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Kim, Doy; Swart, Michael I.; Schenck, Kelsey E.; Nathan, Mitchell J. – Grantee Submission, 2021
This study investigates the associations of spontaneous "dynamic gesture" and "transformational speech" with the production of "deductive proofs" in participants' reasoning about geometric conjectures (N=77). Although statistical analysis showed no significant association, the result suggests that purposefully…
Descriptors: Nonverbal Communication, Geometry, Logical Thinking, Mathematical Logic
Zengin, Yilmaz – Education and Information Technologies, 2022
The study focused on how university students constructed proof of the Fundamental Theorem of Calculus (FTC) starting from their argumentations with dynamic mathematics software in collaborative technology-enhanced learning environment. The participants of the study were 36 university students. The data consisted of participants' written…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, College Students
Walkington, Candace; Woods, Dawn; Nathan, Mitchell J.; Chelule, Geoffrey; Wang, Min – Grantee Submission, 2018
Gestures are associated with powerful forms of mathematical understanding. However, determining the causative role of gestures has been more elusive. In the present study, we inhibit students' gestures by restraining their hands, and examine how this impacts their problem-solving when presented with geometric conjectures to prove. We find no…
Descriptors: Nonverbal Communication, Mathematical Logic, Problem Solving, Geometry
Maarif, Samsul; Alyani, Fitri; Pradipta, Trisna Roy – Journal of Research and Advances in Mathematics Education, 2020
Proof is a key indicator for a student in developing mathematical maturity. However, in the process of learning proof, students have the difficulty of being able to explain the proof that has been compiled using good arguments. So we need a strategy that can put students in the process of clarifying proof better. One strategy that can explore…
Descriptors: Mathematical Logic, Validity, Geometry, Mathematics Instruction
Flórez, Rigoberto; Mukherjee, Antara – PRIMUS, 2020
We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…
Descriptors: Mathematics Instruction, College Mathematics, Secondary School Mathematics, Undergraduate Study
Buchbinder, Orly – International Journal of Mathematical Education in Science and Technology, 2018
The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…
Descriptors: Mathematical Logic, Validity, Geometry, Geometric Concepts
Nathan, Mitchell J.; Schenck, Kelsey E.; Vinsonhaler, Rebecca; Michaelis, Joseph E.; Swart, Michael I.; Walkington, Candace – Journal of Educational Psychology, 2021
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…
Descriptors: Mathematical Logic, Validity, Geometry, Knowledge Level
Sagge, Roberto G., Jr.; Bacio, Salvador P., Jr. – Journal of Science and Mathematics Education in Southeast Asia, 2019
Purpose: This study presents the competence level of education students in College Geometry and the development of a Computer Generated Instructional Materials (CGIM). Method: This research used the model for research and development by Borg and Gall (2003) with revision. The researchers developed a CGIM, specifically, the worktext paired with…
Descriptors: College Students, College Mathematics, Geometry, Mathematics Skills
Nathan, Mitchell J.; Schenck, Kelsey E.; Vinsonhaler, Rebecca; Michaelis, Joseph E.; Swart, Michael I.; Walkington, Candace – Grantee Submission, 2020
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…
Descriptors: Mathematical Logic, Validity, Geometry, Knowledge Level
Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2018
The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…
Descriptors: Teaching Methods, Validity, Mathematical Logic, High School Students
Leung, Kui Chiu Issic; Lee, Chun Yeung – Mathematics Teacher Education and Development, 2017
By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful…
Descriptors: Mathematics Instruction, Preservice Teachers, Beginning Teachers, Knowledge Level
Williams, Caroline C.; Walkington, Candace; Boncoddo, Rebecca; Srisurichan, Rachaya; Pier, Elizabeth; Nathan, Mitchell; Alibali, Martha – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
The role of reasoning and proof in mathematics is undeniably crucial, and yet research in mathematics education has repeatedly indicated that students struggle with proof production. Our research shows that proof activities can be illuminated by considering action and gesture as a modality for crucial aspects of mathematical communication. We…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Nonverbal Communication
Zandieh, Michelle; Roh, Kyeong Hah; Knapp, Jessica – North American Chapter of the International Group for the Psychology of Mathematics Education, 2011
We explore ways that university students handle proving statements that have the overall structure of a conditional implies a conditional, i.e., (p [right arrow] q) [implies] (r [right arrow] s). We structure our analysis using the theory of conceptual blending. We find conceptual blending useful for describing the creation of powerful new ideas…
Descriptors: College Students, Mathematical Logic, Validity, College Mathematics
Koichu, Boris – International Journal of Mathematical Education in Science and Technology, 2010
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
Descriptors: Mathematics Education, Problem Solving, Calculus, Knowledge Level
Hollebrands, Karen F.; Conner, AnnaMarie; Smith, Ryan C. – Journal for Research in Mathematics Education, 2010
Prior research on students' uses of technology in the context of Euclidean geometry has suggested that it can be used to support students' development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships…
Descriptors: Geometric Concepts, Geometry, College Mathematics, College Students
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