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.

A lab experiment on metals separation and recovery from waste ink-jet cartridges as a non-formal appealing learning activity for students of secondary schools

Abstract Since 2004, the Italian Ministry of Education, University and Research (MIUR), the Conference of Science and Technology Headmasters, and Confindustria, have been promoting the National Plan for Scientific Degrees (PLS) aimed at supporting students in acquiring scientific skills better responding to contemporary society challenges and increasing vocations in basic sciences. This paper describes a successful experience of the University of Cagliari together with selected local secondary schools, in which the hot topic of technological waste valorization was selected to create an orientation laboratory for students towards chemistry disciplines. Specifically, students and teachers were guided into the challenging world of e-waste production and treatment through the practical activity of noble metals recovery from real waste ink-jet cartridges. A specific emphasis was placed on fundamental chemical aspects – separation and recovery of metals driven by redox processes favored by a complexing agent – as well as on the chance to play on coordination chemistry to promote a green chemistry approach. The close collaboration between school and university teachers in planning and implementing laboratory activities is the element that characterizes PLS actions and promotes the development and strengthening of relations between secondary school and university courses in science, technology, engineering, and mathematics (STEM).

Self-regulated use of retrieval practice: associations with individual differences in non-cognitive and cognitive factors

AbstractRetrieval practice is a learning strategy that has repeatedly been found to have positive effects on memory and learning. However, studies indicate that students rarely use retrieval practice on a voluntary basis. The objective of the present study was to examine students’ self-regulated use of retrieval practice, and to determine whether sex and individual differences in cognitive and non-cognitive aspects are related to optional use of practice testing. A classroom study was conducted with 146 upper-secondary school students taking courses in mathematics and Swedish. An ABAB design was used to compare students’ optional and non-optional use of retrieval practice (i.e., repeated online quizzing). Students performed cognitive tasks to assess working memory capacity and fluid intelligence and completed self-reports of non-cognitive factors related to school achievement, such as grit, need for cognition (NFC), conscientiousness and openness. Quiz use was then compared using paired- and independent-samples t-tests, and hierarchical linear regression analyses explored relations to individual differences. The results showed that students completed significantly fewer quizzes in the optional sections than in the non-optional sections, and that females completed significantly more optional quizzes than males in Swedish, but not in mathematics. Further, the results showed that conscientiousness predicted optional quiz use in mathematics, whereas sex, NFC, conscientiousness, and openness predicted quiz use in Swedish. To conclude, although the findings show a relatively low optional/self-regulated use of practice testing, in line with earlier research, they suggest that sex and non-cognitive factors, such as personality characteristics, can predict optional use of practice testing.

“Imagine, maths is used anywhere, and we don’t get to know this”—upper secondary students and the relevance of advanced mathematics

People are more motivated to put effort into learning when they know they will be able to put the learnt content to use. These relevance perceptions play a motivating role in the learning of mathematics, a subject renowned for its abstraction, hard examinations, and usefulness in many fields in society (research, industries, etc.). In this article, we describe a study on upper secondary students in an advanced mathematics course and their perception of the relevance of mathematics in future professions, in particular regarding two concepts in their curriculum (logarithms, trigonometry). We defined relevance as a connection between an object (relevance of what?), a subject (relevant for whom?), an asserter (relevant according to whom?), and a purpose (relevant to what end?). The aim of the study was to know (1) what relevance perceptions students held regarding the advanced abstract mathematical concepts, and (2) how students can develop these considering that students do not yet know exactly what future is ahead of them. We interviewed pairs of students (n = 14, 17–19 years old) in two parts. The first part of the interview revealed that students learned mathematics within a traditional school culture that emphasized practice-and-drill of pure mathematics and that did not in any way inform students about the use of mathematics in research and workplaces. After exposing students to authentic applications of logarithms and trigonometry, the second part of the interview showed the power of imagination when it connected students to future professions for which mathematics was relevant. Instrumental in effectively prompting students’ imagination were visualizations showing applications of the mathematical concepts within workplace contexts. Drawing on Leont’ev’s version of Activity Theory, we theorize students’ assertions of the relevance of mathematics through the dialectics of self and collective (relating one’s own goals and more general motives), the dialectics of use-value and exchange-value (needing mathematics for later life or for examinations), and the dialectics of mathematization and de-mathematization (while mathematics is used in many workplaces, it is hidden in instruments).

Impact of Growth, Purpose, and Sense of Belonging (GPS) Mindset Intervention on Student Retention Rates in Asynchronous Mathematics Courses

This study aims to study the effects of incorporating a Growth, Purpose, and Sense of Belonging (GPS) mindset intervention on student retention rates within asynchronous mathematics courses. Specifically, the research hypothesis suggests that integrating the GPS mindset intervention into these courses will yield a statistically significant improvement in student retention rates. Data were collected from Calculus III, Differential Equations, and Linear Algebra courses across multiple semesters—Fall 2018, Spring 2019, Fall 2022, and Spring 2023 to evaluate the impact. Comparative analysis was performed to explore the effectiveness of the intervention. Preliminary findings from the study indicate that the GPS mindset intervention plays a pivotal role in elevating student retention rates in asynchronous mathematics courses. These results contribute to the ongoing discourse on academic retention strategies and underscore the potential benefits of mindset interventions in educational settings.

Introduction English for Mathematics Course: What are the Student Difficulties and Causing Factors?

English for Mathematics is a required university course designed to bridge the gap between general English proficiency and the specific linguistic demands of mathematics. This study aims to explore the challenges students face in adapting to this specialized curriculum, aiming to deepen our understanding of the educational hurdles posed by evolving academic requirements for graduates. Employing a descriptive qualitative research design, the research examines the experiences of 35 students enrolled in the English for Mathematics course at the Mathematics Study Program of Universitas PGRI Sumatera Barat. Data were collected through semi-structured questionnaires, revealing five principal areas of difficulty: listening, reading, writing, and speaking skills, along with comprehension of mathematical content. The study identifies several factors contributing to these challenges, including limited vocabulary, inadequate prior knowledge, misinterpretations of course material, a lack of effective learning aids, and frequent writing errors. The findings suggest that these obstacles hinder student performance and impact their engagement and satisfaction with the course. The study calls for targeted interventions by educators and curriculum designers to enhance instructional methods and learning materials, thereby improving student outcomes and making learning more engaging and effective. These insights have broader implications for curriculum development and instructional strategies in specialized English education settings.

METHODOLOGY OF TEACHING ELEMENTS OF COMBINATORICS AT THE COMPREHENSIVE SECONDARY SCHOOL

The object of the study is the elements of combinatorics at the comprehensive secondary school. The aim of the article is to improve the methodological system of teaching elements of combinatorics at the comprehensive secondary school. The article discusses methodological issues and problems of studying combinatorics elements in the process of teaching mathematics. The methodological features of studying combinatorics elements at the comprehensive secondary school are identified and characterized, their role in the course of mathematics from the point of view of improving the effectiveness of learning is considered. The methods and methodical techniques of teaching combinatorial material, which were previously tested in our educational process, are presented. The possibilities and expediency of their application in connection with the age peculiarities of students are substantiated. Methodological guidelines for teaching individual topics of combinatorics are given. Within the framework of teaching each topic, interesting tasks of applied significance are presented. Effective methods of their solution are given. The presented tasks have been tested for years in our teaching practice. In the process of teaching the elements of combinatorics, methods of cooperative learning, mathematical modeling, graphical modeling, coding, methods that promoting inter- and intra-subject connections were used.

Students' Errors in Constructing Mathematical Proofs by Direct Method

In mathematics, there are several methods for proving mathematical statements, two of them are direct method and indirect method. Both the methods were included in the mathematics curriculum at senior high school level as a learning topic. It implied that the teachers or pre-service teachers must master these methods. In addition, learning advanced mathematics courses also needed the ability of mathematical proving. The direct method was often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to 13 college students. They were pre-service mathematics teachers in one of the public universities in Aceh, Indonesia, and were asked to prove the statements by direct method. The data were analyzed by using Miles and Huberman step. The results showed that there were three main errors, (1) errors in using definition correctly, (2) errors in algebraic process, and (3) proving by examples. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs. Keywords: constructing mathematical proofs, direct method, students’ errors

Perspectives from students and teachers about the challenges of teaching and learning STEM subjects in Ghana

Ghana has recently renewed its commitment to build a strong Science, Technology, and Innovation (STI) base for improved socio-economic development. This commitment hinges on recognizing that the strength of the nation’s STI policy depends on the quality of pre-tertiary education and training in science and mathematics to produce a critical mass of young people well-prepared for Science, Technology, Engineering, and Mathematics (STEM) courses at the tertiary level. However, despite numerous interventions to improve upon STI, Ghana still performs poorly, along with other Sub-Sahara Africa (SSA) countries with common STI indicators in the Global Innovation Index. Using Ghana as a lens, this article highlights the challenges in STEM teaching and learning throughout the sub-region. The qualitative research approach was adopted to allow an in-depth exploration of participants’ perspectives. Six pre-tertiary schools (three Junior High Schools and three Senior High Schools) and the University of Ghana, Legon, were selected due to the availability of their students and teachers to participate in the interviews in Accra, the capital city. This article argues that, to develop the critical mass of human capital needed for sustainable development, there is a need to improve the performance of students in STEM subjects at the pre-tertiary level. In addition, performance improvement, which is linked to student interest in the study of STEM subjects, should increase the quality of students entering tertiary education institutions. These students will then be trained to meet the quality of human resources needed to run the STI system—a step toward achieving sustainable development this article recommends the redesign of STEM curriculum at the pre-tertiary level to align with tertiary STEM education as that in turn aligns with Ghana’s STI system.

Investigating Billingual Education as A Language Framework and Its Application for Successful Social Engagement

Objective: The research reveals the impact of the course on English and English for mathematics conversations, highlighting improvements and identifying challenges in expressing mathematical ideas. Overall, it aims to analyze code-switching types and reasons in the English for Mathematics course context.   Method: This qualitative case study explores code-switching in English for Mathematics courses, unveiling the nuanced types employed by lecturers and students during classroom interactions. From tag-switching to intra-sentential and inter-sentential code-switching, the classroom becomes a dynamic linguistic canvas. The study investigates motivations behind this interplay, including internal factors like language proficiency and fear of linguistic missteps, and external influences like participant dynamics and contextual nuances.   Research Findings and Discussions: Although this course is due in English, the use of the Indonesian language also happens for both lecturers and students. The occurrences of code-switching itself are on the type of tag switching, intra-sentential, and inter-sentential switching. Internal and external factors influence code-switching in classroom interactions. Internal factors, such as language ability and preferences, impact students' comfort with using specific languages. External factors, including participants, context, and lesson topics, also shape code-switching occurrences in educational settings.   Research Implications: The research implied to improve students' English proficiency in mathematics, emphasizing understanding mathematical terms and delivering presentations in English. By implementing the code switching.   Originality/Value: This research offers lecturers and students point of views related to the types of code switching used by both of them in the process of teaching and learning as well as it is also reasons for using code switching where it contributes for both of them to understand and master the English for Mathematics Course. Then, this exploration offers insights into the symbiotic relationship between language and subject matter within the English for Mathematics classroom, revealing the vibrant tapestry of this linguistic and educational dynamic.    

“I’m a bit out of place here.”—Preservice teachers’ positioning in the figured world of university mathematics

AbstractPreservice mathematics teachers are sometimes trained in programs so that they have both their own courses and joint courses with mathematics majors from the beginning of their studies. While this is thought to provide them with both deep mathematical knowledge and teaching-specific content right from the start, many of them report disaffection with and disengagement from mathematics during their very first semester. Current approaches often frame this from an individual’s perspective, investigating cognitive and affective individual differences among students. In contrast, we aim to understand this issue from a sociocultural perspective, examining underlying social processes. In this study, we thus explored preservice teachers’ experiences of the mathematics component of their training, using Holland and colleagues’ theory of figured worlds as a theoretical lens. Three group interviews with 14 preservice higher secondary teachers in a common mixed setting in Germany (one course specific to preservice teachers, one general mathematics course together with major students) were analyzed. Our findings displayed that the preservice teachers experienced two dichotomous figured worlds of mathematics and mathematics teaching. Our further analysis of their positioning between these worlds provided new insights to explain their disaffection, disengagement, and consequent learning behavior. We discuss practical implications, focusing on different teaching systems and interventions in teacher education.

Positioned as a burden: Analyzing the participation of multilingual students of color in undergraduate mathematics courses that use groupwork

More college mathematics classrooms are adopting active learning practices like groupwork. These practices typically foreground vocal communication and interpersonal interactions, both of which are mediated by language. Given that undergraduate classrooms in the U.S. are also becoming more racially and linguistically diverse, this study focuses on multilingual students of color, whose learning experiences have often been overlooked. Specifically, this study aims to learn more about the relationship between groupwork and equity in classrooms with linguistic diversity. Using positioning theory, this study analyzes the learning narratives of 26 multilingual students of color about their experiences working with peers in groups. Findings demonstrate that while multilingual students described enacting a range of different positional identities during groupwork, they were more likely to report being positioned by others in deficit ways. Results highlight how the positional identities perceived to be available to students were often constrained by normative classroom Discourses about language, participation, and mathematics.

Dataset and Development of Learning Analytic Tool to Extract Manifestations of Students’ Agency from Texts of Comments from MOOCs

The study is devoted to the automatic identification of manifestations of various components and sources of student agency from the texts of reviews of MOOCs, as well as descriptions of internal and external transformation among students in the process of studying MOOCs. To extract descriptions corresponding to individual, relational and contextual sources of students’ agency, a dataset of 3445 English-language comments on the most popular mathematics courses presented on the Udemy platform was generated, and additionally 1787 comments on practice-oriented MOOCs and entrepreneurship MOOCs were extracted to understand the descriptions corresponding manifestation of internal and external transformation in MOOC listeners. The paper proposes a methodological approach based on the use of natural language processing methods such as topic modeling, sentiment analysis and N-gram frequency analysis for extracting keywords and their combinations from MOOCs’ comments texts to describe the manifestation of the components of an individual source of student agency in the form of self-efficacy , increased sense of confidence in solving problems and motivation; components of the relational source in the form of support and accompaniment of the online course by the tutor with the help of quick answers and well-structured educational material; components of the contextual source in the form of the ability to make decisions when choosing alternative online courses, as well as descriptions of the manifestation of internal transformation of students, expressed in the transition from internal struggle - overcoming fears, uncertainty, difficulties in perceiving MOOC content to understanding the purpose of learning and external transformation, expressed in the texts of comments on MOOCs in the form of creating a new or changing the structure of an existing product, startup or business through a change in thinking.

Students' Perspectives on Selecta Capita of Mathematics Online Course on Their Ability to Develop Mathematics Task

The main problem in implementing online lectures is how to adjust what students expect with the achievement of learning quality. This study examines students’ perspectives on effective lectures on the ability to develop mathematics task. Quantitative descriptive research has been carried out on students of the mathematics education study program Universitas Negeri Semarang who took the Selecta Capita of Mathematics course. The subjects in this study were 101 first-year students in the mathematics education study program at Semarang State University for the 2021/2022 academic year. The data were obtained through questionnaires and analyzed by the descriptive statistics. The data that had been obtained and then tabulated in a table, the average value is searched, and presented in the appropriate graph. The results of the study indicate that the availability of learning modules and videos as learning resources is the most important thing that must be prepared during lectures. Furthermore, several other things such as synchronous lectures, discussions using the WhatsApp Group, the use of the learning management system, group assignments, virtual face-to-face meetings, and project assignments need to be prepared during lectures. These results are needed to be applied on team-based project learning models to develop students’ abilities in developing math tasks.
 Keywords: students’ perspectives, selecta capita, mathematics online course, mathematics task

The Online Game Design Uses Scratch, Geogebra, and Geogebra AR Through Mathematics Education Multimedia Lectures

This study aims to design online mathematics games using Scratch, Geogebra, and Geogebra AR through multimedia education mathematics courses. This study used the multimedia development life cycle. Participants in the study were 41 students (13 male and 28 female) of fifth-semester in a multimedia course in mathematics education at a university in West Java, Indonesia. The research instrument was a questionnaire through Google Forms, performance appraisal, observation, and interviews. Based on the research results it is known that Scratch, Geogebra, and Geogebra AR can be used in math game design even though previous students have not studied both, but the results are good. The author suggests that students can try out these math games at school during research or teaching practice. In addition, the authors hope that the game can be published on the internet so that it can be used by many students.
 Keywords: game online, scratch, geogebra AR

Formation and Development of Mathematical Literacy in the Context of PISA-2021 Program Concep

This article presents the results of pedagogical experiments, which revealed educational problems that teachers face in the process of teaching mathematical literacy to schoolchildren: a low proportion of practice-oriented tasks in the total number of educational tasks in school mathematics intended for 15-year-old schoolchildren, a passive attitude of teachers to the formation of mathematical literacy among schoolchildren. The analysis of the experimental data made it possible to conclude that the knowledge and skills of teachers on the issues of reducing the standard task of the school mathematics course are insufficient to problem situations in the context of the PISA assessment tasks, compiling task systems for these tasks, containing an algorithm for solving the assigned problem, description of a visual object that allows the visualization of the task. To solve these problems, the paper proposes to apply a modular learning technology in the process of teaching schoolchildren mathematical literacy, an algorithmic method for reducing a standard task to assessment-learning tasks in the context of the PISA-2021 program concept. In the work, examining the task to the problem situation as an object of mental activity of students, the main components of the "Mathematical Reasoning" of the student are highlighted. Namely: recognizes the area of the task; singles out the main components of the tasks; to bring data under known concepts; establishes interdisciplinary links; applies induction, interdisciplinary knowledge in the preparation of a mathematical model; solves a mathematical problem; interprets, evaluates the solution in the context of the phenomenon under consideration. The analysis of algorithms for solving tasks made it possible to identify the following key structural components of mathematical literacy: understanding the context of tasks; the ability to establish correspondences between various objects, apply induction and knowledge, build mathematical models, find solutions to mathematical models of tasks, interpret and evaluate the solutions obtained; have mathematical reasoning skills. The final experimental study confirmed the effectiveness of the developed methodology for the formation and development of mathematical literacy at 15 year old schoolchildren.

Analysis of students' difficulties in writing skills in English mathematics courses

This research aims to analyze the difficulties faced by students in developing their writing skills in the Mathematics English course. Through a qualitative approach, this research explores the factors that influence student difficulties, including language aspects and mathematical concepts.. The research subjects taken were 5th semester mathematics education students. The data collection methods used were documentation methods, test methods, and observation methods. The documentation method was used to obtain data about the list of names of students who were used as research subjects. The test method is used to obtain data on student completion of English courses, the observation method is used to determine objective conditions during English teaching and learning activities and to determine factors that can influence the learning process. The location of students' difficulties in learning English lies in abilities including writing ability and listening ability. The difficulty of spelling errors is 30%, vocabulary errors are 40%, listening errors are 10%, and language errors are 20%. This shows that the level of student ability has a role in the student learning process and can be one of the factors that influence the level of student academic achievement.

Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics

Linear algebra is one of the service mathematics courses that students in many programs take as part of their undergraduate study. Previous studies indicate that linear algebra courses are often challenging for undergraduate students, leading some to seek help from other resources, including online resources such as YouTube. Through a multiple case study, I focused on identifying the opportunities that YouTube resources could offer students to learn about eigenvalues and eigenvectors, which are among the key concepts in introductory linear algebra. I utilized a combination of APOS (Action-Process-Object-Schema) and Tall’s three worlds of mathematics to analyze two highly viewed YouTube videos on this topic. The two analyzed files had different emphases (one more on the embodied world, and the other on the proceptual-symbolic world), catering to students with different levels of understanding of linear algebra. The findings suggest that, overall, these resources could provide students with opportunities to learn about eigen theory in the embodied and proceptual-symbolic worlds, with more focus on action. Lecturers and teacher assistants could benefit from familiarizing themselves with these available resources and considering the possible integration of these resources into their teaching and/or support they provide for students to meet their academic needs and preferences.

Unequal Access to the Mathematics Course Ladder for Rural Students in the Southern States

A lack of access to a sequence of introductory to top-level curricula in rural schools has widened the achievement disparity between rural and urban students and influenced the number of college degree holders in rural areas. Recently, surging diversity and differentiation in income levels across nonurbanized areas can serve as determinants of the development of academically rigorous course pipelines in rural schools. This study examines differentiation in spatial access to the curriculum ladder for rigorous mathematics in three southern U.S. states during the 2017–18 school year: Alabama, Arkansas, and Mississippi. Policy variations in these states yield different effects on the sequence of rigorous mathematics courses in rural high schools. Given that the mathematics course pipeline reinforces college access, access to academically challenging courses likely outweighs the rural disadvantages of college readiness in non-urban students and the persistence of inequality in public education.

Designing and analysing a teaching proposal about linear algebra through the dialogue of two theories

In this paper we propose a new strategy of dialogue between theories, considering a semiotic cognitive analysis and a praxeological analysis. We examine the implementation of a teaching and learning sequence for introducing eigentheory in a linear algebra course taught during the first year of an engineering degree programme. Initially, the semiotic cognitive analysis based on the Action, Production and Communication space (APC) approach is used in the preliminary, a priori and in vivo phases of the didactic engineering process to propose a teaching strategy that incorporates a variety of semiotic resources. In a second moment, the praxeological analysis intervenes to reformulate the preliminary analysis and to progress on the consideration of a reference epistemological model about eigentheory in a first course of mathematics for engineers. This model is then used in the a priori and a posteriori analysis to integrate the semiotic and epistemological dimensions in the design and implementation of the teaching proposal. The results show the productivity of this new networking strategy and the complementarity of connecting the semiotic with the epistemological analysis.