A concerted effort is underway in STEM education to help students more effectively use their mathematical knowledge in science disciplines like physics, chemistry, biology, or computer science (among others). However, these efforts depend, in part, on whether the students learn the prerequisite mathematics in a way that lines up with when they would need to use that mathematics in their science classes. For example, students may need to use integration or power series before having completed the mathematics courses that deal with those topics. The way in which mathematics and science curricula may or may not align with each other has received very little attention by the undergraduate mathematics education community, other than anecdotal evidence to suggest mismatches. This working group invites RUME participants in both mathematics education research and science education research to bring their knowledge together to shed light on how mathematics and science curricula may or may not align. The participants will be asked to think of common undergraduate classes in their respective fields (mathematics, physics, chemistry, and so forth) and outline the mathematical concepts typically taught in those courses. We then plan to compare the mathematics learned in common undergraduate mathematics courses with when that same mathematics is used in science courses. From this we hope to identify mismatches that might exist in curricula in order to better understand challenges students face in trying to use mathematics in their science courses.

In the context of the current political climate and rapidly shifting demographics of the US population, perspectives and research in undergraduate mathematics education that focus on issues of equity and social justice have the potential to play a transformative role in the way our profession organizes/positions itself relative to these broader social issues. Specifically, we argue this context creates an urgent need to understand equity issues in undergraduate mathematics education and ways that equity-focused perspectives can complement existing research in RUME. To address this need, this working group serves as a collective of scholars and practitioners aimed at advancing equity agendas in undergraduate mathematics by exchanging constructive feedback on related scholarly work, instructional and curricular resources, and other artifacts related to their professional practice. Particularly, the group aims to address the following questions: 1) In what ways can equity considerations conceptually and methodologically enhance the quality of research in RUME?; 2) Alongside the broader policy changes in higher education at large, how do we see issues of equity in the day-to-day teaching and learning experiences across undergraduate mathematics classrooms and other related learning contexts? 3) How can we leverage insights from K-12 mathematics education research to further advance the equity research agenda and inform more equitable teaching and learning opportunities in undergraduate mathematics? Informal and sustained mentorship will be encouraged within the working group considering the variation across members’ stages of academic and professional development.

This long-standing working group focuses on research on the professional development and growth of college mathematics instructors regardless of their level of experience or expertise, though many current members have a particular interest in the professional growth of novice college teachers (e.g., graduate student teaching assistants). The group meets online periodically throughout the year and face-to-face at the RUME conference annually. The group’s goals, historically and currently, continue to drive the focus of annual meetings.
Working Group meeting time is structured to bring in researchers new to the field through a variety of scholarly activities: explore and discuss the literature, give and receive feedback on research projects that are in progress, brainstorm potential collaborations and mentoring relationships for both long- and short-term studies, and continued discussion of issues central to the field and ways to address them. Participants in this group include researchers in all areas of the professional preparation, induction, and development of college mathematics instructors, from across institutional types. Research areas include, but are not limited to, factors that shape instructional practices, experiences of instructors as they attend to student thinking in their instruction, and changes in instructional orientations, planning, and practices as teaching experiences accumulate. Researchers need not present their own work to participate in the group or to provide feedback to others. Dissemination from the group is broad, from publications aimed at education research audiences to practice-oriented college mathematics instructor and mathematician communities. What drives the working group is meeting the needs of the group. Regular online meetings during the year sustain collaborations and communication among group participants. Working group facilitators have been involved in various related groups (e.g., MAA-AMS Joint Committee on Teaching Assistants and Part-Time Faculty, MAA Committee on Professional Development), have conducted grant-funded research in the area, and have presented at the Conference on RUME previously.

This working group brings together researchers and practitioners invested in geometry instruction at the college level. In this working group, we will problematize critical issues facing undergraduate geometry courses, design potential projects to address these issues, and introduce GeT: A Pencil, an emerging inter-institutional system for collaborating on these projects. The organizers of this working group include co-investigators of NSF-funded projects to design educative curricula for undergraduate courses for pre-service secondary teachers (MODULE(S2), where MODULE(S2) stands for Mathematics of Doing, Understanding, and Learning for Educating for Secondary Schools) and to develop the GeT: A Pencil platform to support instructors improve undergraduate geometry courses (GeT Support, where GeT stands for Geometry for Teachers). Both projects draw inspiration from the approach to improvement proposed by Bryk, Gomez, Grunow, and LeMahieu (2015), where the distinction between researchers and practitioners is blurred for the sake of including a wide array of stakeholders to form a networked improvement community.
We propose to use the opportunity of a RUME working group session to connect with the members of the RUME community who already participate in GeT Support as well as to involve new potential participants in this network. We will share initial gleanings from interviews of instructors and provide specifics about activities sponsored by the project during the current year, including instruments that have been developed and are being used to understand the variability in curriculum, instruction, and achievement in courses on geometry for secondary teachers.
The working group will build on two inquiry projects that geometry instructors have identified as useful. One is to identify and refine elements of the mathematical knowledge needed for teaching high school geometry and the other is to create and review tasks that could be used in the teaching of geometry for future teachers. Geometry instructors are already using GeT: A Pencil to collaborate on these projects. Our team will provide expertise in research in teaching geometry and mathematical knowledge for teaching geometry while managing these interactions with the participants. Participants in the working group may want to join the networked improvement community and continue ongoing collaboration via GeT: A Pencil.

Although most universities in the United States offer mathematics tutoring for undergraduate students (Bressoud, Mesa, & Rasmussen, 2015), there is little research related to mathematics tutoring at the university level. The existing research mainly focuses on the evaluation of mathematics tutoring centers in the United Kingdom, Ireland, and Australia (Matthews, Croft, Lawson & Waller, 2012; Perkin, Croft, & Lawson, 2013). A few studies give descriptions of the interactions between mathematics tutors and students (Chi, 1996), though the context for these studies is often not collegiate mathematics tutoring. Some studies report that tutors do not utilize the same practices as teachers (Chi, Siler, Jeong, Yamauchi, & Hausmann, 2001; Grasser, D’Mello, & Cade, 2011), but there are almost no recommendations for mathematics-specific tutor training in the literature. There is a need for research on the evaluation of mathematics resource centers (henceforth called MRCs) in the United States (Matthews, Croft, Lawson & Waller, 2012), research on the interactions between tutors and students, and research-based recommendations for mathematics-specific tutor training. To meet these goals, we must bring together directors of MRCs and mathematics education researchers. A working group at the RUME conference will allow tutoring center directors to interact with each other, develop a research agenda, and provide an outlet for presenting research related to mathematics learning in a tutoring environment. We have held a working group at the RUME conference for the past two years, have met in online weekly meetings, and have attended two workshops together in May 2017 and May 2018 on the campus of Oklahoma State University in Stillwater.
The justification for this working group is that much of RUME research focuses on the classroom context and that students’ learning of mathematics outside the classroom is currently largely unexplored. Many of the MRC leaders who gathered in 2018 believe that MRCs have the potential for high impact on student learning: MRCs have fewer constraints that classroom settings, and it may be easier to train tutors to adopt research based strategies compared to instructors.
The research areas proposed at the 2018 RUME working group were refined at the Stillwater meeting, and research teams were formed. The research teams are interested in continuing this work at the 2019 RUME conference. We welcome new participants to join these research teams and recognize the potential to form new groups if other areas of interest emerge.

This working group solicits persons interested in learning about and pursuing research on the teaching and learning of undergraduate statistics. This includes, but is not limited to, theoretical analysis or empirical research situated within the introductory statistics sequence, pre-service teacher courses, or advanced undergraduate statistics courses. Additionally, we encourage persons interested in investigating problem spaces that are shared among the undergraduate mathematics and statistics education communities (e.g., function, probability, modeling, etc.) with the hope that such research may inform the practices and research agendas of both communities.
This is the second year of the Statistics Education RUME working group. We will continue the work started last year by sharing the project that last year’s group began with a presentation of the project and a continued conversation of possible directions that work may lead. Data on the project will be shared, such that participants might work on possible projects related to the collected data or help further the project with new data collection. Further, we will invite any participant to share their current work or present ideas for future work to the group.
Join us as our community grows. We are a small and supportive group and want to help anyone with an interest in statistics education.

The goal of this working group is to bring together researchers who focus on teaching and learning in the unique and significant context community college mathematics.
Roughly half of all U.S. undergraduates, college graduates, and current mathematics majors attend community colleges. These students are more likely to belong to groups that have traditionally been both underrepresented in mathematics and that are at higher risk of not earning a credential: they are often the first in their families to attend college, they tend to be older, have work and family responsibilities, and have weak pre-college preparation. At the same time, mathematics outcomes for these students are significantly poorer—the majority of these students are placed into developmental mathematics courses and only a minority of those ever successfully complete a credit-bearing college mathematics course. There is a significant need for research in this domain of mathematics education research that overlaps research in both K-12 and RUME settings, but that has its own unique questions.
Supported through past working group sessions at RUME and committee work within AMATYC, a growing group of researchers has been collaborating to advance a national agenda and create a web of community college mathematics education research. Projects have been funded, collaborative research has been undertaken, and the dissemination of findings is ongoing. We propose to leverage the RUME working group session to continue a discussion about editing a special issue of a mathematics education journal to highlight this work. We welcome new working group participants who are conducting research in mathematics teaching and learning at community colleges and are looking for a venue to publish their findings.

When students are coming to understand how to construct proofs, as well as how mathematicians use proofs in their work, the role of the instructor cannot be overstated. In this paper, we present an investigation into how an instructor uses her authority to empower students as legitimate proof producers and learners of mathematics. We view this empowerment and student learning through a situated lens, accounting for relationships of disciplinary authority and student agency. In our investigation, we analyzed the transcripts from three classroom episodes in an inquiry-based transition-to-proofs course. We identified instances when the instructor leveraged her institutional authority as well as her mathematics expertise authority to support students’ engagement in the dance of agency, asserting their own creative ideas as learners of mathematics while still adhering to the norms and standards of the discipline.

Recently, Ely & Ellis (2018) described a new mode of covariational reasoning—scaling-continuous reasoning—and conjectured that it might support productive student thinking in calculus. We investigate that hypothesis by analyzing how calculus students employed scaling-continuous covariational reasoning when discussing differential calculus ideas. The interviewed students who took a course based on a “local straightness” approach to calculus used scaling-continuous reasoning in their description of the derivative at a point, particularly in their imagery of zooming in on a function at a point to reveal its slope. The interviewed students who took a course based on an “informal infinitesimals” approach to calculus used scaling-continuous reasoning in their account of how zooming in on a neighborhood reveals the coordination between a bit of x (dx) and the corresponding bit of y (dy), a relationship that gives a differential equation for that curve.

In this paper, we share findings around four prospective secondary mathematics teachers’ attention to varying curricula while planning an algebra lesson. We specifically address how their attention interacted with their interpretations of and responses to the curriculum materials via idea sequences, and further we study how the format of the curriculum materials plays a role in influencing these interactions. We discuss the result that sequences of interpretations and responses are always initiated by attention for PSTs, which itself is influenced by curriculum elements and format. We end with a discussion of implications around the need for curriculum use practices in teacher education and professional development.

We utilize two analyses to confirm a multidimensional framework for analyzing contributions to classroom discourse, previous analysis using the framework and analysis of instances of sociomathematical norm negotiation juxtaposed with it (Cobb & Yackel, 1996). The framework considers social, epistemic, and argumentative activities exhibited in talk-turns during whole class discussion. In this study we show that collective and individual development occurred in an inquiry-oriented differential equations course and discuss patterns in ways learning partners participated in whole class discussions during sociomathematical norm negotiation.

Undergraduate mathematics instruction contributes to marginalization among women and racially minoritized individuals’ experiences. This report presents an analysis from a larger study that details variation in minoritized students’ perceptions of potentially marginalizing events in undergraduate mathematics instruction. With past research on undergraduate mathematics experiences largely focused on students’ post-hoc reflections and one or two race-gender intersections, this analysis extends prior work by attending to variation in students’ in-the-moment perceptions of mathematics instruction across various race-gender intersections. Findings highlight how issues of underrepresentation, stereotypes, and instructor care contributed to interpretations of instruction-related events as potentially marginalizing. The report concludes with implications for teaching practices in undergraduate mathematics that academically support and socially affirm students from historically marginalized backgrounds.

In this study of mathematics teaching, we explore how to measure inquiry-oriented practices of college mathematics instructors. We offer a conceptualization of inquiry-oriented instruction organized by the instructional triangle (Cohen, Raudenbush, & Ball, 2003) and introduce an instrument developed to explore the extent to which elements of inquiry-oriented instruction are present in the teaching of university mathematics courses. This scale has been developed to explore what practices instructors currently use and eventually investigate the relationship between beliefs and practice. We show how we have operationalized inquiry-based instruction as self-report items and report preliminary findings that indicate our scales are performing well. We show that some inquiry-oriented practices are significantly more present in upper-division courses than lower-division courses. This suggests that at least some components of inquiry-oriented instruction are not reducible to individual differences (whether the instructor is an inquiry-based instructor), but also dependent in the context of instruction.

Homework accounts for the majority of undergraduate mathematics students' interaction with the content. However, we do not know much about what students learn from homework. This paper reports on a pilot study of why professors chose particular homework problems, what they hoped students would learn from them, and whether students' engagement with the problems reflected those outcomes. Results show students gained the desired familiarity with notation and procedures. The results also speak to how professors manage the content between what they discuss in class, homework problems, and intentional overlap between the two.

The symbol “dx” is one example of a differential, which is a calculus symbol that is found in a variety of settings and expressions. We wanted to explore how expert mathematicians think about differentials in some of these settings and expressions, in order to see what levels of consistency might appear among their views. To that end, we created an interview protocol that contained differentials in the contexts of derivatives, definite and indefinite integrals, and separable differential equations, interviewed seven mathematicians, and analyzed their responses using a form of thematic analysis. Overall, we found no instances of total agreement among all subjects, but did find several common and recurring themes, including some that were unexpected and not found in our previous studies.

Undergraduate mathematics instructors are called by recent standards to promote prospective teachers’ learning of a transformation approach in geometry and its proofs. The novelty of this situation means it is unclear what is involved in prospective teachers’ learning of geometry from a transformation perspective, particularly if they learned geometry from an approach based on the Elements; hence undergraduate instructors may need support in this area. To begin to approach this problem, we analyze the prospective teachers’ use of the conceptual link between congruence and transformation in the context of congruence. We identify several key actions involved in using the definition of congruence in congruence proofs, and we look at ways in which several of these actions are independent of each other, hence pointing to concepts and actions that may need to be specifically addressed in instruction.

We study how the mathematical beliefs and knowledge of peer mentors in a summer mathematics program influenced their efforts to help high school students learn to write proofs in number theory. Using Schoenfeld’s framework for understanding decision making, we analyze interviews of three undergraduate student mentors for evidence of how their views of the role of proof, norms for proof writing, and mathematical knowledge for teaching informed their pedagogical decisions. We find that each mentor developed a distinctive approach to providing feedback on student work consistent with their own values, and present evidence that the success of each approach depended on the mentor’s resources for interpreting student work.

Calculus is often an essential milestone during a students’ time in college and can be especially impactful for students wishing to major in in a math or science field. Given its relative importance, the ways in which calculus courses are delivered can have a lasting impact on a student’s trajectory and relationship with mathematics. In this study we document the ways in which three calculus course variations at the same University operate to promote different mathematics identities for students. Drawing on the Holland et. al.’s (1998) framework of figured worlds we showcase the ways in which these course variations act as if they are different calculus worlds that constitute socially organized and produced realms of being. We highlight the ways in which these figured worlds position or fail to position students with the opportunity to refigure themselves and others as learners and doers of mathematics.

This study presents findings from a series of interviews in which we observed undergraduate students’ moment-by-moment Reading of Mathematical Proof (ROMP) activity. This methodology is adapted from a validated assessment of narrative reading comprehension developed by cognitive psychologists. We demonstrate the fruitfulness of the method by describing four relatively novel phenomena that we observed in our interviews, and highlight ROMP activities that seemed to distinguish less productive and more productive readers.

The undergraduate preparation of pre-service teachers requires attention to the factors that enable and constrain their application of mathematical knowledge to positive effect in the classroom. In this paper, we examine how the instructional decisions of three in-service secondary mathematics teachers were influenced by individually consistent patterns of such mediating factors. Acknowledging that such factors might be content-dependent, we focus on teachers’ instruction of exponential functions, a topic foundational to both secondary and collegiate mathematics. We developed models of each teacher’s implicit learning theory, professional identity, values and goals for students’ learning, and beliefs about the nature of mathematics and about what constitutes genuine mathematical engagement. We illustrate these results by summarizing our analyses of a selection of mediating factors for each teacher. We conclude with a discussion of the implications of our findings for the preparation of pre-service mathematics teachers at the undergraduate level.

There is evidence that instructors who are responsive to students’ thinking tend to provide more positive learning experience for students. Additionally, effective instruction relies on an instructor’s ability to respond to student thinking, which is especially relevant due to the increased attention on improving college mathematics instruction. In order to investigate instructor responsiveness to student thinking as a disposition (that guides action) and responsiveness to student thinking as an action (the enacted evidence of the underlying disposition), eight college Calculus instructors were interviewed three times over the course of one academic year. A thematic analysis of the task-based interviews indicated that instructors who exhibited a responsive disposition to their students’ thinking enact this through eliciting student thinking, reflecting on student thinking, and responding to student thinking. Further, these instructors view themselves as decision-makers, and thus feel empowered to act on their responsive disposition.

Previous research has illuminated and defined meanings and understandings that students demonstrate when reasoning about graphical images. This study used verbal and physical cues to classify students’ reasoning as either static or emergent thinking. Eye-tracking software provided further insight into precisely what students were attending to when reasoning about these graphical images. Eye-tracking results, such as eye movements, switches between depictions of relevant quantities, and total time spent on attending to attributes of the graph depicting quantities, were used to uncover patterns that emerged within groups of students that exhibited similar in-the-moment meanings and understandings. Results indicate that eye-tracking data supports previously defined verbal and physical indicators of students’ ways of reasoning, and can document a change in attention for participants whose ways of reasoning over the course of a task change.

In this study we investigated how a small sample of students used variational reasoning while discussing ordinary differential equations. We found that students had flexibility in thinking of rate as an object, while simultaneously unpacking it in the same reasoning instance. We also saw that many elements of covariational reasoning and multivariational reasoning already discussed in the literature were used by the students. However, and importantly, new aspects of variational reasoning were identified in this study, including: (a) a type of variational reasoning not yet reported in the literature that we call “feedback variation” and (b) new types of objects, different from numeric-quantities, that the students covaried.

In this study, two universities created and implemented a student-centered graduate student instructor observation protocol (GSIOP) and a post-observational Red-Yellow-Green feedback structure (RYG feedback). The GSIOP and RYG feedback was used with novice graduate student instructors (GSIs) by experienced GSIs through a peer-mentorship program. Ten trained mentor GSIs completed 50 sets of three observations of novice GSIs. Analyzing 151 GSIOPs and 151 RYG feedback meetings longitudinally provided insight to identify what types of feedback informed and influenced GSIOP scores. After qualitatively coding feedback along multiple dimensions, we found certain forms of feedback were more influential for GSI development than others with respect to change in GSIOP score. Our results indicate contextually-specific feedback leads to more observed changes and improvement across multiple observations than decontextualized feedback.

When trying to examine instructors’ instructional practices, specifically lecturing, qualitative studies have indicated the necessity to consider their beliefs. However, there is a dearth of quantitative belief measures specific to instructors of undergraduate mathematics courses. No one specific instrument captures the relationship between beliefs and lecturing. This paper, therefore, attempts to establish a foundation of significant factors for researchers to consider when developing belief measures to predict lecturing. We use pre-existing data from Calculus and Abstract Algebra courses to conduct factor analyses and develop composite variables. We then use multiple regression to examine composites with significant effects on time spent lecturing. Results suggest that beliefs related to a focus on skills and content, knowledge facilitation authority, expectations of student success, and the importance of particular concepts are of particular importance.

This study investigates instructor perceptions of their teaching, as well as their students’ learning, obstacles encountered, and methods of implementation from the use of Primary Source Projects (PSPs). PSPs are curricular modules designed to teach core mathematical topics from primary historical sources rather than from standard textbooks. In essence, they are a form of inquiry-based-learning that incorporates the history of mathematics through original sources. We provide an overview of results from two semesters of implementation reports and surveys administered at the beginning and end of the semester by instructors who implemented PSPs in their undergraduate mathematics class.

While there has been research on students’ understanding of the meaning of the equals sign, there has yet to be a thorough discussion in math education on a strong meaning of the equals sign. This paper discusses the philosophical and logical literature on the identity relation and reviews the math education research community’s attempt to characterize a productive meaning for the equals sign.

Students taking courses below calculus are an understudied population in undergraduate mathematics education, as are students with mathematics difficulty or disability. Students seeking additional help are likely to seek YouTube and other outside resources, which may not mesh with in-class instruction. Since secondary education research suggests that targeted tutoring is beneficial to students with mathematics difficulty or disability, this single case study investigated if there was a functional relationship between a Smartpen to create videos for a student with a mathematics disability to listen to during tutoring sessions and her achievement on synthetic division problems over a four week intervention.

Mathematics achievement, both in high school and early in college, is one of the strongest predictors of college completion. Research conducted within the framework of expectancy-value theory has shown that math interest, utility, engagement, self-efficacy, and identity are related to mathematics achievement. Hence, this study uses structural equation modeling to evaluate Ford’s (2017) empirical model linking mathematics beliefs and achievement with a sample of students enrolled in multiple sections of two algebra-focused remedial math courses at a community college near a midsize metropolitan southern city in the United States.

The aims of this study are to explore student perspectives on the use of an open educational resources (OER) platform in blended learning, and to examine student achievement, engagement, and opportunity for learning mathematics. As a mixed project, the data was collected from 423 students in 15 sections of Elementary Statistics during four semesters. The results of this study showed that the use of an OER learning platform in blended learning promoted student engagement and significantly increased student opportunity for learning. There were not significant differences in student achievement between adopting an OER learning platform in blended learning and adopting commercial resources in regular classes.

This study explored adjunct instructors’ opportunities for learning as they faced challenges while implementing a research-based mathematics curriculum. Three case studies explored adjunct instructors’ experiences as they implemented a research-based precalculus curriculum for the first time over the course of two semesters. The similarities and differences between the challenges faced by the instructors and the opportunities for their learning were analyzed.

Integrating innovative pedagogical initiatives within the learning environment at the Lebanese American University in Beirut, Lebanon, has been set as a strategic goal. Active learning, as one medium of instruction, has seen widespread implementation in mathematics classrooms. This study reports on an inquiry oriented differential equations class offered in spring 2018. The focus is on the role of the curriculum in guiding students reinvent successfully key mathematical notions covered in any introductory differential equations class.

Students are engaged in various reasoning and proving tasks corresponding to the increased emphasis on reasoning and proving in mathematics education. Students routinely encounter differing language present in prompts for these reasoning and proving tasks. The semantic meaning of the language used in these prompts is not usually explicitly discussed and thus may cause inconsistencies in students’ responses to these tasks and in the assessment of their work. The preliminary results imply Calculus I students have various conceptions for prompts such as “prove”, “explain”, “show”, and “convince”. This poster will focus on students’ various conceptions on the two prompts “prove” and “show.”

Research has shown that faculty benefit from support and collaboration when introducing student centered instruction into their teaching (Henderson, Beach, & Finkelstein, 2011; Speer & Wagner, 2009). The RUME community has some knowledge about how these supports take shape and grow (e.g., Hayward, Kogan, & Laursen, 2015), but work is still needed. A crucial component is researching the facilitation of these supports. In this study, we focus on how the facilitation of online working groups occurs. Our preliminary results indicate that the actions facilitators take play crucial roles in how to use discussions of mathematics to proactively engage in student thinking.

This study (a) validates a measure “bold problem solving” for postsecondary students and (b) examines patterns in bold problem solving tendencies within and across various math classes. A confirmatory factor analysis demonstrates the general construct holds for the postsecondary population. Course and gendered differences in bold problem solving tendencies exist.

Observation protocols allow researchers to document moments of teaching and learning, as well as reveal inequities and opportunities for improvement. In two undergraduate mathematics courses, I used the OPAL protocol to understand if and how active learning strategies created equitable learning environments. In this poster, I share findings from observations and discuss possibilities for adapting observation protocols to align with equitable teaching practices.

In this poster we introduce a new learning modality called MathChavrusa. Inspired by the ancient rabbinic approach to Talmudic study, the chavrusa model pairs students in a partnership of deep text-based analysis, discussion, and debate. Over centuries the model has proved its ability to generate thorough understanding, build skills, develop the courage to question, and demonstrate to students the value of both independent thinking and collaboration. MathChavrusa is a complementary model to other accepted modalities for generating student understanding in mathematics. It is particularly effective when employed after a lecture class. In teaching about the model, we will discuss its origins, how it facilitates deep learning and understanding in mathematics, and techniques for implementation. We have begun to utilize the model in our classes, and are gathering data about its real-world effectiveness. Preliminary data implications will be discussed.

The Mathematical Knowledge for Teaching (MKT) theoretical framework describes effective mathematics teaching in a way that relies both on an instructor’s subject matter knowledge (SMK) and on their pedagogical content knowledge (PCK). This proposal reports our initial effort to understand MKT within chemistry instruction, namely what MKT could support chemistry instructors’ efforts to help students develop a deeper understanding of the mathematics used in general chemistry. Coding of several types of general chemistry problems involving ratios and proportions and covariation are provided as examples.

This work focuses on the preparation of graduate Teaching Assistant in the mathematics department of a large urban midwestern R1 university. We explore the author’s experience with three different versions of the course in three varying capacities: as a student, a mathematics education researcher and a co-facilitator. As we delve into the author’s reflections on the evolution of the teaching preparation within this timeframe, we highlight some issues with the course structure and execution. This leads to the development of another, more realistic version of the preparation course.

We present the methodology and preliminary findings from a pilot study undertaken at three institutions during Spring 2018. Our purpose is to uncover student reasoning around volumes of solids of revolution. Initial findings suggest issues arise in the Product layer of the Riemann Integral Framework (Sealey, 2014).

Many undergraduate students experience significant difficulty in learning to prove mathematical propositions nationwide. A previous study by David & Zazkis (2017) used document analysis of publicly available syllabi to create a national portrait of approaches to supporting students’ transition to proof across a large sample of R1 and R2 universities. Liberal arts colleges (LACs) operate under different sets of institutional constraints and thus offer the possibility of different approaches to this issue. We report results of a preliminary survey study, the goal of which was to enhance previous work on approaches to the transition to proof by specifically focusing on the case of LACs. Analysis of the survey data show that LACs’ approaches have distinctive features as compared to R1 and R2 universities. Notably, discrete mathematics courses served as a transition to proof course in almost half of the surveyed institutions.

Using a stakeholder-centered design, this interactive poster presents a research framework for attending to equity and supporting transformative change for faculty who teach courses for future K-8 teachers. The poster reports on a research and development project that is creating and examining the impact of professional learning modules for these faculty. One aim of the project is intentional awareness development among faculty about their own views of mathematics and opportunities to learn it, those of their undergraduate students, and those of the children their students will one day teach. The particular focus of the poster is our research attempt to identify and capture aspects of equity that factor into instructor decisions in each phase of their professional learning experience (motivation, construction, and organization).

This poster presentation will highlight the results of a qualitative, multicase study which explored the use of alternative scoring practices in collegiate mathematics classes. Specifically, the researchers explored the use of two different scoring practices: one in an entry-level College Algebra course and one in an upper-level Modern Geometry course. In addition to classroom observations, data collection for each case consisted of two interviews for each course instructor, one interview with each course designer, and interviews with students in each course. This poster presentation will detail themes from cross case analysis which suggest important details for successful implementation of alternative scoring practices in collegiate mathematics courses.

Research on Mathematical Knowledge for Teaching has helped the education community understand the complex, knowledge-related factors that shape instructors’ practices and the learning opportunities they create for students. Much of this work has occurred in the context of K-12 teaching. Although expanding, research on knowledge for teaching undergraduate mathematics is not extensive. A similar situation exists in science education. To help support these research efforts and theory development, we analyzed existing literature on knowledge for teaching undergraduate STEM content. Findings take the form of cross-disciplinary themes and differences that can help inform research efforts in this area. We seek feedback from the RUME community about our representations of knowledge for teaching, ideas about findings from research on Mathematical Knowledge for Teaching that have been especially useful, and/or ideas for research investigations that would be particularly useful to inform curriculum development, professional development for teaching or theory.

I report on the first stage of my dissertation project which sought to understand engagement in a Precalculus course at a four-year public university. Breaching instructional activities, student interviews, and classroom recordings were used to study the development of several sociological and psychological constructs to help characterize students’ engagement. Despite the instructor’s attempts to negotiate productive norms, data analysis shows that some students’ detrimental practices and beliefs remained unchanged or were even supported by the course. I examine the roots and consequences of this phenomenon.

Small groups teaching as part of first semester was studied through observations of the seminars, analysis of the tasks, and students’ responses in surveys and interviews. The research question posed is how the teaching activities enabled the students to develop their conceptual and procedural knowledge. The results show a desire for a development of conceptual knowledge but the demands on procedural knowledge placed the students with conflicting aims.

Survey data for community college algebra students reveals relationships between a student’s attitudes towards mathematics and the student’s STEM career interests. Results show that while students may not always have a clear understanding of the tasks related to a chosen STEM career area, the student’s math interest predicts interest in some STEM careers and not others.

This research explores preservice teachers (PSTs) views of students’ mathematical capabilities (VSMC) within mediated field experiences (MFEs) and the role of beliefs on instructional decisions. In MFEs, teacher educators serve as instructors, coaches and supervisors as PSTs plan, enact, and debrief instruction (McDonald et al., 2014). The research questions were: What is the nature of PSTs VSMC across an MFE cycle? How might PSTs beliefs impact instructional decisions? What role might MFEs play in developing productive VSMC? Findings showed that some teachers believed students were incapable of engaging in rigorous instruction, and consequently, would not always respond to student difficulty in ways that helps students participate in rigorous mathematical environments. Results suggest the need to study how teachers might develop more productive VSMC and better support students who struggle. The analysis also revealed how daily debriefs within MFEs supported PSTs to glean general instruction principles to inform their teaching.

This preliminary report will focus on how college precalculus teachers, mainly graduate teaching assistants, interact with department-provided curriculum materials. We specifically address what collegiate teachers notice in curriculum resources while planning. Comparisons will be drawn between first-time instructors and those with more experience, ultimately informing what and how collegiate teacher educators might incorporate experiences for precalculus teachers to develop curriculum use practices.

The purpose of this study is to examine the meanings and interpretations a student has about the derivative at a point versus the derivative as a function. The responses given by the student is representative of many Calculus 1 students and their beliefs about derivative.

The IMAGEMath project combines inquiry based learning with an application-inspired approach. Students first learn about an application, and then, in an inquiry framework they develop the mathematics necessary to investigate the application. A novel feature of this approach is that the applied problem inspires the mathematics, rather than the applied problem being presented after the relevant mathematics has been learned. In this poster, we give an overview of the IMAGEMath modules that use image and data applications (radiography, tomography and heat diffusion) to inspire linear algebra topics. We present results from implementing the modules on a small scale at a few institutions, including student and faculty feedback. We also provide information for faculty interested in using IMAGEMath materials.

Student success in introductory calculus is imperative to obtaining a degree in STEM. Calculus I is a main gatekeeper course for STEM majors, and many students leave the class with a diminished motivation to pursue further courses related to mathematics. This poster reports a qualitative case study from a larger mixed-methods project aimed at exploring the relationship between course structures (hybrid, traditional, and large active learning) and student motivation in calculus. Using the theoretical framework of self-determination theory (SDT), six students were interviewed to investigate how each course structure was related to students’ perceptions of their competence, autonomy, and relatedness. Emerging themes showing differences in student motivation between the three course types will be presented.

We observed recordings of instances from a graduate course in topology where students engaged in proving theorems on the whiteboard in a collaborative environment. We considered the written component on the whiteboard as “the proof”, which was aided, in 17 out of 20 instances by some form of verbal explanation. The peculiarity of the class structure allowed each lesson to be followed by an open discussion regarding “the proof”. As a result of the discussions, the written component of each proof would undergo improvements. When analyzing the developments of the proofs in this course, we employed the thematic of proof introduced by Mariotti. Stemmed by these proof-presentations, we introduce the idea of proving as a “work-in-progress” activity.

This poster presents conceptual analysis and hypothetical learning trajectory for learning proportionality which was previously limited only to figure out missing value using cross-multiplication. Based on a series of clinical interview that investigated students’ meaning of proportionality in an online format, I found that students tend to use only cross-multiplication strategy to reason proportionally which did not help them to reason proportionally. That emphasizes how learning proportionality along with the constant rate of change among quantities given in any specific word problem helps to reason proportionality conceptually.

This pilot study sought to understand how, if at all, computational thinking influenced mathematical understanding, specifically within the context of integration. Interviews conducted with STEM students probed conceptual understanding of integration by eliciting justification of solutions and application to an integration problem most readily solved graphically.

We suggest a 4-step cycle for helping prospective teachers transform their mathematical understandings from procedurally-based to more conceptually-based understandings. We use Mezirow’s (1991) idea of Transformative Learning Theory (TLT), which is an application of androgogy, or the methods of teaching adults. In this poster, we share our model of a TLT cycle and illustrate it using an example of a proportional reasoning problem for prospective teachers.

It is well-known that too many students abandon a STEM career because of their calculus requirement. Therefore, being able to identify early on which students may be at risk of failing is important. Using indicators of mathematical readiness (SAT/ACT and PCA) and attitudes toward mathematics (MAPS), we build models predicting final grades. Our analyses show that all three indicators are significant predictors of success in calculus.

In order to determine preservice secondary mathematics teachers’ (PSMTs) conceptual understanding following an inquiry-based lesson on the constructed meanings of the equals sign and the distinctions between the concepts of function and equation, we utilized a scripting task in which the PSMTs individually continued a dialogue between two hypothetical students with opposing viewpoints with respect to an equation arising from a function context. This study is part of the Enhancing Explorations in Functions for Preservice Secondary Mathematics Teachers Project which is developing research-based tasks and explorations together with instructor materials to be used in mathematics courses for PSMTs. The goal of this poster presentation is to discuss our implementation of the scripting task to gauge PSMTs’ understanding of the nuances between function and equation. We also wish to gather feedback and suggestions on the study design and potential implications of our research.

Undergraduate students in a History of Mathematics course engaged with various historical mathematical problems. Reflective journals and interviews were used to analyze their perspectives on meta-issues of mathematics. The results indicate some revision of their metaperspectives and new cultural awareness.

Our initial project focused on assessing conceptual understanding of key topics in Calculus I, specifically measuring changes in the achievement gap between underprepared and prepared students in Active and Traditional classrooms. However, a main hurdle is the lack of inventory for assessing Calculus readiness. In this poster, we present results of student understanding of continuity in Active vs. Traditional settings from 16 sections of Calculus I. We present ideas for refining this study to be able to better assess student growth by creating and validating questions regarding students’ initial understanding of Calculus topics: continuity, differentiability, limits, and area. We present our study design and initial findings; we look forward to feedback as we enter the latter half of our project.

As part of an ongoing effort to understand how mathematics departments in the U.S. can better support graduate students teaching in precalculus and calculus courses, we are interested in investigating plans (or potential plans) departments are making toward improving their graduate teaching assistant (GTA) professional development (PD) programs. Contributing to a larger national project of first-year mathematics, this study looked at mathematics departments’ survey responses to three items regarding changes to GTA PD programs. Out of the 223 departments that responded to the survey 66 of them indicated some level of plans of change to their program. For those schools, we analyzed the open-ended responses elaborating on the current status of the GTA PD program and found several noticeable themes regarding changes or plans to change their programs.

In an attempt to bring more realistic situations into college mathematics classroom environments, lessons were created that utilized culturally relevant pedagogy for a college algebra course at a large historically black college/university (HBCU) in the south. These lessons were aimed at the growing population of diverse students in an effort to gauge their effectiveness with students, in regards to achievement and self efficacy. This poster will illuminate the conceptual developmental process of four “experimental” lessons and provide some preliminary findings of the course that utilized these lessons in comparison with a control class that did not.

In this study, we explore how quantum mechanics students understand linear algebra concepts in the context of two spin-½ probability problems, the second of which required a change of basis. In particular, our research question is: what problem solving approaches do students use, what mathematical concepts are involved in that approach, and how do students reason about basis and change of basis as they engage with the problems? Data come from individual, semi-structured interviews with twelve quantum mechanics students from two different universities. Our poster will share preliminary results for all parts of the research question.

In this poster we share a qualitative study aimed at investigating creativity in problem solving for non-mathematics tracked students enrolled in a calculus course. Three task-based semi-structured interviews with volunteered participants were analyzed using a modified whole-to-part inductive approach (Erickson, 2006). Our findings suggest that even though students may perceive creativity as a process, this understanding may not necessarily be reflected in their written work. Teachers therefore need to create opportunities in the classroom to challenge and push students to take risks to develop their mathematical creativity.

Recommendations for the teaching and learning of introductory statistics at the tertiary level have been set forth by the research community, including recommendations outlining desirable pedagogical strategies such as the use of student-centered instruction and the integration of technology and resampling methods to support the development of students’ conceptual understanding. Yet, surprisingly little is known about how introductory statistics is being taught at colleges and universities across the United States. The research presented here aims to shed light on these aspects of the introductory statistics course by reporting preliminary findings from an instructor survey that was recently completed by 148 instructors nationwide.

We investigate links between units coordination schemes and covariation schemes.