digital holograms are layered over the real world, is rapidly being applied to different educational domains, including mathematics education. However, little is known about how AR can be effectively designed for collaborative use. There are both practical and theory-based reasons to set up collaboration in AR in different ways, which result in different costs and opportunities for learning. Here we compare parallel …
Action Predictions Facilitate Embodied Geometric Reasoning
Task‐relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action‐cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements—imagined as well as real ones operating on real or imaginary objects—activate feedforward mechanisms for the plausible predicted out…
Learning vector addition using concreteness fading
Multimodal analysis of interaction data from embodied education technologies
The emergence of immersive digital technologies, such as shared augmented reality (shAR), virtual reality (VR) and motion capture (MC) offers promising new opportunities to advance our understanding of human cognition and design innovative technology-enhanced learning experiences. Theoretical frameworks for embodied and extended cognition can guide novel ways in which learning in these environments can be understood and analyzed. This conceptual …
Your body tells how you engage in collaboration
Collaborative learning, driven by knowledge co‐construction and meaning negotiation, is a pivotal aspect of educational contexts. While gesture's importance in conveying shared meaning is recognized, its role in collaborative group settings remains understudied. This gap hinders accurate and equitable assessment and instruction, particularly for linguistically diverse students. Advancements in multimodal learning analytics, leveraging sensor tech…
Inference making and learning from text via embodied situation models
The adventures of John Bransford
Materialist epistemology lends design wings
Embodied geometric reasoning
Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts (N = 44) were asked to judge the truth and to justify their judgments for four geometry conjectures.…
The Future of Embodied Design for Mathematics Teaching and Learning
A rising epistemological paradigm in the cognitive sciences—embodied cognition—has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experienc…
Learning from an avatar video instructor
Teachers often produce gestures, and, in some cases, students mimic their teachers’ gestures and adopt them into their own repertoires. However, little research has explored the role of gesture mimicry in technology-based learning contexts. In this research, we examined variations in the rate and form of students’ gestures when learning from a computer-animated pedagogical avatar. Twenty-four middle school students received a lesson on polynomial…
Teachers’ attitudes about gesture for learning and instruction
We developed and tested a survey instrument to measure teachers’ attitudes about gesture in learning and instruction (TAGLI). Teachers ( N = 192) generally believed that instructional gestures are beneficial for learning, and not distracting for students. Teachers had positive expectations, both for gestures that are redundant with (i.e., match) the accompanying speech, and gestures that are complementary to (i.e., mismatch) speech. However, teac…
Improving Students’ Learning With Effective Learning Techniques
Many students are being left behind by an educational system that some people believe is in crisis. Improving educational outcomes will require efforts on many fronts, but a central premise of this monograph is that one part of a solution involves helping students to better regulate their learning through the use of effective learning techniques. Fortunately, cognitive and educational psychologists have been developing and evaluating easy-to-use …
Students learn more when their teacher has learned to gesture effectively
Teachers’ gestures are an integral part of their instructional communication. In this study, we provided a teacher with a tutorial about ways to use gesture in connecting ideas in mathematics instruction, and we asked the teacher to teach sample lessons about slope and intercept before and after this tutorial. In response to the tutorial, the teacher enhanced his communication about links between ideas by increasing the frequency with which he ex…
Embodiment in Mathematics Teaching and Learning
Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for ea…
Learning sciences
The aims of the learning sciences (LS) are to understand the nature of learning from a broad range of perspectives, and to shape the ways that learning environments and resources are designed and used. LS incorporates both systemic and elemental approaches to investigating questions about learning, as a complement to the primarily elemental approach emphasized in cognitive science research. Thus, its greatest potential is in the integration of sy…
Unresolved Contradiction as a Condition for Promoting Socially Mediated Learning
In ‘Collaborative group work in middle childhood: Joint construction, unresolved contradiction and the growth of knowledge,’ Howe [this issue] addressed what appears to be a central, but often untested, assumption in the literature on effects of collaboration on learning; namely, that knowledge growth is achieved (primarily) through one of two means: assimilation of a relatively advanced contribution proposed by one child because it is accepted w…
Expert Blind Spot Among Preservice Teachers
This study (N = 48) examined the relationship between preservice secondary teachers’ subject-matter expertise in mathematics and their judgments of students’ algebra problem-solving difficulty. As predicted by the “expert blind spot” hypothesis, participants with more advanced mathematics education, regardless of their program affiliation or teaching plans, were more likely to view symbolic reasoning and mastery of equations as a necessary prereq…
The Symbol Precedence View of Mathematical Development
This study examined a corpus of 10 widely used pre-algebra and algebra textbooks, with the goal of investigating whether they exhibited a symbol precedence view of mathematical development as is found among high school teachers. The textbook analysis focused on the sequence in which problem-solving activities were presented to students. As predicted, textbooks showed the symbol precedence view, presenting symbolic problems prior to verbal problem…
Embodiment in Mathematics Teaching and Learning
Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for ea…
Students learn more when their teacher has learned to gesture effectively
Teachers’ gestures are an integral part of their instructional communication. In this study, we provided a teacher with a tutorial about ways to use gesture in connecting ideas in mathematics instruction, and we asked the teacher to teach sample lessons about slope and intercept before and after this tutorial. In response to the tutorial, the teacher enhanced his communication about links between ideas by increasing the frequency with which he ex…
Learning sciences
The aims of the learning sciences (LS) are to understand the nature of learning from a broad range of perspectives, and to shape the ways that learning environments and resources are designed and used. LS incorporates both systemic and elemental approaches to investigating questions about learning, as a complement to the primarily elemental approach emphasized in cognitive science research. Thus, its greatest potential is in the integration of sy…
Learning vector addition using concreteness fading
Inference making and learning from text via embodied situation models
The Symbol Precedence View of Mathematical Development
This study examined a corpus of 10 widely used pre-algebra and algebra textbooks, with the goal of investigating whether they exhibited a symbol precedence view of mathematical development as is found among high school teachers. The textbook analysis focused on the sequence in which problem-solving activities were presented to students. As predicted, textbooks showed the symbol precedence view, presenting symbolic problems prior to verbal problem…
The Symbol Precedence View of Mathematical Development
This study examined a corpus of 10 widely used pre-algebra and algebra textbooks, with the goal of investigating whether they exhibited a symbol precedence view of mathematical development as is found among high school teachers. The textbook analysis focused on the sequence in which problem-solving activities were presented to students. As predicted, textbooks showed the symbol precedence view, presenting symbolic problems prior to verbal problem…
Expert Blind Spot Among Preservice Teachers
This study (N = 48) examined the relationship between preservice secondary teachers’ subject-matter expertise in mathematics and their judgments of students’ algebra problem-solving difficulty. As predicted by the “expert blind spot” hypothesis, participants with more advanced mathematics education, regardless of their program affiliation or teaching plans, were more likely to view symbolic reasoning and mastery of equations as a necessary prereq…
Unresolved Contradiction as a Condition for Promoting Socially Mediated Learning
In ‘Collaborative group work in middle childhood: Joint construction, unresolved contradiction and the growth of knowledge,’ Howe [this issue] addressed what appears to be a central, but often untested, assumption in the literature on effects of collaboration on learning; namely, that knowledge growth is achieved (primarily) through one of two means: assimilation of a relatively advanced contribution proposed by one child because it is accepted w…
Learning sciences
The aims of the learning sciences (LS) are to understand the nature of learning from a broad range of perspectives, and to shape the ways that learning environments and resources are designed and used. LS incorporates both systemic and elemental approaches to investigating questions about learning, as a complement to the primarily elemental approach emphasized in cognitive science research. Thus, its greatest potential is in the integration of sy…
Embodiment in Mathematics Teaching and Learning
Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based in perception and action, and it is grounded in the physical environment. We present evidence for ea…
Improving Students’ Learning With Effective Learning Techniques
Many students are being left behind by an educational system that some people believe is in crisis. Improving educational outcomes will require efforts on many fronts, but a central premise of this monograph is that one part of a solution involves helping students to better regulate their learning through the use of effective learning techniques. Fortunately, cognitive and educational psychologists have been developing and evaluating easy-to-use …
Students learn more when their teacher has learned to gesture effectively
Teachers’ gestures are an integral part of their instructional communication. In this study, we provided a teacher with a tutorial about ways to use gesture in connecting ideas in mathematics instruction, and we asked the teacher to teach sample lessons about slope and intercept before and after this tutorial. In response to the tutorial, the teacher enhanced his communication about links between ideas by increasing the frequency with which he ex…
Teachers’ attitudes about gesture for learning and instruction
We developed and tested a survey instrument to measure teachers’ attitudes about gesture in learning and instruction (TAGLI). Teachers ( N = 192) generally believed that instructional gestures are beneficial for learning, and not distracting for students. Teachers had positive expectations, both for gestures that are redundant with (i.e., match) the accompanying speech, and gestures that are complementary to (i.e., mismatch) speech. However, teac…
The Future of Embodied Design for Mathematics Teaching and Learning
A rising epistemological paradigm in the cognitive sciences—embodied cognition—has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experienc…
Learning from an avatar video instructor
Teachers often produce gestures, and, in some cases, students mimic their teachers’ gestures and adopt them into their own repertoires. However, little research has explored the role of gesture mimicry in technology-based learning contexts. In this research, we examined variations in the rate and form of students’ gestures when learning from a computer-animated pedagogical avatar. Twenty-four middle school students received a lesson on polynomial…
Materialist epistemology lends design wings
Embodied geometric reasoning
Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts (N = 44) were asked to judge the truth and to justify their judgments for four geometry conjectures.…
The adventures of John Bransford
Multimodal analysis of interaction data from embodied education technologies
The emergence of immersive digital technologies, such as shared augmented reality (shAR), virtual reality (VR) and motion capture (MC) offers promising new opportunities to advance our understanding of human cognition and design innovative technology-enhanced learning experiences. Theoretical frameworks for embodied and extended cognition can guide novel ways in which learning in these environments can be understood and analyzed. This conceptual …
Your body tells how you engage in collaboration
Collaborative learning, driven by knowledge co‐construction and meaning negotiation, is a pivotal aspect of educational contexts. While gesture's importance in conveying shared meaning is recognized, its role in collaborative group settings remains understudied. This gap hinders accurate and equitable assessment and instruction, particularly for linguistically diverse students. Advancements in multimodal learning analytics, leveraging sensor tech…
Inference making and learning from text via embodied situation models
Action Predictions Facilitate Embodied Geometric Reasoning
Task‐relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action‐cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements—imagined as well as real ones operating on real or imaginary objects—activate feedforward mechanisms for the plausible predicted out…
Learning vector addition using concreteness fading
The impact of different collaboration formats on mathematical problem-solving in augmented reality
Augmented reality (AR), where digital holograms are layered over the real world, is rapidly being applied to different educational domains, including mathematics education. However, little is known about how AR can be effectively designed for collaborative use. There are both practical and theory-based reasons to set up collaboration in AR in different ways, which result in different costs and opportunities for learning. Here we compare parallel …
Psychology (15 works) · Computer Science (13 works) · Artificial Intelligence (9 works) · Hearing Impairment and Communication (9 works) · Mathematics education (9 works) · Gesture (7 works) · Cognitive psychology (6 works) · Cognitive science (6 works) · Embodied cognition (6 works) · Innovative Teaching and Learning Methods (6 works)