We report on semi-quantitative research into students' difficulties with integration in an intermediate-level electromagnetism course with cohorts of about 50 students. We have found that before they enter the course, students view integration primarily as a process of evaluation, even though viewing integration as a summation process would be more fruitful. We confirm and quantify earlier results that recognizing dependency on a variable is a strong cue that prompts students to integrate and that various technical difficulties with integration prevent almost all students from getting a completely correct answer to a typical electromagnetism problem involving integration. We describe a teaching sequence that we have found useful in helping students address the difficulties we identified.

In their study of physics beyond the first year of University -termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-thebook style problems, and from trying to develop an understanding of the underlying physics through solving such problems. Some of the research at the upper-division focuses on how students use mathematics in these problems, and what challenges students encounter along the way. There are a number of different and diverse research studies on students' use of mathematics in the upperdivision. These typically utilize one of two broad approaches, with some researchers primarily seeking out and addressing challenges students face, and others working chiefly to unpack students' in-the-moment reasoning. In this paper, we present and discuss both approaches, and then review research efforts that strive to connect these two approaches in order to make sense of students' use of mathematics as well as to uncover particular challenges that students encounter. These recent efforts represent a small step towards synthesizing the two approaches, which we argue is necessary to more meaningfully impact student learning at the upper-division. We close our review and discussion with suggested refinements for future research questions for the physics education research community to consider while it works to understand how students use math in upperdivision courses.

Identity production is a complex process in which a person determines who he or she is via internal dialogue and sociocultural participation. Understanding identity production is important in biology education, because students’ identities impact classroom experiences and their willingness to persist in the discipline. Thus, we suggest that educators foster spaces where students can engage in producing science identities that incorporate positive perceptions of who they are and what they have experienced. We used Holland’s theory of identity and Urrieta’s definitions of conceptual identity production (CIP) and procedural identity production (PIP) to explore the process of students’ science identity production. We interviewed 26 students from five sections of a general biology course for majors at one higher education institution. The interview protocol included items about students’ identities, influential experiences, perceptions of science, and perceptions of their classroom communities. From the interviews, we developed hierarchical coding schemes that focused on characterizing students’ CIP and PIP. Here, we describe how students’ socially constructed identities (race, gender, etc.) and their experiences may have impacted the production of their science identities. We found that authoring (i.e., making meaning of) experiences and recognition by others as a community member influenced students’ science identity production.

Student success in large enrollment undergraduate science courses which utilize "active learning" and Learning Assistant (LA) support is a complex phenomenon. It is often ill-defined, is likely impacted by many factors, and regularly interacts with a variety of treatments or interventions. Defining, measuring, and modeling student success as a factor of multiple inputs is the focus of our work. Because this endeavor is complex and multifaceted, there is a need for strong theoretical framing. Without such explicit framing, we argue that our findings would be uninterpretable. In this paper we describe our efforts to define that theoretical framework, present the framework, and describe how it defines our methodological approach, analyses, and future work.

Abstract. End-of-course assessments play important roles in the ongoing attempt to improve instruction in physics courses.Comparison of students' performance on assessments before and after instruction gives a measure of student learning. In addition, analysis of students' answers to assessment items provides insight into students' difficulties with specific concepts and practices. While open-ended assessments scored with detailed rubrics provide useful information about student reasoning to researchers, end users need to score students' responses so that they may obtain meaningful feedback on their instruction. One solution that satisfies end users and researchers is a grading rubric that separates scoring student work and uncovering student difficulties. We have constructed a separable rubric for the Colorado Classical Mechanics/Math Methods Instrument that has been used by untrained graders to score the assessment reliably, and by researchers to unpack common student difficulties. Here we present rubric development, measures of inter-rater reliability, and some uncovered student difficulties.