College Mathematics Research Articles

Koneksi Analisis Riil dan Matematika Sekolah: Identifikasi pada Mahasiswa Calon Guru Matematika

There is a significant gap between secondary school mathematics and university mathematics courses. This study aims to identify how mathematics education students understand the connection between topics in Real Analysis and school mathematics content. The research method used in this study is a qualitative descriptive method with the research subjects being students who are pre-service mathematics teachers who are taking the Real Analysis course. Data analysis was carried out in 3 stages, namely: data condensation (data reduction), data presentation, and drawing conclusions. Concept-by-concept connections between Real Analysis topics and mathematics in secondary schools are categorized based on Suominen's categorization of mathematical connections. The research findings reveal that pre-service teachers have limitations in identifying the connections between Real Analysis and school mathematics topics. The connections that students identified were limited to general ideas. It is necessary to prepare a structured learning method in the Real Analysis course that can facilitate the gap between university mathematics and school mathematics.

Exploring Students’ Responses to Reading Assignments in First-year University Mathematics Courses

ABSTRACT Although reading homework is common in university courses, compliance rates vary. Using interviews, this study explored how five students responded to reading assignments in their introductory college mathematics classes and how they viewed reading and reading-related activities relative to their academic successes. Qualitative content analysis of the interview data and resultant case studies revealed that the participants completed their readings and undertook associated activities to produce gains in confidence, preparedness, mastery, achievement, and self-responsibility. This research offers an in-depth view of students’ reading and reading-related practices, highlights the importance they attributed to these behaviors, reveals how their mathematics comfort levels influenced their approaches to reading assignments, exposes complicating factors that impacted their academic achievements, and points to the value of using pedagogic interventions to encourage reading in math courses.

The Application of Interactive Effect Evaluation Model in the Teaching of College Mathematics Courses

Mathematics courses in higher education (advanced mathematics, linear algebra, etc.) are characterized by abstract concepts, many easily confused concepts, many nature theorems, and large amount of calculation of many difficulties. In most cases, due to the knowledge level, knowledge structure, and requirements of the teaching process, the traditional mathematics teaching adopts the straight-to-point approach to the introduction of mathematical concepts, and the explanation of property theorems mostly adopts the method of giving the theorems first and then analyzing and proving them for the calculation problems are mostly manual calculation. Educators are mainly concerned with how to organize teaching so that the trainees can acquire more knowledge, while ignoring the subject status of the trainees, and it is often related to the talents of higher education. The training goals are consistent. The traditional mathematics teaching only reflects a function of knowledge inheritance, but lacks the function of knowledge innovation. The lack of concept generation process in teaching makes the abstraction stronger; the lack of case analysis process makes the applicability weaken; and the serious separation of engineering problem solving and computer operation makes it lack of practicability. The current mathematics knowledge and curriculum make students in a passive position in the process of mastering basic knowledge. From the study about the present condition of the math education and the real requirement, the thesis will talk about content, characteristics, and the relationships for the practical education along with interactive teaching process. What is more, the ways of education and online education is able to be presented. At the same time, this paper also obtains the maximum weight value of each teaching quality evaluation index through analytic hierarchy process, introduces the quadratic fuzzy comprehensive calculation method of fuzzy operator, and determines the maximum component of the evaluation level as the final evaluation level according to the most subordinate degree criterion of fuzzy comprehensive evaluation. Especially in the formulation of teaching quality evaluation model in China, the qualitative description is processed quantitatively by the method of fuzzy mathematics and statistics, so that the qualitative index and the quantitative index are organically combined.

The transition from school to university mathematics in different contexts: affective and sociocultural issues in students’ crisis

Understanding the secondary–tertiary transition is not only an educational matter, but also an inclusion and equality matter as mathematics qualifications lead to better employment and better earning for students. Research on what causes the crisis associated to this transition has so far focused on the impact of cognitive and epistemological changes in university mathematics. Recently, attention has been given to sociocultural and affective issues, which indicate the impact of diverse contexts on such event in the students’ life. Here we present a study investigating the experiences of first-year mathematics students in three European countries. The study adopted the framework of transition as a rite of passage and to detect the changes in attitudes towards the mathematics which originated the crisis, the three-dimensional model for attitude towards mathematics (TMA) was used. Data consist in one questionnaire translated into three languages and administered to students in the first year of study. Most of the questions were open-ended, and the data were analysed first qualitatively and then quantitised. Results show that while the transition experiences of the students may seem on the surface uniform, some significant differences emerge for motivation to join mathematics degrees, motives for changes in perceived competence, and impact of university mathematics formalism. We hypothesise a link between these changes and the differences in educational environments in the three countries. We conclude with highlighting the need for more research of this kind to understand the secondary–tertiary transition in the educational context in which it happens.

Reflecting on the Overview of University Mathematics Education Research by INDRUM

Reflecting on the Overview of University Mathematics Education Research by INDRUM

Artificial Intelligence Evaluation for Mathematics Teaching in Colleges under the Guidance of Wireless Network

Comprehensively improving the quality of teaching is the highlight of current higher education. Also, it meets the basic needs of China’s current transformation into a country for strong education. Mathematics is one of the most important subjects in education these days, which is widely applied in research, social life, and understanding various science theories and laws. Hence, improving the quality of teaching mathematics in colleges becomes an important task in modern college teaching. In particular, the wireless integration of information has enriched and diversified the teaching methods of higher education. Vigorously promoting the application of wireless network technology in mathematics teaching is not only an effective way to solve the insufficient supply of educational resources but also a bold attempt to innovate the mathematics teaching mode in colleges and universities. Firstly, this work proposes an IACO-BP (improved ant colony optimization-based backpropagation) network to evaluate teaching quality for higher level mathematics in a wireless network environment. It improves the traditional ant colony optimization algorithm from three aspects, namely ant colony pheromone adaptive volatility coefficient, pheromone iterative elite selection strategy, and population iteration, adding a variation factor to construct IACO. Then, we use IACO to optimize initial weight and threshold to solve the issue of BP network’s falling into local optimum and improve network performance. Secondly, this work puts forward a series of countermeasures for the construction of mathematics teaching system in colleges. The correctness and superiority of the proposed strategy are verified by comparing the mathematics teaching quality in colleges before and after using the proposed strategies. Various aspects of mathematics teaching, such as teaching objectives, teaching content, and teaching process, are evaluated before and after using these strategies. These features are improved by a significant margin, up to 2.6%, after applying the proposed strategies.

An in-depth study on the integration of mathematics teaching into ideological and political education in colleges and universities

In the development of modern education innovation, mathematics teaching, as a basic course for colleges and universities to cultivate professional talents, has a positive impact on the cultivation of students' thinking ability and comprehensive quality, so it is the key and difficult point of practical education construction and curriculum innovation. In the new educational environment, according to the current situation and main problems of college mathematics curriculum construction, the comprehensive infiltration of ideological and political education elements can promote the accurate transmission of mathematical knowledge. Therefore, on the basis of understanding the current situation of mathematics teaching in modern colleges and universities, this paper makes clear the feasibility of integrating ideological and political education elements, and discusses how to integrate ideological and political education elements in mathematics teaching in colleges and universities, so as to provide effective basis for the guidance of modern education.

An in-depth study on the integration of mathematics teaching into ideological and political education in colleges and universities

In the development of modern education innovation, mathematics teaching, as a basic course for colleges and universities to cultivate professional talents, has a positive impact on the cultivation of students' thinking ability and comprehensive quality, so it is the key and difficult point of practical education construction and curriculum innovation. In the new educational environment, according to the current situation and main problems of college mathematics curriculum construction, the comprehensive infiltration of ideological and political education elements can promote the accurate transmission of mathematical knowledge. Therefore, on the basis of understanding the current situation of mathematics teaching in modern colleges and universities, this paper makes clear the feasibility of integrating ideological and political education elements, and discusses how to integrate ideological and political education elements in mathematics teaching in colleges and universities, so as to provide effective basis for the guidance of modern education.

An analysis of the relationship between high-school pre-calculus and university calculus grades

First-year mathematics instructors at universities across North America and the globe have been noticing a decline in the mathematics skills and preparation of their incoming students, who have been failing out of first-year mathematics courses at alarming rates. Though some universities have implemented placement or diagnostic tests to measure students’ preparedness, many still use high school grades as the only indicator of readiness for university mathematics. However, researchers have questioned how effective these high school grades are at predicting success in university mathematics classes due to factors such as mis-aligned teaching methods, curriculum, and grade inflation. This study analyzes the relationship between grade 12 Pre-Calculus grades and first year university Calculus grades at a large Canadian university over the period from 2001–2015 in an attempt to quantify previous research in a large-scale, longitudinal manner. Results show that there is a significant disconnect between these grades, that the disconnect has been growing over time, and that it is is quite significant for students who are not performing well at the Calculus level. Recommendations moving forward include the implementation of placement examination in a wide-scale manner, and increased communication and collaboration between K-12 and university mathematics educators and administrators.

Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students

As earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher education is proposed, consisting of relevance content and relevance reasons. We investigate students' relevance perceptions of mathematical topics and of topics’ complexities, as well as their rating of individual and societal/ vocational relevance reasons, all in relation to their perception of the relevance of their overall program of study. Contrary to earlier research findings, our results suggest that mathematics teaching students already do attribute relevance to many content areas and that a preparation for the teaching profession is not the only reason for them to assign relevance. There also seem to be many students who would attribute relevance if they could develop as individuals and pursue their interests. We suggest that giving students opportunities to set individual priorities in their studies could hence support their relevance assessments. As low relevance assessments seem to be connected to students’ motivational problems, students might profit from motivational support, as well.

Whose Math and For What Purpose? A Community Seminar on Identity, Culture, and Mathematics

In the spring of 2018, the Pomona College mathematics department hosted a community seminar on identity, culture, and power in the discipline and education of mathematics. The seminar was free and open to all students, faculty, and staff of the college. In this paper I describe the specifics of the seminar, what types of issues we discussed, what a typical seminar session looked like, and what we all gained from the experience. Similar community seminars might support mathematics departments and faculty in their own endeavors to create inclusive and healthy mathematical communities.

EXPLORING LEGITIMATE PERIPHERAL PARTICIPATION OF STUDENTS IN A COLLEGE MATHEMATICS COURSE

Students, by just listening to and being observant of mathematical procedures to gain conceptual knowledge in mathematics, do not often lead valuable performance. Students need to participate. Learning is initiated and enhanced via continuing legitimate participation in a community of practice. Hence, this study explores students' legitimate peripheral participation in a college mathematics course, explicitly to describe the (1) activities students do to refine practice, (2) barriers students face to advance to full participation, and (3) participation support structures that allow students' legitimate peripheral participation. This study used qualitative-exploratory research design via the qualitative tool—reflective journal—comprising second-year teacher education students (N = 42) from a state university in Bulacan, Philippines, taking the Logic and Set Theory course as study participants, obtained purposively. Data were analyzed through thematic coding. This study showed that the activities of students that refine their practice could be thematized as individual engagement or collaborative involvement. Students faced both intrinsic and extrinsic barriers in progressing to full participation. The participation support structures facilitating students' legitimate peripheral participation were the manifestation of a welcoming environment that offered students additional practice activities to work into supplemented with constructive feedback, joined with the convenience of peer groups where they could go when needed. Inspirational life quotes, fascinating lessons that stir interest, and closed knowledge gaps equally enable student participation. A legitimate peripheral participation activity cycle may still arise when faced with difficulties as participants gradually try to work independently. A friendship-based collaborative group is suggested for Filipino learners.

Readiness in using blended approach in college education

This study explores readiness in using blended approach in teaching and learning of mathematics in colleges of education in the Northern Region of Ghana. 15 participants were purposively selected made up of College Vice Principals, Quality Assurance Officers, Head of Mathematics Departments, and ICT heads from the three colleges of education. Structured interview was used to collect information regarding policy on the blended approach, supportive environment for effective implementation, availability of ICT equipment and internet connectivity among others. Data were analyzed using coding, theme, and content analysis. It revealed that, colleges of education integrate the blended approach in teaching and learning. There is availability of computer labs, internet connectivity, tutors were assisted in acquiring data, and there was provision of smart phones to trainees, as well as a well-structured timetable. Tutors have ideas about the blended approach but lack the necessary skills and knowledge to use it effectively. It is recommended that college management should collaborate with stakeholders to improve upon the computer laboratories, the Internet connectivity, and up-date the skills of mathematics tutors.

University Mathematics Assessment Practices During the Covid-19 Pandemic

In response to the global Covid-19 pandemic departments of mathematical sciences within the UK and Ireland needed to adapt their teaching approaches and methodologies from March 2020 to incorporate not only government social distancing requirements, but also periods of national lockdown and the fact that students were necessarily studying online. In planning for the many different and possible scenarios, universities implemented a range of emergency measures and regulation changes to provide frameworks for adapting teaching, learning and assessment approaches, and at a subject level, departments also needed to correspondingly respond to specific disciplinary needs. Here we specifically consider the changes made by mathematical sciences departments to their assessment practices in the period from March 2020 until January 2021 and their proposed adjustments for the remainder of the 2020/21 academic year. We found that departments were using a range of different approaches regarding the release of their assessments and this paper considers the implications of each for future practice. In particular we identified a concerning issue that emerged across a number of departments in relation to academic misconduct that will now require a community-wide approach if open-book online assessments are to prove a valid, reliable and fair method of assessment in the longer-term.

Motivational states in an undergraduate mathematics course: relations between facets of individual interest, task values, basic needs, and effort

According to situated expectancy-value models, motivational variables play an important role in students’ engagement in academic mathematics courses and achievement. However, for academic mathematical learning, only a few studies provide information regarding the fluctuation of task values on different occasions (situation-specificity, state) and the extent to which task values depend on individual characteristics (personal-specificity, trait). Thus, answering these questions provides information about the extent to which adequate situational characteristics, such as relevance interventions, can influence students’ motivation to engage in the learning process. To contribute to this discussion of the situation- and personal-specificity of task values, I surveyed 181 undergraduate students attending an advanced mathematics course. These students reported on their task values and effort three times in four different lessons during a course in linear algebra. I focused on the following three questions: (1) situation-specificity: to what extent do task values fluctuate between situations (and between persons)? (2) predictions of task values: to what extent do personal characteristics and situational perceptions predict task values? (3) predictions of effort: to what extent do personal characteristics and situational perceptions predict effort? These questions were answered by applying linear mixed models. The analysis results indicate that task values fluctuate only slightly in different situations and are strongly predicted by individual characteristics, such as interest in university mathematics, and task values predict effort. The theoretical and practical implications of the results are discussed.

Teacher education students’ assessment of modular distance learning during the COVID-19 pandemic

This research investigated the teacher education students’ assessment of modular distance learning (MDL) during the coronavirus disease 2019 pandemic using a descriptive comparative research design. There were 295 respondents who are taking up Bachelor of Secondary Education major in Mathematics in a state university. The respondents were identified using stratified random sampling. They answered a four-part survey questionnaire that assessed their profile, perception, benefits and challenges they encountered while learning through MDL. The results showed that they have a positive perception of MDL. At the same time, they found this modality to be beneficial. However, they often encountered the challenges that MDL brings. Moreover, there is a significant difference in the students’ perception, benefits and challenges that MDL brings when grouped according to their year level. Thus, it is recommended that school administrators and teachers consider students’ diversity relative to their needs and provide other instructional support while students are engaging in MDL.
 
 Keywords: Benefits, challenges, modular distance learning, perception, teacher education students

A Research on the Strategy of Integrating PBL with Curriculum Ideological and Political Elements – Taking College Mathematics as an Example

Taking college mathematics as an example, a questionnaire was designed for college mathematics teachers and students to fully comprehend the teaching situation. This paper mainly discusses the problems existing in the teaching of college mathematics and proposes the strategy of integrating PBL with curriculum ideological and political elements in college mathematics, so as to change the teaching process and improve the teaching quality.

Measurement Model and Adaptation of Self-Efficacy toward Mathematics Reasoning among University Students

Mathematics self- efficacy is generally defined as individuals' beliefs or perceptions regarding their mathematical abilities. The aim of this quantitative study was to conduct a validity analysis of a self- efficacy instrument toward mathematics reasoning among 184 undergraduate public university students. Students clearly distinguished between their self-efficacy in doing and understanding mathematics reasoning and their self-efficacy in accomplishing assignments in their university mathematics lesson. In these quantitative studies, self-efficacy which demonstrated convergent and discriminant validity was performed, which corresponded to the Bandura theory and included three dimensions: course self-efficacy, exam self-efficacy, and future self-efficacy. The research design utilized casual correlation technique to investigate the effect of self-efficacy on mathematics reasoning. The reliability analysis of Cronbach Alpha internal consistency reliability revealed that self-efficacy instrument that was constructed was extremely reliable and can be utilized by researchers to measure university students' self-efficacy toward mathematical reasoning.

Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching

Abstract The article uses ordinary differential to solve inhomogeneous equations by the constructivist learning concept. We use the equivalent equations to study the n-th order non-homogeneous linear ordinary differential equations with constant coefficients and get the method of solving this equation. Then we use the Filippov transformation and comparison theorem to prove the boundedness of all system trajectories. Numerical results show that the calculation formula is effective for solving stiff ordinary differential equations.

Study on OBE Teaching Concept in the Context of Deep Learning for the Construction of University Mathematics Microcourses

Outcome-Based Education (OBE) is a goal-based educational system in which each part of education is around outcomes. By the end of the course, every student should have achieved the goal. Outcome-Based Education (OBE) involves various teaching methods and is not restricted to any specified way of teaching. Based on the targeted results, the teacher will mentor the students by acting as an instructor, trainer, and facilitator. The Deep Learning Technology of Artificial Intelligence is applied in various applications to carry out automation and physical tasks without human intervention along with data transfer through wireless networking. In this research, an Apriori Algorithm supports the identification of a suitable method for the teaching process (the OBE Teaching concept) through the outcome of the learning process. This optimization of identification of suitable method is performed with the implementation of Ant Colony Optimization (ACO) in the construction of the University Mathematics Course. The study results proved that the proposed algorithm provides an accuracy of 98.87%. The proposed algorithm can be trained further based on different rules to attain some increased performance of the methodology.