Secondary Mathematics Teachers Research Articles

Examining teachers' relational noticing: promoting equity through positive interactions in mathematics education

AbstractHow teachers attend to and interpret positive relational interactions shapes how they enact instructional practices for equity. We draw on frameworks from equitable mathematics instruction, relational interactions, and teacher noticing to conceptualize mathematics teachers’ relational noticing. Using noticing interview and classroom observation data from a research collaborative between secondary mathematics teachers and university-based teacher educators, we document the range and diversity of ten teachers’ relational noticing. We use this analysis to examine how teachers’ relational noticing supports enacting equitable instructional practices. Our findings indicate five themes of teachers’ relational noticing that are informed by their personal histories, understanding of dominant narratives of mathematics education, and their local sociopolitical school context. Additionally, teachers enacted a range of practices for creating positive relational interactions, with attending to student thinking being the most enacted practice. Our findings suggest that mathematics teachers’ relational noticing can support the three axes of equitable instruction.

A systemic analysis of secondary school mathematics teachers' attitudes toward assessment of learning

Aware of the various issues involved in assessing learning, but also of the difficulties encountered in classroom practice of this pedagogical act, we set out in this article to explore and analyze the assessment practices of secondary school mathematics teachers and the conceptions they underlie. The study was conducted from a systemic perspective. We therefore targeted three aspects in our study: the conceptual, the institutional, and the docimological. Analysis of the attitudes declared by a random sample of mathematics teachers enabled us to confirm that pedagogical, and in particular cognitive, issues do not represent a priority for them in assessment practices. They focus more on the organizational aspect of examinations, with a remarkable lack of concern for docimological considerations to give credibility to the assessments carried out.

Mathematical Connections in Preservice Secondary Mathematics Teachers’ Solution Strategies to Algebra Problems

This study investigated the mathematical connections found in the solutions provided by 22 preservice secondary mathematics teachers to a set of algebra problems. Interest in, and research on, mathematical connections has gained prominence of the past decade. Here, we use the Extended Theory of Mathematical Connections or ETMC to explore the types of connections that this framework does and does not capture in the preservice teachers’ solutions. The ETMC surfaced four types of mathematical connections across four problems: ‘different representations’, ‘procedural’, ‘part-whole’ and ‘meaning’. The other types of connections defined in ETMC such as ‘reversibility’ or ‘feature’ were not found in our data, perhaps because of the specific problems that were used. Some mathematical connections were not highlighted when examining the solutions through the lens of ETMC (‘meaning’, ‘implication or if/then’ and modelling) addressing areas in which ETMC might be limited in its capacity to support researchers in identifying mathematical connections in different contexts.

Radian π: Concept images evoked by quantitative representations of radian angle measure

ABSTRACT This article investigates evoked concept images (CIs) of seven secondary preservice mathematics teachers (PMTs) as they interact with different types of representations of radian angle measure. A thematic analysis indicates that representations emphasizing quantitative aspects of angle measure evoke conceptions that are attuned to quantitative elements of radian angle measure. Specifically, quantitative representations evoked CIs relating the length of the arc subtending the angle to the radius. Non-quantitative representations evoked CIs of radian in terms of π or in relation to degrees, even when the representation did not contain angles in these measurements. To foster a quantitative understanding of radian angle measure, teachers and curriculum developers are encouraged to consider how visual representations might support students in conceptualizing radian angle measure quantitatively.

Effects of teaching internships on preservice teachers’ noticing in secondary mathematics education

Effects of teaching internships on preservice teachers’ noticing in secondary mathematics education

Improving mental arithmetic ability of primary school students with schema teaching method: An experimental study.

Skillful utilization of mental arithmetic can significantly improve students' mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability improvement. This paper devises a set of graphic teaching aids for primary school students' mental arithmetic improvement based on mental arithmetic strategies, schema theory, and working memory. To validate the effectiveness of schema teaching in enhancing mental arithmetic ability among primary school students, a controlled experiment was conducted with two groups of third-grade students randomly selected from a primary school in Jingshan City. The results, obtained through descriptive statistical analysis and the multitrait-multimethod approach (MTMM), indicated that the experimental group (n = 52) demonstrated significant improvements in speed, accuracy, and stability in mental addition and subtraction after a 14-day instruction period in schema teaching. This study offers a potent mental arithmetic teaching strategy for elementary mathematics education, which can lead to a comprehensive enhancement of students' mental calculation abilities. It also holds promise for inspiring innovative teaching methodologies in primary and secondary mathematics education in the future.

Computational Thinking in Secondary Mathematics Education with GeoGebra: Insights from an Intervention in Calculus Lessons

AbstractNowadays, mathematics teachers in K–12 strive to promote their students‘ mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students’ views toward them. In this work, we present the results of a research study, which included the design of a six-lesson learning activity aimed at fostering 16- to 17-year-old secondary students’ CT skills in calculus lessons using the dynamic mathematics software GeoGebra. Our goal was to investigate how students experienced the CT-embedded calculus lessons with GeoGebra and what challenges they faced during their interaction with the learning material and software. We collected and analyzed data from students’ code in GeoGebra, workbooks, semi-structured interviews, and questionnaires. Our findings suggest that most students mastered using CT concepts in calculus activities to a satisfactory degree and could reason about their computational solutions using GeoGebra and the generated graphs. Students’ understanding of the mathematical content knowledge introduced was essential to complete the lesson series successfully and unnoticed gaps in prior knowledge emerged. Our study shows that students appreciate the CT-embedded calculus lessons and GeoGebra’s exploratory approach to mathematics problems when provided with appropriate support. We conclude that an integrated approach to mathematics education and CT is viable and can contribute not only to fostering CT but also to increasing interest in mathematics.

Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development

AbstractResearch has shown that there is a need to examine prospective teachers’ development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16–18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing their noticing of students’ mathematical thinking of this concept in teacher education programs is crucial to achieve high school student mathematics achievement. This study examines how prospective secondary school mathematics teachers (PTs) notice students’ mathematical thinking about the limit concept as they participated in a teaching module. PTs had to anticipate and interpret students’ mathematical understanding and make instructional decisions to support students’ conceptual progression using information about high school students’ understanding of the limit concept. We examined PTs changes related to how they anticipated, interpreted and made instructional decisions during the teaching module. We identified a change in how PTs conceived the understanding of the dynamic limit concept: from all-or-nothing dichotomy to progression; and a change in the instructional decisions they made: from decisions focused on changing the type of discontinuity to conceptual decisions. These changes allow us to characterise development noticing pathways. Our findings also help to identify the teaching module characteristics that support the development of PTs noticing.

Effects of a professional development programme on teachers’ classroom practices in Colombia

ABSTRACT The professional development for teachers is an important component of the quality of education. However, few systems for monitoring and analysing the quality and impact of teacher professional development programmes have been created. In this article, we present the effects on classroom practices of a Colombian professional development programme for in-service secondary mathematics teachers. We compare the teachers’ classroom practices of planning, implementation, and assessment, before and after participating in the programme. We found that the professional development programme shows a statistically significant and positive effect on planning, implementing and assessment practices. These results serve as evidence of teacher training policy in terms of changes in classroom practices.

Secondary school teachers’ interest and self-efficacy in implementing STEM education in the science curriculum

This study examines the role of Namibian secondary school science, technology, engineering and mathematics (STEM) teachers’ interest in STEM education and self-efficacy in implementing STEM education in science education curricula. Furthermore, it aimed to distinguish male and female Namibian teachers’ interests and self-efficacy regarding STEM education and investigate how different teaching subjects affect them. To achieve this goal, a survey was completed with (n=200) secondary school teachers, both males and females. Data were analyzed quantitatively using exploratory factor analysis and analyzed covariance. The results show that most teachers were highly interested and confident in implementing STEM subjects into science curricula. While Namibian teachers indicated a high level of interest, they also revealed a high lack of interest in STEM, implying that at least some teachers felt bored and meaningless in implementing STEM education. However, gender plays a significant role in teachers’ negative self-efficacy, with male teachers being less confident than female teachers in implementing STEM education. Moreover, teachers in the present study have high positive and negative self-efficacy levels regarding implementing STEM education. Therefore, these findings highlight the need for a paradigm shift, especially in the Namibian science curricula, to promote STEM subjects and to improve science education. Potential implications from this research also suggest that teachers’ participants benefit significantly from learning within a community by engaging in solutions to real-world problems.

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.

Using different digital tools in designing and solving mathematical modelling problems

AbstractWhile existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.

The impact of online lesson study on students’ achievement in mathematics in China

ABSTRACT Chinese education has been striving to enhance student achievement in mathematics, and one approach that has shown promise is the improvement of teacher preparation. However, the implementation of formalized Lesson Study (LS) in China necessitates the establishment of new and effective structures to facilitate its practice. Additionally, due to the 2019 coronavirus pandemic, distance education has become increasingly prevalent. To investigate the potential benefits of combining LS with online education, the authors conducted an action research study of classroom practices. This mixed-method study aimed to determine whether the use of O-LS (Online Lesson Study) among in-service secondary mathematics teachers would improve student performance in mathematics and to explore the factors that influenced teachers’ pedagogical practice. For the quantitative research component of the study, a sample size of 68 was selected from two intact mixed-ability classes in a secondary school population, with 34 participants in each of the experimental and control groups. This action research study highlights the significance of O-LS in the context of Chinese society and demonstrates the successful integration of online education with LS to improve student achievement in mathematics.

Life Story Analysis of the Longer-term Effects of Kenya’s Strengthening of the Mathematics and Science in Secondary Education Project on the Attitudinal and Behavioural Changes of Former Secondary Students

The aims of this study were to (a) qualitatively determine former students’ perceptions of environment, personal and behaviour factor changes that were due to the teachers involved in the Strengthening of Mathematics and Science in Secondary Education (SMASSE) project in Kenya and (b) reveal the long-term influence of these qualitative changes on their lives. The study also clarified the significance of using life story analysis to this end. The theoretical framework we utilised is social learning theory. Data collected from interviews were examined using Steps for Coding and Theorisation (SCAT) analysis, as well as NVivo, to identify respondents’ experiences as former SMASSE students. First, SCAT analysis revealed that participants’ lives were influenced in the long term owing to changes in: (a) environmental factors, such as interaction with SMASSE teachers and collaboration with other students; (b) personal factors, such as changes in cognitive and affective aspects; (c) behavioural factors, such as learning methods. Second, by using NVivo to integrate all the stories, we showed that former students’ perceptions of the environmental, personal and behaviour changes that were due to the teachers involved the SMASSE project were mutually interrelated. The analysis has also identified long-term effects on various aspects of human resource development: post-graduation career development, employment opportunities, and mindset. Finally, the results of this study emphasise the robustness of qualitative research in identifying the qualitative changes in the participants in a multi-dimensional manner for this international project.

Exploring the Roots of Poor Mathematics Performance: A Stakeholder Perspective in Adamawa State, Nigeria

In numerous countries worldwide, poor performance in mathematics remains a critical concern, and Adamawa State in Nigeria is no exception. This study investigates the perspectives of key stakeholders, including students, teachers, and headmasters, regarding the roots of poor mathematics performance within Shangui and Hong Government Senior Secondary Schools, Adamawa State. Through quantitative and qualitative approaches, data were collected from 151 senior secondary school participants, including 121 students, 11 mathematics teachers, 10 heads of departments, and 9 head teachers from randomly selected secondary schools in the Hong Local Government Area of Adamawa State. The findings revealed a prevalent negative attitude among students towards mathematics. Moreover, the study has identified a significant factor contributing to poor performance, which was the secondary schools' ineffective mathematics curriculum. In addition, many elementary school teachers lacked the aptitude and skills necessary to teach mathematics, which significantly impacted pupils' disinterest and resulted in low achievement in secondary education. The study recommends crucial interventions, including the revision of the final year mathematics curriculum, the incorporation of technology in mathematics education, enhancement of the quality of secondary mathematics teachers, a reduction in the emphasis on examinations, and the integration of internal assessments, projects, and fieldwork into the mathematics curriculum. This comprehensive stakeholder inquiry sheds light on the multifaceted challenges faced by the educational system in addressing and improving mathematics performance in Adamawa State.

Evolution of teachers’ and researchers’ praxeologies for designing inquiry mathematics tasks: the role of teachers’ beliefs

AbstractThis paper is focused on the collaborative work of two communities, one of teachers and one of researchers, during a teacher professional development program on the inquiry-based learning approach in mathematics, addressed to lower secondary school in-service mathematics teachers. We conceptualize the design of inquiry mathematics task as the boundary object on which the two communities work collaboratively. We aim to study the evolution of teachers’ and researchers’ meta-didactical praxeologies for designing inquiry mathematics tasks, with the Meta-Didactical Transposition framework, to understand if and how their collaboration favors their convergence toward shared components of final meta-didactical praxeologies. In the results, we show that this convergence is reached thanks to internalization processes of praxeological components for designing inquiry mathematics tasks, as a consequence of the learning mechanisms activated by the common work on the boundary object. In this paper, we address also the issue of understanding the complex relationship between teachers’ beliefs on inquiry mathematics tasks and the meta-didactical praxeologies of teachers and researchers. As a result, we propose a model in which the evolution of teachers’ beliefs is taken into account both as an agent and a consequence of the evolution of the meta-didactical praxeologies of the two communities involved in the teacher professional development program.

Investigating boundaries and boundary crossing between mathematics and visual art teaching in a collaborative setting

Our study explores boundaries and boundary crossing between communities of mathematics teaching (MT) and visual art teaching (AT). We focus on teacher collaboration, draw on communities of practice and examine the existing boundaries and the way collaborating members handle them. We present data from 17 group meetings of secondary school art and mathematics teachers who try to develop ways of linking ΜΤ and ΑΤ. Results indicate the emerging boundaries by means of discontinuities regarding mathematical practices and tools used in MT and AT, and the disciplines’ teaching and curriculums. Via analysis of the central boundary – the analytical or visual ways of thinking – we present members’ boundary handling that indicates the development and developmental process of integrated practice. The study incorporates boundary crossing processes and learning mechanisms in which the two separate ways of thinking are gradually transformed into an integrated one and reveals possible ways of integration in teaching and learning.

Successfully preparing future mathematics teachers for digital technology integration: a literature review

Over the last several decades, digital technology (DT) integration in teaching and learning mathematics has received considerable attention, as such integration has not led to the expected results. Teacher education is a critical factor – even more important than access to tools and devices – in technology-enhanced teaching and learning. The purpose of this literature review is to examine and systematise core findings of studies that inform mathematics teacher education that supports the integration of digital technologies. We explore key considerations in mathematics teacher education for successfully preparing Prospective Secondary Mathematics Teachers (PSMT) for digital technology integration. This review includes 25 theoretical and empirical articles found using the keywords ‘Digital Technology’ and ‘Mathematics Education’. The review explores different topics that impact teachers’ technology integration classified into six categories according to their varying nature: (1) Mathematical digital competence, (2) Empirical and theoretical justifications, (3) Stages in DT integration, (4) Pedagogies for DT integration, (5) Mathematical skills, and (6) Systemic factors. It articulates and connects several findings reported in the extant literature previously seen as isolated and disconnected.

Challenges and supports for secondary science and mathematics teacher retention

AbstractMore research related to effective ways to support and retain teachers in the teaching profession is necessary as the need for science and mathematics teachers continues to grow. Understanding how teachers perceive challenges and experience support early in their career can contribute to building environments which foster teacher retention. This mixed‐method study explored the influences on the self‐efficacy and career satisfaction of a group of 21 early‐career (2–6 years of classroom experience) secondary science and mathematics teachers who participated in a traditional university preparation program and scholarship program to prepare them for teaching in high‐need school districts. Using data from an efficacy survey and semistructured interviews, this study measured changes in teacher efficacy and described teacher leadership experiences, perceived teaching challenges, and valued supports. Results found no change in teachers' self‐efficacy scores although mean outcome expectancy scores decreased. Teachers' identification as a teacher leader was correlated with science or mathematics teaching self‐efficacy. Qualitative coding of the interviews revealed ways in which assessments, workload, school structures and polices, administration, students, and teacher community either contributed to teachers reported difficulties or supported them as early‐career teachers. The discussion offers suggestions for ways to increase secondary science and mathematics teachers' job satisfaction.

Secondary Mathematics Teachers’ Anticipations of Student Responses to Cognitively Demanding Tasks

ABSTRACT This study examines secondary mathematics teachers’ anticipations of student responses related to a series of cognitively demanding mathematics tasks from multiple mathematical domains presented in the context of voluntary and asynchronous online professional development modules. We analyze 283 anticipations made by 127 teachers to 17 mathematics tasks and present four distinct foci of teachers’ anticipations. Teachers participating in this study focused on actions students might take when engaging with the task — including the representations, strategies, and resources they might use — as well as aspects of students’ mathematical thinking, such as potential difficulties they might have, prior understandings they might use, and mathematical connections they might make. Teachers also attended to how students might react emotionally when presented with tasks and what actions they might take in advance or in response to their anticipations. We conclude with a discussion of ways our results can inform efforts to support improvements in mathematics teachers’ practice of anticipating.