Theory Of Mathematics Education Research Articles

The sociopolitical turn in mathematics education and decolonial theory

This literature review examines how the theoretical perspectives aligned to the sociopolitical turn in mathematics inform social justice mathematics education. While existing literature has established the importance of social justice frameworks informed by critical theory, there has been limited exploration of critical race theory, poststructuralism and feminist theory, perspectives that offer a broader and more complex understanding of the social and political. After examining how these perspectives contribute to social justice mathematics, we explore the potential contributions of decolonial theory, particularly the way it unsettles accepted notions of social justice. By drawing and building on the sociopolitical turn in mathematics education, this article argues that decolonial thought can also assist in reimagining social justice mathematics education theoretically, methodologically and pedagogically. Ultimately, the article argues that there is no social justice without cognitive/epistemic and ontological justice, meaning that social justice loses ethical and political weight when modernity’s violent epistemic and ontological foundations are not questioned by social justice mathematics education research.

An Overview of the Study of Cognitive Load Theory in Mathematics Education

An Overview of the Study of Cognitive Load Theory in Mathematics Education

Do Instructional Strategies Impact Students’ Situational Interests in Learning Mathematics? A Case Study of Secondary School Students in Guyana

This experimental study investigates which instructional strategies are effective in promoting situational interest in learning mathematics among secondary school students. This research study builds on established theories of interest and mathematics education. Situational interest is an important facet of learning engagement, and it can potentially enhance students’ interest and motivation in class. A total of 165 students were engaged in this study, selected from three diverse secondary schools in Georgetown, Guyana, encompassing different grade levels and varying motivating profiles. This study employed a quantitative research design, providing a comprehensive understanding of the relationship between instructional strategies and situational interest. Participants were given a carefully constructed questionnaire that entails questions about their level of situational interest and their perceptions of various instructional strategies used in their mathematics classroom. Results suggested visual aids, inquiry-based learning, and collaborative learning are most effective in promoting situational interest. These findings highlight the interplay between pedagogical approaches and students’ motivation, and how closely connected they are. This emphasizes the importance of using teaching strategies that align with students’ interests and needs.

Learning mathematics through experience

The aim of this research is to explore the application of experiential mathematics education to enhance the enthusiasm of second-grade students in the context of Vietnamese education. The research methodology is based on conducting a specific theoretical study of the benefits of experiential mathematics education and the significance of mathematical enthusiasm. This paper provides an overview of the theory of experiential mathematics education, focusing on understanding the importance of mathematical enthusiasm in the teaching process and evaluating the current state of mathematics education for second-grade students in Vietnam. The research results emphasize that learning mathematics through experience can create an exciting and effective learning environment for second-grade students. This method helps them grasp mathematical knowledge with greater enthusiasm and provides opportunities for active participation in the learning process. However, it also poses some challenges in implementation, such as adapting to the Vietnamese educational context and ensuring that teachers have the knowledge and skills to effectively apply this method. In conclusion, this paper's research highlights the importance of applying experiential mathematics education to enhance the mathematical enthusiasm of second-grade students in Vietnam and provides theoretical foundations for its effective implementation in the Vietnamese educational environment.

Contributions of the Theory of the Inclusion of the Other to Inclusive Mathematics Education

Background: The post-colonial and anti-colonial theories in mathematics education, difference and inclusion led Souza and Skovsmose to create the term deficiencialism. Objective: To present the potential of Jurgen Habermas’s theory of the inclusion of the other to contribute to concepts of inclusive mathematics education. Design: Considering that Habermas is a German philosopher who defends ethical communication to solve social problems, we believe that his concepts can help understand the idea of inclusion in teaching to guide the academic community towards a better understanding and positioning about who the Other is. Setting and participants: Jurgen Habermas (2018, 2019) and Ole Skovsmose (2014). Data collection and analysis: Bibliographical and theoretical study. Results: We found possible similarities between Habermasian theories and the critical mathematics education by Ole Skovsmose, each concept with its particularities converging on ethical communication that can favour a more inclusive mathematics education.

Piaget's Theory in Mathematics Education in Elementary School

Since the passing of Law No. 2 of 1989, the landscape of education in Indonesia should be distinguished by the consistency of its system, thus by a series of adjustments. Some possible adjustments to the primary school curriculum to the high school level include (1) imbalances in the effective learning offered. This is supported by the fact that, since the implementation of the national exam (in elementary schools), the field of mathematics studies has one of the lowest average values among national exam subjects. (2) The ongoing curriculum's requirements not fit with students intellectual development. This study will employ theory of learning based on Piaget's intellectual development from a variety of learning theories based on cognitive theory. According to Piaget's hypothesis, a child's development progresses over the course of 4 sequential phases, consisting :(1) Sensory motor period (ages 0 to 2 years), (2) per-operational period (ages 2 to 7 years), (3) concrete operational period (ages 7 to 11 years), and (4) formal operational period (ages 11 and onwards).The purpose of this research is to determine the level of effectiveness in teaching geometry unit math based on the conservation aspects of Piaget's theory. These goals can be summarized as follows: 1) Determining the amount of efficacy in teaching geometry unit math using Piaget's theory's conservation components;2) Identifying differences in the influence of age (9, 10, and 11) on receiving geometry unit math teachings based on the conservative aspects of Piaget's theory. To accomplish the study's objectives, the research utilized a per-experimental research design, particularly a pre-test-post-test design with one group. The results indicated that the learning accomplishment of geometry unit math based on the conservation aspects of Piaget's theory did not vary by age (9, 10, or 11 years). The study's findings indicate that there is no interaction effect between the ages of 9 and 10 on math learning achievement, (2.2) that there is no interaction effect between the ages of 9 and 11 on math learning achievement, (2.3) there is no interaction effect between the ages of 10 and 11 on math learning achievement, and (2.4) that there is no interaction effect between the ages of 9 and 10 on math learning achievement. Keywords: Mathematics, elementary school.

The Role of Teaching and Learning Theories in Preparing Student Teachers to Teach Mathematics and Enhancing Learners' Readiness to Learn: A Case Study of Bia Lamplighter College of Education in Ghana

Aim: The study aimed to investigate the role of teaching and learning theories in preparing teachers to teach mathematics and in enhancing students' readiness to learn. Specifically, the study explored the application of constructivist and pedagogical content knowledge (PCK) theories in a teacher preparation program and in classroom instruction.
 Study Design: The study employed a case study design and involved pre-service teachers and their students in a mathematics classroom. Data was collected through interviews, observations, and document analysis.
 Methodology: The study employed a case study design to investigate the application of constructivist and PCK theories in a teacher preparation program and in classroom instruction. The study involved pre-service teachers and their students in a mathematics classroom. A purposive sampling technique was used to select ten (10) final year student teachers who can provide rich and detailed information about their readiness to teach and learn mathematics, as well as their understanding and application of learning and teaching theories. Also, one hundred (100) students were purposively selected for the study. Data was collected through interviews, observations, and document analysis and was analyzed using thematic analysis.
 Results: The findings revealed that pre-service teachers who were exposed to constructivist and PCK-based instruction in their teacher preparation program were better equipped to design and deliver mathematics lessons that promote active learning and deep understanding of mathematical concepts. Moreover, students who were taught in a constructivist and PCK-based learning environment demonstrated higher levels of readiness to learn mathematics. The study provides insights into the effectiveness of using learning and teaching theories in mathematics education and highlights the importance of incorporating these theories in teacher preparation programs.
 Conclusions: Based on the findings and analysis of this study, it can be concluded that the application of constructivist and PCK-based instruction in mathematics teacher preparation programs has a positive impact on pre-service teachers' readiness to teach mathematics.
 To successfully incorporate constructivist and PCK-based instruction in mathematics teacher preparation programs, it is important to provide adequate support and training for instructors and to engage in ongoing evaluation and refinement of these programs. By doing so, we can help to ensure that future mathematics teachers are prepared to effectively facilitate learning and promote mathematical understanding in their classrooms.

Karl Marx’s thoughts on critical pedagogy, reproduction, and aesthetic literacy in STEAM education and praxis

This article sheds new light on Karl Marx’s theoretical legacy to promote educational philosophy and theory in science, technology, engineering, arts, and mathematics (STEAM) education. Accordingly, this article selects Marxian thought as an exemplar case to elaborate critical pedagogy and aesthetics and culminate with an overview of the Marxian approach to the theoretical underpinnings of STEAM education. Hence, the article critically reviews Marx’s original works and earlier Marxian scholars’ contributions to extending critical pedagogy and its applications to the STEAM paradigm and informational and communication technology (ICT) development. This article critiques notable structural problems of STEAM education that produce power differentials such as educational gaps and digital divides in the current age of digital capitalism. Given the context, this article refines art and communication theories through the lens of his biography and writings. Additionally, this article incorporates the Marxian viewpoints about reproduction and aesthetic literacy into STEAM education. Overall, this article reviews the theoretical legacy of Marx and his essential critical and pedagogical theory, calling on scholars to pay close attention to re-orienting STEAM pedagogy as an emerging multidisciplinary field.

Formative Assessment in Secondary Mathematics: Moving Theory to Recommendations for Evidence-Based Practice

Mathematics teacher educators play a key role in supporting secondary mathematics teachers’ development of effective, research-based formative assessment (FA) practices. We used qualitative research synthesis as a tool to identify actionable recommendations for mathematics teacher educators as they work with teachers on FA practices in secondary classrooms. These recommendations can strengthen the research-based practices of mathematics teacher educators as they support teachers’ collections and uses of FA data to move student thinking forward in secondary mathematics. We share and discuss recommendations for mathematics teacher educators to connect pedagogical content knowledge of students, teaching, and curriculum to FA practices. We also highlight the usefulness of the qualitative synthesis method, meta-aggregation, for generating research-based connections between theory and practice in mathematics education.

Abordagem semiótica do feixe e abordagem OntoSemiótica: um diálogo entre duas teorias sobre um problema aritmético-algébrico

Abstract This research rests on the analysis of a mathematical task, concerning an arithmetic-algebraic problem and its solution, using theoretical tools from two main frames: the Semiotic Bundle Approach (SBA) and the Onto-Semiotic Approach (OSA). The activity has been examined by two original video recordings of the group consisting of five pupils of primary education. By presenting an empirical case of networking of theories, the objective is to begin a dialogue with the two approaches, reading the asymmetries found between their languages, with the aim of getting some new insights into the mathematical problem. Whereas the SBA, in a systematic approach, is particularly apt to focus on the relationships among the different multimodal semiotic resources used by the students in the short timescales of the classroom story (an embodied cognitive focus), the OSA incorporates a set of conceptual tools to address the analysis of the different facets that interact in a mathematical education process. Mainly the SBA describes the importance of the bundle of signs (like gestures, words, written signs) for mathematical thinking and communication and its multimodality, whereas the OSA favours the description of objects and processes that emerge from the mathematical practices. The results from this joint analysis provide a rich insight into the observed phenomenon and help initiate a dialogue between theories in Mathematics Education, within a Semiosphere generated by the networking between SBA and OSA.

Creating a context for graduate student learning through constructivist inquiry: Introduction to academia as learning through play

ABSTRACT In this article, I explore the impact of receiving mentorship into research and theory of the field that was guided by a social constructivist learning lens. I reflect on the ways that my conception of research and research agenda were framed subconsciously by early experiences investigating my secondary mathematics teaching practice under the mentorship of Dr. Terry Wood. Terry mentored through listening, posing questions, creating cognitive conflict, and encouraging my autonomous exploration. What stood out from this process are the parallels between her words about constructivism, applied to the elementary mathematics classroom, and her ways of mentoring me into the space of mathematics education research, theory, and practice. Her patient and student-centered mentorship had a profound impact on my ways of framing and studying teacher learning.

The Impact of Challenges Experienced by Teachers and Learners on Mathematics Performance in Relation to their Socio-Economic St

Objective – This paper explores the challenges experienced by mathematics teachers and learners of seven high schools in South Africa. A mixed method approach involving interviews and questionnaires was used. Methodology – The sample included 7 principals or deputy principals, 7 departmental heads who supervised mathematics, 1 mathematics teacher who taught mathematics in grades 10 to 12, and 1 mathematics teacher who taught Mathematics in grades 8 and 9. In addition, 1 learner from each grade 8 to 12 was included in the sample. Each participant was interviewed using a structured interview schedule, followed by participants completing a questionnaire. Findings – Vygotsky's socio-cultural and conceptual development theories in mathematics education formed the basis of this study. The 'Inputs, Processes and Output" model of Howie and Kilpatrick's model of the five strands of achieving 'mathematics proficiency was adopted. We identified many systemic, societal, and pedagogical challenges that teachers and learners experienced, which affected their mathematics teaching and learning. Our findings correlated with research in the literature review. Novelty – The researchers concluded there were always intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers and learners of mathematics, thus improving their socio-economic standing. Type of Paper: Review JEL Classification: A14, 19. Keywords: Challenges, Strategies, Blended Learning, Scaffolding, Conceptual Development, Collaborative Learning. Reference to this paper should be made as follows: Brijlall, D; Ivasen, S.J. (2022). The impact of challenges experienced by teachers and learners on Mathematics performance, in relation to their socio-economic standing, J. Bus. Econ. Review, 7(2), 112–126. https://doi.org/10.35609/jber.2022.7.2(1)

A Rasch Analysis of Students' Academic Motivation toward Mathematics in an Adaptive Learning System.

Despite the criticality of considering student academic motivation as it influences learning, research within the field of adaptive learning technologies for education has so far focused more on customising instruction to implement personalised learning, than investigating how personalised learning is associated with learners’ motivation. Given this, a robust instrument is required to gather information about student academic motivation within the context of adaptive learning technologies. This study sought to validate the Academic Motivation Toward Mathematics Survey (AMTMS) currently used to measure motivation based on self-determination theory in mathematics education at pre-tertiary levels (grades 11 and 12) in Asia. A total of 196 participants recruited via availability sampling took part in this study, after interacting with an in-house mathematics adaptive learning system within a tertiary educational institution. The validation was performed based on modern test theory given that it overcomes some limitations of classical factor analytic approaches. Results supported the factorial structure of the AMTMS but 12 of the original 21 items had to be rescored to establish ordered thresholds. Further, the bifactor equivalent solution suggested the possibility of reporting a singular motivation index comprising the five factors within the AMTMS. Along with the results, this study offers researchers a robust and validated instrument to measure motivation toward mathematics that can be used within an adaptive learning environment.

Designing a teaching model based on the Realistic Mathematics Education (RME) approach and its application in teaching calculus

The trend of applying mathematical knowledge to solve practical problems has become a top priority goal of many mathematics educations in the world, including Vietnam. The pioneer in the concept of “realistic mathematics education” is Freudenthal (1991). He believes that “math teaching needs to be connected with situations related to everyday life, to general society to be of value to learners”. Freudenthal’s (1991) thought opened the way for the formation of a very developed theory of mathematics education in the Netherlands, called realistic mathematics education (RME), with two basic principles that mathematics must not only be linked with the real but also mathematics needs to be viewed as a human activity. By applying this theory, in this article, we have designed a teaching model based on RME, the feasibility of the model has been verified by us through two experimental teaching periods in the classroom. With positive results, we believe that the model that we have proposed according to RME’s approach can meet the goal of mathematics education in Vietnam in the current period and in the coming 21st century, and it needs to be widely studied and applied in math teaching in Vietnam.

Approach to Realistic Mathematics Education in Teaching Calculus for High School Students: A Case of the Application of Derivatives

The purpose of the study is to systematize some core principles of Realistic Mathematics Education (RME) theory in the design of mathematics teaching so that we can design a teaching model “applying derivatives” in the topic of calculus in high school. The feasibility of the model has been verified by us through two experimental lessons in class. With the positive results, we believe that the model we propose according to RME’s approach can improve the effectiveness of teaching and learning the topic of calculus at high schools in Vietnam today.

POTENTIAL OF APPLYING REALISTIC MATHEMATICS EDUCATION TO THE TEACHING OF PROBABILITY - STATISTICS AT THE UNIVERSITIES OF MEDICINE AND PHARMACY

RME is a theory of mathematics education with a history of more than 50 years, widely deployed in many developed education systems around the world. Many research papers have confirmed the compatibility of RME with the principles and orientation of mathematics education, as well as with the education practices in Vietnam. Based on an overview of RME, this paper presents the potential of applying RME for teaching Probability - Statistics at the Universities of Medicine and Pharmacy.

INTRODUCTION OF ELEMENTS FROM PROBABILITY THEORY IN THE EDUCATION IN MATHEMATICS FOR PRIMARY SCHOOL

The article considers the prerequisites for the inclusion of problems with elements of probability theory in mathematics education in grades 1-4. This type of task is generally not present in the compulsory curriculum in mathematics in primary school, but they could be used in classes for compulsory, extended, and additional training, thus creating conditions for implementing developmental learning.
 Some theoretical statements about the theory of probabilities are systematized, related to the tasks included in the constructed and approbated methodological system of work. Some of its characteristics are presented. This article offers some of the tasks for grades 1-4.
 A longitudinal empirical study was conducted with students of the 1-4th grade in the period 2015 to 2020. The results of the outgoing diagnostics in 4th grade are processed by mathematical and statistical methods and are presented graphically. They show that fourth-graders successfully solve problems with elements of probability theory, and a primary school teacher could use them in the systematic work in mathematics at the initial stage of the basic educational degree.
 Solving non-standard mathematical problems is an element of probability theory that helps arouse interest, motivate students, and place them in an active cognitive position by solving problem situations in the pedagogical interaction in mathematics in primary school.

The Interrelationships between Metacognition and Modeling Competency: The Moderating Role of the Academic Year

<p style="text-align:justify">Several concerted movements toward mathematical modeling have been seen in the last decade, reflecting the growing global relationship between the role of mathematics in the context of modern science, technology and real life. The literature has mainly covered the theoretical basis of research questions in mathematical modeling and the use of effective research methods in the studies. Driven by the Realistic Mathematics Education (RME) theory and empirical evidence on metacognition and modeling competency, this research aimed at exploring the interrelationships between metacognition and mathematical modeling and academic year level as a moderator via the SEM approach. This study involved 538 students as participants. From this sample, 133 students (24.7%) were from the first academic year, 223 (41.4%) were from the second and 182 (33.8%) were from the third. A correlational research design was employed to answer the research question. Cluster random sampling was used to gather the sample. We employed structural equation modeling (SEM) to test the hypothesized moderation employing IBM SPSS Amos version 18. Our findings confirmed the direct correlation between metacognition and mathematical modeling was statistically significant. Academic year level as a partial moderator significantly moderates the interrelationships between the metacognitive strategies and mathematical modeling competency. The effect of metacognition on mathematical modeling competency was more pronounced in the year two group compared to the year one and three groups.</p>

MERIA – Conflict Lines: Experience with Two Innovative Teaching Materials

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestration supported by these scenarios. The context of the study is the Erasmus+ project MERIA – Mathematics Education: Relevant, Interesting and Applicable, which aims to encourage learning activities that are meaningful and inspiring for students by promoting the reinvention of target mathematical concepts. As innovative teaching materials for mathematics education in secondary schools, MERIA scenarios cover specific curriculum topics and were created based on two well-founded theories in mathematics education: realistic mathematics education and the theory of didactical situations. With the common name Conflict Lines (Conflict Lines – Introduction and Conflict Set – Parabola), the scenarios aim to support students’ inquiry about sets in the plane that are equidistant from given geometrical figures: a perpendicular bisector as a line equidistant from two points, and a parabola as a curve equidistant from a point and a line. We examine the results from field trials in the classroom regarding students’ formulation and validation of the new knowledge, and we describe the rich situations teachers may face that encourage them to proceed by building on students’ work. This is a crucial and creative moment for the teacher, creating opportunities and moving between students’ discoveries and the intended target knowledge.

Development of an Exploring System: An Integrated Approach to Children’s Math Education in China

In terms of the leap-forward development for education experiment, both the Chinese and English educational experiment have been very successful, while the progress of the children’s mathematics education experiment in China has been relatively slow. It is believed that the main reason for this is the lack of an efficient cognitive tool or system that supports students’ study and exploration and correspondingly covers the whole curriculum of children’s math education. In recent years, basic mathematics education cognitive tools have undergone rapid development, whereas the lack of a common normalization method for continued in-depth inquiry of the relationships among Objects, Algebra, and Geometry (OAG) has led to the fragmentation of students’ mathematical knowledge. Thus, it is difficult for students to develop a systematic understanding of mathematics. Therefore this project attempts to construct a Children’s Mathematics Exploring System (CMES), which integrates with cognition theory, method, and contents of basic mathematics education to query the essence of the relationships among OAG. Specifically, the functions of CMES include the following: (1) providing cognitive tools with typical characteristics for the relationships among OAG; (2) offering a general normalized open system on which sustainable in-depth research can be conducted and a conversion tool through which the complete textbook unit of the basic mathematics education can be converted to reveal the relationships among OAG; and (3) presenting a set of cognitive theories, methods, and a system of basic mathematics education to further explore the relationships among OAG. This project will accelerate the development of cognitive technology in basic mathematics education, widen its practical applications, reduce the difficulty of mathematics cognition, and finally improve the quality and efficiency of basic mathematics education.