Mathematics Pedagogy Research Articles

Modelling mathematics for educational research and practice: a comparison of two theoretical approaches

AbstractThe production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within Subject Matter Didactics (Stoffdidaktik). The second is the notion of praxeology from the Anthropological Theory of the Didactic, which originated in France. After presenting the genesis and interpretation of these notions as theoretical modelling tools, we provide a detailed case study of actual models produced with these tools, concerning the notion of limits and derivatives. Furthermore, we identify similarities and differences of both models in how they can support didactical research and practice, for instance, by identifying important phenomena or problems. We conclude that the two approaches offer important, different and, to some extent, complementary positions and perspectives.

Decolonising mathematics education: Teachers’ initial experiences of using ethnomathematical games in the intermediate phase

The African Agenda 2063 strives to attain the goals of peace and prosperity, and to do so, there must be a process of political liberation and decolonisation. In the South African context, decolonisation involves transforming the mathematics curriculum to one that is African by employing cultural approaches such as ethnomathematics. However, South African mathematics teachers still rely on Eurocentric methods for teaching mathematics. To decolonise mathematics in the Intermediate Phase, a project was initiated that utilised indigenous games for teaching mathematics. This paper aims to identify whether such efforts to decolonise mathematics education will be accepted or rejected by the mathematics teachers involved in this study. The paper is framed by the Critical Mathematics Pedagogy Theory. A qualitative case study approach was employed to collect data through a focus group interview with ten mathematics teachers who teach in rural and semi-rural areas of KwaZulu-Natal, South Africa. The findings demonstrate that ethnomathematical games encourage mathematics learning, that teachers’ initial apprehensions gave way to enthusiasm, that learners were excited to play and learn, and that teachers found it effortless to integrate mathematical concepts such as addition, subtraction, multiplication, factorisation, and quadrilaterals with the indigenous games of Morabaraba, Tshetershere, Diketo, and Kgati. Recommendations include that mathematics educational policies incorporate ethnomathematics as a policy directive and that teachers receive training in alternative cultural pedagogical practices for teaching mathematics, such as the use of ethnomathematics. Future research endeavours should focus on finding avenues to sustain ethnomathematics in the classroom.

Toward a framework of culturally relevant science and mathematics pedagogy: a pedagogical and analytical tool for teacher education

Toward a framework of culturally relevant science and mathematics pedagogy: a pedagogical and analytical tool for teacher education

INTEGRATING SERVICE LEARNING INTO MATHEMATICS PEDAGOGY FOR DEVELOPING PROSPECTIVE TEACHERS' METACOGNITION, PROBLEM-SOLVING SKILL AND PROFESSIONALISM

Service learning is an educational approach that integrates community service with academic instruction and reflection to enrich the learning experience, teach civic responsibility, and strengthen communities. Integrating service learning into mathematics pedagogy for developing prospective teachers can have significant benefits in various areas, including metacognition, problem-solving skills, and professionalism. This research study objectifies to explore the strategies incorporated for integrating service learning into math pedagogy for developing prospective teachers’ metacognition and problem-solving skills which is an essential skill for a math teacher to develop. The study aims to explore various strategies of social learning to develop prospective teachers’ professionalism and last but not least, the study also aims to find out the influence of metacognition and problem-solving skills, gained through social learning, on the prospective teachers’ professionalism development. For this study systematic literature review is followed to collect data and thematic analysis is done. The findings of this piece of research study ensure a great educational implication by integrating service learning into mathematics pedagogy. These strategies aim to create authentic learning experiences that integrate mathematical problem-solving, community engagement, and reflective practices. By implementing these strategies, prospective teachers can develop metacognitive awareness, enhance their problem-solving skills, and cultivate essential professional dispositions and competencies necessary for effective teaching and community service. The result of the study also shows that by integrating service learning into mathematics pedagogy, prospective teachers have the opportunity to develop metacognitive skills, problem-solving abilities, and professional dispositions in authentic contexts. These experiences can contribute to their overall professional growth, preparing them to become effective, reflective, and socially responsible educators who are equipped to navigate the complexities of the teaching profession. KEYWORDS: Service learning, Mathematics pedagogy, Prospective teachers, Metacognition, Problem solving skill, Professionalism.

Context of Contextualized Teaching Situations in the Initial Training of Mathematics Teachers at the Popular University of Cesar

The purpose of this research is to reflect on the role of the context environment of the contextualized situations of teaching school mathematics, which make significant contributions to the initial training of the mathematics teacher at the Universidad Popular del Cesar-Valledupar-Colombia, where the informants were the twelve students enrolled in the subjects of Elective III, Mathematics Didactics, History and Epistemology of Mathematics and Degree Work II, of the VI, VII, VIII and IX semesters respectively, of the Bachelor's Degree in Mathematics program; assigned to the Faculty of Education, of the Universidad Popular del Cesar. The study was situated in the qualitative paradigm, under the epistemological approach of sociocultural constructivism, with the recapitulations of the foundations and orientations of the phenomenological-transcendental methodology. It is concluded that it is feasible to change the mathematics master class for a space where students can interact in the teaching-learning process, with the necessary knowledge to understand the messages of the context of the habitat of the subject who learns; and for this reason, the relationships of the trio: Teacher-School Mathematical Knowledge-Students and these with the context can always be placed in the context of mathematics education.

Teaching practice: Contributions to Spanish prospective mathematics teachers

Prospective primary education (PE) teachers of mathematics are trained on university programs which include core subjects in the field of the didactics of mathematics. However, these subjects have no general practical component. Therefore, this research aims to analyze the contribution of practical courses to the development of good practice in mathematics education. For this purpose, an ethnographic study was carried out with the participation of 23 prospective teachers who completed a questionnaire with closed and open-ended questions. The closed responses were analyzed by frequency and percentage, and the open-ended responses were analyzed using the ATLAS.ti software (v. 22) (ATLAS.ti, 2022). The results show that most of the prospective teachers identified principles of good practice in mathematics classes, and most of them found a relationship between their initial training and what they experienced in these classrooms. In the light of the results, contributions are made to improve the initial training of mathematics teachers in PE.

A Socio-Constructivist Perspective on Problem-Solving Approaches in Mathematics: Perceptions of Future Primary Education Teachers

This study investigates the perceptions of future primary education teachers regarding the implementation of a problem-solving teaching approach from a socio-constructivist perspective. Although previous research has shown the benefits of problem-solving in mathematics education, few studies have yet focused on preservice teachers in primary education, particularly within a socio-constructivist framework. Therefore, this study addresses this gap by exploring the effectiveness and challenges of the Building Thinking Classrooms approach developed by Peter Liljedahl. The study was conducted through a case study design involving 36 first-year preservice teachers enrolled in a mathematics didactics course at a public university in Chile. Qualitative and quantitative data were collected through surveys, field logs, and classroom observations. The data analysis included descriptive statistics and content analysis to understand the students’ perceptions of problem difficulty, engagement, and the overall approach. The findings reveal that the problem-solving approach was positively perceived by the participants, highlighting its role in fostering critical thinking, collaboration, and a deep understanding of mathematical concepts. However, challenges were identified, particularly regarding group work and the autonomy required in solving problems. Furthermore, the study identified areas in which additional support could enhance the effectiveness of problem-solving approaches. This research underlines the importance of integrating problem-solving approaches into teacher education programmes and highlights the need for future research on the long-term impacts and strategies needed to support autonomy and collaborative learning.

Inteligencia Artificial en educación matemática: Una revisión sistemática

[Objective] This study aims to analyze the current state of research on artificial intelligence (AI) in mathematics education, its applications, and its role in teaching and learning processes. [Methodology] A systematic review of the literature was conducted in three stages: identification, selection, and inclusion of articles from three recognized databases, resulting in 29 articles. These articles were thoroughly analyzed to identify participants, instruments used, the country of the authors' affiliation, year of publication, type of research, methodological approach, and the role of AI in these studies. [Results] There is a noticeable increase in research related to AI in mathematics education, with most studies being empirical and quantitative. The most frequently used instruments are questionnaires and interviews, with half of the studies employing at least two data collection instruments. Additionally, most studies focused on intelligent learning systems to enhance learning and support teaching, particularly for online assessment. [Conclusions] The reviewed articles show no evidence of research at the early childhood education level and very little related to teacher training. Few studies demonstrate the use of theoretical frameworks or approaches from the Didactics of Mathematics.

Pre-service teachers’ use of the jump strategy on the empty number line for mental computation

Background: South African teachers’ mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics.Aim: The aim of this article is to share how pre-service teachers (PSTs) used the empty number line (ENL) to demonstrate the jump strategy (JS) for efficient mental computation, related to the national Mental Starters Assessment Project (MSAP).Setting: This study was conducted at a tertiary institution in the Eastern Cape province of South Africa, with 40 first-year intermediate phase PSTs, during their mathematics didactics course.Methods: The data comprised 40 micro-teaching videos, analysed thematically, following an analytical model for video-recorded data. Videos were categorised according to the way they faithfully followed or departed from the MSAP teacher resources.Results: Findings suggest that more than 70% of the PSTs faithfully followed the teacher resources to teach the JS on the ENL, with regards to use of at least three of the four key elements, namely: ENL, jumps, gesturing, and key phrases and terminology.Conclusion: We suggest PSTs receive explicit instruction on the above-mentioned key elements for teaching mental calculation strategies with the ENL and opportunities to practise teaching these to their peers.Contribution: Most PSTs successfully used the ENL to demonstrate the JS for efficient mental computation, enabled by the opportunity to engage in developing (and reflecting on their) micro-teaching videos.

The algebraic learning of middle school students’ evolution during a school year: a statistical large-scale study based on results in mathematics didactics

AbstractThis large-scale study characterizes the algebraic learning of a cohort of nearly 800 French students during the last year of middle school (9th grade, 14–15 years old) and examines their evolution in relation to the composition of the classes to which the students belong. Based on the Anthropological Theory of the Didactic (ATD), the study is founded both on a reference model of elementary algebra and on technological-theoretical levels characterizing the students’ reasoning and their knowledge regarding institutional expectations. These are used to code the data and define the statistical variables on which multivariate descriptive analyses are carried out. Students’ learning is analyzed through Pépite, an algebra test given at the beginning and at the end of the year. A cluster analysis resulted in three distinct clusters of similar classes and of similar students both at the beginning and end of the grade 9 school year. They are interpreted didactically and could be useful for a teacher who has to manage the heterogeneity of learning in a class. Some classes and students move from one cluster to another between the beginning and the end of the year, showing a wide variety of ways in which students’ algebra learning progresses or regresses over a school year.

Didáctica de la Matemática: Una reflexión sobre su evolución

The didactics of mathematics has allowed an evolution in terms of the learning and teaching of mathematics in different parts of the world, achieving its existence was and is a challenge since, although the years go by, its evolution is continuous, for various reasons including the generations of teachers and students who day after day face new challenges to achieve their goal, teach or learn mathematics in the best way.

Innovative Strategies in Math Education: The Impact of PBL and TaRL on Concept Mastery and Classroom Dynamics

In scrutinizing the amalgamation of Problem-Based Learning (PBL) and Teaching at the Right Level (TaRL) approach within mathematics pedagogy, extant scholarship scarcely offers a holistic evaluation of their synergistic efficacy. Prior research predominantly accentuates scholastic outcomes, frequently neglecting the ramifications of these models on classroom dynamics, including the nuances of student-teacher interactions and student engagement and participation levels. This study probes the integration of PBL and TaRL models to augment students' comprehension of mathematical principles, employing a mixed-methods research design encompassing qualitative and quantitative methodologies. The investigation centered on seventh-grade students in junior high school, utilizing test instruments to evaluate mathematical comprehension and observational protocols to document student and teacher engagement for enriched insights. Comprehensive qualitative and quantitative data analyses were executed. The findings disclosed significant advancements in students' grasp of mathematical concepts, with observations revealing heightened student engagement and more favorable teacher-student interactions. Statistical analyses evidenced substantial disparities between pre-test and post-test scores (p < 0.05). The results proffer recommendations and pragmatic implications for enhancing mathematics education, underscoring the imperative for teacher professional development in deploying this integrative pedagogical model to elevate the quality of mathematics instruction at the secondary school echelon.

Social justice implications of digital science, technology, engineering and mathematics pedagogy: Exploring a South African blended higher education context

AbstractHigher Education institutions robustly adopted digital pedagogy during the coronavirus (COVID-19) pandemic. This article reports on a study focussing on postgraduate students’ first-hand experiences of digital pedagogy for Science, Technology, Engineering and Mathematics (STEM) education. This study was conducted at one higher education institution in South Africa post-COVID-19. The study was framed by the technology acceptance model and a self-constructed conceptual model focusing on key concepts and ideas related to social justice. Forty-seven postgraduate STEM education students participated in the study. A mixed-methods approach guided the data generation for this study, whereby one questionnaire was used to generate quantitative data and four semi-structured focus group interviews assisted in generating qualitative data. Thematic coding, interpretative techniques and NVivo were used to analyse the qualitative data. Excel was used to analyse the quantitative data. The results exhibit the strengths, limitations and implications of digital STEM pedagogy for higher education in a developing country. This study adds to the developing knowledge concerning digital pedagogy for STEM education and social justice issues in developing countries. Using postgraduate STEM education students’ personal experiences of digital pedagogy, this study seeks to contribute to the growing body of research on the social justice implications of using digital pedagogy in higher education. By examining the implications of digital pedagogy for STEM education through a social justice lens, this research can inform curriculum development and pedagogical practices that encourage more inclusive and equitable learning environments.

Didactics of mathematics, free software and resource development through Learnr and Shiny.

Didactics of mathematics, free software and resource development through Learnr and Shiny.

Effectiveness of Problem-Based Learning in the Unplugged Computational Thinking of University Students

Computational thinking is recognized as a critical competency in contemporary education, preparing individuals to tackle complex challenges in a digitally pervasive world. In this quasi-experimental design study with pretest and post-test measures, the possibility of developing computational thinking from the field of didactics of mathematics in higher education students was investigated. This was performed via a problem-based learning (PBL) methodology using problem solving in the experimental group or, alternatively, focused on the analysis of solved problems in the control group. After the intervention, the control group experienced a statistically significant improvement in the scores obtained in the post-test measure. Thus, PBL and problem solving did not lead to an improvement in the students’ computational thinking, whereas the analysis of solved problems approach did. Therefore, the results suggested the potential benefits of this latter methodology for teaching computational thinking.

On resolving the tension between visiting mathematical works and questioning the quantum world

For the past 40 years, researchers in didactics of mathematics have developed and utilised didactic engineering as a methodology for design-based research. In this article we discuss its second step, the so-called a priori analysis. In the framework of the Anthropological Theory of the Didactic, engineering is in the form of the implementation of a study and research path (SRP), an inquiry-based course. SRPs may be either finalised, that is aimed at the teaching of a particular piece of knowledge, or rather open, that is solely aimed at answering a given question. This tension between sometimes competing goals especially shows in the a priori analysis of SRPs, a phenomenon we address in this paper. Our study is based on pieces of evidence collected by setting up an SRP two years in a row at the interface between mathematics and quantum mechanics, in third year of bachelor's degree. We take a particular care in explicating the rationale behind the a priori analysis and its connection with the preliminary analysis. We bring out the significance of spelling out one's epistemological stance, as didactic engineer, emphasising the value of the notion of reference epistemological models to do so.

Developing teachers’ cultural competencies through co-design of robot-coding mathematics activities for Latinx and Black elementary school students

This year-long case study involved the professional development of teachers in New York City elementary schools, who co-designed with researchers culturally relevant robot-coding mathematics activities to advance teachers’ understanding of culturally responsive mathematics pedagogy. Study findings indicated that co-designing culturally relevant robot-coding mathematics activities led to the development of teachers’ cultural competencies, deeper understanding of culturally responsive mathematics pedagogy and their students’ cultures, stronger agency, and ability to integrate culturally responsive pedagogy into their mathematics curriculum. Teachers also began to perceive the robot as a mathematical tool rather than a motivational add-on, and started to develop their own cultural lens while focusing less on school structure constraints. The study emphasises the importance of engaging teachers as active co-designers of culturally relevant coding curriculum in professional development programmes.

Research on Integrated Teaching of Mathematical Units from the Perspective of HPM

In recent years, unit holistic teaching has been continuously focused on as an effective way to implement core competencies. This teaching method takes a global perspective, organizes teaching content from a unit perspective with systematic thinking, and emphasizes the improvement of students' basic abilities and the development of core competencies. At the same time, teaching based on the history of mathematics is highly valued, HPM (History and Pedagogy of Mathematics) entered the mathematics classroom teaching. HPM teaching can transform science oriented mathematics into education oriented mathematics, thereby maximizing the educational value of the history of mathematics. HPM teaching coincides with unit teaching. This article conducts in-depth research on the overall teaching of mathematical units, sorts out the development of mathematical history, explores the historical background of mathematical knowledge, calculates the evolution process, and effectively integrates mathematical history resources into unit teaching design. The introduction of M-perspective can effectively enrich the content of mathematics teaching, enhance students' interest in learning, deepen their cognitive depth, and help cultivate students' innovative thinking ability in mathematics. Explore the overall teaching implementation strategy of mathematical units, propose corresponding teaching suggestions, and provide reference for mathematics educators.

Factors affecting success and failure in higher education mathematics: Students' and teachers’ perspectives

BackgroundStudents from Bangladesh pursuing STEM education often encounter obstacles when tackling diverse mathematical problems within various educational settings. Frequently, they find themselves lacking the essential prerequisite knowledge and strong foundational skills necessary to engage with the teaching and learning resources utilized at the undergraduate level, resulting in a significant number of students needing to seek readmission annually. ObjectiveThe objective of this study is to explore the determinants of academic achievement among university undergraduates majoring in mathematics in Bangladesh. Employing a mixed-method research approach, the study combines quantitative and qualitative data analysis to examine the viewpoints of both students and educators concerning these factors. The authors primarily emphasize classifying the factors that impact the efficacy of mathematics pedagogical methods. MethodologyThe study is structured into three phases: i. An initial exploratory qualitative survey. ii. A quantitative triangulation survey. iii. Followed by explanatory semi-structured interviews. FindingsTo begin, the initial qualitative survey identified significant factors that contribute to students' achievements and setbacks in mathematics. Subsequently, the quantitative analysis verified both similarities and distinctions in the perspectives of students and educators. Furthermore, the correlation coefficient analysis revealed that male students frequently exhibit inconsistency and a lack of enthusiasm for studying, resulting in subpar performance. Conversely, female students frequently cited challenges like the difficulty of connecting mathematical theories to real-world applications, heavy course loads, and limited resources as reasons for their academic difficulties. Lastly, insights from interviews with students highlighted their acknowledgment of inadequate study practices, excessive reliance on memorization, suboptimal teaching methods, low motivation, and external distractions as key factors leading to their struggles. They also recognized the importance of consistent practice, a solid comprehension of concepts, regular study routines, and effective learning strategies for successful mathematics education. In contrast, educators emphasized the significance of students having clear concepts, natural aptitude, motivation, and a sense of curiosity as pivotal elements for successful learning in mathematics. ConclusionThis conclusion suggests a new beginning in the realm of local mathematics pedagogy, achieved by scrutinizing teacher-student feedback about the factors influencing success and failure, considering the diverse individual and contextual variables at play. To foster mutual trust and understanding between students and teachers, it may be beneficial to engage in open discussions and interactions.

Empowering Mathematics Education in Greek Primary Schools: Bridging the Divide through ICT Integration and Interactive Boards for Enhanced Teacher ICT Literacy

This article advocates for a tech-enriched teaching approach using Information and Communication Technologies (ICT) and interactive boards to enhance students’ understanding and problem-solving skills. Overcoming challenges requires systematic planning, progressive policies, dedicated funds, and regular teacher training. The essay also discusses the benefits and limitations of ICT, the key principles of interactive whiteboard application in pedagogy, and the dynamic challenges faced by Greek elementary schools in redesigning mathematics pedagogy with ICT. It proposes blending modern technologies with traditional instructions, emphasizing the need for continuous teacher development and a positive attitude toward technology. The way forward involves leveraging Optical Character Recognition (OCR) systems and interactive boards, necessitating strategic planning, training programs, and infrastructure investment for a tech-enriched teaching future in Greek primary schools.