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Katalenic, Ana; Cižmešija, Aleksandra; Milin Šipuš, Željka – International Journal of Science and Mathematics Education, 2023
This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a "reference epistemological model" to describe the knowledge about asymptotes for upper secondary…
Descriptors: Preservice Teachers, Mathematics Teachers, Knowledge Level, Mathematical Concepts
Hong, Dae S. – International Journal of Science and Mathematics Education, 2023
We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…
Descriptors: Calculus, Mathematics Instruction, Mathematics Teachers, Genetics
Özgeldi, Meriç; Aydin, Utkun – International Journal of Science and Mathematics Education, 2021
This study investigates how three widely used calculus textbooks realise integrals as a potential to prompt mathematical competencies, adapting the rating scheme used in Boesen et al. ("The Journal of Mathematical Behavior," 33:72-87, 2014), Pettersen and Braeken ("International Journal of Science and Mathematics Education,"…
Descriptors: Mathematics Instruction, Calculus, Textbook Content, Textbooks
Jones, Steven R. – International Journal of Science and Mathematics Education, 2019
The calculus concepts of concavity and inflection points are critical for a complete understanding of quantities' behavior, making them important topics of research for those interested in the intersections of STEM disciplines. This study seeks to provide insight into this area by reporting on trends in students' concept projections of these…
Descriptors: Calculus, Mathematical Concepts, STEM Education, Concept Formation
Adu-Gyamfi, Kwaku; Bossé, Michael J.; Chandler, Kayla – International Journal of Science and Mathematics Education, 2017
When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…
Descriptors: Mathematics Skills, Mathematical Concepts, Algebra, Graphs
Jones, Steven R.; Lim, YaeRi; Chandler, Katie R. – International Journal of Science and Mathematics Education, 2017
Past research in calculus education has shown that Riemann sum-based conceptions of the definite integral, such as the multiplicatively based summation (MBS) conception, can have important value in interpreting and making sense of certain types of definite integral expressions. However, additional research has shown that students tend to not draw…
Descriptors: Calculus, Concept Teaching, Mathematical Concepts, Introductory Courses
Dahl, Bettina – International Journal of Science and Mathematics Education, 2017
Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…
Descriptors: College Freshmen, Nonmajors, STEM Education, Definitions
Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi – International Journal of Science and Mathematics Education, 2016
Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…
Descriptors: Calculus, Textbooks, Teaching Methods, Mathematics Instruction
McGee, Daniel Lee; Moore-Russo, Deborah – International Journal of Science and Mathematics Education, 2015
In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of…
Descriptors: Mathematics Instruction, Mathematical Concepts, Calculus, Semiotics
Verhoef, Nellie; Tall, David; Coenders, Fer; van Smaalen, Daan – International Journal of Science and Mathematics Education, 2014
This study combines the Japanese lesson study approach and mathematics teachers' professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of…
Descriptors: Foreign Countries, Mathematics Instruction, Teaching Methods, Lesson Plans
Calculus Students' and Instructors' Conceptualizations of Slope: A Comparison across Academic Levels
Nagle, Courtney; Moore-Russo, Deborah; Viglietti, Janine; Martin, Kristi – International Journal of Science and Mathematics Education, 2013
This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…
Descriptors: Calculus, Qualitative Research, Mathematical Concepts, College Students
Garcia, Mercedes; Llinares, Salvador; Sanchez-Matamoros, Gloria – International Journal of Science and Mathematics Education, 2011
This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between…
Descriptors: Evidence, Undergraduate Students, Correlation, Mathematics