Mathematics Teaching Practices 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.

Case study Based on Ogane's Problem-solving Process

In the 1980s, there were problems in the teaching of problem-solving in mathematics in the former Soviet Union, such as formulaic solutions and a lack of emphasis on teaching mathematical thinking. Therefore, Oganesian believes that in the traditional education system and in a large number of mathematical teaching practices, the role of mathematical exercises in developing students' mathematical level is limited. Mathematical exercises are difficult to test students' other aspects of mathematical development and ideological education factors. Introducing new teaching models is an urgent need for teaching mathematical problem-solving. Based on this, Oganesian proposed four steps for solving problems in his book "Teaching Methods for Primary and Secondary School Mathematics": understanding the problem conditions-developing a solution plan - implementing the solution plan - researching the obtained solutions. The article takes the "theorem for determining the perpendicularity of a straight line to a plane" in mathematics as an example, and analyzes its application based on the process of solving problems using the Oganesian method. By introducing mathematical problems into the Oganesian phase problem-solving process, gradually solving problems, delving into the vertical relationship between lines and planes, and analyzing their significance and role in practical applications. Assist students in cultivating thinking methods and problem-solving strategies for mathematical problem-solving systems, guide them to solve mathematical problems more deeply and accurately, enhance the problem-solving ability of mathematical learners, and optimize their thinking logic.

“Mathematics is a battle, but I’ve learned to survive”: becoming a disabled student in university mathematics

AbstractIn university mathematics education, students do not simply learn mathematics but are shaped and shape themselves into someone new—mathematicians. In this study, we focus on the becoming of disabled mathematical subjects. We explore the importance of abilities in the processes of being and becoming in university mathematics. Our interest lies in how teaching and assessment practices provide students with ways to understand themselves as both able and disabled, as disabilities are only understood with respect to the norm. We analyse narratives of nine university students diagnosed with learning disabilities or mental health issues to investigate how their subjectivity is constituted in discourse. Our analysis shows how the students are shaped and shape themselves as disabled mathematicians in relation to speed in mathematical activities, disaffection in mathematics, individualism in performing mathematics, and measurability of performance. These findings cast light on the ableist underpinnings of the teaching and assessment practices in university mathematics education. We contend that mathematical ableism forms a watershed for belonging in mathematics learning practices, constituting rather narrow, “normal” ways of being “mathematically able”. We also discuss how our participants challenge and widen the idea of an “able” mathematics student. We pave the way for more inclusive futures of mathematics education by suggesting that rather than understanding the “dis” in disability negatively, the university mathematics education communities may use dis by disrupting order. Perhaps, we ask, if university mathematics fails to enable accessible learning experiences for students who care about mathematics, these practices should indeed be disrupted.

Factors influencing students’ attitude towards science subjects in Secondary Schools: A case study of Secondary Schools in Kisseka Sub County, Masaka District.

As a result of its earliest history, science has faced a minimal level of interest in secondary schools by students and few teachers qualified for teaching. The study, therefore, was about factors influencing students’ attitudes towards science subjects in secondary schools. The study was carried out in Kisseka Sub County, Masaka District. The study was aimed at analyzing factors that influence students' attitudes towards the sciences, analyzing current teaching and learning practices in science and mathematics, and establishing strategies that have been adopted to improve students’ attitudes towards the science subjects. Various data collection methods were used to elicit information from the respondents. These included a self-administered questionnaire, key informant interviews, and a documentary review. The data was analyzed both qualitatively and quantitatively using a computer package known as Microsoft Excel. Excel was used to generate tables, charts, and graphs. From the findings, it was found that students’ attitudes towards science subjects were generally negative. The negative students’ attitudes toward science subjects were attributed to a lack of necessary laboratory equipment, a lack of confidence and trust that the students may have towards the teachers handling the subject, low commitment by teachers, old students influence, and poor teaching methods. The teaching methods used by science teachers were said to include the use of notes and explanations, the use of practicals in the laboratory, setting constant tests for the science students, and the use of discussions. These teaching methods varied according to different secondary schools and according to their different capacities. With the above background, there is a need to encourage science and mathematics teachers to improve their classroom practices and create a conducive learning environment for students to motivate them to offer science subjects. Also, the school head teachers, in conjunction with the district education department, should recruit more trained and qualified science teachers to effectively handle science students’ needs. Keywords: Students, Science teachers, Secondary schools, Teaching methods

Adult education in mathematics and numeracy: a scoping review of recent research

AbstractThe paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education.

An exploration of Scottish teachers’ perceptions of equitable teaching practices in mathematics

An exploration of Scottish teachers’ perceptions of equitable teaching practices in mathematics

REMOTE: First insights into assessing and evaluating remote learning practices in STEM

The rapid transition to remote learning practices in Science, Technology, Engineering, and Mathematics (STEM) education necessitates a comprehensive assessment and evaluation of their effectiveness. This article presents the first findings of the UE funded project REMOTE “Assessing and evaluating remote learning practices in STEM” (ref: 2022-1-ES01-KA220-HED-000085829) project: a literature review focused on assessing and evaluating remote learning practices in STEM. Drawing on a wide range of scholarly articles, reports, and studies, this article review examines various dimensions of remote learning, including instructional design, student engagement, assessment methods, and instructor-student interaction associated with remote STEM learning in Higher Education Institutions (HEIs). The set of academic contributions detected can be classified into four major typologies according to the area in which they are focused: students, teaching methodologies, teaching staff and technologies. In consequence, the review carried out, summarized in a categorization of the research developed so far, allows a broad and critical view of the state of the art. The findings of this article contribute to the broader conversation surrounding remote learning and serve as a valuable resource for stakeholders involved in STEM education.

Discrete Mathematics Teaching Reform and Practice for Engineering Certification in Computer Science

Engineering education professional certification is the certification of engineering majors in higher education institutions in accordance with the standards and processes of the Washington Agreement. It is an effective means to improve the quality of engineering education, promote continuous improvement of the profession, and enhance the international competitiveness of professional talents. Discrete mathematics is the core backbone course of computer science and technology and related majors. Under the guidance of the certification concept of engineering education, the curriculum outline of discrete mathematics, the core basic course of computer science and technology, has been revised to focus on cultivating students’ graduation abilities, refine teaching objectives, closely adhere to graduation requirements, support graduation indicators, and continuously reform teaching methods, teaching modes, and assessment forms. Teaching practice has shown that students’ mastery of computer mathematics theoretical knowledge is more solid, their ability to solve complex engineering problems is improved, and good teaching results are achieved.

The Teaching Demonstration in the Transitioned Times: Pedagogical Practices in New Normal Classrooms

College Graduating Students Batch 2022 of the Philippine Education is tagged as the experimental batch since they were the first recipients of the full K-12 implementation and a COVID-19-caught transition of education from the full face-to-face classroom to flexible learning. In the City College of Calamba, March 2020 shifted their instruction to full modular distance learning and it took the college two semesters to implement an online learning system, hence the first batch of students with this transition did their practice teaching internship in a new normal class where three-fourths of their learning came from the transitioned education set-up. Now, the study’s focus was to assess their performance as evaluated by the cooperating teacher, cooperating school head, and practice teaching supervisor despite the minimal guidance during the learning of academic and pedagogical principles years. The hypothesis is tested if significant differences can be found in the areas of teaching pedagogies when grouped according to specialization. The study used a simple random sampling technique, 432 evaluations were noted from the observers accumulated for each specialization including secondary education including English education, mathematics education, and science education practice teachers’ assessment constituting a total of 108 respondents. Due to the test of normality and homogeneity failure, the Kruskal-Wallis test was used. Based on the findings, areas in lesson planning, teaching method, classroom management, communication skills, and teacher’s personality had significant differences among all specializations except content mastery. Although there were weak indicators per area, it implied that teaching pedagogical practices were different depending on the specialization orientation of the practice teacher, but they have equal content mastery levels. Therefore, despite the transition of the educational system of these students and now practice teachers, it was comprehensively understood that they are well-equipped in terms of pedagogical practices. Keywords: Lesson Planning, Content Mastery, Teaching Method, Classroom Management, Communication Skill, Teacher’s Personality, Pedagogical Practices, Transitioned Practice Teachers, Teaching Demonstration, New Normal.

Briefly Recalling Moments in Mathematics Education History:

Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedegogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetivive drill of procedures. This continued until pedegogical alternatives to this approach were offered by innovative textbook writers, most notably William Colburn and his 1825 text First Lessons in Arithmetic on the Plan of Pestalozzi. In this article, the teaching of arithemtic in the early United States and the influence of Colburn's text is discussed and is later contextualized through their influence on modern mathematics education practice.

Enhancing Mathematics Teaching Practice Supervision in an Open Distance E-Learning Context: Challenges and Successes with 4IR

Enhancing Mathematics Teaching Practice Supervision in an Open Distance E-Learning Context: Challenges and Successes with 4IR

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.