Mathematical Experiences Research Articles

Study on School Students’ Blended Learning Experiences and Mathematical Self-Concept during Covid-19

The self-perception of one's mathematical abilities is a critical component that academics study to improve mathematics education. Amidst the Covid-19 pandemic, the majority of educational institutions used a blended learning method, specifically including both online and modular distance learning. This research investigated the contribution of blended learning experiences in mathematics to learners' self-perception of their mathematical abilities in the new learning environment. This research used deliberate sampling to select and conduct focus group conversations with ten (10) students studying Science, Technology, Engineering, and Mathematics (STEM). The data obtained underwent thematic analysis. The findings revealed that students' experiences of the teacher’s mastery of the topic, observations about learner-learner relations, the importance of rereading transcripts, and utilisation of internet-based resources fostered their mathematics self-perception, while their experiences such as inadequate teacher-student connections, distracting educational settings, clashes with domestic obligations, and sensations of solitude hindered it. The findings show that comprehending these encounters in this demanding educational setting presents a constant prospect for students to enhance their mathematical learning and their perception of their own ability to excel in the topic.

Introducing the ProInterest model

This study introduces the ProInterest model, a novel framework designed to foster long-term student engagement in mathematics. ProInterest model identifies features that trigger initial interest and subsequently sustain student interest towards mathematics activities. We explore the interplay between these features based on a focused narrative review and demonstrate their application through a case analysis of two mathematics tasks that look different on the surface, yet can be identified to share common features fostering interest when looked through the lense of the ProInterest model. We also apply the model to tasks generated by experts and AI. We show that applying the model to identify features that can trigger and maintain student interest towards a task, one can reveal shortcomings in typical mathematics tasks: humour and creativity are typically missing, and even tasks aimed to be tailored to appeal to students may utilise unimaginative layout and structure. This research bridges a critical gap in the knowledge of interest promoting mathematics tasks by providing a practical tool for educators and instructional designers to create engaging mathematics experiences.

Paths into and out of STEM fields: A qualitative study of women and students of color at a predominately white institution

AbstractThis phenomenological study examines how women and Students of Color who attend a small undergraduate predominately white institution (PWI) make meaning of their experiences in science, technology, engineering and mathematics (STEM) and how individual and contextual factors influence whether they decide to stay, leave, or add an STEM major. We conducted qualitative interviews with 50 juniors and seniors across three participation pathways: (1) students who entered college with an interest in an STEM major and are still an STEM major, (2) students who entered college with an interest in a non‐STEM major and switched to an STEM major, and (3) students who entered college with an interest in an STEM major and changed to a non‐STEM major. Students' descriptions of the factors that influenced their academic choices support the tenets of the situated expectancy‐value theory. Themes related to expectancies for success, value beliefs, and teachers and peers are presented. Implications of these findings for retaining underrepresented students in STEM majors are discussed.

The pedagogical insights of mathematics teachers integrating artificial intelligence in rural upper primary schools of Namibia

This paper presents a qualitative intervention study that explores the pedagogical experiences of mathematics teachers integrating Artificial Intelligence (AI) technologies into teaching mathematics in rural upper primary schools in Namibia. The Technological Pedagogical Content Knowledge (TPACK) framework, which intersects teachers’ understanding of technology integration with pedagogical techniques and subject matter knowledge, was adopted for the study. The research involved 13 mathematics teachers selected through purposive sampling. Data collection included two sharing circle discussions, lesson observations, and semi-structured interviews. A thematic analysis approach was employed to interpret the collected data. The findings reveal a diverse range of AI tools used by the selected teachers, such as Geogebra, Khan Academy, Virtual Tutors, and various problem-solving mobile applications, including Photomath, Mathway, and Microsoft Math Solver. These AI resources were noted for enhancing the visualisation of mathematical concepts, providing adaptive learning experiences, and promoting independent, paced learning that supports learners' learning styles. Teachers reported a marked improvement in learners’ comprehension and problem-solving abilities attributable to AI integration. Despite the benefits of AI in education, challenges remain, particularly in rural areas. Key issues include inadequate infrastructure, limited access to devices, and the need for ongoing teacher training in technological pedagogical content knowledge. Additionally, the lack of culturally relevant AI technologies hinders effective AI-supported learning in diverse contexts. Greater investment in localised AI educational tools is needed to achieve equitable and effective learning outcomes.

Review of Digital Educational Resources for Use in Mathematics Classes

The article discusses a wide range of digital educational resources designed for use in mathematics classes. These resources represent innovative tools that contribute to a more interactive and engaging learning experience in mathematics. The article also considers several classifications of digital educational resources, their potential in mathematics education.

Preservice Teachers’ Experiences With, Beliefs About, Self-Efficacy In, and Instructional Practices for Mathematical Writing

ABSTRACT Students across grades K-12 may communicate their mathematical understanding via writing. Mathematical writing (MW) can include journaling about prior mathematical experiences, reflecting on a problem-solving strategy, providing feedback on a peer’s strategy, and generating a mathematical proof. Although there are a wide range of MW activities, many teachers report that they do not provide MW instruction or utilize writing activities with their students. Such instructional decisions are tied to teachers’ prior experiences with MW, beliefs about MW, and self-efficacy in teaching MW. Thus, in an effort to increase MW instruction for K-12 students, this study examined pre-service teachers’ (PSTs’) prior MW experiences and the impact of an online learning module on self-efficacy in teaching, beliefs about, and instructional decisions for MW. Participants were 111 elementary, special, or dual-education PSTs at one of the two universities. Findings indicated that PSTs had minimal prior MW experiences in their K-16 schooling but believed that MW was important before the module. After the module, PSTs’ self-efficacy in teaching MW significantly increased. Further, PSTs’ saw greater benefits of MW and demonstrated more sophisticated ways to utilize MW in mathematics teaching and learning.

Pre-service Elementary Mathematics Teachers' Opinions on the School Experience Course Conducted through Distance Education

This study aims to examine the experiences of pre-service elementary mathematics teachers regarding the school experience course conducted through distance education due to the Covid-19 pandemic. The study was conducted with 64 volunteer participants, from students who took the School Experience course in the fall semester of the 2021-2022 academic year at a state university, which was determined by convenience sampling among the universities in Turkey. The data was gathered using Google form at the end of the fall semester, using a data collection tool including 4 open-ended questions. These questions were about general evaluation, contributions, faced problems, and suggestions about the school experience course process. The study is phenomenological research from qualitative research types, and the content analysis method was used to analyze the data. Based on the analysis of the collected data, the following codes were obtained: positive, neutral, and negative under the heading of general evaluation; no contribution, getting to know students, professional skills, and time under the heading of contributions; technological problems, lack of professional skills, professional satisfaction, and communication under the heading of faced problems; and active participation, changing the course content, educational support, face-to-face education, student participation, and technological support under the heading of suggestions.

Teacher Educators’ Use of Formative Feedback During Preservice Teachers’ Simulated Teaching Experiences in Mathematics and Science

Teacher Educators’ Use of Formative Feedback During Preservice Teachers’ Simulated Teaching Experiences in Mathematics and Science

STEM Cooperating Teachers’ Professional Growth: The Positive Impacts of a Year-Long Clinical Residency Collaboration

Teacher residency programs integrate coursework with clinical practice in a year-long residency in which pre-service teachers work under the guidance of a cooperating teacher who has demonstrated excellence in teaching and mentoring. The purpose of this study was to examine the reasons for serving as a cooperating teacher and investigate how clinical residency pre-service teachers promote growth in the professional practice of cooperating teachers as teachers and teacher leaders. In this longitudinal qualitative study, we gathered data through semi-structured interviews and responses to survey questions over a five-year period. Ten STEM cooperating teachers (six female and four male) with 7 to 18 years of full-time teaching experience in biology, chemistry, or mathematics participated. A thematic analysis was used to analyze the interview transcripts and survey responses. The primary motivation for serving as a cooperating teacher was the desire to share experiences and support new teachers. Cooperating teachers described the following benefits: increased self-reflection and continuing reflective practice; meaningful collaboration with pre-service teachers; learned new teaching strategies to enrich their own teaching practice; improved communication skills; and the impetus to become teacher leaders. These findings support that clinical residency teaching programs are beneficial for STEM cooperating teachers and promote their professional growth.

Identifying queer discourses and navigational strategies in mathematics for undergraduate STEM students

IntroductionWhile research has explored racialized and gendered discourses in mathematics, there is a gap in understanding the experiences of Queer students and the discourses related to sexual identity in mathematics. This study aims to identify the discourses about mathematics that Queer STEM students describe in relation to their Queer identity and how they navigate these discourses.MethodsUsing phenomenology, individual interviews were conducted with 17 Queer STEM students at four universities in the United States. The interviews explored their life histories, experiences in mathematics, and responses to vignettes depicting mathematical scenarios. Grounded theory was leveraged to analyze the interviews to build a framework for Queer discourses and navigational strategies.ResultsSeven Queer discourses in mathematics were identified with underlying notions of exclusion and irrelevancy. The most prevalent discourses cast Queer identity as being irrelevant (erasure), unseen (heteronormative), or discriminated against (marginalized) in mathematics. At the same time there were some beliefs that Queer identity acceptance was unknown (ambiguous) was treated equally (normalized) or was accepted and even valued in math. Key findings from the study help theory build an exclusion-irrelevancy space to network together mathematical discourses and highlight how Queer marginalization is acted upon based on notions of rightful presence and not mathematical success.DiscussionThis study highlights the need to recognize and address the marginalization of Queer students in mathematics. By understanding the discourses and navigational strategies employed by these students, educators can create more inclusive and equitable STEM environments. It is critical to recognize and build upon the unique strengths of Queer students in mathematics, rather than focusing only on the challenges they face.

Insights on usability testing: The effectiveness of an adaptive e-learning system for secondary school mathematics

The study evaluates the Mythematix prototype, an innovative adaptive e-learning system designed specifically to enhance secondary school students’ understanding and proficiency in mathematics. Utilizing a mixed-methods approach, it combines qualitative and quantitative research methodologies to thoroughly assess students’ perceptions and experiences with the Mythematix prototype. The study involved a group of 30 students participating in a comprehensive usability survey, which included a range of Likert scale questions alongside an open-ended response. This survey was designed to evaluate the usability of the prototype, pinpointing its strengths and weaknesses from the students’ perspectives. The analysis of the survey results provided detailed insights into the most and least effective aspects of the prototype. Overall, the study contributes valuable insights into the effectiveness of adaptive e-learning platforms in enhancing and enriching students’ learning experiences in mathematics, and it lays the groundwork for future research in this evolving educational field.

Quantile regression model on how logical and rewarding is learning mathematics in the new normal

Learning mathematics through distance education can be challenging, with the “logical” and “rewarding” nature proving difficult to measure. This article aimed to articulate an argument explaining the “logical” and “rewarding” nature of online mathematics learning, elucidating their causal factors. Existing data from the literature that involving students at Visayas State University, Philippines, were utilized in this study. The study used statistical measures to capture descriptions from the data, and quantile regression analysis was employed to forecast the predictors of the logicality and rewarding nature of learning mathematics at a distance. Results indicate that learning mathematics in the new normal is perceived as “logical” and moderately “rewarding”. The regression and correlation analyses revealed a significant positive association between the perceived “logical” nature and the rewarding experience of learning mathematics. The constructed statistical models depicted that the determinants of logicality in learning mathematics include family income, money spent on the internet, learning environment, household size, social status, and health. Moreover, causal factors such as family income, money spent on the internet, learning environment, leisure activities, social status, and health significantly determine the rewarding nature of learning mathematics online. Conclusively, institution must support college students with their online learning needs. Furthermore, mathematics instructors should create lively and exciting online discussions that boost their logical thinking. Providing problem-solving task that are intrinsically rewarding can contribute to a more fulfilling learning experience.

Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem

Eigenvalue-eigenfunction problems frequently appear in many physical areas. Some mathematical experience is needed to identify whether the differential system is an eigenvalue-eigenfunction problem or not. Apart from the mathematical nature of the problem, the eigenvalue-eigenfunction solutions have physical interpretations which have to be addressed properly for real problems. The rotating beam problem is treated to exploit the mathematical and physical nature of such problems and the conditions to divert from the eigenvalue-eigenfunction problem. The rotation of a beam about its symmetry axis along its length and about another axis parallel to its symmetry axis changes the nature of the problem. While the former is an eigenvalue-eigenfunction problem, the latter is not. The interpretations of the physical consequences of the solutions are discussed in detail. The problem can be used as supplementary material in undergraduate courses such as differential equations, mechanics and dynamics.

Remembering learning mathematics – we can run but we can’t hide

ABSTRACT The adult participants in this study range in age from 20 to 50 years. They describe their remembered experiences of learning mathematics in both primary and secondary education. None of the participants achieved the qualifications in mathematics which would allow them access to higher education. They are now studying mathematics after many years away because it is required to achieve their ambitions. Each participant has considerable mathematics anxiety, which, they reported, resulted in reactions towards mathematics ranging from avoidance to fear and distress. The research uses narrative methodologies to collect and analyse these data. Common emergent themes were unsupportive relationships with their teachers and memories of being excluded and humiliated. The data suggests their teachers did not see supporting students’ well-being as part of their role, resulting in strong negative emotional reactions. The article concludes that where warm, respectful, relationships are built, barriers to learning mathematics can be overcome.

Humanoid Robots as Learning Assistants? Useability Perspectives of Grade 6 Students

AbstractDespite the increasing number of robots in educational settings, they are relatively new, with ambiguous research findings regarding a robot’s influence on students’ learning, psychosocial aspects, and gender differences. In this study, 17 Grade 6 students in a Norwegian school participated in a human–robot interaction (HRI) session with mathematics and programming tasks followed by focus group interviews to explore their experiences. Thematic analysis resulted in four main themes: (1) Technical aspects, (2) Robots as educational assistants, (3) Robot features, and (4) Attitudes regarding robots. Overall, the students found the robot entertaining, providing mastery experiences in mathematics and programming. Some technical difficulties were experienced, and the robot’s lack of facial expressions, emotions, and tailored feedback created interaction challenges. Gender differences regarding interest in people versus things were found. The implementation of robots in education shows potential, however, more research is needed, especially longitudinal exploring the impact of HRI in education.

Developing an instruments to measure prospective teacher beliefs about mathematical problem-solving using the Rasch model

Beliefs in solving mathematical problems become the basis for action, the basis for change, and the basis for learning mathematics. This research describes the development of an instrument for measuring prospective teachers beliefs in solving mathematical problems. One hundred sixty prospective teachers’ with experience in problem-solving and learning mathematics became research respondents. The research data was analysed using the Rasch model. The results of the data analysis show that the instrument developed is considered reliable and valid. Fifty-five items can be used to measure prospective teachers’ beliefs about solving mathematical problems. The instruments that have been developed can be used as initial assessments in implementing problem-based learning to help students develop problem-solving skills to face challenges in real life.

From Switching Languages to Switching Units

Switching languages enriches the mathematical experience of all students in the classroom during the problem-solving process.

AlephZero and mathematical experience

This essay explores the impact of automated proof construction on three key areas of mathematical cognition: on how we judge the role one piece of mathematics plays in another, on how we make mistakes in reasoning about mathematical objects, and on how we understand what our theorems are truly about. It concludes by speculating on a new form of mathematical experience that these methods could make possible: “glitching”, a game-like search for uncanny consequences of our definitions.

Analyzing Students’ Thinking in Mathematical Problem Solving Using Vygotskian Sociocultural Theory

Objective: This study aims to investigate students' thinking in solving mathematical problem solving (MPS) using the Vygotskian sociocultural theory (SCT) in the form of mathematical objects. Method: This qualitative study involved 34 high school students in Palembang, 20 female and 14 male students. Data were obtained from students' work and video recordings when students solved problems. The analysis of students' work was reviewed from the semiotic system to see the students' semiotics, including languages (natural and alphanumeric), concepts and propositions, procedures, and arguments. The video recordings were analyzed to assess communication and collaboration among students during problem-solving activities. Research Findings and Discussions: Analyzing students' work and video recordings revealed significant insights into their problem-solving strategies and sociocultural interactions. Through semiotic analysis, it was possible to observe how students expressed and communicated mathematical ideas. Moreover, examining video recordings elucidated communication and collaboration dynamics within the classroom context. These findings shed light on the effectiveness of integrating Mathematical Problem Solving (MPS) with Socio-Cultural Theory (SCT) principles in fostering algebraic thinking and enhancing students' mathematical abilities. Research Implication: The findings of this study hold implications for both research and practice in mathematics education. They provide valuable insights for designing instructional approaches that promote collaborative problem-solving and facilitate the development of algebraic thinking skills. Additionally, the application of Vygotskian SCT in mathematics classrooms offers a promising avenue for cultivating a supportive sociocultural environment conducive to learning. Originality/Value: This study contributes to the existing literature by offering a comprehensive exploration of MPS through the lens of Vygotskian SCT, mainly focusing on using mathematical objects as mediational tools. By examining students' semiotic systems and sociocultural interactions, this research enhances our understanding of the complex processes involved in mathematical problem-solving and underscores the importance of sociocultural factors in shaping students' mathematical experiences.

Development of a Mathematical Experience from a STEM and Sustainable Development Approach for Primary Education Pre-Service Teachers

Advances in education are increasingly important, and it is necessary to look for methodological strategies that enhance the value of mathematics in society and promote integrated training that helps students reason critically and rigorously. In this sense, math trails with a focus on STEM and sustainable development are a good resource to connect mathematics with the environment in a transversal way with other disciplines. A total of 35 postgraduate students in secondary education and 30 undergraduate students in primary education participated in this research and received a training course from experts in mathematics teaching. During the experience, the graduate students designed trails that were tested by the undergraduate students after a prior review by three in-service primary teachers. Likert scale questionnaires and open questions were asked of the students to evaluate the training received and the execution of the experience. Likewise, it was also decided to hold a debate with the participants and a guided interview with in-service teachers to assess the possible application of the resource in primary education courses. The results show a very positive assessment of the experience and allow us to support this approach to promote a change in the teaching–learning of mathematics in the last years of primary education.