• An Inquiry-Based Approach to Teaching Introduction to Proof

      Gentle, Adrian P.
      In recent years I have become increasingly dissatisfied with the depth of engagement and student learning in my classes. As a result, in fall 2016 I implemented an inquiry-based learning (IBL) approach to teaching introduction to proof, a required course for mathematics majors which aims to introduce students to careful mathematical reasoning and transition them away from an algorithmic view of mathematics. IBL engages students in guided discovery, and in this talk I describe my transition to this evidence-based, student-centered approach. Rather than follow a traditional textbook, students work through carefully sequenced notes which contain key definitions and statements of important theorems, and students are required to construct proofs and solve non-trivial problems. Class time is spent with students presenting their work on the board, or working in small groups, with students responsible for building understanding through discussion and questioning. A significant increase in student engagement and community was observed in the first semester of the IBL class. I will discuss what worked and what did not, and argue that a transition to evidence-based teaching not only benefits students, but provides instructors with an opportunity to revitalize their classrooms.
    • Does Precalculus Hurt More Than It Helps?

      Gentle, Adrian P.; Wilding, William
      Precalculus is intended as a rigorous preparation for calculus, developing students abstract reasoning skills, algebraic thinking, and deepening their understanding of a variety of mathematical functions. We ask whether USIs precalculus courses are achieving these goals. In a recent national study, Bressoud (2014) found that success rates in precalculus are relatively low, while only 50-60% of those who succeed in precalculus actually continue to calculus. For the students who do make it to calculus, there is evidence that precalculus does little to increase their chances of success, and the additional semester may actively discourage some students, especially those from underrepresented groups (Sonnert and Sadler, 2014). In light of these studies, we investigate the effects of precalculus at USI on students attitudes towards mathematics, and their subsequent performance in Calculus I. We present preliminary data on student attitudes gathered over several semesters in USIs three credit-hour precalculus course. While we observe a negative impact on attitudes towards mathematics, these changes are not out of line with previous studies (Sonnert 2015). Using a decade of data on student grades in USIs Calculus I course, we match students by SAT score and then compare success rates in Calculus I for the cohort who took precalculus at USI with the cohort who proceeded directly to calculus. Our initial analysis suggests that a semester of precalculus doesn't improve success rates in calculus. We will discuss ways in which this initial analysis can be improved using high school GPA, together with other data. References: Bressoud, D (2014). Attracting and Retaining Students to Complete Two- and Four-Year Undergraduate Degrees in STEM: The Role of Undergraduate Mathematics Education. National Academy of Sciences; Washington, DC: 2014. (Commissioned for the Committee on Barriers and Opportunities in Completing 2-Year and 4-Year STEM Degrees). Sonnert, G. (2015) The Impact of Instructor and Institutional Factors on Students Attitudes, in Insights and Recommendations from the MAA National Study of College Calculus, Bressoud D., Mesa V., Rasmussen, C. (Eds.), MAA Press. Sonnert, G. and Sadler, P. M. (2014). The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance, International Journal of Mathematical Education in Science and Technology, v45 n8 p1188-1207.
    • Flipping Precalculus to Improve Student Learning

      Gentle, Adrian P.; Wilding, William; Wilding, William
      Precalculus is designed to prepare students for college-level calculus, and as such the course serves students majoring in a variety of STEM disciplines and pre-professional programs. Its efficacy, however, is unclear. Precalculus courses tend to have a high failure rate, while those students who actually proceed to calculus may not gain much benefit from the course (Sonnert & Sadler 2014). We describe a quasi-experimental study in which we flip an undergraduate precalculus course with the goal of improving student learning and increasing success rates through the implementation of evidence-based teaching strategies. While there is some evidence for the effectiveness of flipped pedagogy in improving student learning (Talbert 2017), positive outcomes are likely critically dependent on the specific implementation of the flipped classroom (O'Flaherty & Phillips 2015). In particular, improvements in student learning outcomes may be largely attributable to the active learning occurring during class (DeLozier & Rhodes 2017). Our flipped course structure is guided by these findings, together with the evidence-based design principles outlined by Lo, Hew & Chen (2017). Two sections of precalculus were flipped during a recent semester, with students expected to watch a short video (approximately 15 minutes), attempt a few introductory problems, and complete a brief reflection quiz before class. During class the students actively engaged in group-based problem solving with the support of the instructor. The student learning outcomes in these flipped sections are compared with a traditional “interactive lecture”-based section of precalculus taught by the same instructor in the same semester. In addition to comparing student learning outcomes, we use the Short Attitudes Towards Mathematics Inventory (Lim & Chapman 2013) to track affective changes, including enjoyment, the perceived value of mathematics, and mathematical efficacy (self-confidence) between the flipped and control sections.
    • Understanding Retention Pathways and Bottlenecks of STEM Majors: Implications for Student Success

      Elliot, William S.; Deligkaris, Christos; Greenwood, Eric S.; Gentle, Adrian P.; Chan Hilton, Amy B.; Blunt, Shelly B.
      The goals of this project are to increase faculty member's knowledge about evidence-based student retention, instructional best practices, and understanding bottlenecks and other factors impeding student progress in STEM at University of Southern Indiana (USI). In particular, hands-on experiences through group work and engaging students with early undergraduate research contribute significantly to student learning. To accomplish these goals, a working group consisting of faculty members from across the Pott College of Science, Engineering, and Education initiated discussions in Fall 2017 to examine retention factors and bottlenecks. In order to support these activities, the working group secured an Innovation Grant through the Pott College with the goal of developing individualized projects focusing on increasing retention of STEM majors and improving student learning. To assist with our shared efforts, reference materials are made available through SharePoint, Trello is used to document developing hypotheses and activities of the working group, and in-person meetings are held at least once a month to discuss the readings and to share updates on individualized projects. Initially, a systems map was created by the working group to analyze retention pathways of STEM majors at USI. Systems thinking is an effective way to understand the complexity of a topic, identify links among themes, and discover potential individualized research directions. Each working group member then created their own systems map to better constrain their specific area of interest. Research projects that originated from this process include: (1) comparing student attitudes towards group work implementations in introductory Physics courses; (2) evaluating the effectiveness of Pre-Calculus as a preparation for college-level Calculus; (3) exploring the impact of course repeats on student success in the Pott College; (4) increasing retention rates of STEM majors through an early undergraduate research program; and (5) using a faculty learning community and systems mapping to engage faculty members with pedagogical research. Selected student learning outcomes of these projects include: (1) improved comprehension and problem solving skills through group work and active learning, and (2) enriched student engagement through early undergraduate research. Furthermore, faculty members supported one another through the process of Institutional Research Board (IRB) training, the IRB approval process, and securing student data from the Office of Planning, Research, and Assessment. The results from this project will support longer-term retention initiatives and inform strategies to improve student success and retention of STEM majors in the Pott College at USI. In addition, these projects will better position the Pott College to seek external funding (such as National Science Foundation S-STEM program or Howard Hughes Medical Institute Inclusive Excellence program) to support student retention efforts. Finally, classroom strategies that result in improved student learning will be expanded to other sections of introductory courses in mathematics and physics.