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Giovanni Vincenzi – International Journal of Mathematical Education in Science and Technology, 2025
Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…
Descriptors: Mathematical Logic, Validity, Numbers, Mathematics
Montero-Moguel, Luis E.; Vargas-Alejo, Verónica; Carmona Domínguez, Guadalupe – North American Chapter of the International Group for the Psychology of Mathematics Education, 2021
This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…
Descriptors: Mathematical Models, College Students, Mathematics, Numbers
Ghergu, Marius – International Journal of Mathematical Education in Science and Technology, 2018
We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.
Descriptors: Mathematics, Mathematics Instruction, Mathematical Concepts, Numbers
Herzinger, K.; Kunselman, C.; Pierce, I. – International Journal of Mathematical Education in Science and Technology, 2018
Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…
Descriptors: Algebra, Mathematics Instruction, Mathematical Formulas, Mathematics
Nel, Benita P. – South African Journal of Education, 2020
Learners intending to enter some higher education (HE) institutions in South Africa write the National Benchmark Tests (NBTs) that are expected to provide a measure of their readiness for HE. A large gap exists between the quantitative literacy competencies of many of these learners and expectations at HE level. In this article I explore the…
Descriptors: Benchmarking, Foreign Countries, College Readiness, College Bound Students
Tempier, Frédérick – Journal of Mathematics Teacher Education, 2016
Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…
Descriptors: Mathematics, Mathematical Concepts, Mathematics Instruction, Mathematical Logic
Fagan, Emily R.; Tobey, Cheryl Rose; Brodesky, Amy R. – Teaching Children Mathematics, 2016
This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…
Descriptors: Formative Evaluation, Individualized Instruction, Mathematics, Mathematics Instruction
Soares, A.; dos Santos, A. L. – International Journal of Mathematical Education in Science and Technology, 2017
In this article, we revisit the concept of strong differentiability of real functions of one variable, underlying the concept of differentiability. Our discussion is guided by the Straddle Lemma, which plays a key role in this context. The proofs of the results presented are designed to meet a young audience in mathematics, typical of students in…
Descriptors: Introductory Courses, Mathematics Instruction, Calculus, Mathematical Logic
Sears, Ruthmae; Kersaint, Gladis; Burgos, Fernando; Wooten, Rebecca – PRIMUS, 2019
This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…
Descriptors: Middle School Mathematics, Preservice Teachers, Knowledge Level, Mathematics Education
Goldenberg, E. Paul; Carter, Cynthia J. – Mathematics Teacher, 2017
A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…
Descriptors: Algebra, Secondary School Mathematics, Numbers, Mathematics Teachers
Moru, Eunice Kolitsoe; Nchejane, John; Ramollo, Motlatsi; Rammea, Lisema – African Journal of Research in Mathematics, Science and Technology Education, 2017
The reported study explored undergraduate science students' validation and comprehension of written proofs, reasons given either to accept or reject mathematical procedures employed in the proofs, and the difficulties students encountered in reading the proofs. The proofs were constructed using both the Comparison and the Integral tests in the…
Descriptors: Undergraduate Students, College Students, Mathematical Logic, Validity
Breda, Ana Maria D'azevedo; Dos Santos, José Manuel Dos Santos – Teaching Mathematics and Its Applications, 2016
Complex functions, generally feature some interesting peculiarities, seen as extensions of real functions. The visualization of complex functions properties usually requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the…
Descriptors: Mathematics Instruction, Geometry, Algebra, Computer Software
de Moura Fonseca, Daila Silva Seabra; de Oliveira Lino Franchi, Regina Helena – Teaching Mathematics and Its Applications, 2016
This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…
Descriptors: Geometric Concepts, Geometry, Algebra, Computer Software
Grant, Ken – Australian Senior Mathematics Journal, 2015
In 1859, on the occasion of being elected as a corresponding member of the Berlin Academy, Bernard Riemann (1826-66), a student of Carl Friedrich Gauss (1777-1855), presenteda lecture in which he presented a mathematics formula, derived from complex integration, which gave a precise count of the primes on the understanding that one of the terms in…
Descriptors: Mathematical Formulas, Mathematics, Numbers, Equations (Mathematics)
Zazkis, Rina; Zazkis, Dov – Research in Mathematics Education, 2014
Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…
Descriptors: Numbers, Mathematics, Teacher Education, Mathematics Education