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Burns-Childers, Annie; Vidakovic, Draga – International Journal of Mathematical Education in Science and Technology, 2018

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Protocol Analysis

Zeynivandnezhad, Fereshteh; Bates, Rachel – International Journal of Mathematical Education in Science and Technology, 2018

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…

Descriptors: Mathematics Instruction, Equations (Mathematics), Computer Uses in Education, Educational Technology

Hyland, Diarmaid; van Kampen, Paul; Nolan, Brien C. – International Journal of Mathematical Education in Science and Technology, 2018

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore,…

Descriptors: Foreign Countries, Outcomes of Education, Teaching Methods, Equations (Mathematics)

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

Leavy, Aisling; Hourigan, Mairead – International Journal of Mathematical Education in Science and Technology, 2018

Mathematics education research has given increasing attention to the role of affective factors in the learning process. While 'affect' is used to refer to a variety of aspects including feelings, emotions, beliefs, attitudes and conceptions, this paper focuses on 'beliefs' of elementary pre-service teachers. In particular, the study evaluates the…

Descriptors: Mathematics Instruction, Teacher Education Programs, Elementary School Teachers, Preservice Teachers

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki – International Journal of Mathematical Education in Science and Technology, 2018

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus…

Descriptors: Calculus, Mathematical Concepts, Imagery, Schemata (Cognition)

Bicer, Ali; Capraro, Robert M.; Capraro, Mary M. – International Journal of Mathematical Education in Science and Technology, 2018

The purpose of this paper is to demonstrate Hispanic students' mathematics achievement growth rate in Inclusive science, technology, engineering, and mathematics (STEM) high schools compared to Hispanic students' mathematics achievement growth rate in traditional public schools. Twenty-eight schools, 14 of which were Texas STEM (T-STEM) academies…

Descriptors: Hispanic American Students, STEM Education, Mathematics Achievement, Achievement Gains

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2018

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…

Descriptors: Mathematics Instruction, Calculus, Problem Solving, Case Studies

Gkioulekas, Eleftherios – International Journal of Mathematical Education in Science and Technology, 2018

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original…

Descriptors: Problem Solving, Equations (Mathematics), Mathematical Concepts, Algebra

Vandenbussche, J.; Ritter, L.; Scherrer, C. – International Journal of Mathematical Education in Science and Technology, 2018

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Descriptors: Calculus, Mathematics Instruction, Remedial Mathematics, At Risk Students

Abernethy, Gavin M. – International Journal of Mathematical Education in Science and Technology, 2018

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.

Descriptors: Mathematical Models, Mathematics, Equations (Mathematics), Mathematical Concepts

Prendergast, Mark; Breen, Cormac; Bray, Aibhin; Faulkner, Fiona; Carroll, Brian; Quinn, Dominic; Carr, Michael – International Journal of Mathematical Education in Science and Technology, 2018

Many studies over the past 30 years have highlighted the important role of students' beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students' (n = 975) beliefs about the…

Descriptors: Secondary School Students, Beliefs, Student Attitudes, Mathematics Education

Turgut, Melih – International Journal of Mathematical Education in Science and Technology, 2018

In this work, students' thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students' thinking modes and representation types of linear algebra. The participants were 74 undergraduate…

Descriptors: Interaction, Algebra, Correlation, Undergraduate Students

Umugiraneza, Odette; Bansilal, Sarah; North, Delia – International Journal of Mathematical Education in Science and Technology, 2018

Paying attention to the planning of lessons represents a crucial teaching task. This paper analyses teachers' framing of lesson objectives and their descriptions of how they would introduce particular mathematics topics. Connections between the objectives and the instructional strategies employed, were also studied. The study involved 75 South…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Mathematics Teachers

Olteanu, Constanta – International Journal of Mathematical Education in Science and Technology, 2018

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

Descriptors: Arithmetic, Mathematics Instruction, Mathematical Models, Problem Solving