Peer assessment has great potential to improve student learning. However, assessment is not an everyday activity for students, and thus providing appropriate guidance to students is a key component of creating a successful peer assessment experience. This paper explores how to structure peer feedback in the guided process Peer-Assisted Reflection…

Academic programs targeted for first-time students can help their persistence in STEM majors. Our project, ASCEND STEM, included three first-year experiences (FYEs) designed to offer students the skills that would help them successfully traverse potential barriers to academic success. In the FYEs, we sought to strengthen the learning power,…

A student, Stuart, related perimeter to pixels and the professor, Beth, moved back and forth between "reserved believing" and "reserved doubting" and "doubting" teacher actions (Elbow, 1986; Harkness & Noblitt, 2017) while assessing the merit of his conjecture in the moment. Video allowed the researchers to…

Tutorials/discussion classes are seen as an essential part of the teaching mix in the natural sciences, because that is where problems can be solved and course content is applied. Learning support provided by teaching assistants may free up the lecturer to do research, but are these assistants sufficiently well trained and well informed? Do…

The University of Wollongong's first locally developed and hosted Massive Open Online Course (MOOC) "The Reluctant Mathematician" was run in the last four weeks of our summer holiday, prior to Autumn session in 2014. It was developed to lift maths skills at our university and also in the community--where maths skills continue to be a…

We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the…

Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Teachers often promote care in doing calculations, but for most students a single mistake rarely has major consequences. This article presents several real-life events in which relatively minor mathematical errors led to situations that ranged from public embarrassment to the loss of millions of dollars' worth of equipment. The stories here…

Estimating the effect of campus math tutoring support, this study demonstrates the use of propensity score weighted and matched-data analysis and examines the correspondence with results from parametric regression analysis.

This paper demonstrates how questions of "provability" can help students engaged in reinvention of mathematical theory to understand the axiomatic game. While proof demonstrates how conclusions follow from assumptions, "provability" characterizes the dual relation that assumptions are "justified" when they afford…

A new law, Assembly Bill 705 (Irwin), is driving dramatic changes in how California Community Colleges place students into English and math courses. Beginning in fall 2019, AB 705 requires the colleges to use students' high school grades as the primary means of placement; restricts colleges from denying students access to transferable,…

Analyses of literacy and numeracy levels worldwide by the Organisation for Economic Cooperation and Development suggest that the U.S. population has one of the lowest numeracy levels among developed nations. Sixty-four percent of American adults are unable to use math and interpret math problems that most higher-level jobs require, and a full 30…

Many college students are required to take at least one developmental math course, but as many as half of them fail to complete their developmental math requirements and never matriculate into college-level courses. To address this issue, the Charles A. Dana Center at the University of Texas at Austin created the Dana Center Mathematics Pathways…