More Like this

1. Case Studies of Undergraduate Students’ Agentive Participation in the Parallel Spaces of Calculus I Coursework and Peer-Led, Inquiry-Oriented, Complementary Instruction

   Yu, K; Greenstein, S (February 2024, Research on Undergraduate Mathematics Education (RUME))

   Calculus has long been known as a “gateway course” to STEM fields in postsecondary education. To address this issue, researchers in the Math Department at Mountain State University (pseudonym) designed a model of complementary instruction that features peer-facilitated workshops where Calculus I students work in groups on inquiry-oriented, groupworthy tasks. The purpose of this multiple-case study is to seek answers to the question, "How do undergraduate Calculus I students experience and navigate their learning of calculus in the parallel spaces of coursework and inquiry-oriented complementary instruction?" The findings of one case study are presented here and include characterizations of the different forms of agentive participation afforded to students in each of the two spaces, as well as their complementary nature relative to learning calculus with understanding. Implications for dismantling the persistent barriers imposed by calculus on access to postsecondary STEM fields are also discussed. 

   more » « less
2. Novel Representations of the Experiences of Calculus I Students’ Participation in the Parallel Spaces of Coursework and Complementary Instruction

   https://doi.org/10.31756/jrsmte.318SI  

   Yu, Karmen Tracy; Greenstein, Steven (January 2024, Journal of Research in Science, Mathematics and Technology Education)

   Calculus has long been known for its gatekeeping role in postsecondary students' pursuit of STEM careers. In addressing this pressing issue, researchers at Montclair State University developed a model of peer-led complementary instruction to engage Calculus I students in small-group, collaborative problem solving on inquiry-oriented, groupworthy tasks. This work comes from a multiple-case study that sought to address the question, “How do undergraduate students experience and navigate their calculus learning in the parallel spaces of coursework and inquiry-oriented complementary instruction?” The analytic representations that were constructed to represent the findings of that study are presented here. Those findings include characterizations of the different forms of Calculus I students’ agentive participation and the figured worlds of class and complementary instruction. The analytic representations depict those findings in the form of word clouds and Venn diagrams. The analytical representations of “Victor’s” participation are presented and discussed here, and an argument is made for their particular representational power and efficiency. As such, this work seeks to make a methodological contribution to education research that seeks to characterize the nature of participation by the actors in figured worlds. 

   more » « less
3. Establishing a new standard of care for calculus using trials with randomized student allocation

   https://doi.org/10.1126/science.ade9803  

   Kramer, Laird; Fuller, Edgar; Watson, Charity; Castillo, Adam; Oliva, Pablo Duran; Potvin, Geoff (September 2023, Science)

   Calculus, the study of change in processes and systems, serves as the foundation for many STEM disciplines. Traditional, lecture-based calculus instruction may present a barrier for students seeking STEM degrees, limit their access to STEM professions, and block their potential to address society’s challenges. A large-scale pragmatic trial with randomized student allocation was conducted to compare two calculus instruction styles: active student engagement (treatment condition) versus traditional, lecture-based instruction (control condition). A sample of 811 university students were studied across 32 sections taught by 19 instructors over three semesters at a large, US-based Hispanic-serving institution. Large effect sizes were consistently measured for student learning outcomes in the treatment condition, which demonstrates a new standard for calculus instruction and increased opportunities for completion of STEM degrees. 

   more » « less
4. Detailing Racialized and Gendered Mechanisms of Undergraduate Precalculus and Calculus Classroom Instruction

   https://doi.org/10.1080/07370008.2020.1849218  

   Leyva, Luis A.; Quea, Ruby; Weber, Keith; Battey, Dan; López, Daniel (January 2021, Cognition and Instruction)

   null (Ed.)

   Undergraduate mathematics education can be experienced in discouraging and marginalizing ways among Black students, Latin
   students, and white women. Precalculus and calculus courses, in particular, operate as gatekeepers that contribute to racialized and gendered attrition in persistence with mathematics coursework and pursuits in STEM (science, technology, engineering, and mathematics). However, student perceptions of instruction in these introductory mathematics courses have yet to be systematically examined as a contributor to such attrition. This paper presents findings from a study of 20 historically marginalized students’ perceptions of precalculus and calculus instruction to document features that they found discouraging and marginalizing. Our analysis revealed how students across different race-gender identities reported stereotyping as well as issues of representation in introductory mathematics classrooms and STEM fields as shaping their perceptions of instruction. These perceptions pointed to the operation of three racialized and gendered mechanisms in instruction: (i) creating differential opportunities for participation and support, (ii) limiting support from same-race, same-gender peers to manage negativity in instruction, and (iii) activating exclusionary ideas about who belongs in STEM fields. We draw on our findings to raise implications for research and practice in undergraduate mathematics education. 

   more » « less
5. Student attitudes in an innovative active learning approach in calculus

   https://doi.org/10.1080/0020739X.2021.2023771  

   Castillo, Adam J.; Durán, Pablo; Fuller, Edgar; Watson, Charity; Potvin, Geoff; Kramer, Laird H. (February 2022, International journal of mathematical education in science and technology)

   A study conducted by the Mathematical Association of America showed that calculus not only has significant effects on students’ decision to pursue STEM fields, but also on their attitudes towards mathematics. Inspired by this large-scale study, the present study sought to deepen the current understanding of the impact of calculus on student attitudes towards mathematics. Results of an implementation of the Modeling Practices in Calculus (MPC) model, an innovative active learning in mathematics (ALM) approach, in Calculus I at a large, urban, research intensive (R1) institution are presented. Using a randomized-control trial research design, stu- dents were randomly assigned to either traditional, lecture-based classrooms, or MPC classrooms. The Attitudes Towards Mathematics Inventory (ATMI) was used to measure student attitudes at the begin- ning and end of the course and results were compared from both MPC and traditional sections. Overall, MPC sections showed improve- ment over traditional instruction by having less negative impact on student attitudes. The enjoyment and self-confidence ATMI sub- scales showed significant differences at course completion for both semesters, when controlling for pre-ATMI score and term. Further- more, the MPC model had a positive impact on female students’ self-confidence as opposed to male students, acting as a gender equalizer. 

   more » « less