College Mathematics Research Articles

AN ASSESSMENT-DIRECTED, STUDENT-CENTERED, AND MASTERY-BASED MODEL OF TEACHING AND LEARNING IN MATHEMATICS

This is a descriptive article illustrating a multi-year research study in mathematics education of college students in the U.S. It focuses on the first two years in the undergraduate mathematics curriculum. The study presents the theory, practice, and results of an innovative instructional program (Keystone model) applied to algebra classes at the college. The research investigated two areas of student learning outcomes: performance in mathematics and improvements in students’ concentration skills. Under the application of this program, students not only achieved significant outcomes in mathematics, as evidenced by formative and summative assessments but also improved their concentration skills, as demonstrated in the gains in national reading comprehension tests. In the following, we present, in extensive detail, the elements of the Keystone approach and its implementation in a learning environment, such as a college mathematics classroom.

Conflicting mathematical worldviews

University mathematics education and civic education through mathematics emphasise different aspects of the mathematical worldview. The present study qualitatively analyses 21 mathematics students’ mathematics-specific intrinsic motivation for choosing a mathematics study programme referring to different aspects of their mathematical worldview before the beginning of their study. The results show that many preservice teachers enjoy schematic aspects of mathematics, which does neither correspond to the type of mathematics taught at universities nor to civic education through mathematics. These findings contribute to explaining demotivation and frustration of preservice teachers with university mathematics as well as challenges for implementing civic education through mathematics in classrooms.

Community college mathematics instructors of color on the pursuit of supporting developmental students’ self-efficacy

As of 2017, colleges in the state of Texas in the United States of America are transitioning to a corequisite model where students take developmental and traditional mathematics classes concurrently. Using a self-efficacy framework, this qualitative study aimed to explore the perceptions of four mathematics instructors of color at two community colleges in Texas that have adopted the corequisite model mentioned above. Semi-structured interviews were used to inquire how instructors perceived to best support students through this new model. Using thematic analysis, five overarching themes emerged: feelings of encouragement, vulnerability, and empathy, challenges in supporting students’ development of self-efficacy, relatedness to students. The instructors voiced many challenges in helping students. However, most of the instructors also displayed some level of attending to their student’s social and emotional needs to overcome these challenges. In many ways, instructors expressed that they have to be vulnerable with their students to overcome challenges and open themselves up so students are more willing to learn. Instructors discussed instances in which they have been oppressed, which have shaped their educator identity, influenced their current practice, and impacted their relatedness with students. Furthermore, instructors expressed constantly trying to form connections with their students. These instructors discussed how their similar social identities, such as language, race, national origin, and mathematical experiences, are an important middle ground that connects them to their students. Through relatedness and vulnerability, instructors discussed getting students to open up and become more receptive to learning, achieving the necessary outcomes to succeed. The five themes discussed in this paper foreground (a) instructors’ ability to provide student encouragement, typically through vulnerability, (b) challenges that negatively influence students’ self-efficacy and (c) relatedness and empathy to help students succeed, resulting in a higher perceived self-efficacy in their students’ part.

Mathematical Modeling Through the Eyes of Elementary and Middle Preservice Teachers

Mathematical modeling is a useful pedagogy in mathematics education, but preservice teachers (PSTs) conceptualization of the teaching and learning of modeling practices is an ongoing concern. This research study examined 31 elementary and middle grades PSTs’ conceptualization of mathematical modeling and their experiences with such modeling. The study participants were recruited from two, four-year university mathematics methods courses located in northeastern and midwestern United States. Data for this study was collected through a questionnaire and analyzed using qualitative and quantitative methods. Results indicated that most of the PSTs had little understanding of the intersection of mathematical modeling, and the teaching and learning of mathematics. As such, many perceived mathematical modeling as an exclusive action reserved for teachers. Additionally, the results revealed that most participants had minimal, if any, experience with mathematical modeling. These limited experiences portrayed mathematical modeling as a show and tell method or step-by-step explanation. Our results expand the inadequate research into elementary and middle grades PSTs’ knowledge of and experiences in mathematical modeling and warrant the exigency for the inclusion of extensive mathematical modeling practices into methods and content courses for PSTs. The directions for future research and implications for researchers and teacher education programs are also discussed.

Digital Twin for Math Education: A Study on the Utilization of Games and Gamification for University Mathematics Education

Gamification has emerged as a promising strategy for engaging students and enhancing learning outcomes across various disciplines, including education. It involves incorporating game-like elements into non-game contexts to motivate and engage users. Extensive research has demonstrated the positive impact of gamification on student engagement, motivation, and learning outcomes in diverse subjects, including mathematics. Nevertheless, there is a paucity of research on the effectiveness of gamification in mathematics education. To bridge this gap, we investigated the effects of gamification in college mathematics education, with a specific emphasis on students from liberal arts backgrounds who may lack foundational mathematical knowledge. In this work, we designed and implemented a gamified mathematics course tailored for liberal arts students in a Korean university. Leveraging digital twin technology for game and gamification, we created an immersive learning environment that allows students to visualize mathematical concepts through games, pair gamification factors on physical and virtual worlds, and engage in interactive problem-solving activities. The effectiveness of this gamified course in improving students’ engagement, motivation, and learning outcomes was thoroughly evaluated. Digital twin technology, in conjunction with gamification, holds immense potential to revolutionize the way mathematics is taught and learned, making it more accessible, interactive, and engaging for students from diverse educational backgrounds.

Retracted: Characteristics Analysis of Applied Mathematics in Colleges and Universities Based on Big Data Mining Algorithm Model

Retracted: Characteristics Analysis of Applied Mathematics in Colleges and Universities Based on Big Data Mining Algorithm Model

An updated conceptualization of the intuition construct for mathematics education research

To improve instruction, conduct communicable studies on student intuition, and provide an entry point for researchers interested in this area, the meaning of intuition in mathematics education needs to be addressed. This paper reviews 816 journal papers from top tier mathematics education journals to obtain an updated conceptualization of the intuition construct. Different research camps, such as a camp focused on instructional design that leverages learners’ primary intuitions in the classroom and a camp concerned with sources of errors through the lens of intuitive rules theory, emerged. A critical discussion of theoretical choices for intuition research will be followed by several directions for future research on intuition specific to university mathematics education.

STATISTICAL METHODS FOR EVALUATING EXPERIMENTAL DATA ON THE USE OF MATHEMATICAL COMPETENCIES IN STUDY FOR A RESILIENT ECONOMY

The description of the problems, solved within the statistics evaluation of the results of educational (pedagogical) experiment in resilient economy is given. Comparison of the two average samplings and hypothesis verification relative to dispersions of the two samplings are considered. It is shown the hypothesis that teaching and methodical training system of subjects of higher mathematics in technical universities, suggested on the base of the modern interactive technologies, significantly improves the quality of the base level of professional competence of future engineers. The methods for statistical processing of the obtained results, which very thoroughly research all the indexes which compose the suggested learning and methodical system for teaching higher mathematics in technical universities are used.

On the relationship between school mathematics and university mathematics: a comparison of three approaches

This paper examines how different approaches in mathematics education conceptualise the relationship between school mathematics and university mathematics. The approaches considered here include: (a) Klein’s elementary mathematics from a higher standpoint; (b) Shulman’s transformation of disciplinary subject matter into subject matter for teaching; and (c) Chevallard’s didactic transposition of scholarly knowledge into knowledge to be taught. Similarities and contrasts between these three approaches are discussed in terms of how they frame the relationship between the academic discipline and the school subject, and to what extent they problematise the reliance and bias towards the academic discipline. The institutional position implicit in the three approaches is then examined in order to open up new ways of thinking about the relationship between school mathematics and university mathematics.

Theorizing university mathematics teaching: the Teaching Triad within an Activity Theory perspective

In this paper, we draw on our recent research to inspect again some of the theoretical perspectives we have been using to analyze data and to characterize teaching-learning in university settings. We focus particularly, within a sociocultural perspective on Activity Theory and the construct the “Teaching Triad,” seeking to embed the Triad within an Activity Theory perspective. To achieve this, we relate the Teaching Triad with aspects of the sociocultural setting both in and beyond direct interactions in face-to-face teaching. While this is mainly a theoretical paper, an example is taken from observations of teaching in university lectures in a Greek university to show how these theoretical perspectives have provided insights to the institutional and cultural complexities involved and in what ways the Triad construct has evolved.

Research on the Mixed Teaching Mode based on the New Form Textbook of Linear Algebra

The new form of textbooks combines paper textbooks with new media resources, teaching with modern technology, and compensates for the content that paper textbooks cannot carry. The new form teaching materials of Linear algebra, including the integrated design of teaching content, strengthen the problem orientation, fully reflect the concepts of Flipped classroom, mixed teaching mode, inquiry learning, etc., improve the creativity, progressiveness and effectiveness of college mathematics teaching activities, and promote the benign development of college mathematics teaching.

Physical and Mechanical Characteristics Analysis of Partition Composite Board Made of Coconut Shell Material

This research aims to examine the effect of the thickness of coconut shell composite board on elasticity, sound absorption, water absorption, and density. The elasticity test was conducted using the tensilon RTF2350 machine at the Faculty of Mechanical Engineering and the sound absorption test was conducted using the sound level meter GM1352 at the Faculty of Science and Mathematics of the State University of Yogyakarta. The thickness of the composite board was varied, and its elasticity was measured using the tensilon RTF2350 machine, the sound absorption measurement was determined using a sound level meter with a sound source from a sound generator with a frequency of 1000Hz and intensity of 20 dB, while the thickness was varied. The elastic modulus decreased with the increase in partition thickness, sound absorption decreased with the increase in partition thickness, and water absorption increased with the increase in partition thickness. Water absorption was determined by submerging the partition into distilled water for 30 seconds and observing the mass before and after immersion into the water.

곡선 아래 넓이에서 리만합의 극한으로

The transition from high school to university mathematics presents significant challenges for understanding definite integrals. In high school, students learn that definite integral is the difference between the two antiderivatives evaluated at the endpoints. However, in university calculus, the definition of the definite integral is based on the limit of Riemann sums. To facilitate students’ transition, we employed commognitive theory to design teaching and learning activities that incorporated the history of definite integrals. Our study aimed to document changes in students’ discourse on definite integrals and analyze the conflicts they encountered in the transition. In the pre-survey, most students believed that the area under a curve was the definition of the definite integral. However, in the post-survey, many students accepted the limit of Riemann sums as the formal definition. Moreover, students demonstrated growth in substantiating narratives on the connection between areas (or the limits of Riemann sums) and antiderivatives. Utilizing the history of mathematics, we provided suitable contexts to discuss explicitly the change in word use of the definite integral. Students’ self-reports indicated that history helped them understand the reasons behind the new definition of definite integral. Additionally, rather than disregarding the high school definition as incorrect or imprecise, students could relearn it in connection with the university discourse. Our study contributes to designing a smooth transition from high school to university mathematics and for mathematics teachers to adapt to the inverse transition.

Professed vis-à-vis Enacted Knowledge: Topic-Specific Pedagogical Content Knowledge of University Mathematics Teachers

This study aimed to determine and observe the topic-specific pedagogical content knowledge of university mathematics teachers before and during limit and continuity concept instruction, and compare the teachers’ perceptions of their teaching to what happened in their classrooms using the case study method. The study involved five university mathematics teachers who teach ‘Applied Mathematics I’ to pre-engineering students at Assosa University, Ethiopia. Classroom observation sessions and pre-lesson teacher interviews were used as data sources. The data were analyzed by identifying common themes in each of the knowledge components prior to and during the lesson, and then by comparing the two phases. The findings from the teacher cases provided detailed contextual information and revealed knowledge manifestations in their lesson design and actual teaching processes. The study’s findings revealed that teachers had a good understanding of topic-specific pedagogical content knowledge components prior to the lesson, but did not demonstrate most of these in their actual teaching of limit and continuity; their reported and enacted knowledge differed. According to this study, individual teachers varied in their implementation of what they had mentioned about various components of topic-specific pedagogical content knowledge. The study proposes that understanding teachers’ knowledge during the lesson design phase and actual teaching could help fill the gap as a means of professional development, and thereby, improve pre-engineering students’ mathematics learning.

Uji Distribusi Binomial Pada Data Lama Masa Studi Mahasiswa

The length of study time for students at a higher education institution varies quite a lot. Many factors cause students to finish college on time or not on time. The length of study period is one indicator of the success of a tertiary institution. The faster students complete their education, the better the quality of service from an educational institution. This study aims to test the binomial distribution on data on length of study of students of the Tribuana University Mathematics Study Program (Untrib) Kalabahi. The binomial distribution is a distribution of discrete random variables with n trials and two outcomes. The data was obtained from the mathematics study program (prodi) document, in the form of the length of study period of 105 graduate students in 2017-2021. Then a binomial distribution test was carried out with successful data categories, namely students who completed college ≤ 8 semesters and the failed category, namely students who completed college > 8 semesters. The results of the study show that the average success rate for mathematics students is not equal to 50% of the total students in each batch

Making university mathematics matter for secondary teacher preparation

Internationally, questions about the perceived utility of university mathematics for teaching school mathematics pose an ongoing challenge for secondary mathematics teacher education. This special issue is dedicated to exploring this topic and related issues in the preparation of secondary mathematics teachers—by which we mean teachers of students with ages, approximately, of 12–18 years. This article introduces this theme and provides a semi-systematic survey of recent related literature, which we use to elaborate and situate important theoretical distinctions around the problems, challenges, and solutions of university mathematics in relation to teacher education. As part of the special issue, we have gathered articles from different countries that elaborate theoretical and empirical approaches, which, collectively, describe different ways to strengthen university mathematics with respect to the aims of secondary teacher education. This survey paper serves to lay out the theoretical groundwork for the collection of articles in the issue.

Important Evaluation Model of University Mathematics Curriculum

Mathematics is the foundation of all subjects, and every great progress of human beings has the strong support of mathematics. Mathematics has shown an extremely important role in university education and the importance of mathematics is increasing. With the differentiation of objective environment, the personalization of individual disciplines, the subjective learning attitude, and the interactive influence between various disciplines, a lot of precise statistical requirements are put forward. In this context, the study of the importance model of university mathematics curriculum is helpful for college students to better study and plan, and also provides a reference for other industries such as education. This paper combines the performance data of mathematics students of each major and each class. It also combines the relevant characteristics of college students themselves, and puts forward suggestions on the connection of middle school and university mathematics and the subsequent study.

Assessment considerations during lockdown in Norway: An exploratory case study with focus on misconducts in university mathematics

The present paper raises a discussion about assessment formats in mathematics courses at Norwegian universities during the Covid lockdown. This proved to be challenging since the European GDPR regulations are strictly interpreted in Norway, making proctoring at home difficult. Based on analyses of nine university teachers’ feedback on how exams were carried out at their university during lockdown, a discussion is raised about assessment modes and misconducts. The result shows how a framework from another research field can be adjusted to analyze data about the assessment situations. Next, by utilizing the different components (themes) of the adjusted framework, we shed light on perspectives on misconducts in un-proctored home exams. In doing so, the paper informs the discussion on challenges related to assessing students in mathematics at home. Results are relevant for future educational settings since change in the demographic profile of students increase topicality of online assessment.

Strengthening mathematical orientation: how university mathematics courses can gain relevance for pre-service teachers

The aim of the article is to discuss how university mathematics courses can become more relevant for pre-service teachers (PSTs). We therefore introduce a concept we call mathematical orientation and develop an analytical framework based on Felix Klein’s pervasive approach to elementary mathematics from a higher standpoint and the work of the practical philosopher Stegmaier on orientation. This framework is used to analyze the mathematical orientation of PSTs on two mathematics courses in Norway and Switzerland. In a qualitative empirical approach, we analyzed 85 reflections written by PSTs on the topic of decimal expansions and reconstructed aspects of their individual mathematical orientation. Our results show that mathematical orientation varies across PSTs to a certain extent. In particular, different points of reference, perspectives, standpoints, and types of links between the mathematical content and teaching situations could be identified. We therefore propose that mathematical orientation can be considered a key variable in addressing the mathematical needs of PSTs in university courses.

Teaching Mathematics Through Online at the University Level: An Ethnographic Inquiry

Teaching mathematics at the university level expects a more complex form of algorithmic and theoretical exploration which sometimes could not be delivered as enough as the curriculum demands. In this context, this study primarily focused on exploring the opportunities and challenges of online classes while teaching-learning mathematics at the university level. It is an ethnographic study in which three students and a teacher who had a long experience in online teaching-learning practices were taken as the key respondents. The key informants were requested for writing the reflection about their experiences of learning mathematics through online mode. And, the responses of the students were analyzed and presented in different themes. Based on the responses of the key respondent students, poor networking, unavoidable disturbance, teacher’s artificial pretending, negligence of the teachers, and less ICT-friendly curriculum & teachers were found as the major challenges for the online class. From the perspective of teachers' preparing documents for teaching, students’ negligence, ICT being used only as a means of sharing, taking more time to complete the course, less interactive class, and evaluating the students were found as the major challenges. However, online education provided the teachers and student both with a friend in crisis, sitting home reaching school, reducing unnecessary expenditures, and utilizing video records of the classes. Similarly, for teachers; providing opportunities for professional development, web browsing, any time anywhere teaching-learning, and developing the skills for designing different online evaluation tools have been observed as the major opportunities. Based on these conclusions, even having many challenges of using ICT in teaching university mathematics, its appropriate use leads for the deeper and wider understanding of mathematical contents.