This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

Preservice teachers study an academic discipline (e.g. mathematics) and -- just like students majoring in that discipline -- have a certain level of connectedness to it. While studying, students may compare themselves to peers studying the same discipline within alternative degree programs, characterized by different study contexts. Notably,…

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,…

The University of Minnesota Talented Youth Mathematics Program (UMTYMP) is a selective, five-year accelerated mathematics program for students in grades 6-12. During the program, students take college mathematics courses on University of Minnesota campuses, starting with algebra and continuing through logic and proofs, linear algebra, and…

This study focuses on the potential of university mathematics courses to advance teachers' knowledge regarding an important component of knowledge about the nature of mathematics as a scientific discipline, namely the mutual contribution between mathematics and various fields: mathematics contributes to solving problems in different fields, and…

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

In the mathematical community, two notions of "function" are used: the set-theoretic definition as a univalent set of ordered pairs, and the Bourbaki triple. These definitions entail different interpretations and answers to mathematical questions that even a secondary student might be prompted to answer. However, mathematicians and…

The purpose of this study was to investigate the gender differences in students' attitude toward mathematics and how attitude impacts achievement in the course. The sample consisted of 172 undergraduate health science students (123 women, 49 men) enrolled in mathematics courses at a University in the Midwestern United States. Data were collected…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

The widely used Draw a Scientist Test was revised to focus on statistics and 110 Elementary Statistics students were asked to draw a statistician. In addition, to better understand students' drawings and have some relative comparison, 173 College Algebra students were asked to draw a mathematician. A detailed analysis of students' images and…

To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete…

This paper reports the results of three questionnaires applied to sixty-seven students preparing to become university-level mathematics teachers; the questionnaires were focused on knowing their conceptions and their mastery of the representations of functions in the development of power series. The theoretical and methodological background rests…

Despite the function concept being fundamental to mathematics, an adequate understanding of this concept is often lacking. This problem is prevalent at all levels of education and is reported in many countries. This article reports on a new pedagogical strategy based on exploring photographs or digital images as functions. The objective of this…

To prevent difficulties in learning mathematics, effective and innovative teaching methodologies should be used. The present study presents the results of a relational and comparative study between the application of the open number-based algorithm (ABN) and the closed number-based algorithm (CNB) method. The research was of a descriptive…

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First,…