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Oxman, Victor; Sigler, Avi – International Journal of Mathematical Education in Science and Technology, 2021
In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…
Descriptors: Geometry, Mathematics Instruction, Validity, Mathematical Logic
Yan, Xiaoheng; Zazkis, Rina – International Journal of Mathematical Education in Science and Technology, 2022
Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Algebra
Philip Slobodsky; Mariana Durcheva – International Journal for Technology in Mathematics Education, 2023
The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…
Descriptors: Mathematics Instruction, Learning Processes, Algebra, Validity
Kimberly Dwyer; Angela M. Kelly – Journal for Research in Mathematics Education, 2025
This quantitative correlational study examines school-level longitudinal outcomes of eighth-grade algebra universal acceleration in 15 U.S. school districts when compared with selective acceleration in 289 school districts. Universally accelerated school districts had higher enrollments, with large effect sizes, in geometry, algebra 2, and…
Descriptors: Algebra, Grade 8, Mathematics Instruction, Acceleration (Education)
Simsek, Zulfiye Zeybek – International Journal for Mathematics Teaching and Learning, 2020
This study focused on investigating the ability of 58 pre-service mathematics teachers (PSMTs) to construct-evaluate-refine mathematical conjectures and proofs. The PSMTs enrolled in a three-credit mathematics education course that offered various opportunities to engage with mathematical activities including constructing-evaluating-refining…
Descriptors: Preservice Teachers, Mathematics Teachers, Mathematical Logic, Validity
Oxman, Victor; Stupel, Moshe; Weissman, Shula – International Journal of Mathematical Education in Science and Technology, 2021
The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…
Descriptors: Mathematics Instruction, Teaching Methods, Computer Assisted Instruction, Geometry
Petrilli, Salvatore J., Jr. – PRIMUS, 2021
The Department of Mathematics and Computer Science at Adelphi University engaged in a year-long program revision of its mathematics major, which was initiated by a longitudinal study and the publication of the 2015 Curriculum Guide by the MAA's Committee on Undergraduate Programs in Mathematics. This paper stands as a short story, so to speak, of…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, 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
Akkurt, Yasemin Yilmaz; Durmus, Soner – Journal of Research and Advances in Mathematics Education, 2022
The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…
Descriptors: Validity, Mathematical Logic, Mathematics Instruction, Classification
Julius, Rafael; Halim, Muhammad Syawal Abd; Hadi, Normi Abdul; Alias, Azrul Nizam; Khalid, Muhammad Hafiz Mohd; Mahfodz, Zulfadli; Ramli, Fariesha Farha – EURASIA Journal of Mathematics, Science and Technology Education, 2021
This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…
Descriptors: Bibliometrics, Mathematics Education, Databases, Algebra
Kanellos, Ioannis; Nardi, Elena; Biza, Irene – Mathematical Thinking and Learning: An International Journal, 2018
In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture…
Descriptors: Secondary School Students, Secondary School Mathematics, Validity, Mathematical Logic
Sachs, Robert – PRIMUS, 2017
A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the "complex precalculus" part of the course. In…
Descriptors: Mathematics Instruction, Undergraduate Study, Validity, Mathematical Logic
Oxman, Victor; Stupel, Moshe – International Journal of Mathematical Education in Science and Technology, 2018
A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive 'mathematical toolbox'. Investigation of the property that appears in the task was carried out using a computerized tool.
Descriptors: Mathematics Instruction, Problem Solving, Geometry, Algebra
Askey, Richard; Matsuura, Ryota; Sword, Sarah – Mathematics Teacher, 2015
NCTM's Connections Standard recommends that students in grades 9-12 "develop an increased capacity to link mathematical ideas and a deeper understanding of how more than one approach to the same problem can lead to equivalent results, even though the approaches might look quite different" (NCTM 2000, p. 354). In this article, the authors…
Descriptors: Arithmetic, Geometry, Mathematics Instruction, Mathematical Concepts
Weiss, Michael – Mathematics Teacher, 2016
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
Descriptors: Algebra, Mathematics, Mathematical Formulas, Mathematics Teachers