Longitudinal Success of Calculus I Reform

This paper describes the second year of an ongoing project to transform calculus instruction at Boise State University. Over the past several years, Calculus I has undergone a complete overhaul that has involved a movement from a collection of independent, uncoordinated, personalized, lecture-based sections, into a single coherent multi-section course with an activelearning pedagogical approach. The overhaul also significantly impacted the course content and learning objectives. The project is now in its fifth semester and has reached a steady state where the reformed practices are normative within the subset of instructors who might be called upon to teach Calculus I. Gains from the project include a rise in the pass rate in Calculus I, greater student engagement, greater instructor satisfaction, a general shift toward active learning pedagogies, and the emergence of a strong collaborative teaching community. Project leaders are seeking to expand these gains to other areas of the curriculum and to broaden the community of instructors who are fully accepting of the reforms. Common concerns expressed by faculty resistant to the overhaul include suspicion that pass rate gains might reflect grade inflation or weakened standards, and that altering the traditional content of Calculus I might leave students unprepared for Calculus II. External stakeholders also have a vested interest in ensuring students receive a solid preparation in Calculus I. In this paper we develop a response to ensure solid evidence of Calculus II readiness that we hope will be useful to change agents and campus leaders in many other settings. We address concerns about Calculus II readiness by conducting a natural experiment, tracking two cohorts of students through Calculus I and into Calculus II. The “treatment” cohort consists of students who reach Calculus II after passing the reformed Calculus I. The “control” cohort consists of students who reach Calculus II after passing non-reformed Calculus I at Boise State University. The experiment has no designed randomizing, but enrollment data shows that both cohorts spread out across all sections of Calculus II with apparent randomness. Our research question is: “Does the treatment cohort perform any worse than the control cohort in Calculus II?” Data on pass rates and grades in Calculus II will show that the answer is “No.

The Crux: Promoting Success in Calculus II

In the 2013-14 school year, Boise State University (BSU) launched a major overhaul of Calculus I. The details of the reform, described elsewhere, involved both pedagogical and curricular changes. In subsequent years, we developed several assessment tools to measure the effects of the project on students’ grades and retention. The toolkit includes: (1) pass rate and GPA in Calculus I, (2) longitudinal analysis of pass rates and GPA in subsequent courses, (3) impact of Calculus I on retention in STEM and retention at BSU, (4) all of the above comparing students in reformed Calculus vs traditional Calculus, (5) all of the above for underrepresented minorities, women, or other demographic subsets. While these tools were originally developed to study the Calculus I project, they are available for studying the effects of other courses on student academic performance and retention. In this paper, we briefly describe a rebuild of Calculus II, overhauled in the 2015-16 school year following the same general plan as was used for Calculus I. We then present the results of applying the full toolkit to the new Calculus II course. Pass rate and GPA improvements in Calculus II were evident immediately after scale up in the spring of 2016. Sufficient time has now passed so that we can apply the full set of assessment tools built for Calculus I to measure the effectiveness of the Calculus II transformation on academic performance in post-requisite coursework and on student retention in STEM

Using Active Learning Strategies in Calculus to Improve Student Learning and Influence Mathematics Department Cultural Change

An interdisciplinary team of physics, education, math and chemistry faculty developed MATH-GAINS (Growing as Adaptive INstructors) creating an ecosystem where mathematics faculty persistently and sustainably apply active learning strategies in their teaching of calculus courses. As a result of implementation, MATH-GAI NS proposed to positively affect the wide-spread adaptation of active learning strategies by department faculty as well as student learning, retention and graduation of over 900 students annually. The objective of this paper is to provide details on how the project was conceived and implemented; instruments, research methodologies and active learning strategies used; and examples of faculty projects and preliminary results of the study. Results of the study add to the growing body of knowledge of how research-based instructional strategies designed in other STEM disciplines work in math courses, as well as an understanding of the critical factors that influence math faculty’s teaching practices

Calculus Reform: Increasing STEM Retention and Post-Requisite Course Success While Closing the Retention Gap for Women and Underrepresented Minority Students

Boise State University (BSU) implemented an across-the-board reform of calculus instruction during the 2014 calendar year. The details of the reform, described elsewhere (Bullock, 2015), (Bullock 2016), involve both pedagogical and curricular reform. Gains from the project have included a jump in Calculus I pass rate, greater student engagement, greater instructor satisfaction, a shift toward active learning pedagogies, and the emergence of a strong collaborative teaching community. This paper examines the effects of the reform on student retention. Since the curricular reform involved pruning some content and altering course outcomes, which could conceivably have negative downstream impacts, we report on student success in post-requisite mathematics and engineering coursework. To explore the effects of the Calculus reform on retention we focused on whether or not students are retained at the university immediately subsequent to the year in which they encounter Calculus I. We divided 3002 student records into two groups: those who encountered the new version of Calculus and those who had the traditional experience. We then compared retention rates for the two groups. We found that the new Calculus course improved retention (relative to the old) by 3.4 percentage points; a modest, but statistically significant (p = 0.020) result. University retention rates for women, under-represented minorities (URM), and Pell-eligible students were also computed. All three subgroups showed gains, with URM leading with 6.3 percentage points of improved retention (p = 0.107) We then considered retention within STEM as a measure of how the Calculus reform influenced students. For the same groups of students, we computed the rate at which STEM majors were retained in STEM. Once again we found a modest overall gain of 3.3 percentage points (p = .078). We found strong effects on women and underrepresented minorities (URM). The new Calculus course improved retention for both of these groups by more than 9 percentage points, a large effect. At this university, under the old Calculus, women used to lag men in STEM retention by about 8 percentage points. After the Calculus reform this gap nearly vanished, shrinking to 0.5 percentage points. Under the old Calculus, STEM retention of URM students used to lag that of non-URM. After the Calculus reform the gap flipped, so that underrepresented minority students are now retained in STEM at higher rates than non-URM. As a final result we examined student success in courses that typically follow Calculus I. Here the metric is pass rate, and we compared pass rates between the students who took the new Calculus against those who took the old. For additional comparison we also included students who transferred into post-Calculus course work. Once again the reformed Calculus course led to better results

Secondary implementation of interactive engagement teaching techniques: Choices and challenges in a Gulf Arab context

We report on a "Collaborative Workshop Physics" instructional strategy to deliver the first IE calculus-based physics course at Khalifa University, UAE. To these authors' knowledge, this is the first such course on the Arabian Peninsula using PER-based instruction. A brief history of general university and STEM teaching in the UAE is given. We present this secondary implementation (SI) as a case study of a novel context and use it to determine if PER-based instruction can be successfully implemented far from the cultural context of the primary developer and, if so, how might such SIs differ from SIs within the US. With these questions in view, a pre-reform baseline of MPEX, FCI, course exam and English language proficiency data are used to design a hybrid implementation of Cooperative Group Problem Solving. We find that for students with high English proficiency, normalized gain on FCI improves from = 0.16+/-0.10 pre- to = 0.47+/-0.08 post-reform, indicating successful SI. We also find that is strongly modulated by language proficiency and discuss likely causes. Regardless of language skill, problem-solving skill is also improved and course DFW rates drop from 50% to 24%. In particular, we find evidence in post-reform student interviews that prior classroom experiences, and not broader cultural expectations about education, are the more significant cause of expectations at odds with the classroom norms of well-functioning PER-based instruction. This result is evidence that PER-based innovations can be implemented across great changes in cultural context, provided that the method is thoughtfully adapted in anticipation of context and culture-specific student expectations. This case study should be valuable for future reforms at other institutions, both in the Gulf Region and developing world, facing similar challenges involving SI of PER-based instruction outside the US.Comment: v1: 28 pages, 9 figures. v2: 19 pages, 6 figures, includes major reorganization and revisions based on anonymous peer review. v3: 19 pages, 6 figures, minor revisions based on anonymous peer revie

Scientific reasoning abilities of non-science majors in physics-based courses

We have found that non-STEM majors taking either a conceptual physics or astronomy course at two regional comprehensive institutions score significantly lower pre-instruction on the Lawson's Classroom Test of Scientific Reasoning (LCTSR) in comparison to national average STEM majors. The majority of non-STEM students can be classified as either concrete operational or transitional reasoners in Piaget's theory of cognitive development, whereas in the STEM population formal operational reasoners are far more prevalent. In particular, non-STEM students demonstrate significant difficulty with proportional and hypothetico-deductive reasoning. Pre-scores on the LCTSR are correlated with normalized learning gains on various concept inventories. The correlation is strongest for content that can be categorized as mostly theoretical, meaning a lack of directly observable exemplars, and weakest for content categorized as mostly descriptive, where directly observable exemplars are abundant. Although the implementation of research-verified, interactive engagement pedagogy can lead to gains in content knowledge, significant gains in theoretical content (such as force and energy) are more difficult with non-STEM students. We also observe no significant gains on the LCTSR without explicit instruction in scientific reasoning patterns. These results further demonstrate that differences in student populations are important when comparing normalized gains on concept inventories, and the achievement of significant gains in scientific reasoning requires a re-evaluation of the traditional approach to physics for non-STEM students.Comment: 18 pages, 4 figures, 3 table

Does Retention Interval Matters in Mathematics Performance?

This study describes and investigates if an association exist between the retention intervals of the three-grouped student respondents in high school and their performance in the basic algebra. The respondent’s performances were categorized into different proficiency levels namely the far below basic, below basic, basic, above basic and proficient. Results revealed that a highly significant association was found between the retention intervals and the level of performance of the respondents. The level of performance of the respondents significantly increased with varying retention interval. An improved shift in the level of performances were observed from test to retest. The recall of information in the basic algebra was strengthened as retention interval increases particularly to high performing students. Respondents’ exposure to related advance academic mathematics learnings, practice as well as maturity may have contributed to the mathematical performance across retention intervals of the respondents

The Interactions of Relationships, Interest, and Self-Efficacy in Undergraduate Physics

This collected papers dissertation explores students’ academic interactions in an active learning, introductory physics settings as they relate to the development of physics self-efficacy and interest. The motivation for this work extends from the national call to increase participation of students in the pursuit of science, technology, engineering, and mathematics (STEM) careers. Self-efficacy and interest are factors that play prominent roles in popular, evidence-based, career theories, including the Social cognitive career theory (SCCT) and the identity framework. Understanding how these constructs develop in light of the most pervasive characteristic of the active learning introductory physics classroom (i.e., peer-to-peer interactions) has implications on how students learn in a variety of introductory STEM classrooms and settings structured after constructivist and sociocultural learning theories. I collected data related to students’ in-class interactions using the tools of social network analysis (SNA). Social network analysis has recently been shown to be an effective and useful way to examine the structure of student relationships that develop in and out of STEM classrooms. This set of studies furthers the implementation of SNA as a tool to examine self-efficacy and interest formation in the active learning physics classroom. Here I represent a variety of statistical applications of SNA, including bootstrapped linear regression (Chapter 2), structural equation modeling (Chapter 3), and hierarchical linear modeling for longitudinal analyses (Chapter 4). Self-efficacy data were collected using the Sources of Self-Efficacy for Science Courses – Physics survey (SOSESC-P), and interest data were collected using the physics identity survey. Data for these studies came from the Modeling Instruction sections of Introductory Physics with Calculus offered at Florida International University in the fall of 2014 and 2015. Analyses support the idea that students’ perceptions of one another impact the development of their social network centrality, which in turn affects their self-efficacy building experiences and their overall self-efficacy. It was shown that unlike career theories that emphasize causal relationships between the development of self-efficacy and the subsequent growth of student interest, in this context student interest takes precedence before the development of student self-efficacy. This outcome also has various implications for career theories