Pub Date : 2023-12-02DOI: 10.1007/s40753-023-00230-2
Jocelyn Rios
Active learning practices, like groupwork, are becoming more widely used in post-secondary mathematics classrooms. These practices are often talk-intensive and require interpersonal interactions. As such, it remains an open question the extent to which practices like groupwork equitably support students with different social identities, including identities that center language. The goal of this paper is to use critical quantitative methodology to analyze the experiences of students in introductory college mathematics courses, particularly in courses that require peer collaboration. The data for this paper stems from surveys completed by 464 undergraduate students with different language backgrounds. The analysis identifies relationships that existed between the identities students brought to the classroom and the identities they developed in introductory mathematics courses. Using linear regression models, the study found that students’ comfort speaking during class and the language they preferred to do mathematics in were associated with practice-linked identities, like sense of belonging among peers. Findings also suggest an interaction between these variables and the frequency that students engaged in peer collaboration. This study contributes to the growing body of literature documenting how students with marginalized identities may have differential experiences with active learning practices, like groupwork.
{"title":"Language, Comfort Speaking, and Collaboration: A QuantCrit Analysis of Multilingual Students’ Experiences in Introductory College Mathematics Courses","authors":"Jocelyn Rios","doi":"10.1007/s40753-023-00230-2","DOIUrl":"https://doi.org/10.1007/s40753-023-00230-2","url":null,"abstract":"<p>Active learning practices, like groupwork, are becoming more widely used in post-secondary mathematics classrooms. These practices are often talk-intensive and require interpersonal interactions. As such, it remains an open question the extent to which practices like groupwork equitably support students with different social identities, including identities that center language. The goal of this paper is to use critical quantitative methodology to analyze the experiences of students in introductory college mathematics courses, particularly in courses that require peer collaboration. The data for this paper stems from surveys completed by 464 undergraduate students with different language backgrounds. The analysis identifies relationships that existed between the identities students brought to the classroom and the identities they developed in introductory mathematics courses. Using linear regression models, the study found that students’ comfort speaking during class and the language they preferred to do mathematics in were associated with practice-linked identities, like sense of belonging among peers. Findings also suggest an interaction between these variables and the frequency that students engaged in peer collaboration. This study contributes to the growing body of literature documenting how students with marginalized identities may have differential experiences with active learning practices, like groupwork.</p>","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-24DOI: 10.1007/s40753-023-00229-9
Katrina Stullken Rothrock, A. Susan Gay
Knowing what first-time freshmen in mathematics believe to be true about themselves as they arrive on a college campus provides valuable perspectives about freshman mathematics learners. We investigated how gender, high school mathematics course history, and university mathematics course placement are related to first-time freshmen’s mathematical mindset, identity, self-efficacy, and use of self-regulated learning strategies. A survey was completed by 293 first-time freshmen at a four-year university in the United States. Participants were enrolled in one of three university mathematics courses and completed a survey during the first week of class in Fall 2018. Results found that students’ mean scores for mathematical self-efficacy and use of self-regulated learning strategies were close to 4, and mathematical mindset and identity were close to 3 on a 5-point scale, where larger values corresponded to a more positive response. A multivariate analysis of variance was conducted on mean subscale scores, followed by analyses of variance. Calculus I students expressed significantly stronger mathematical identity than Intermediate Algebra students, and students who took advanced mathematics courses in high school expressed both stronger mathematical identity and self-efficacy than those who had taken only up to Algebra 2. Gender was not a significant differentiator among students, and neither mathematical mindset nor use of self-regulated learning strategies varied significantly across any subgroups.
{"title":"What College Freshmen Believe About Themselves: An Investigation of Mathematical Mindset, Identity, Self-Efficacy, and Use of Self-Regulated Learning Strategies in Mathematics","authors":"Katrina Stullken Rothrock, A. Susan Gay","doi":"10.1007/s40753-023-00229-9","DOIUrl":"https://doi.org/10.1007/s40753-023-00229-9","url":null,"abstract":"<p>Knowing what first-time freshmen in mathematics believe to be true about themselves as they arrive on a college campus provides valuable perspectives about freshman mathematics learners. We investigated how gender, high school mathematics course history, and university mathematics course placement are related to first-time freshmen’s mathematical mindset, identity, self-efficacy, and use of self-regulated learning strategies. A survey was completed by 293 first-time freshmen at a four-year university in the United States. Participants were enrolled in one of three university mathematics courses and completed a survey during the first week of class in Fall 2018. Results found that students’ mean scores for mathematical self-efficacy and use of self-regulated learning strategies were close to 4, and mathematical mindset and identity were close to 3 on a 5-point scale, where larger values corresponded to a more positive response. A multivariate analysis of variance was conducted on mean subscale scores, followed by analyses of variance. Calculus I students expressed significantly stronger mathematical identity than Intermediate Algebra students, and students who took advanced mathematics courses in high school expressed both stronger mathematical identity and self-efficacy than those who had taken only up to Algebra 2. Gender was not a significant differentiator among students, and neither mathematical mindset nor use of self-regulated learning strategies varied significantly across any subgroups.</p>","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-15DOI: 10.1007/s40753-023-00231-1
Ghislaine Gueudet, Elena Nardi, Elise Lockwood
{"title":"A Tribute to Anna Sierpińska","authors":"Ghislaine Gueudet, Elena Nardi, Elise Lockwood","doi":"10.1007/s40753-023-00231-1","DOIUrl":"https://doi.org/10.1007/s40753-023-00231-1","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-14DOI: 10.1007/s40753-023-00228-w
Eng Guan Tay
{"title":"Review of Practice-oriented Research in Tertiary Mathematics Education by Biehler et al. (2022)","authors":"Eng Guan Tay","doi":"10.1007/s40753-023-00228-w","DOIUrl":"https://doi.org/10.1007/s40753-023-00228-w","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135804008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1007/s40753-023-00227-x
Tommy Dreyfus, Michal Tabach, Chris Rasmussen
{"title":"Bafflement in an Inquiry-based College Mathematics Classroom","authors":"Tommy Dreyfus, Michal Tabach, Chris Rasmussen","doi":"10.1007/s40753-023-00227-x","DOIUrl":"https://doi.org/10.1007/s40753-023-00227-x","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-30DOI: 10.1007/s40753-023-00225-z
Vahid Borji, Rafael Martínez-Planell, María Trigueros
{"title":"University Students’ Understanding of Directional Derivative: An APOS Analysis","authors":"Vahid Borji, Rafael Martínez-Planell, María Trigueros","doi":"10.1007/s40753-023-00225-z","DOIUrl":"https://doi.org/10.1007/s40753-023-00225-z","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136342643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 10.1007/s40753-023-00226-y
Amelia Stone-Johnstone
Abstract Many postsecondary institutions across the United States have adopted the corequisite model of academic support to facilitate student learning and the successful completion of introductory mathematics courses within students’ first year of college enrollment. While research have highlighted the benefits of corequisites in terms of academic outcomes, there is little qualitative research on the impact of this model of academic support on students beyond course grades. Through student narratives, this study documents how one university implemented their College Algebra corequisite and investigates the impact of the classroom climate of a corequisite course on students’ attitudes toward mathematics. This study shows that though the classroom climate positively impacted the participants’ attitudes toward mathematics in general, the climate of the corequisite specifically had a greater impact on their beliefs about mathematics and perceptions of themselves as learners of mathematics. However, there were some identified drawbacks to the corequisite course including time-consuming coursework and occasionally unproductive group collaboration. These findings highlight the potential for corequisites to foster positive attitudes toward mathematics, yet it also demonstrated a need for greater intention in the course development to ensure a coherent course structure where course activities and assessments give way to meaningful and productive student engagement.
{"title":"Exploring the Impact of the Corequisite Classroom Climate on Students’ Attitudes Toward Mathematics","authors":"Amelia Stone-Johnstone","doi":"10.1007/s40753-023-00226-y","DOIUrl":"https://doi.org/10.1007/s40753-023-00226-y","url":null,"abstract":"Abstract Many postsecondary institutions across the United States have adopted the corequisite model of academic support to facilitate student learning and the successful completion of introductory mathematics courses within students’ first year of college enrollment. While research have highlighted the benefits of corequisites in terms of academic outcomes, there is little qualitative research on the impact of this model of academic support on students beyond course grades. Through student narratives, this study documents how one university implemented their College Algebra corequisite and investigates the impact of the classroom climate of a corequisite course on students’ attitudes toward mathematics. This study shows that though the classroom climate positively impacted the participants’ attitudes toward mathematics in general, the climate of the corequisite specifically had a greater impact on their beliefs about mathematics and perceptions of themselves as learners of mathematics. However, there were some identified drawbacks to the corequisite course including time-consuming coursework and occasionally unproductive group collaboration. These findings highlight the potential for corequisites to foster positive attitudes toward mathematics, yet it also demonstrated a need for greater intention in the course development to ensure a coherent course structure where course activities and assessments give way to meaningful and productive student engagement.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134960287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-25DOI: 10.1007/s40753-023-00224-0
Martin Mayerhofer, Marko Lüftenegger, Michael Eichmair
Abstract The transition from secondary to tertiary education is an exciting and yet challenging event in the educational biography of students. During this transition, students often meet with unexpected challenges, which may cause them to drop out from their degree program. Many universities offer bridging courses or longer-term interventions to support their incoming students in this period. To examine the effect of a bridging course designed to reduce gaps in prior mathematical knowledge, promote social-emotional well-being, and foster learning skills, we implement a repeated-measures intervention study. We analyze the outcomes of the intervention, which features tutors with special training, autonomous choice of topic areas, peer learning, and materials for self-directed learning. We measure the development of motivational beliefs reflecting the will to learn (achievement goals, satisfaction of basic psychological needs, implicit theories, self-efficacy) and the skills to learn (reactions to errors, self-regulated learning) at the secondary-tertiary transition. These aspects are captured at multiple measurement points among students (N = 679) who participate in the bridging course (intervention group) and those who do not (control group). The intervention boosts motivational beliefs related to social embeddedness and learning skills in the short term. The observed decrease in autonomy, competence, and self-efficacy might be explained by higher standards that students use for their self-assessment in the new peer group. In the long term, all aspects of the will to learn, except for social relatedness, show stable to strongly negative developments in both groups. Among those students who do not participate in the bridging course, mostly strongly negative developments are observed. The results suggest that the peer tutoring strategy is highly effective and the need for longer-term interventions to uphold the positive short-term effects.
{"title":"Impact of a Mathematics Bridging Course on the Motivation and Learning Skills of University Students","authors":"Martin Mayerhofer, Marko Lüftenegger, Michael Eichmair","doi":"10.1007/s40753-023-00224-0","DOIUrl":"https://doi.org/10.1007/s40753-023-00224-0","url":null,"abstract":"Abstract The transition from secondary to tertiary education is an exciting and yet challenging event in the educational biography of students. During this transition, students often meet with unexpected challenges, which may cause them to drop out from their degree program. Many universities offer bridging courses or longer-term interventions to support their incoming students in this period. To examine the effect of a bridging course designed to reduce gaps in prior mathematical knowledge, promote social-emotional well-being, and foster learning skills, we implement a repeated-measures intervention study. We analyze the outcomes of the intervention, which features tutors with special training, autonomous choice of topic areas, peer learning, and materials for self-directed learning. We measure the development of motivational beliefs reflecting the will to learn (achievement goals, satisfaction of basic psychological needs, implicit theories, self-efficacy) and the skills to learn (reactions to errors, self-regulated learning) at the secondary-tertiary transition. These aspects are captured at multiple measurement points among students (N = 679) who participate in the bridging course (intervention group) and those who do not (control group). The intervention boosts motivational beliefs related to social embeddedness and learning skills in the short term. The observed decrease in autonomy, competence, and self-efficacy might be explained by higher standards that students use for their self-assessment in the new peer group. In the long term, all aspects of the will to learn, except for social relatedness, show stable to strongly negative developments in both groups. Among those students who do not participate in the bridging course, mostly strongly negative developments are observed. The results suggest that the peer tutoring strategy is highly effective and the need for longer-term interventions to uphold the positive short-term effects.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135817654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-14DOI: 10.1007/s40753-023-00223-1
Jonathan Troup, Hortensia Soto, Aubrey Kemp
{"title":"Developing Geometric Reasoning of the Relationship of the Cauchy Riemann Equations and Differentiation","authors":"Jonathan Troup, Hortensia Soto, Aubrey Kemp","doi":"10.1007/s40753-023-00223-1","DOIUrl":"https://doi.org/10.1007/s40753-023-00223-1","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82851353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.1007/s40753-023-00220-4
L. Alcock, N. Attridge
{"title":"Refutations and Reasoning in Undergraduate Mathematics","authors":"L. Alcock, N. Attridge","doi":"10.1007/s40753-023-00220-4","DOIUrl":"https://doi.org/10.1007/s40753-023-00220-4","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79625045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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