We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read and discuss mathematics critically, reach a consensus on correctness and clarity as a group, and verbalize what…

A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways.…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was…

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

Previous studies have shown that students who have completed differential and integral calculus often accept and employ empirical arguments as proofs, but this is not the case for students who have had at least one upper-level proof course; these students tend toward the use of deductive proofs. This paper finds that a majority of the students…

We have observed that over 90% of our students, both undergraduate and graduate, know little about the existence and multiplicity of real roots of real numbers; for example the fifth root of -2. Most of those who may know the answers are unable to give a logical explanation of the validity of their answers.

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,…

This research is generally conducted to solve the difficulties of students in understanding courses in mathematics education especially in the real analysis course, in addition, this research specifically aims to examine, describe and compare differences in the ability to think mathematically critically between students who obtain learning concept…

While proof is often presented to mathematics undergraduates as a well-defined mathematical object, the proofs students encounter in different pedagogical contexts may bear salient differences. In this paper we draw on the work of Dawkins and Weber (2017) to explore variations in norms and values underlying a proof across different pedagogical…

The Math Immersion intervention was designed to aid the transition-to-proof phase of the undergraduate mathematics major. The Immersion was co-taught by two instructors, one for Intro to Proofs and Abstract Algebra and another for Probability and Statistics and Linear Algebra. This case study documented that efficiency gains directly attributable…

Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original problem setting (Wild and Pfannkuch, Int Stat Rev 67(3):223-248, 1999). Assessment in introductory statistics…

For several decades, literature on the history and pedagogy of mathematics has described how history of mathematics is beneficial for the teaching and learning of mathematics. We investigated the influence of a history and philosophy of mathematics (HPhM) course on students' progress through the lens of various competencies in mathematics (e.g.,…

As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof. We examine some of the reasons behind this discrepancy and to what degree it affects doing, teaching and learning mathematics in college. We also…