Higher Mathematics Teaching Research Articles

Assessment as a barrier to inclusion

I argue that the methods used to assess mathematics in higher education too often prevent people from achieving their potential and have the (presumably unintended) consequence that the diversity of the mathematical community is reduced as a result.

Student Engagement with Technology-Enhanced Resources in Mathematics in Higher Education: A Review

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics.

Information and communication technology integration and teaching mathematics in higher education

The purpose of the study is to develop a model for the application of information and communication technology in the teaching of higher mathematics at the level of school education. The leading method for studying this issue is testing developed by V.E. Milman "Diagnostics of motivational structure of personality", which allows studying the level and features of motivational sphere of the researched based on characteristics of their personality with prevailing emotional background of interest, which are directly connected with motivational sphere and due to which it is possible to influence the level of motivation and mastering of the material on topics of higher mathematics based on given parameters of its increase. The identified indicators enable determining the success of using information and communication technologies within the framework of the created model improving the educational process of studying elements of higher mathematics at school. This will enable students to understand how the knowledge they are learning will be put into practice in their lives in the future, allowing them to be highly motivated in their approach to learning the subject, as well as within the framework of imaginative reconstructions of mathematical figures from different angles, graphs of various parameters, imaginative explanations of formulae, theorems and mathematical rules, which will be displayed in 3D on a large screen, thus enabling students, through their visualization, to understand their essence from different perspectives, which will be reinforced by their practical application.

The application of statistics in the teaching of advanced mathematics

Advanced mathematics is one of the compulsory courses in the process of college learning, but its knowledge is obscure and difficult to understand, and the access threshold for learning is high, which also has a certain impact on students' learning. The introduction of statistics in the classroom of higher mathematics will help students understand the knowledge of higher mathematics. Based on this, this paper discusses the development of higher mathematics and statistics, and analyzes the similarities between higher mathematics and statistics, laying a solid foundation for the application of statistical knowledge in higher mathematics teaching, and puts forward some countermeasures for the use of statistical knowledge in higher mathematics teaching, with a view to providing help for teachers' teaching work.

Higher mathematics teaching design based on military problem

Integrating military cases into the teaching of higher mathematics can stimulate students’ interest in learning and lay a good foundation for students to consciously apply mathematical knowledge and methods to solve military problems they will face in the future. Therefore, this paper first expounds the significance of integrating military problems into higher mathematics, then expounds the selection principles of integrating military problems into higher mathematics, and finally combines part of the teaching content of higher mathematics with practical problems with military background, and uses the "problem solving" of military problems to design the classroom content. Demonstrate the use of mathematical methods in solving practical problems.

Analysis of the feasibility of integrating innovative education into higher mathematics education

Analysis of the feasibility of integrating innovative education into higher mathematics education

A systematic review of studies on self-regulated learning in Higher Education Mathematics

Resumo Esta revisão sistemática buscou analisar os estudos sobre a autorregulação da aprendizagem (ARA) da matemática no ensino superior. Os métodos aplicados foram baseados na recomendação PRISMA. As bases de dados pesquisadas foram Scielo, ScienceDirect, Scopus e Web of Science, e os critérios de elegibilidade foram definidos a partir dos elementos população (estudantes do ensino superior), contexto (matemática) e conceito (ARA), sem restrição quanto ao período e idioma de publicação. Foram incluídos 28 estudos, de 2008 a 2021, dos quais quase a metade foi realizada nos Estados Unidos. Doze estudos realizaram intervenções com o objetivo de promover a ARA dos estudantes, e seus resultados apoiam a eficácia das intervenções na promoção da ARA da matemática no ensino superior. As demais pesquisas, de forma geral, procuraram analisar, no âmbito da ARA da matemática, os efeitos dos fatores motivacionais e emocionais, das estratégias de aprendizagem e da administração do estudo. Os resultados apontam que os fatores motivacionais, em especial a autoeficácia, são bons preditores para o desempenho acadêmico. Os estudos sobre a ARA no contexto específico da matemática no ensino superior estão em crescimento e ainda há muito a ser explorado, principalmente no Brasil. As limitações e as sugestões para pesquisas futuras são discutidas ao final da revisão.

Teaching Strategy of Higher Mathematics Based on the Training of Mathematical Modeling Ability

Advanced mathematics is an important basic course of science and engineering. It mainly introduces the basic theories and methods of mathematics and trains students' thinking. Abstraction is its most basic and significant feature. Mathematical modeling is an important means to solve practical problems with mathematical tools. This paper attempts to take "mathematical modeling" as a breakthrough, so it is particularly important to improve the teaching strategy of advanced mathematics based on mathematical modeling methods in higher mathematics teaching. Based on this, this paper simply discusses the teaching strategy of advanced mathematics under the background of mathematical modeling method.

Co-operative Learning in Undergraduate Mathematics and Science Education: A Scoping Review

To cope with an unpredictable future, higher education in mathematics and science (MS) needs to educate a knowledgeable and skilled workforce. Co-operative learning (CL) is a teaching method associated with increased academic achievement and development of generic skills. Thus, the purposes of this scoping review are to assess the evidence base of CL in undergraduate MS education to inform teaching practices and to identify potential knowledge gaps to inform future research. The review covers 24 empirical studies conducted from 2010 to 2020 on the prevalence, uses, and outcomes of CL elements in undergraduate MS education. The results show that there are few such studies, and these are rarely conducted outside the US or in disciplines other than chemistry. The most frequently implemented CL elements in the included studies are heterogeneous group formation, the use of roles, and different CL structures. The most prevalent student outcome of implemented CL elements in the reviewed studies is enhanced academic success, followed by student attitudes, generic skills, and psychological health. The results have implications for future implementation of and research on CL in international MS higher education.

Mathematics Lecturers’ Views on the Student Experience of Emergency Remote Teaching Due to COVID-19

Due to the COVID-19 pandemic, university closures were commonplace worldwide from March 2020, meaning that lecturers and students had to adapt to emergency remote teaching with little or no notice. In this paper, we report upon the results of an online survey undertaken with university mathematics lecturers during May–June 2020. There were 257 respondents from 29 countries who gave their reactions to emergency remote teaching due to the COVID-19 pandemic. Here, we focus upon lecturers’ perceptions of how their students coped with this style of teaching, considering any particular difficulties they reported to their lecturers, their attendance at online teaching sessions, and their engagement in a general way. Lecturers reported students struggling with both hardware and software issues, particularly in relation to fast, reliable broadband. Childcare issues also emerged as a challenge for students during this timeframe, as well as students’ personal circumstances in terms of living situations and financial stability. Overall, lecturers reported lower levels of engagement with online learning compared to in-person lectures, which occurred prior to the pandemic. However, four-fifths of respondents were still in regular contact with their students during this time. Many of the studies exploring the impact of COVID-19 on the teaching and learning of mathematics in higher education are small-scale, sometimes single-module studies. Restrictions differed greatly between countries, and indeed between regions, meaning that the results of any regional study cannot be generalised to a more international experience. In addition, the experience of students studying mathematics as their degree programme differed from those who undertook only one mathematics module as part of a science, engineering, or business degree. This paper provides a more global insight into the student experience during the COVID-19 pandemic. By focusing on lecturers, rather than asking students directly, the experiences of those students who may not have engaged with such a study have been included; oftentimes, these students were those who struggled the most with this new format of learning.

E-assessment in mathematics in higher education: a student perspective

Assessment is among the inevitable components of a curriculum and directs students’ learning. E-assessment, as prepared and administered with the use of ICT, provides opportunities to make the process easier in some aspects, but also brings certain challenges. This paper presents an e-assessment framework from a student perspective. Our study lasted for one academic year and incorporated a total of 631 students’ responses to questionnaires conducted three times in two different mathematics courses. The courses are compulsory for undergraduate informatics students. The research included a three-step factor analysis: two exploratory factor analyses and a confirmatory factor analysis. It yielded a model of a student perspective on e-assessment consisting of four factors: Transparency and fairness of assessment, Formative and summative assessment and feedback, Meaningful use of technology in assessment and Difficulty of learning outcomes. The students’ opinion about the use of e-assessment was generally positive. The students appreciated the student-centred approach based on sound pedagogical alignment of all teaching and learning elements with assessment. They found it important that technology should not distract students during assessment tasks and considered cheating in a controlled e-assessment environment to be no more frequent than in face-to-face assessment.

Evaluating digital mathematical games in improving the basic mathematical skills of university students

Technical skills related to basic mathematics in higher education have been a key foundation for further allied courses across primary programmes. While the traditional learning strategies appear to be inadequate to enhance the basic mathematics skills of university students, digital mathematical games pose the potential to improve such a set of skills by means of mobile learning. This work focuses on investigating the influence of digital mathematical games on students’ basic mathematics skills under four various academic programmes. To illustrate the proposed scheme, a case study is conducted in a state university in the Philippines across undergraduate programmes in information technology, hospitality management, industrial engineering, and education. It was found that the use of digital games can improve the skills of students in basic mathematics. Thus, the educational system may be redesigned along with the positive effects of digital games on traditional skill enhancement initiatives.

Mathematics self-belief comparison and examination of pre-service teacher (PST) through a flipped-open calculation based on numbers (ABN) learning method

Teaching mathematics in higher education has been followed traditionally by teacher-centered methodology. With this methodology, there are always certain difficulties in mathematics learning, revealing students are not capable of dealing properly with calculations and/or problems. This research presents the comparison and examination of two different instruction methodologies, traditional-classroom methodology (TCM) and flipped-classroom methodology (FCM) about self-belief of pre-service teacher (PST) in a mathematics course. Here, an open calculation based on numbers (ABN) method originally from the Spanish teaching methodology (abierto basado en números) was used in both teaching methodologies. The 274 PSTs participated in the course: 131 students to T-ABN and 143 students to F-ABN. The results after applying the questionnaire (Cronbach's α = 0.897) showed F-ABN had significant influences in PSTs' self-belief toward the course and made classes more interactive based on parametric-statistical tests. PSTs' self-belief for four studied groups (pre- and post-test in control and experimental group) indicated significant differences found by ANOVA test. Additionally, significant differences were only observed in educational background not in gender of PSTs' self-belief according to factorial ANVOA. In all cases, when significant differences were found, effect size and post-hoc tests were conducted. Therefore, more student-centered methodology allowed to build positive teaching/learning environment for PSTs as future teachers, which consequently expects better learning outputs for children as their future students.

Klassklättring och matematik-kapital. En fallstudie.

Breaking the class ceiling? A case study of a university mathematics student from a non-academic background. In this paper we report from a case study of a student from non-academic background, who has continued on to study mathematics in higher education. Bourdieu’s concepts of capital, habitus, and field were used to analyse the student’s trajectory into university mathematics, with a particular focus on mathematics specific capital. Data was collected through classroom observations and three semi-structured interviews, over a period of three years. The analysis showed how the student acquired mathematics capital by acting as an informal teaching assistant, thus receiving recognition from both peers and teachers for his mathematical abilities. The longitudinal interviews also demonstrated how the student has continuously been able to expand his social capital related to mathematics and science. We argue that it is important for higher education researchers and teachers to consider disciplinary specific capital, and also to provide students with opportunities to acquire such capital.

Digital Resources for Targeted Mathematics Support

SPIRIT Maths (Students’ Perceptions Informing and Redefining Innovative Teaching of Mathematics in Higher Education) is a project that was established in Munster Technological University (MTU) to investigate students’ attitudes towards mathematics and to explore a more student-centred development of mathematics resources. One of the aims of the project was to create a collection of student-preferred digital materials with a view to improving student engagement, building students’ confidence in mathematics and helping students to succeed in their mathematics modules.The findings of a survey disseminated to first year students in MTU indicated that students would be most likely to use the resources if they were geared towards their specific module; to maximise impact, resources were developed for two modules, one in Engineering and one in Business, that are each taken by large numbers of students. The resources were integrated on the learning management system and are available to all MTU students taking a mathematics module. Three interlinked digital resources were developed: (1) a series of interactive self-assessment questions, (2) corresponding videos showing worked solutions and (3) an associated bank of practice questions developed using a digital tutor to provide instant feedback. It is hoped that the complementary resources will facilitate student learning through a combination of active learning, explicit instruction and the ready availability of the resources.This article describes these resources and how they were developed, and outlines how these are being promoted to students. We also report on the feedback received from a small number of students who tested the resources and discuss how to measure student engagement with the resources.

Quality Assessment Method of Information Model Reform of Higher Mathematics Education Based on Big Data

The quality of higher mathematics teaching in colleges and universities is related to a variety of influencing factors, and the changing laws are very complex, which makes the current model unable to accurately evaluate the quality of higher mathematics teaching in colleges and universities. In order to solve the deficiencies in the current teaching quality evaluation process in colleges and universities and improve the correct rate of college teaching quality evaluation, a quality evaluation method based on big data is proposed, which reforms the information model of college teaching quality evaluation. The literature related to mathematics teaching quality evaluation is researched and analyzed, and the influencing factors of higher mathematics teaching quality evaluation in colleges and universities are established. Then, collect the data of the influencing factors of higher mathematics teaching quality in colleges and universities, and establish a learning sample of college teaching quality evaluation through the star rating of the teaching quality of colleges and universities by experts. Finally, the neural network and decision tree of big data technology are introduced to train the learning samples to form an evaluation model of higher mathematics teaching quality in colleges and universities. The results show that our method can achieve high accuracy.

Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy

The education sector, among others, was severely affected by the coronavirus disease 2019 (COVID-19) pandemic. Because mathematics has always been singled out as a subject that needs more verbal communication and interaction, rapid adjustments had to be made by mathematics lecturers in higher education institutions to try and facilitate normal teaching and learning remotely through emergency open distance methods. Lecturers were forced to examine prevailing practices with a view to creating innovative and workable solutions to the emergency challenges without compromising the quality previously experienced during face-to-face classroom interactions. The article developed through a simple technology a conceptual framework for emergency remote teaching (ERT) in an emergency techno-response pedagogy (ETRP). The key was to demonstrate an innovative instructional strategy for teaching mathematics using a simple technology instead of an advanced or complicated mathematics software in the move from face-to-face to fully online teaching during a crisis. A development qualitative virtual case study was conducted that involved observing live and recorded mathematics lectures and interviewing an innovative lecturer of mathematics in the delivery of complex numbers at a graduate school in South Africa. The facilitation of the lesson through a simple and inexpensive technology (Microsoft OneNote) guided the development of a conceptual framework for ERT within an ETRP. The Context, Input, Process, and Product (CIPP) evaluation model was used as a theoretical framework to guide the analysis and conceptualisation of the lessons. Results provided guidelines through a conceptual framework for ERT that included a unique model of a lesson plan and advantages of using a simple technology in ERT instead of advanced mathematical software. The article contributes to the knowledge base in planning future ERT interventions.

Engaging with Maths Online - teaching mathematics collaboratively and inclusively through a pandemic and beyond

This case study details several concrete approaches to integrating the use of student-loaned iPads in the teaching of mathematics in Higher Education. Although there is a scarcity of rigorous studies into the efficacy of tablet devices for improved educational outcomes, previous case studies have argued that tablet devices, if used, should be integrated into the whole learning experience. The mathematics teaching team at Middlesex University have developed an inclusive digital pedagogy over the last five years that enabled us to effectively respond to the remote teaching imposed by the COVID-19 pandemic by loaning iPads to all students on specialist mathematics programmes. As we begin the return to campus, we continue to integrate these devices into our teaching to address the observed “digital divide” in Generation-Z students which is characterised not by access to smart devices but by the digital skills to use them as effective learning tools. This is particularly relevant at Middlesex University which is disproportionately affected by digital poverty amongst its student population. We discuss the use of virtual whiteboard apps, the necessity of handwritten mathematics, the rich integration of multimedia content, persistent collaborative “problem solving spaces”, and how a common hardware platform allows for varied and equitable inclusive assessment. We also report the results of students’ surveys of iPad use during the remote-only 2020-21 academic year.

Switching to Fully Online Teaching and Learning of Mathematics: The Case of Norwegian Mathematics Lecturers and University Students During the Covid-19 Pandemic

Towards the end of 2019, a novel coronavirus, known as COVID-19, was detected and quickly spread worldwide. The resulting pandemic led many countries to lockdown and teaching and learning switched to fully online provision. This study explores how Norwegian higher education lecturers and students of mathematics experienced online provision following this switch in March 2020 when the national lockdown was imposed. Data are generated and analysed using an exploratory sequential mixed methods approach that first entailed interviews with ten mathematics lecturers and six undergraduate students as the foundation for developing a survey instrument. The instrument was designed to explore further how a larger sample of mathematics lecturers and students perceived their experiences following the switch to online teaching and learning. One hundred and twenty-seven university students from four universities and eighteen mathematics lecturers from seven universities responded to the survey. The data generated indicate that advanced technology and the internet were not entirely successful in supporting many students and lecturers to adjust to the lockdown environment. Additionally, it appears that some mathematics lecturers were not aware of several challenges that students experienced following the switch. This paper aims to increase the awareness of the mathematics education community at the tertiary level about the challenges mathematics lecturers and students experience through online education. Further, it is hoped to prompt collaboration within the community to address these challenges in order to be better equipped for any use of online teaching and learning of mathematics in higher education.

Remote Teacher Actions of Mathematics Teachers in Higher Education

Background: the investigation of teacher actions in face-to-face teaching has become a fertile line of research both in mathematics and in other areas. The pandemic moment that Brazil has been going through since March 2020, which forced teaching to take place remotely, provided conditions for the research to be extended to this type of teaching. Objectives: investigate teacher’s actions in remote education to understand what teachers actually did and do in their classes in this teaching format. Design: This research is characterised as qualitative, with the focus of observation on synchronous and asynchronous classes held by teachers. Setting and Participants: Eleven teachers who teach mathematics in higher education remotely at different institutions in the state of Paraná participated in the research. Data collection and analysis: Data were collected through interviews conducted via Google Meet, recorded, transcribed and analysed using discursive textual analysis. Results: From the analysis, the remote teaching actions were grouped into two moments, called Poscênio [Backstage] and Execution. The Backstage covered a set of seven actions (Self-education, Acquire, Organise, Elaborate, Send, Communicate, and Evaluate) that involved 35 different microactions, when the teacher carried out the preparation of the discipline and classes, as well as their closings asynchronously. The Execution moment comprised six actions (Operationalise, Write, Explain, Answer, Wait, and Interrupt) and 24 microactions, in which the teacher synchronously put into practice what was prepared in Backstage. Conclusions: Based on the results (large number of actions and micro-actions in Backstage), we conclude that remote teaching has required a great effort from teachers in the search for information and elaborate planning for the realisation of classes, which perhaps explains the anxieties revealed by them during interviews.