Mathematics Teaching Practices Research Articles

Facilitating effective mathematical teaching practices in preschool

Initial seeds for mathematics literacy are planted during early childhood. Children benefit when they are exposed to and provided with opportunities for math experiences that emphasize their holistic development and not just mathematics proficiency in isolation. This way of viewing and presenting mathematics to young children requires teachers who are equipped with strong mathematics teaching skills. This study examined a 21-hour professional development series for public school preschool teachers on early numeracy, geometry, mathematical reasoning, and teaching pedagogies. This professional development series aimed to help preschool teachers incorporate effective mathematical practices and increase their comfort level in teaching mathematics. Participants noted this professional development series impacted their ability to foster children’s early numeracy development, engage in math talkpose questions that helped children process early numeracy, and contextualize early numeracy through stories and/or word problems. The study demonstrates change takes time, and the impact of this professional development series is dependent on preschool teachers’ readiness and their perception of their teaching context needs.

수학교육의 교수학적 실천과 연구 측면에서 AI 언어 모델 활용 방안 탐색

Due to the recent development of technology, the possibility of using AI language models in various fields is drawing attention. This study attempted to explore ways to utilize the AI language model in terms of pedagogical practice and research in mathematics education. To this end, the matching rate between the meaning of the Korean dictionary and the mathematical term presented by the AI language model was compared and analyzed using ChatGPT. ChatGPT is one of the AI language models that can process natural language and organize answers according to input text. As a result of the analysis, it was possible to explore the various possibilities of using AI language models for teaching and learning design, evaluation, and research from the basis of answers and analysis of Korean dictionaries and AI language models. However, considering the volatility of the AI language model, it is required to find a way to secure the validity and reliability of the research.

Advance Practices In Mathematical Education System

Practices in mathematics education are essential to foster effective learning. They provide structured approaches for teaching, help build foundational skills, enhance problem solving abilities, and promote a deeper understanding of mathematical concepts. Consistent practices also contribute to standardized assessments and ensure a more cohesive educational experience for students. Practices in mathematics education are crucial for several reasons. They offer a systematic framework for teaching and learning, ensuring that students receive consistent and structured instruction. These practices help educators adapt to diverse learning styles and provide a basis for assessing student progress. Additionally, established practices contribute to the development of critical thinking, problem solving skills, and a deeper understanding of mathematical concepts. Overall, they play a key role in creating a more effective and standardized learning experience In this paper we will discuss some new advance practices in Mathematics education. Here we will see the actual advance practice then the objective, procedure and finally benefits of it.

Facing and challenging language ideologies towards a more inclusive understanding of language in mathematics education research—the case of sign languages

Research on language in mathematics education is largely dominated by a ‘normalcy’ of spoken languages. This modal hegemony does not only affect a whole group of learners in failing to provide access that is epistemologically equitable—those using sign language as their preferred mode for mathematical discourse—it also obscures our view on the roles language can play in mathematical thinking and learning. As a field, we can only win from seeking to understand Deaf learners of mathematics beyond a disability, as learners of mathematics with a specific linguistic background that influences mathematical thinking and learning in peculiar ways. In this contribution, I suggest a shift in mindset towards a more inclusive view on language in mathematics education research and practice. I propose basic principles to inform a perspective for reconsidering the role of language in mathematics thinking and learning, inspired by work of philosopher Francois Jullien. This perspective counters a perspective that merely integrates sign language into existing research and instead searches for dialogue between linguistic modalities in learning mathematics, looking beyond language as spoken or written. This approach will be illustrated by the case of the modal affordance of iconicity foregrounded in signed mathematical discourse, its role in Deaf students’ mathematics thinking and learning, and how this can inform existing research and practice dealing with language in mathematics education.

Mathematics Teachers’ Beliefs About Which Practices They Implement: A Q-Sort Analysis

ABSTRACT The Mathematics Teaching Practices identified by the National Council of Teachers of Mathematics are eight research-based practices that promote mathematics teachers’ implementation of specific knowledge to support student understanding. We wondered which practices mathematics teachers perceived as most characteristic and least characteristic of their teaching and if groups of mathematics teachers might have similar beliefs about their use of the MTPs in their teaching. Data from 39 mathematics teachers of grades 5–12 and one administrator who completed the Teacher Action Q-Sort revealed three distinctive groups: predominantly high school teachers and teachers with post-baccalaureate degrees, predominantly early career middle school teachers, and predominantly beginning middle school teachers. We describe each group, provide a visualization for each group’s composite Q-sort, and report the similarities and differences across the groups of teachers. We also include implications and recommendations for teachers of mathematics and those who provide professional development to teachers of mathematics.

P4C Practices in Mathematics Education: The Case of Math Stories

Bu araştırma, ortaokul öğrencilerinin "Çocuklar için Felsefe (P4C)" etkinlikleri sırasında oluşturdukları soruları incelemeyi amaçlamaktadır. Araştırma nitel araştırma desenlerinden durum çalışmasıdır. Araştırmanın katılımcıları bir devlet okulunda öğrenim göre ortaokul 7. sınıf öğrencileridir. Araştırma kapsamında, beş adet matematik hikayesi videosu öğrencilere uyaran olarak izletilmiş daha sonrasında öğrencilerden izledikleri bu videolara yönelik sorular oluşturmalarını ve akabinde tartışmaları istenmiştir. Araştırma kapsamında 97 adet geçerli soru üretilmiştir. Öğrencilerin oluşturdukları bu sorular, araştırmacılar tarafından geliştirilen dört farklı kategori içeren bir gösterge analiz edilmiştir. Bu kategoriler; "Temel Bilgi ve Hatırlama”, “Neden-Sonuç Analizi” Eleştirel Düşünme ve Değerlendirme” ve “Empati Kurma ve Düşüncelerini İfade Etme” dir. Kategoriler araştırma süresince soruları analiz ettikçe ortaya çıkmıştır. Bulgulara göre, ilk kategorideki sorular öğrencilerin temel bilgileri anlama ve hatırlama yeteneklerine yönelik; kim, ne, nerede, ne zaman ve nasıl gibi sorulardır. İkinci kategorideki sorular daha çok neden-sonuç ilişkilerini anlama becerileri ile ilgili olup, öğrencilerin daha derinlikli ve analitik düşünmelerini gerektirmiştir. Araştırmanın üçüncü kategorisinde, öğrencilerin eleştirel bir bakış açısı ile konuları sorguladığı ve olabilecek farklı senaryoları ele aldığı tespit edilmiştir. Son olarak, dördüncü kategoride öğrencilerin kendi düşüncelerini ifade etme ve farklı bakış açılarını anlama ve kabul etme yetenekleri ile ilgili sorular ürettikleri tespit edilmiştir. Öğrenciler etkinliklere başladığında daha çok bilgi ve hatırlama kategorisinde sorular üretirken etkinlikler ilerledikçe empati kurma, eleştirel düşünme gibi farklı düşünce becerilerini kullanarak bu yönde sorular ürettikleri ve bu becerilerinin zamanla geliştiği gözlemlenmiştir. Sonuç olarak, araştırma ortaokul öğrencilerinin P4C etkinlikleri sırasında soru üretme becerilerini ve düşünce süreçlerini anlamak için önemli bir perspektif sunmaktadır.

Toward culturally sustaining supervision practices in mathematics education: what do Pasifika research students value most about their supervisors?

Disrupting forms of exclusion in higher education requires culturally sustaining practices. However, in some areas of higher education, the notion of culturally sustaining practice remains unexplored. The present study addresses this disparity by exploring the concept of culturally sustaining supervision in the specific case of Pasifika research students in mathematics education. In particular, this case study examines what a group of 22 Pasifika research students in mathematics education valued most about their respective supervisors. Using talanoa (respectful and free-flowing conversation and discussion) to gather data, three characteristics of supervisors that the participants valued most were identified via thematic analysis: (a) being available and accessible; (b) developing the student’s confidence; and (c) providing support beyond the thesis. The characteristics are discussed with respect to the Pacific concept of vā (relationships), which refers to the intricate relational and spatial realm in which connections among people exist and evolve.

The Fascists Are Coming! Teacher Education for When Right-Wing Activism Micro-Governs Classroom Practice

U.S. educational reform is often the harbinger of global demands on mathematics education practices globally. It behooves teacher education to ‘catch up’ on current trends, hopefully, to stave off the worst of the fascist tendencies of contemporary politics of education. Past foci on research-based ‘best practices’ and ‘mathematics for all’, grounded in liberal multiculturalism (confirming expectations from critical mathematics education scholarship), have become the targets of activists and politicians, turning once-exemplary teachers and their students into casualties. The four phases of currere are employed to study this phenomenon and to identify strategies and tactics for teacher education programs. The currere methodology indicates that the content of such programs must reduce time devoted to evidence and research-based practice in order to accommodate techniques and knowledge bases for the recognition of right-wing tactics, clowning, slogan parody, and political organizing. Teacher education must further place mathematics teachers’ embrace of expertise, authority, and neutrality within broader perspectives on the politics of education, organizational infrastructure strategies and tactics, resource curation, and personal safety planning. Teacher educators themselves must prepare responses to threats on their careers, lives, and families, and proactive ‘game plans’ for the development of new program curricula.

Redesigning mathematics preservice teachers’ preparation for teaching with technology: A qualitative cross-case analysis using TPACK lenses

This qualitative cross-case study examined how a university redesigned instructional course for a preservice program supported the development of mathematics preservice teachers' Technological Pedagogical Content Knowledge (TPACK) regarding the use of Information and Communication Technologies (ICT) in their instruction. This research occurred on the context of a redesigned Mathematics Teaching Practice IV course. This course was redesigned to include in it the six SQD-model (Synthesis of Qualitative Evidence) micro level for preparing preservice teachers to use ICT in mathematics teaching and learning practices and was taught by professors with strong ICT profiles. These course activities were organized and used during an entire semester and the combination of these group of activities was called Studying, Learning and Teaching mix. We observed the preservice teachers' practices in their design and teaching of high school lessons and conducted semi-structured interviews to assess their TPACK development. While there were observable features of TPACK development in the early TPACK levels as a result of the participants' experiences, the authentic teaching experience clearly challenged their attitudes and beliefs about teaching and learning mathematics and the role ICT might play in this process. The course experience provided multiple teachable moments for the course professors as they observed and described the preservice teachers’ TPACK levels. In the end, we found that the Case 1 of preservice teachers demonstrated multiple descriptors from the Accepting TPACK level while those in Cases 2 and 3 displayed descriptors primarily associated with the Recognizing TPACK level. Results suggest that their attitudes and beliefs were challenged through a constructive and iterative process that ultimately supported their TPACK development.

Microteaching and Peer Assessment in Mathematics Teaching Practice

Considering the characteristics that teachers should have, concepts such as critical thinking, active learning, taking responsibility, evaluation, analysis, self-evaluation and reflective thinking are important. In this context, micro-teaching and peer assessment methods come to the fore. Micro-teaching is defined as sharing a part of the course with peers and receiving feedback from peers or advisors. Peer assessment, on the other hand, involves providing constructive suggestions among peers, reviewing and giving feedback according to predetermined criteria. In the study, pre-service teachers' views on micro-teaching and peer assessment methods were evaluated. The study was designed as a case study, one of the qualitative research methods. The participants of the study consisted of eight pre-service mathematics teachers studying in the Department of Elementary Mathematics Teaching at a university in Turkey. Questionnaires about microteaching and peer assessment were used as data collection tools. A 14-week microteaching and peer assessment implementation process was carried out with the participants. As a result of the applications, pre-service mathematics teachers' opinions about these concepts were obtained. As a result, the pre-service teachers stated that the application provided positive developments in their cognitive, affective and psychomotor behaviors and that they gained professional experience.

Teaching-learning practices of mathematics in semester system: A case study of Tribhuvan University, Nepal

This study explores the practice of mathematics teaching and learning in the semester system in Nepal. Three teachers and six students of Master of Education from the Faculty of Education, Tribhuvan University (TU) were selected purposively for the interview. In addition, 21 students were also selected for focused group discussion (FGD), and classroom observation and FGD were used to collect information from the participants in the study. Thematic analysis is used in the study. It is concluded that the semester system at TU, Central Department of Education, particularly in mathematics, has a radical shift in pedagogical practices. There is the provision of supportive internal and external evaluation systems to promote multiple skills and knowledge in mathematics or the holistic development of learners. The assessments were to encourage and motivate the students in learning. The study supported to enhance the weakness of teaching-learning activities in the semester system. It is the supportive document for effective teaching-learning in the semester system for Nepal.

고등학교 <확률과 통계>의 통계적 추정 단원 재구조화 방안 탐색

This study aimed to improve statistical estimation teaching practices in school mathematics, support the development of textbooks according to the 2022 revised mathematics curriculum, and the implementation of the curriculum in the schools. Apropos this, the directions of restructuring the statistical estimation unit were derived by synthesizing the results of previous studies related to statistical estimation. Based on these, specific restructuring suggestions for the statistical estimation unit are proposed as follows. First, in relation to the meaning of the sample and sampling method, it is necessary to focus on the bias in the sampling process to promote conceptual understanding in terms of sample representativeness and to promote the recognition of sampling variability using technologies. Second, in relation to sampling distribution, it is necessary to construct contents that promote conceptual understanding of sampling distribution and the relationship between sample size and sampling variability using simulation. Third, in relation to the confidence interval, it is necessary to construct contents that promote the recognition of the confidence levels as probabilistic confidence and provide interpretation and evaluation opportunities of estimation results using sampling errors. In addition, some examples from foreign mathematics textbooks, that can be referred to when implementing each restructuring suggestion, are explored and presented.

Sustainable Development Education for Training and Service Teachers Teaching Mathematics: A Systematic Review

This study conducted a systematic review following the guidelines of the PRISMA statement, with the aim of analyzing the scientific production on Education for Sustainable Development (ESD) in in-service and pre-service mathematics teachers. Out of 211 articles identified in the indexed databases, WOS, SCOPUS, and SciELO, 16 were selected for an exhaustive analysis. It was determined that this topic is still in the process of development, focusing on aspects such as learning content, pedagogy, and the learning environment. Most studies employed qualitative methodologies. Contextualization in sustainability is the most advanced competency. The results highlight the importance of continuing to investigate and develop effective strategies to integrate ESD in the continuous education and training of mathematics teachers. It is essential to address the development of competencies in ecological and mediational facets, ensure solid knowledge of mathematical content, employ adequate pedagogical strategies, and understand the relationship between the environment and mathematics. These findings offer insights into the prevailing trend of integrating ESD into mathematics education through ESD elements and didactic competencies, as evidenced by recent studies involving both practicing and pre-service teachers. This understanding may promote the enhancement of the quality of mathematics education practices within this domain.

Is it only about technology? The interplay between educational technology for mathematics homework, teaching practice, and students’ activities

Current research on the use of digital technology in education has overgrown. It is becoming clear that technology will not unfold its pedagogical potential outlined in the literature on its own. To harness its full benefits, it is paramount to thoroughly understand the educational context and underlying pedagogical principles. This research reports how an educational technology can support students’ knowledge development from homework mathematics learning practices for 11 to 14 year-old students. The article describes the shift learning goals from producing the correct answer to understanding how to address current and future mathematical challenges as an important interaction between educational technology, teaching practices and student learning activities. The study revealed specific features of technology integration with mathematics teaching and learning practices. The findings highlighted the effectiveness of digital support for homework activities, indicating that there were benefits only when students and teachers used the full range of features and engaged in the process. Finally, the report provides practical tips and ground rules that can contribute to the successful implementation of educational technology for homework activities.

Towards a socio-ecological practice of mathematics teacher education

This theoretical article is a response to UNESCO’s call for a new social contract for education, in the context of mathematics teacher education. The article sets out four principles behind “socio-ecological” practices in mathematics education: not taking nature as a fixed background for concerns; avoiding the epistemological error of taking the individual as the unit of learning; questioning what is centred in our work; moving towards a dialogic ethics. The article considers the “what” and the “how” of mathematics teacher education, from this socio-ecological perspective. In terms of the “how”, it is argued a dialogic ethics prompts attention to the potential for a mathematics teacher educator taking a “meta-perspective” in relationships with prospective teachers, recognising those prospective teachers as “teachers”, from the start of a teacher education course. In contexts where the “what” of mathematics teacher education is highly constrained, the “how” of socio-ecological practices may still be possible to enact.

Outstanding Mathematics Teachers’ Teaching Practices: A Collective Case Study

This collective case study explored the teaching practices of outstanding mathematics teachers who were purposely chosen using a selection guide by a team of mathematics administrators in Panay Island, Philippines. Researcher-made classroom observation tools (COT), interview protocols, field and reflection notes, lesson plans, and focus group discussions from students were used to gather multiple sources of data. Analyses of pedagogical strategies, including the interactive classroom collaborations, and explanations for those decisions from the teachers were included in the within-case analysis and cross-case analysis. The study depicted detailed verbatim interactions between the teachers and the students during actual teaching episodes to give the reader naturalistic examples of the explanation patterns and strategies that the outstanding teachers used to further students’ understanding of mathematical concepts and procedures. The Philippine Professional Standards for Teachers (PPST) framework was used as guide in the analysis, interpretation, and presentation of the results. These outstanding teachers were noted to be exemplary in planning the teaching and learning process, proficient in using teaching and learning resources including ICT, and excellent in managing the classroom; applied successful teaching strategies in the development of critical and creative thinking as well as of higher-order thinking skills; used appropriate formal and non-formal assessment tools; provided feedback to their learners to rationalize and to improve learning; and constantly communicated their learners’ progress and achievements to parents. Keywords: teaching practices, outstanding mathematics teachers, collective case study DOI: 10.7176/JEP/14-12-07 Publication date: April 30 th 2023

Examining the changes in mathematics teachers’ technology dispositions through GeoGebra-mediated professional development

Drawing on a technology dispositions framework, this study examined the changes in teachers’ beliefs, attitudes, competence, and behavioral intentions toward the use of technology in the mathematics classroom, following their engagement in professional development (PD) mediated by GeoGebra software. In a case study research design, 11 mathematics teachers from a senior high school in Ghana were purposively selected to engage in a 1-year PD program. They worked in teams to design and enact GeoGebra-based mathematics lessons. A self-report questionnaire, semi-structured interview, and lesson observation were used for data collection. Self-report data were analyzed using mean, SD, paired sample t-test, and Hedges’ g. Interview and lesson observation data were analyzed using a thematic approach. The results indicated that teachers’ pedagogical beliefs, affective attitudes, and competence toward technology changed following the PD. To some extent, they were able to make the goals of their mathematics lessons explicit and sequenced their instructional activities to engage students’ geometric and algebraic thinking. However, their intention to put the new pedagogy into classroom practice in the future depended on multiple contextual factors: administrative support, continual professional training, and provision of adequate technology facilities. These findings have implications for practices in mathematics education, technology dispositions frameworks, and PD.

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.

Factors that influence STEM faculty use of evidence-based instructional practices: An ecological model.

Traditional teaching practices in undergraduate science, technology, engineering, and mathematics (STEM) courses have failed to support student success, causing many students to leave STEM fields and disproportionately affecting women and students of color. Although much is known about effective STEM teaching practices, many faculty continue to adhere to traditional methods, such as lecture. In this study, we investigated the factors that affect STEM faculty members' instructional decisions about evidence-based instructional practices (EBIPs). We performed a qualitative analysis of semi-structured interviews with faculty members from the Colleges of Physical and Mathematical Sciences, Life Sciences, and Engineering who took part in a professional development program to support the use of EBIPs by STEM faculty at the university. We used an ecological model to guide our investigation and frame the results. Faculty identified a variety of personal, social, and contextual factors that influenced their instructional decision-making. Personal factors included attitudes, beliefs, and self-efficacy. Social factors included the influence of students, colleagues, and administration. Contextual factors included resources, time, and student characteristics. These factors interact with each other in meaningful ways that highlight the hyper-local social contexts that exist within departments and sub-department cultures, the importance of positive feedback from students and colleagues when implementing EBIPs, and the need for support from the administration for faculty who are in the process of changing their teaching.

Necessity is the Mother of Invention: How the Need for Online Schooling Impacted Mathematics Teaching Practices and Student Engagement

In this paper, we document elementary school teachers’ attitudinal and pedagogical changes during the rapid move from brick-and-mortar to virtual schooling initiated by the COVID-19 pandemic. We administered four online surveys (in September and October 2020, and in March and June 2021) to determine teachers’ perceived challenges and successes in using online technology, as well as applied mixed-methods action research to identify their approaches to teaching mathematics online. The initial challenges included gaining skills, resources, and know-hows for teaching online, and supporting students and their families in the swift transition, while also maintaining instructional goals and overcoming stress. The later challenges included dealing with workload and engaging students in learning. As their comfort with technology increased, teachers started realizing that many old pedagogies were either impossible or inadequate in the online environment, and they began to innovate with virtual classrooms that encompassed students’ homes, parents, and the outdoors. Mathematics manipulatives were found in the kitchen and measurements were done in the home or during walks outside. Mathematics concepts became more real-life centered, and learning became more playful and problem-oriented. Technology helped to create and sustain learning communities, and exposed student thinking at their comfort level. For some students, this approach worked better than brick-and-mortar schools; for most teachers, it created opportunities to provide and receive feedback differently, collaborate widely, reinvent their practice, and contribute to changing norms. We conclude by providing suggestions for moving forward.