Introductory Mathematics Courses Research Articles

Linking self-regulated learning to community of inquiry in online undergraduate courses: A person-centered approach

AbstractThe Community of Inquiry (CoI) framework has gained widespread recognition as a theoretical model for understanding student learning in online environments. Despite its prevalence, CoI has been critiqued for its limited emphasis on learners’ proactive roles in self-regulating their own learning. To address this, researchers have suggested integrating self-regulated learning (SRL) into the CoI framework. This integration calls for empirical research to explore the relationship between SRL and the three established CoI presences: teaching, social, and cognitive. Using a person-centered approach, this study examines how varying SRL skills among 750 undergraduate students in an online introductory mathematics course are related to the three CoI components. Latent profile analyses identified five distinct SRL profiles: minimal regulators, low regulators with limited social skills, low regulators, moderate regulators, and competent regulators. We found that students in higher SRL profiles demonstrated higher perception of CoI, whereas those in relatively lower SRL profiles showed lower levels of perceived CoI. Our findings underscore the importance of incorporating self-regulation in the CoI framework for a more comprehensive understanding of online learning.

First-year engineering students’ affective behavior about mathematics in relation to their performance

The present study examines the first-year engineering students’ attitudes towards mathematics, their beliefs and self-efficacy about mathematics, as part of their affective performance, in relation to their mathematical academic performance before and after attending an introductory mathematics course. It aims to contribute on the ongoing discussion about the teaching of mathematics at the level of higher education in engineering programs. First-year engineering students completed a questionnaire and a test after their entrance at the university. Their mathematical performance was examined by using their results at the midterm and the final mathematical mark during AMAT111 course offered at the first semester of their studies. Results indicated that aspects of the affective domain were related with students’ performance, while the predominant role belonged to their previous mathematical knowledge and skills (as learning outcome of the high school education), which undoubtedly need further enhancement. The belief about a formalistic perspective of mathematics and the lack of understanding of the implementation of the mathematical concepts on engineering problem solving situations were obstacles for them on recognizing the importance of attending mathematics courses as part of their engineering studies. Discussion concentrates on the following up steps, which have to be done at the level of higher education in order to face the initial difficulties, which have been identified.

Evaluation of Intertwined Project-Based Learning in Introductory Mathematics and Statistics Courses

Evaluation of Intertwined Project-Based Learning in Introductory Mathematics and Statistics Courses

Exploring the Impact of the Corequisite Classroom Climate on Students’ Attitudes Toward Mathematics

AbstractMany 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.

Enhancing the Success of College Algebra Students by Incorporating Adaptive Technologies

College students in the United States often enrol in introductory mathematics courses to acquire skills and knowledge that will enable them to solve related problems in their careers and daily activities. However, previous studies have shown limited levels of improvement that perpetuate a lack of proficiency. As a result, the gap in performance between top students and those at the bottom continues to increase. Using modern technology has been suggested as part of the solution to help students resolve their difficulties in mathematics and achieve better learning outcomes. This study assesses the longitudinal effect of redesigning College Algebra classes at a large public university, switching from a modified emporium model to a lab-based adaptive model. The results show that after redesigning the course, the pass rate increased from 68% to consistently being over 80%, while the withdrawal rate fell from 8% to 3%.

Predicting Student Success in Co-remediated General Education Mathematics Courses at a Large Urban Public University

Placement and support of students in first-year mathematics courses at institutions of higher education has long been a consequential issue. In a bid to address it, many systems and institutions of higher learning have elected to implement a co-remediation framework in place of pre-remediation, due in large part to the prohibitive cost of the latter, both in terms of financial resource, as well as student academic progress. Accompanying this evolution has been the expansion of the introductory mathematics curriculum beyond algebra to include statistics and quantitative reasoning. The present study discusses three distinct introductory mathematics courses at a large urban public M.S. granting institution in the U.S., with the goal of identifying the characteristics that correlate with success in each. Conditional probability and non-completion rate analyses were implemented to compare student performance in each course. Predictive models were then trained and validated, building insight concerning the differential relationships of demographic and academic covariates with course completion.

Implementasi Pembelajaran Drill and Practice dengan Proyek Untuk Meningkatkan Hasil Capaian Belajar Mahasiswa

The learning of introductory mathematics courses in the Undikma FSTT Mathematics Education Study program has so far been carried out in a monotonous manner. The lecturer explains the material, gives examples of questions, and gives exercises. The impact is the low achievement of student learning outcomes. Therefore, the purpose of this research is to improve student learning outcomes through the application of drill and practice learning with projects. This type of research is classroom action research. Data collection was carried out by evaluating student learning outcomes. The results of the study obtained an average score of student learning outcomes reaching 89.2% in the Very Good category. Thus, it can be concluded that the Implementation of Drill and Practice Learning with Projects able to Improve Student Learning Outcomes

A quantitative exploration of Queer-spectrum students' experiences in introductory undergraduate mathematics courses.

Research into the experiences of students in mathematics with a marginalized sexual identity has remained largely underexplored, relegating these experiences and individuals to remain invisible. In this study, we leverage Queer Theory to address this gap in research by reporting on the experiences of Queer-spectrum undergraduate students (n = 2,454) enrolled in introductory mathematics courses (Precalculus, Calculus 1, and Calculus 2) across the United States. Drawing on student data (n = 24,327) from the Student Post-Secondary Instructional Practices Survey, we examine reported outcomes of math learning experiences and access to learning environments. Overall, within introductory math courses, sexual identity had a significant relationship with accessing learning environments and mathematical learning experiences. Asexual students were among those that reported higher levels of interactions with peers and instructors, a greater sense of community & participation, positive math affect, and were more likely to access learning environments external to the course yet anticipated receiving a lower course grade when compared to straight students. Bisexual students reported lower levels of interactions with instructors, a diminished sense of community & participation, math engagement, positive math affect, and were less likely to access learning environments compared to straight students. These findings suggest that Queer-spectrum students experience mathematical learning in a different manner than their straight peers and in relation to other Queer spectrum identities. Queer-spectrum students with a sexualized identity perceive that mathematics environments are not normative places to be a part of the community, resulting in negative dispositions, reduced interactions, and lower academic success. The impact of sexual identity, although small, contributes to negative indicators of positive mathematical experiences and suggests that the normative discourses in mathematics that are identity neutral, heteronormative, and aligned with binary thinking are differentially impacting Queer-spectrum students.

Predicting STEM persistence from mathematics affect, pedagogical perceptions and Calculus I setting

A significant portion of mathematics education research has focused on factors that impact student pursuit of science, technology, engineering and mathematics (STEM). Low rates of STEM student enrollment combined with high drop-out rates have consistently drawn attention from educators, administrators and policy-makers at all levels. Many studies have been dedicated to the investigation of the influential factors that exacerbate this problem, and one factor that has been cited consistently is the learning experience in a specific introductory mathematics course – first-semester calculus. Research has shown strong relationships between STEM persistence and student affect in this context including their attitudes, beliefs, confidence and enjoyment related to mathematics, and between persistence and student perceptions of pedagogy in these courses. In this paper, we extend prior work by the authors by investigating the impact of three different Calculus I course settings on these relationships and find that some course structures have a moderating effect on these relationships. We present those results and indicate some possible ways to leverage pedagogical structures to improve student persistence in pursuing a STEM major.

Development of an Item Bank for Measuring Students’ Conceptual Understanding of Real Functions

It is known that students have many misconceptions about concepts related to function. By discovering misconceptions using an appropriate measurement instrument, we can determine what changes we need to make in the real functions curriculum to improve learning outcomes. Therefore, we designed an item bank for measuring conceptual understandings of real functions with items that require ability to move from one representation of the same concept to another. By surveying university professors, we conducted an expert judgment and content validity of the test. Altogether 36 multiple-choice items based on concepts related to real function with a single correct answer and three distractors have been field-tested by means of a paper and pencil survey, which included 80 freshman students from the Faculty of Science at the University of Sarajevo. By surveying students, we checked technical characteristics of items and their cognitive validity. Results from surveying university professors and students show that the test meets the requirements of content and cognitive validity. Results from the item analysis (item difficulty index, item discrimination index, and point-biserial coefficient) and test analysis (test reliability and Ferguson’s delta) show that 32 out of 36 items have good psychometric characteristics, and they are reliable for measuring students’ understanding and skills in introductory mathematics courses at universities. We noticed that students have a poor understanding of certain concepts, regardless of the representation, and that there is no coordination between representations of the same concept.

Students' Mathematical Concept Understanding in Introductory Mathematics Course

The Introductory Mathematics Course is an initial course that students must master before they study advanced courses. However, many students still need higher grades in this course. This study aims to analyze the students' mathematical concepts understanding in Introductory Mathematics Course. This study is a descriptive qualitative study involving three mathematics education students at an Islamic University in Jambi. Each has high, medium, and low abilities based on the mathematical concept of understanding test results. The students were also interviewed to confirm their test answers. Data were analyzed descriptively using the method-triangulation. The results of this study indicate that, in general, the students' mathematical concepts understanding in Introductory Mathematics Course is in the medium category. A student with high ability can answer all the questions correctly, while ones with medium and low abilities still need to correct some things. The students with medium and low abilities must train more and get used to working on concept-understanding questions. Learning methods are also needed that further hone their ability to understand mathematical concepts.

Characteristics of interactive classrooms that first year students find helpful

BackgroundImplementing research-based teaching practices has been repeatedly cited as an important factor for student success in university mathematics courses. Many research-based practices increase the amount of student–student and/or student–instructor interaction. However, some instructors are hesitant to implement such practices because they anticipate their students reacting negatively to experiencing an interactive classroom. As part of a larger project studying introductory undergraduate mathematics courses in the United States, we investigated students’ perceptions of the helpfulness of various classroom characteristics, particularly those that require interaction.ResultsFrom analyzing quantitative student data, we found that students reported interactive classroom characteristics (e.g., group work) as less prevalent than other classroom characteristics (e.g., lecture). Moreover, the students tended to regard characteristics that they reported experiencing often as helpful for their learning. From analyzing qualitative data from student focus groups, we found that students considered several indicators when identifying if a characteristic was helpful for their learning. In particular, students suggested that they can identify a characteristic as helpful for their learning when it supported them in solving assigned problems and understanding why the procedures work, earning good grades, building on their knowledge or applying it in different contexts, and teaching others.ConclusionsThe key finding from our work is that students are likely to view classroom characteristics that they experience more often as more helpful for their learning and are less likely to view characteristics that they rarely experience as helpful for their learning. Students view the characteristics that they regularly experience as helping them to solve problems and understand why the procedures work, earn good grades, build on their knowledge or apply it in different contexts, and teach others. We discuss important implications for practice, policy, and research as it relates to both student and instructor buy-in for increasing interactions in class.

Developing the Student Postsecondary Instructional Practices Survey in Mathematics for Measuring Student Experiences in Introductory Mathematics Courses

ABSTRACT Active Learning is becoming a standard method of delivering instruction in mathematics courses across the country. Researchers, administrators, policy makers, and instructors all need access to valid means of measuring practices used in the classroom. Drawing on the Postsecondary Instructional Practices Survey, the Student Postsecondary Instructional Practices Survey in Mathematics (SPIPS-M) was developed to measure the undergraduate student perspective of active learning. Factor analysis from 10 institutions (N = 16,495 surveys) supports a 4-factor model with a plausible theoretical foundation connected to the four pillars of Inquiry-Based Mathematics Education, by measuring the degree to which students perceive 1) their own engagement with meaningful mathematics, 2) collaboration to process mathematical ideas, 3) participation and formation of community, and 4) contribution of their own ideas for immediate instructor feedback. The instrument provides a new mechanism for program evaluation and course formative feedback. Ultimately the SPIPS-M instrument will allow a better understanding of the nuances of student experiences in their mathematics courses.

“It Seems like They Purposefully Try to Make as Many Kids Drop”: An Analysis of Logics and Mechanisms of Racial-Gendered Inequality in Introductory Mathematics Instruction

ABSTRACT Introductory mathematics courses, including precalculus and calculus, largely influence Black and Latin* students’ persistence and sense of belonging in STEM. However, prior research on instruction in these courses for advancing more equitable outcomes is limited. This paper presents findings from a study of 18 Black and Latina/o students’ perceptions of introductory mathematics instruction as a racialized and gendered experience at a large, public, and historically white research university. Sociological perspectives of logics and mechanisms of inequality guided an analysis of Black and Latina/o students’ group interview responses on how instruction perpetuates racial and gendered oppression. Two logics were identified: (i) Instructors hold more mathematical authority than students in classrooms; and (ii) Calculus coursework is used to weed out students ‘not cut out’ for STEM. These logics, coupled with the influence of broader sociohistorical forces (e.g., cultural scripts of behavior, stereotypes), gave rise to mechanisms of inequality through seemingly neutral instructional practices that reinforce racial-gendered distribution of classroom participation and STEM persistence. Our findings inform implications for STEM higher education researchers and mathematics faculty to foster socially affirming STEM instruction, especially in introductory courses.

Detailing Racialized and Gendered Mechanisms of Undergraduate Precalculus and Calculus Classroom Instruction

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.

The effects of instructors' use of online discussions strategies on student participation and performance in university online introductory mathematics courses

This study examines instructor strategies for designing and participating in online discussions and how these strategies influence their students' participation and course performance in university introductory online mathematics courses. The study leveraged data and text mining techniques to examine five years of online discussion data automatically collected by a Learning Management System from 72 introductory online mathematics courses involving over 2800 instructors and students who collectively contributed over 22,000 posts. A classification and regression tree (CART) analysis of instructor strategies revealed four instructor participation variables (open-ended discussion, grading, discussion setting, elaborated feedback) that impacted student course performance and nine that did not. Further, students in courses where instructors used open-ended discussion prompts and graded posts had higher average final course grades. An examination of how instructor discussion strategies influenced student participation found that subgroups of students with lower average final course grades tended to engage in less online speaking and listening, while also contributing more posts categorized as social interactions and fewer related to course content. Students in subgroups with higher average final course grades tended to engage in more online listening and contributed more posts coded as higher in knowledge construction.

For physics majors, gender differences in introductory physics do not inform future physics performance

Analysis of institutional data for physics majors showing predictive relationships between required mathematics and physics courses in various years is important for contemplating how the courses build on each other and whether there is need to make changes to the curriculum for the majors to strengthen these relationships. We used 15 years of institutional data at a US-based large research university to investigate how introductory physics and mathematics courses predict male and female physics majors’ performance on required advanced physics and mathematics courses. We used structure equation modeling (SEM) to investigate these predictive relationships and find that among introductory and advanced physics and mathematics courses, there are gender differences in performance in favor of male students only in the introductory physics courses after controlling for high school GPA. We found that a measurement invariance fully holds in a multi-group SEM by gender, so it was possible to carry out analysis with gender mediated by introductory physics and high school GPA. Moreover, we find that these introductory physics courses that have gender differences do not predict performance in advanced physics courses. In other words, students could be using invalid data about their introductory physics performance to make their decision about whether physics is the right field for them to pursue, and those invalid data in introductory physics favor male students. Also, introductory mathematics courses predict performance in advanced mathematics courses which in turn predict performance in advanced physics courses. Furthermore, apart from the introductory physics courses that do not predict performance in future physics courses, there is a strong predictive relationship between the sophomore, junior and senior level physics courses.

Perceptions of Students on Introductory University Mathematics: Perspective Study on First Year Undergraduate Students

This paper mainly sought to find out how students’ perceptions influence students in their introductory university mathematics: The perspective of first-year undergraduate students of the University of Cape Coast. Specifically, the study sought to find out first-year students’ perceptions about SHS mathematics and also to find out the perception students have about introductory university mathematics. The population size of the study was 600 students. The research design used was the descriptive survey and the stratified random sampling technique was used to select the sample. A questionnaire was designed and used to collect the data. From our findings, it was established that students have a positive perception about SHS mathematics and the introductory university mathematics course. Based on the findings of the study, it was recommended that teachers are encouraged to use learner centered approach of teaching mathematics with little regard to the teacher centered approach since the former ensures active participation of students in the teaching-learning process and facilitates understanding while the latter makes students mere passive listeners Keywords: Perception, introductory, students, undergraduate and first-year DOI: 10.7176/JEP/11-25-01 Publication date: September 30 th 2020

Introductory College Mathematics for the Life Sciences: Has Anything Changed?

This paper focuses on issues concerning the introductory college mathematics sequence with an emphasis on students interested in the life sciences, and concentration on the time after the publication of BIO2010 (BIO2010 in Transforming Undergraduate Education for Future Research Biologists, National Academies of Science, Medicine and Engineering, Washington, 2003). It also explores the potential uses of books targeted at introductory mathematics courses for life science majors today. As relevant background, we look at the evolution of the way that calculus has been taught over the past 50 years, including at the high school level. We also explore the implications of changes in technology and course delivery, such as online education. As we discuss different books and introductory course ideas, we focus on the needs of biology students, the inclusion of real-world problems and models, the role of technology, and the impact of data science. The paper is organized as follows: Sect. 1 provides some personal background with calculus dating back to the 1970s, and changes in calculus prior to BIO2010. Section 2 introduces goals for an introductory mathematics sequence and evaluates the calculus sequence in light of those goals. Sections 3–7 discuss various issues that will help to understand issues and challenges for introductory mathematics for the life sciences: Calculus in high school (Sect. 3), equity issues relative to calculus and other math topics (Sect. 4), the impact of online education (Sect. 5), math as a stumbling block for college students (Sect. 6), and the increasing importance and value of teaching data science (Sect. 7). Section 8 reviews the development of books in light of these issues and challenges. The last section (Sect. 9) summarizes conclusions.

Individual differences in the preference for worked examples: Lessons from an application of dispositional learning analytics

SummaryWorked‐examples have been established as an effective instructional format in problem‐solving practices. However, less is known about variations in the use of worked examples across individuals at different stages in their learning process in student‐centred learning contexts. This study investigates different profiles of students' learning behaviours based on clustering learning dispositions, prior knowledge, and the choice of feedback strategies in a naturalistic setting. The study was conducted on 1,072 students over an 8‐week long introductory mathematics course in a blended instructional format. While practising exercises in a digital learning environment, students can opt for tutored problem solving, untutored problem solving, or call worked examples. The results indicated six distinct profiles of learners regarding their feedback preferences in different learning phases. Finally, we investigated antecedents and consequences of these profiles and investigated the adequacy of used feedback strategies concerning ‘help‐abuse’. This research indicates that the use of instructional scaffolds as worked‐examples or hints and the efficiency of that use differs from student to student, making the attempt to find patterns at an overall level a hazardous endeavour.