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Oehrtman, Michael; Soto-Johnson, Hortensia; Hancock, Brent – International Journal of Research in Undergraduate Mathematics Education, 2019

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics…

Descriptors: Mathematical Concepts, Abstract Reasoning, Mathematical Applications, Theories

Melhuish, Kathleen – International Journal of Research in Undergraduate Mathematics Education, 2019

Introductory group theory provides the foundational course on algebraic structures. Yet, we know little about students' underlying conceptual understandings. In this paper, I introduce the Group Theory Concept Assessment (GTCA), a measure created for the purpose of conducting large-scale studies of student conceptual understanding in group theory.…

Descriptors: Algebra, Mathematical Concepts, Mathematical Logic, Knowledge Level

Chorlay, Renaud – International Journal of Research in Undergraduate Mathematics Education, 2019

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students,…

Descriptors: Definitions, Foreign Countries, Didacticism, Educational Experiments

Dawkins, Paul Christian; Oehrtman, Michael; Mahavier, W. Ted – International Journal of Research in Undergraduate Mathematics Education, 2019

In this paper, we provide an in-depth account of traditional IBL instruction. Understanding the nature and effects of this form of instruction is of growing importance due to the strength and breadth of the IBL movement and its connections to other forms of inquiry in undergraduate mathematics. In this case study of one real analysis course taught…

Descriptors: Active Learning, Inquiry, Student Experience, Undergraduate Students

Deshler, Jessica; Fuller, Edgar; Darrah, Marjorie – International Journal of Research in Undergraduate Mathematics Education, 2019

The identification of factors that impact student success in mathematics courses has been a focus of a great deal of research since the early 2000s. The role of classroom approaches, teacher beliefs, and underlying student backgrounds have been studied in different ways. As a part of this effort researchers have studied the degree to which…

Descriptors: Affective Behavior, College Students, Remedial Mathematics, Self Efficacy

Melhuish, Kathleen; Larsen, Sean; Cook, Samuel – International Journal of Research in Undergraduate Mathematics Education, 2019

Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…

Descriptors: Mathematical Logic, Problem Solving, Algebra, Error Patterns

Schüler-Meyer, Alexander – International Journal of Research in Undergraduate Mathematics Education, 2019

In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses…

Descriptors: Learning Processes, Arithmetic, College Mathematics, Secondary School Mathematics

Kuster, George; Johnson, Estrella; Rupnow, Rachel; Wilhelm, Anne Garrison – International Journal of Research in Undergraduate Mathematics Education, 2019

Here we report on the development process of the Inquiry Oriented Instructional Measure (IOIM), an instrument for scoring a lesson along seven inquiry-oriented instructional practices. The development of the IOIM was a multi-phase, iterative process that included reviewing K-16 research literature, analyzing videos of classroom instruction, and…

Descriptors: Teaching Methods, Inquiry, Undergraduate Study, Pilot Projects

Reinholz, Daniel L.; Bradfield, Kenneth; Apkarian, Naneh – International Journal of Research in Undergraduate Mathematics Education, 2019

This paper describes a method for using instructional analytics to support changes in teaching practice. The study took place in a discourse-focused undergraduate mathematics classroom taught by an experienced instructor. Using the classroom observation tool EQUIP and social network surveys, we generated quantitative data on patterns of student…

Descriptors: Educational Change, Teaching Methods, Student Participation, Student Experience

Lahdenperä, Juulia; Postareff, Liisa; Rämö, Johanna – International Journal of Research in Undergraduate Mathematics Education, 2019

Prior research acknowledges the need to further develop undergraduate mathematics instruction. The aim of this study is to investigate the relationship between instructional design and quality of learning. This quantitative study approaches the learning environment by comparing students' approaches to learning, self-efficacy, and experiences of…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Instructional Design

Troup, Jonathan – International Journal of Research in Undergraduate Mathematics Education, 2019

In this study, a description is provided for the development of two undergraduate students' geometric reasoning about the derivative of a complex-valued function with the aid of "Geometer's Sketchpad" ("GSP") during an interview sequence designed to help them characterize the derivative geometrically. Specifically, a particular…

Descriptors: Geometric Concepts, Mathematics Instruction, Educational Technology, Technology Uses in Education

Kempen, Leander; Biehler, Rolf – International Journal of Research in Undergraduate Mathematics Education, 2019

At the University of Paderborn, the course "Introduction into the culture of mathematics" is required for all first-year students who enter the study program for future mathematics teachers at lower secondary level (grade 5-10). In this inquiry-based transition-to-proof course, we use four different kinds of proofs (the generic proof…

Descriptors: Foreign Countries, College Freshmen, College Mathematics, Required Courses

Faulkner, Brian; Earl, Katherine; Herman, Geoffrey – International Journal of Research in Undergraduate Mathematics Education, 2019

Facing increased pressure to improve retention and graduation rates, engineering departments are increasingly scrutinizing whether they are getting their desired outcomes from core mathematics coursework. Since mathematics courses are a significant source of attrition and many engineering faculty are unhappy with students' mathematical abilities,…

Descriptors: Engineering Education, Mathematics Education, College Mathematics, College Faculty

Laursen, Sandra L.; Rasmussen, Chris – International Journal of Research in Undergraduate Mathematics Education, 2019

In the United States (US) and elsewhere across the world, undergraduate mathematics instructors are increasingly aware of the value of inquiry-based instruction. In this research commentary, we describe the intellectual origins and development of two major strands of inquiry in US higher education, offer an explanation for apparent differences in…

Descriptors: Active Learning, Inquiry, College Mathematics, Undergraduate Students

Iannone, Paola; Simpson, Adrian – International Journal of Research in Undergraduate Mathematics Education, 2019

Existing research posits a relationship between undergraduate mathematics students' mathematics-related epistemological beliefs and their perceptions of summative assessment. This paper reports a study investigating whether there is indeed such a relationship. First and second year mathematics undergraduate students at two universities in the UK…

Descriptors: Epistemology, Beliefs, Summative Evaluation, Preferences