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Challenging mathematics problems were posed as a substantial part of homework in an elective combinatorics course. The intent was to encourage undergraduate students' exploration as well as develop their technical writing skills. The bulk of students' grades on these problems rested on a three-page reflective write-up using a rubric on mathematical creativity, the Creativity-in-Progress Rubric on Proving. Through student reflections, this structure led to a self-reported boost in students' proving confidence and led them to view themselves as practicing mathematicians. Descriptions of the problems, how students used the rubric as their guide, and grading structure are detailed in this article.

A growing body of mathematics education research points to the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative assessment tool, the "Creativity-in-Progress Rubric (CPR) on Proving". This tool is developed to help students evaluate their own proving process, as well as provide instructors insight into students' self-evaluation and process. In this paper, we provide a brief description of the CPR on Proving and explain its implementation in two courses at different institutions. Additionally, we share several students' usages of the CPR and provide some practical implementation suggestions.

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course instructors, including one pre-activity reflection assignment, three modeling activities, and a final project. The Pre-Activity Assignment engages students to draw on their own personal and/or cultural experiences with the concept of love. Three activities focus on developing revision skills in mathematical modeling and practicing methods of solving systems of ordinary differential equations (ODEs). In these activities, students would collaborate to construct a relationship model consisting of a system of first-order linear ODEs and solve different model iterations with the characteristic polynomial, matrix form, or Laplace transform method. The final project connects the reflections in Pre-Activity Assignment with the skills developed in the three activities by inviting students to create a relationship scenario, model, revise, solve it, and present the conclusions. By engaging in this set of assignments, students connect personal and cultural experiences with the concept of love and perceive themselves and their peers in the curriculum, fostering a sense of belonging and relevance. [ABSTRACT FROM AUTHOR]

Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom.

A growing body of mathematics education research points to the importance of fostering students’ mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative assessment tool, theCreativity-in-Progress Rubric(CPR)on Proving. This tool is developed to help students evaluate their own proving process, as well as provide instructors insight into students’ self-evaluation and process. In this paper, we provide a brief description of the CPR on Proving and explain its implementation in two courses at different institutions. Additionally, we share several students’ usages of the CPR and provide some practical implementation suggestions. [ABSTRACT FROM PUBLISHER]

Abdominal aortic aneurysm (AAA) repair may be performed through open or endovascular approaches, but the factors influencing a patient's repair-type preference are not well characterized. Here we performed a qualitative analysis to better understand factors influencing patient preference within the Preference for Open Versus Endovascular Repair of AAA Trial. Open-ended responses regarding primary (n = 21) and secondary (n = 47) factors influencing patient preference underwent qualitative analysis using the constant comparative method with iterative reviews. Codes were used to generate themes and themes grouped into categories, with each step conducted via consensus agreement between three researchers. Relative prevalence of themes were compared to ascertain trends in patient preference. Patient responses regarding both primary and secondary factors fell into four categories: Short-term concerns, long-term concerns, advice & experience, and other. Patients most frequently described short-term concerns (23) as their primary influence, with themes including post-op complications, hospitalization & recovery, and intraoperative concerns. Long-term concerns were more prevalent (20) as secondary factors, which included themes such as survival, and chronic management. The average age of patients voicing only long-term concerns as a primary factor was 11 years younger than those listing only short-term concerns. Short-term concerns relating to the procedure and recovery are more often the primary factor influencing patient preference, while long term concerns play a more secondary role. Long-term concerns are more often a primary factor in younger patients. Vascular surgeons should consider this information in shared decision making to reach an optimal outcome. [ABSTRACT FROM AUTHOR]