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Articles 1 - 8 of 8
Full-Text Articles in Education
Hear What They Say And Watch What They Do: Predicting Valid Mathematical Proofs Using Speech And Gesture, Caro C. Williams-Pierce
Hear What They Say And Watch What They Do: Predicting Valid Mathematical Proofs Using Speech And Gesture, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
In mathematics, practices of proof are notoriously difficult for learners to adopt. In prior work, we found that when providing verbal justifications, learners’ speech patterns predict whether their justifications are mathematically sound. However, current views on the embodied nature of cognition suggest that actions and speech may co-constitute reasoning processes. The current study investigated whether the gestures learners use while formulating proofs also predict proof validity. 120 undergraduates provided verbal justifications for two mathematical tasks. We analyzed speech patterns in participants’ justifications using text analysis software, and we coded participants’ gestures as dynamic or static. Results showed that dynamic gestures …
Being Mathematical Relations: Dynamic Gestures Support Mathematical Reasoning, Caro C. Williams-Pierce
Being Mathematical Relations: Dynamic Gestures Support Mathematical Reasoning, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
In mathematics classrooms, body-based actions, including gestures, offer an important way for students to become mathematical ideas as they engage in mathematical practices. In particular, a type of gesture that we call a dynamic depictive gesture allows learners to model and represent fluid transformations of mathematical objects with their bodies. In this paper, we report on two empirical studies – one in which dynamic gestures were observed, and one where these gestures were directed. We conclude that dynamic gestures are a key element in successful justification and proof activities in mathematics.
Performance Assessments, Caro C. Williams-Pierce
Performance Assessments, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
No abstract provided.
Broadening What We Perceive: A Method For Analyzing Gesture And Language, Caro C. Williams-Pierce
Broadening What We Perceive: A Method For Analyzing Gesture And Language, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
Gesture and language are deeply intertwined, and attending to both simultaneously when examining mathematical processes is a complex yet rewarding task. We share our budding research methodology for analyzing gesture and language and discuss the methodology from a generic perspective that can be easily adapted to different contexts, participants, and mathematical domains. We further share our problem-specific gesture coding scheme as an example of the grain size and foci of such schemes. Finally, we close by discussing the importance of gesture and language to understanding mathematical justifications and proofs.
Correspondence And Covariation: Quantities Changing Together, Caro C. Williams-Pierce
Correspondence And Covariation: Quantities Changing Together, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
Exponential functions are important topic in school algebra and in higher mathematics, but research on students’ thinking suggests that understanding exponential growth remains an instructional challenge. This paper reports the results of a small-scale teaching experiment with students who explored exponential functions in the context of two continuously covarying quantities, height and time. We present two major conceptual paths that occurred in the development of an understanding of exponential growth, the covariation view and the correspondence view, and discuss the influence of each perspective on the growth of students’ understanding.
Strategically Chosen Examples Leading To Proof Insight: A Case Study Of A Mathematician’S Proving Process., Caro C. Williams-Pierce
Strategically Chosen Examples Leading To Proof Insight: A Case Study Of A Mathematician’S Proving Process., Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper we present a case study of one mathematician’s work on a conjecture in which his strategic, intentional use of examples led to a proof of that conjecture. By examining his work in detail, we highlight specific mechanisms by which the mathematician’s examples led to successful proof …
Gesture As A Window To Justification And Proof, Caro C. Williams-Pierce
Gesture As A Window To Justification And Proof, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
The role of the body, particularly gesture, in supporting mathematical reasoning is an emerging area of research in mathematics education. In the present study, we examine undergraduate students providing a justification for a task about a system of alternating gears, which involves concepts of number relating to even/odd patterns. Some participants were directed to perform gestures relevant to alternation and parity before attempting their justification, while others were not. Although these directed actions did not seem to influence the gestures participants used to solve the problem, we found an important relationship between gesture and mathematical reasoning. In particular, certain types …
Five Key Ingredients For Improving Student Motivation, Caro C. Williams-Pierce
Five Key Ingredients For Improving Student Motivation, Caro C. Williams-Pierce
Mathematics and Statistics Faculty Scholarship
Motivation is probably the most important factor that educators can target in order to improve learning. Numerous cross-disciplinary theories have been postulated to explain motivation. While each of these theories has some truth, no single theory seems to adequately explain all human motivation. The fact is that human beings in general and students in particular are complex creatures with complex needs and desires. With regard to students, very little if any learning can occur unless students are motivated on a consistent basis. The five key ingredients impacting student motivation are: student, teacher, content, method/process, and environment. The focus of this …