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Kar, Tugrul; Güler, Gürsel; Sen, Ceylan; Özdemir, Ercan – International Journal of Mathematical Education in Science and Technology, 2018

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, "Everyday Mathematics" (EM) and "Connected Mathematics 3" (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems…

Descriptors: Multiplication, Fractions, Textbook Evaluation, Textbook Content

García-García, Javier; Dolores-Flores, Crisólogo – International Journal of Mathematical Education in Science and Technology, 2018

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Descriptors: Foreign Countries, High School Students, Mathematics Skills, Calculus

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén – International Journal of Mathematical Education in Science and Technology, 2018

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

Descriptors: Geometry, Mathematics, Mathematics Instruction, Geometric Concepts

Caglayan, Günhan – International Journal of Mathematical Education in Science and Technology, 2018

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space R[superscript m x n] in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools…

Descriptors: Algebra, Class Activities, Mathematics Instruction, Computer Uses in Education

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Descriptors: Mathematics, History, College Freshmen, College Science

Ruiz-López, Natalia – International Journal of Mathematical Education in Science and Technology, 2018

This paper, which describes a study undertaken with pairs of future primary teachers using GeoGebra software to solve geometry problems, includes a brief literature review, the theoretical framework and methodology used. An analysis of the instrumental genesis process for a pair participating in the case study is also provided. This analysis…

Descriptors: Geometry, Computer Software, Computer Uses in Education, Preservice Teachers

Howard, Emma; Meehan, Maria; Parnell, Andrew – International Journal of Mathematical Education in Science and Technology, 2018

In "Maths for Business", a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students' specific usage patterns with both of these resources and discuss their reasons for the…

Descriptors: Lecture Method, Mathematics Instruction, Foreign Countries, Mixed Methods Research

Flores, Alfinio; Park, Jungeun – International Journal of Mathematical Education in Science and Technology, 2018

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

Descriptors: Geometry, Mathematics Instruction, Geometric Concepts, Prediction

Cunningham, Daniel W. – International Journal of Mathematical Education in Science and Technology, 2018

Modern calculus textbooks carefully illustrate how to perform integration by trigonometric substitution. Unfortunately, most of these books do not adequately justify this powerful technique of integration. In this article, we present an accessible proof that establishes the validity of integration by trigonometric substitution. The proof offers…

Descriptors: Mathematics Education, Trigonometry, Calculus, Mathematical Concepts

de Camargo, André Pierro – International Journal of Mathematical Education in Science and Technology, 2018

In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…

Descriptors: Mathematics Education, Calculus, Mathematical Logic, Equations (Mathematics)

Green, Simon; McGlynn, Susan; Stuart, Deidre; Fahey, Paul; Pettigrew, Jim; Clothier, Peter – International Journal of Mathematical Education in Science and Technology, 2018

The effect of high school study of mathematics on numeracy performance of sports and exercise science (SES) students is not clear. To investigate this further, we tested the numeracy skills of 401 students enrolled in a Bachelor of Health Sciences degree in SES using a multiple-choice survey consisting of four background questions and 39 numeracy…

Descriptors: High School Students, Mathematics Education, Numeracy, Mathematics Tests

O'Meara, Niamh; Prendergast, Mark – International Journal of Mathematical Education in Science and Technology, 2018

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide…

Descriptors: Foreign Countries, Time Management, Secondary School Mathematics, Mathematics Education

Ferrarello, Daniela; Mammana, Maria Flavia; Pennisi, Mario – International Journal of Mathematical Education in Science and Technology, 2018

In this paper, we show some properties of centroids of geometric figures, such as triangles, quadrilaterals and tetrahedra. In particular, we will prove the properties by means of geometric transformations and by introducing extensions of triangles and quadrilaterals, i.e. by adding one, two or three new vertices to the figure. The study of these…

Descriptors: Geometric Concepts, Transformations (Mathematics), Secondary School Mathematics, Mathematics Instruction

Shahbari, Juhaina Awawdeh – International Journal of Mathematical Education in Science and Technology, 2018

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers'…

Descriptors: Mathematics Instruction, Mathematics Teachers, Teacher Attitudes, Beliefs

Pujol, Jose – International Journal of Mathematical Education in Science and Technology, 2018

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

Descriptors: Mathematics Instruction, Algebra, Geometric Concepts, Problem Solving