Mathematics Education Research Research Articles

Seeing Through the Eyes of Classroom Observers: The Case of Rating Contrasted Groups of Lessons With Classroom Observation Measures

Classroom observations are commonly employed to assess quality of instruction in research and practice in mathematics education. However, there is more to be learned about how sensitive classroom observation protocols are to exemplars of strong mathematics instruction, and continuous refinements to observation protocols or rating processes that may be warranted. In this study, we use the public-released mathematics videos from the Third International Mathematics and Science Study (TIMSS) to examine how classroom observers, using two contemporary classroom observation instruments, rate a set of lessons whose instructional quality is in theory expected to differ, also referred to as contrasted groups. We find that descriptively, the pattern of findings is distinct from prior studies’ conclusions about the relative instructional quality reflected in the TIMSS video pool. We provide qualitative examples to illustrate the findings, and discuss implications for future research. We point to the potential value of exploring classroom observation rubrics’ performance using ‘contrasted groups’ of lesson videos, as a tool to broaden our understanding of how observation instruments are functioning.

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.

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.

A systematic review of TPACK research in primary mathematics education

AbstractThis study is a systematic review of Technological Pedagogical and Content Knowledge (TPACK) studies concerning primary mathematics education published between 2005 and 2022. The aim of the systematic review was to identify the common features of previous TPACK research on primary mathematics education and identify the research gaps based on their contexts. The study used the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) procedure to investigate TPACK-related studies published during the last 17 years in the primary mathematics education domain and to evaluate the characteristics of TPACK instruments used in primary mathematics education. We identified five foci of these studies of TPACK in primary mathematics education research: designing lessons, evaluating mathematics teachers’ knowledge of integrating digital technologies, designing the assessment, evaluating training programs, and informing professional development program designs. Findings from this systematic review of the literature can assist educators in better designing professional development programs to help primary mathematics teachers improve their ability to integrate digital technology into classroom teaching. Also, the findings can assist researchers in locating TPACK instruments that are appropriate and relevant for their research. Finally, we argue that there is a research gap concerning how to measure primary mathematics teachers’ TPACK, how to design a TPACK instrument that includes contextual factors, and how to develop TPACK-oriented teacher training programs for primary mathematics teachers.

Working Interinstitutionally to Apprentice Doctoral Students in Mathematics Education Research

Working Interinstitutionally to Apprentice Doctoral Students in Mathematics Education Research

A Systematic Review of Research on Gender Diversity in STEM Education

Science, technology, engineering, and mathematics (STEM) education research has increased worldwide in recent years. Recognition of STEM education's importance in producing highly skilled scientists and technologists and its economic benefits to society are driving this increase. However, STEM labor force gender representation is a persistent issue. A meta-analysis using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol and a thorough literature search assessed STEM gender diversity. A total of 42 STEM education gender diversity research papers were reviewed using PRISMA. These Scopus papers provide a database from 2013 to 2023. The study used text analysis and synthesis to evaluate and highlight the countries, extract key phrases, identify research issues of interest to scholars, and suggest future research directions. The research findings indicate that current publications primarily focus on developing STEM education programs to attract and provide more opportunities for women. Additionally, other research areas of interest include proposing solutions to enhance gender equality in STEM education, women's awareness, and skills in the STEM field. Furthermore, research gaps have been identified in course design, learning material development for STEM education, and establishing a direction for implementing STEM education starting from early elementary school, with the optimal period being before grade 3. These findings can help academics explore STEM research ideas in new situations. However, the investigation was limited by using only a Scopus catalog database; disregarding alternative sources may have led to material being omitted.

The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking

The purpose of this study was to articulate nuances within the process of learning to notice and to provide a framework for characterizing the capabilities of noticing in prospective mathematics teachers. We collected and analyzed data on teacher noticing based on classroom videos from prospective teachers in a mathematics content course. We analyzed data in accordance with existing research-based frameworks on noticing and in consideration with literature on expertise. We provide the Framework for the Expertise of Noticing, which describes noticing expertise along five dimensions: Evidence-based Noticing; Concrete vs. Abstract Characteristics in Noticing; Individual vs. Pattern Focus in Noticing; Task vs. Contextualized Perspective in Noticing; and Cognitive vs. Metacognitive Characteristics in Noticing. The framework is a tool for mathematics education researchers and teacher educators who study and support the development of noticing in prospective teachers.

A One‐Parameter Diagnostic Classification Model with Familiar Measurement Properties

AbstractDiagnostic classification models (DCMs) are psychometric models designed to classify examinees according to their proficiency or nonproficiency of specified latent characteristics. These models are well suited for providing diagnostic and actionable feedback to support intermediate and formative assessment efforts. Several DCMs have been developed and applied in different settings. This study examines a DCM with functional form similar to the 1‐parameter logistic item response theory model. Using data from a large‐scale mathematics education research study, we demonstrate and prove that the proposed DCM has measurement properties akin to the Rasch and one‐parameter logistic item response theory models, including sum score sufficiency, item‐free and person‐free measurement, and invariant item and person ordering. We introduce some potential applications for this model, and discuss the implications and limitations of these developments, as well as directions for future research.

Mathematics education researchers’ practices in interdisciplinary collaborations: Embracing different ways of knowing

Mathematics education researchers’ practices in interdisciplinary collaborations: Embracing different ways of knowing

Validity evidence of the use of quantitative measures of students in elementary mathematics education

AbstractQuantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in elementary mathematics education. The review includes measures that focus on elementary students as the unit of analyses and attends to validity as defined by current conceptions of measurement. Findings suggest that one in ten measures in mathematics education include rigorous evidence to support intended uses. Recommendations are made to support mathematics education researchers to continue to take steps to improve validity evidence in the design and use of quantitative measures.

Using social network analysis to investigate mathematical connections in U.S. and Chinese textbook problems

Textbooks, as potentially implemented curricula, play an important role in supporting classroom teaching and learning. Mathematical connections, one of the essential and hot topics advocated in mathematics education, have been emphasized in national curriculum reforms in various countries. However, little is known about the connection networks represented in school textbooks; even less has been done to compare textbooks from different countries. In this study, we propose an innovative method for examining how connections are represented in two popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school textbook problems involving quadratic relations. By using social network analysis, we identified 1129 connections, characterized connection networks into dense, moderate, and sparse digraphs, identified influential, prominent, and dual concepts and representations, and evaluated the strength between typical and reverse connections. The results revealed that the Chinese series presented a denser network of balanced between-concept connections but limited within-concept connections. The U.S. series exhibited more within-concept connections but emphasized typical connections, thus validating the potential of this innovative method. From this study, we suggest that our novel method provides a theoretical contribution to textbook analysis and connection analysis, which has rich implications for practice, for example, examining the network of connections students construct as a way to assess and to promote their conceptual understanding, and our approach opens the possibility of adopting new and efficient analytical tools from social network analysis in mathematics education research.

Contributions of the anthropological theory of the didactic to the epistemological programme of research in mathematics education

AbstractIn the early 1980s, the theory of didactic situations put the analysis of mathematical activity at the core of the didactic analysis, thus initiating a new research programme in mathematics education: the epistemological programme. This paper describes and interprets some of the contributions of the anthropological theory of the didactic (ATD) to the development of this programme. These contributions come from the new institutional and ecological perspective provided by the ATD to approach the didactic problem and from the significance it assigns to macrodidactic phenomena characterised by didactic transposition. They are illustrated with research works involving different fields of school mathematics in which the ATD team led by Spanish researchers played a central role: research in school algebra and its relations with functional modelling, differential calculus, and real numbers. The paper concludes by briefly describing the contributions of the ATD to the dialogue between didactic theories, another domain that has notable Spanish contributions.

국내 초⋅중등 수학교육에서 협력학습 연구에 관한 체계적 문헌 고찰

This study aims to conduct a systematic literature review on collaborative learning research in elementary and secondary mathematics education in Korea, explore various characteristics related to the research, and discuss areas for improvement. To achieve this, this study presents a protocol for analyzing research in mathematics education with a focus on collaboration and cooperation, following a systematic literature review methodology. Then analyze the selected studies based on the themes derived from the protocol. As a result of the systematic literature review, research characteristics on collaborative learning were categorized into eight main themes: keywords, small group composition methods, sampling methods, sample size, analysis methods, analytical frameworks, domains of educational goal, and collaborative mathematical competencies in collaborative learning. The research findings revealed several key points: First, many studies conducted at the various school grades and methodologies, help to understand various classroom environments that implement collaborative learning. Second, it was found that the researcher's subjective characteristics were largely reflected in the selection of the sample extraction method and sample size. Third, as the cognitive domain of collaborative learning mainly presents changes as results through pre- and post-academic achievement, in relation to mathematics subject competency, there have been many studies that have derived results in relation to collaborative mathematical problem solving.

Pre-service teachers’ development of digital resource design capacity

AbstractIn the current digital age, (mathematics) teachers are provided with a profusion of digital resources. Consequently, research in mathematics education has focused on teachers’ interactions with resources as the heart of their professional activity. The term Pedagogical Design Capacity (PDC) was introduced to designate teacher’s ability to perceive affordances of resources and to make decisions about how to use them efficiently. PDC has been further conceptualized to define teacher design capacity (TDC) as including a goal or points of reference for the design, a set of design principles, and reflection-in-action. This definition is illustrated with case studies involving teachers’ design of digital resources, yet it does not seem to consider the specificities of the latter. We therefore aim to further refine the concept of TDC by considering crucial components that designing technology-based tasks and their enactment in the classroom entail. We ask: What are the unique components of TDC specific to digital technology and resources? We elaborate a framework to suggest dimensions and components of mathematics teacher Digital Resource Design Capacity (DRDC) to emphasize the focus on design of digital resources. This framework is built on previous studies and on the concept of instrumental orchestration, and is refined taking into account findings from two case studies in France and Israel.

Research on curriculum resources in mathematics education: a survey of the field

AbstractThis survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students’ use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research.

Understanding Problem-Based Learning and its Application in Learning Mathematics Concepts Among Pre-Service Teachers

Learning to teach mathematics has become crucial since its application in real life cannot go unmentioned. The desire of mathematics education researchers to make mathematics concepts easier for pre-service teachers to easily understand has attracted attention. This has become indispensable since after college, pre-service teachers are deployed from K-12 to assist learners in understanding mathematics concepts. The study aimed to ascertain how improvement in the learning of mathematics concepts using the Problem-based learning (PBL) approach could be understood and/or explained among pre-service teachers. This was viewed in two folds: how improvement in learning outcomes using the PBL approach could be explained; and how pre-service teachers’ disposition about the PBL could be explained/understood. Exploratory case study design involving qualitative and quantitative data was concurrently gathered and used. This involved the use of data collection instruments such as focus group discussion, pre-post-test scores, PBL observation protocol, and PBL disposition questionnaire. The study showed that the PBL method improved the learning of mathematics concepts among pre-service teachers. Pre-service teachers also showed a positive disposition (interest, belief, and attitude) toward the PBL intervention. The authors advocated for the conduct of a longitudinal study to understand the direction of change over time.

Eye movements in the development of geometric shape recognition: from sensory-motor processes to theoretical perception

AbstractEfficient recognition of geometric shapes is an important aspect of proficiency in geometry. Building theoretically on the cultural-historical approach enriched by the physiology of activity, we investigate theoretical perception in geometry—the ability to recognize conceptual geometric aspects of visual figures. Aiming to understand the development of theoretical perception, we investigate how sensory-motor processes of eye movements differ between adults and children when perceiving geometric figures. In an empirical study, we explored the variety of perceptual strategies used by first-grade students and compared them with the adults’ perception. The results reveal the contraction of eye movements: with growing expertise, foveal analysis—namely, an inspection of the figures by directing the gaze to their parts—is substituted by extrafoveal analysis—namely, perceiving without looking directly. The variety of the observed children’s perceptual strategies demonstrates that theoretical perception of different figures is heterogeneous. From the suggested theoretical perspective, the direct foveal inspection of particular figures is critical for the development of general anticipatory images of geometric shapes. Our theoretical analysis and empirical findings lead to distinguishing several functions of sensory-motor processes in theoretical perception in geometry. Those functions include positioning the retina in the best way for the comparison of sensory feedback with the geometric shape’s anticipatory image, advancing an anticipatory image based on visual experience, and regulating covert attention. All of these functions need to be taken into account when interpreting the results of eye-tracking studies in mathematics education research. Notably, our research highlights the limitations of the eye-mind hypothesis: direct fixations on a figure are not always needed for its theoretical perception and, the other way around, a fixation position may indicate the comparison of a broad extrafoveal region with an anticipatory image.

Reflecting From the Border Between Mathematics Education Research and Cognitive Psychology

Reflecting From the Border Between Mathematics Education Research and Cognitive Psychology

Appraisement of mathematics tasks—a point of view of Norwegian eighth-grade students

In the large body of literature that is available about the role of motivation in mathematics education, the focus is mostly on students’ attitudes and feelings toward mathematics in general. In the current small-scale explorative study, we zoomed in on what students think about the tasks they can come across in mathematics education. To investigate students’ appraisement of mathematics tasks, that is, their judgment of how much they like mathematics tasks, we used a mixed method approach with an online questionnaire including closed and open questions. We asked 67 Norwegian eight graders to give an appraisal score for 24 tasks and to express in their own words their reasons for liking/disliking them. In addition, the students also had to indicate for each task whether they think they can solve the tasks. The analysis of the data indicated that the students may prefer bare number problems over context problems. Similarly, students inclined to like puzzle-like tasks more than estimation or straightforward tasks. The reasons for liking/disliking a task most often refer to the difficulty or easiness of the task. The data about the perceived solvability revealed that the more the students believed that they can solve the task, the more they liked the task. Given the different appraisals that the students granted to the different task types and the comments they came with, there is much reason to afford students a stronger voice in mathematics education research, particularly when it is about the tasks used in mathematics education.

Investigating the Philosophical View of Teaching Circles Theorem

Circle theorem was seen as the most challenging mathematics topic most students’ in Ghana run away from. During the WASCE, most students run away from answering mathematics questions that are in line with circle theorem. Such challenge has drawn the attention of mathematics teachers and researchers in mathematics education to find out the factors that drives students from attempting circle theorem question and the appropriate approach that can be used to teacher and to solve questions in circle theorem. The study aimed to investigate the philosophical view of teaching circle theorem. The literature review was based on ontological view of circle theorem, axiological view of circle theorem, and epistemological view of circle theorem. The study concluded that, the three philological view of mathematics has a unique significant effect on teaching and learning circle theorem.