Secondary Mathematics Research Articles

Preservice Secondary Teachers’ Mathematical Knowledge for Teaching: Focus on Reflective Practice

ABSTRACT Mathematics education researchers have highlighted that preservice secondary mathematics teachers (PSTs) need opportunities to learn how their content knowledge is contextualized during instruction. Mathematical Knowledge for Teaching (MKT) subdomains provide a way to understand mathematics discipline-specific knowledge that is unique to the profession of teaching. Using a single case study design, we investigated how 11 secondary PSTs described MKT subdomains as they engaged in approximations of practice in the form of lesson planning, peer teaching, and associated guided reflections. The findings demonstrated that the PSTs referenced the MKT subdomains related to planned teacher actions (e.g., posing scripted questions) in their initial reflections. As they progressed through the approximations of practice and associated reflections, they began reflecting on MKT subdomains related to contingency actions and decisions (e.g., modifying mathematical tasks based on students’ thinking). Findings also demonstrated that, after experiences reflecting, the PSTs described a broader set of MKT subdomains (e.g., curricular trajectory) in addition to their responses to the specific prompts. We argue that providing PSTs with opportunities to reflect on their practices through the lens of MKT is an effective way to develop their understanding of how content knowledge is contextualized during mathematics teaching.

Exploring the Integration of Artificial Intelligence-Based ChatGPT into Mathematics Instruction: Perceptions, Challenges, and Implications for Educators

This research investigates how secondary school mathematics educators in the Nsukka Education Zone, Enugu State, Nigeria, perceive the incorporation of artificial intelligence-based ChatGPT into teaching mathematics. The study employed a sequential exploratory mixed-methods strategy, starting with a systematic survey and followed by detailed interviews. The Mathematics Teachers’ Awareness and Perceptions of AI-based ChatGPT Questionnaire (MTAPACQ) used in this study was adapted from an existing online survey and administered to 80 mathematics teachers, who were selected using stratified random sampling to ensure varied representation across different local government areas. The survey explored teachers’ awareness, utilisation, and perceptions of ChatGPT. Following the quantitative phase, in-depth qualitative interviews were conducted with a subset of five teachers who were familiar with ChatGPT to gain deeper insights into their experiences. The findings indicate limited awareness of ChatGPT, with only 17% demonstrating familiarity with the technology. The infrequent utilisation of ChatGPT in mathematics teaching is mainly associated with this limited awareness. Teachers who integrate ChatGPT report positive outcomes, including improved teaching effectiveness, heightened student engagement, and enhanced comprehension of complex concepts. Nevertheless, the overall perceptions of the tool’s impact on mathematics teaching and learning are moderate. The identified challenges in relation to integration include technical adaptability, curriculum alignment, and the need for customisation to accommodate diverse learning styles. This study emphasises the significance of continuous professional development and ongoing support for teachers to integrate AI-based ChatGPT into mathematics instruction proficiently. The insights derived from the findings hold value for educators, policymakers, and technology developers aspiring to elevate the role of artificial intelligence in mathematics education.

Task potential in relation to teaching quality and teacher competence in secondary mathematics classrooms

The potential of tasks to foster mathematical learning and understanding is an important aspect of instruction and their implementation in teaching is thus often viewed to be positively related to the quality of instruction. Both the selection of tasks as well as their implementation in the classroom depend on many factors, with teachers’ knowledge and skills as one of the most important ones. The present study aims to analyze the relations between different aspects of task potential, the quality of instruction, and teachers’ competence in order to investigate whether task potential can be seen as an indicator for teaching quality, for teacher competence, or as an independent construct in models of educational effectiveness. To this end, we draw on data from the TEDS-Validate study, namely tests of mathematics teachers’ competence (n = 31) observations in their classrooms (n = 60), and an in-depth analysis of all tasks used in the respective lessons (n = 2490). Multiple regression analysis suggests that while some facets of task potential are related to either teaching quality or teacher competence, the potential of tasks emerges as an independent construct with some characteristics predicting the teaching quality of the respective lessons. Implications of these results for the role of tasks in educational effectiveness research are discussed.

Dataset collected to evaluate the impact of continuous professional development training on Rwandan upper primary and lower secondary mathematics and science teachers’ content knowledge and beliefs

Dataset collected to evaluate the impact of continuous professional development training on Rwandan upper primary and lower secondary mathematics and science teachers’ content knowledge and beliefs

Supporting students’ participation in collective argumentation: Use of displays in a secondary mathematics classroom

ABSTRACT Thoughtful and purposeful displays can support students’ participation in argumentation. This report addresses how displays are used within collective argumentation. We examined a secondary mathematics teacher’s and her students’ use of displays during selected episodes of collective argumentation. From video classroom observations and interviews with the teacher, we extracted several kinds of displays according to their functions and then investigated how these displays supported collective argumentation as direct contributions to the argument or actions supporting the argumentation. Furthermore, we also considered actions by the teacher that supported her students to display. We found displays can be both part of the mathematical argument and supportive of the mathematical argumentation. This finding has direct implications for studying mathematical discussions because the literature has primarily focused on verbal contributions to the argument over nonverbal contributions such as displays.

Teacher education for mathematical modelling: exploring the experiences of secondary school teachers in two courses

This paper focuses on in-service teacher education as a crucial agent in driving educational paradigm shifts for the teaching and learning of mathematical modelling. Our paper presents empirical research based on two case studies, examining training courses for in-service secondary school mathematics teachers. The first course integrates different modelling approaches, while the second one is based on the anthropological theory of the didactic and uses the proposal of the study and research paths for teacher education. Both experiences conclude with teachers working on the design of modelling tasks to be implemented in secondary schools. Both courses are analysed through the lenses of how teachers progress on the collective identification of conditions and constraints for modelling, when teachers deal with the design of modelling tasks and analyse their implementations. First, the results show the kind of modelling tasks teachers design and the level of disciplinary specificity at which they plan modelling to be implemented. Second, we analyse how teachers address the “ecological analysis”, that is, the identification of conditions and constraints that facilitate or hinder the integration of modelling in secondary school classrooms after their experiences.

Beginning mathematics teachers’ values and beliefs about pedagogy during a time of policy flux

AbstractThis study interrogates how beginning secondary mathematics teachers align their beliefs with their practice when they justify their pedagogical choices in the context of recent English mathematics education policy which is strongly influenced by approaches to mathematics teaching in Shanghai and Singapore currently referred to as ‘mastery’ approaches. It seeks to understand beginning teachers’ perceptions and understandings of these approaches and the extent to which they recognise aspects of ‘mastery’ in practice. In setting the context, pre-service teachers’ beliefs were surveyed and found to be congruent with constructivist approaches to learning. We then draw on qualitative data from semi-structured interviews secondary mathematics teachers in their first year post-qualification. The interviews were designed to interrogate and capture understanding of the features of mastery within their own classrooms. By using vignettes to capture participants’ beliefs, our aim was to present a ‘more nuanced understanding of the phenomena’ (Skilling and Stylianides in Int J Res Method Educ 43(5):541–556, 2019, 10.1080/1743727x.2019.1704243). The analytical framework developed draws on Guskey’s (In: Wright J (ed) International encyclopedia of the social & behavioural sciences, 2015, vol 14, 2nd edn, Elsevier, pp 752–759) interpretation of Bloom’s theory of mastery learning together with features of mastery learning in mathematics articulated by Drury (How to teach mathematics for mastery, 2018, Oxford University Press) and Boylan et al. (Edu Sci 8(4):202, 2018, 10.3390/educsci8040202). This posed a research design challenge given the variation in interpretation of mastery learning as it is understood in practice. The data exposes differences in the interpretation of mastery approaches in the settings where they learn to teach, as well as the tensions that arise between beginning teachers’ beliefs, practice, professional knowledge and agency in their developing classroom roles.

Insights on usability testing: The effectiveness of an adaptive e-learning system for secondary school mathematics

The study evaluates the Mythematix prototype, an innovative adaptive e-learning system designed specifically to enhance secondary school students’ understanding and proficiency in mathematics. Utilizing a mixed-methods approach, it combines qualitative and quantitative research methodologies to thoroughly assess students’ perceptions and experiences with the Mythematix prototype. The study involved a group of 30 students participating in a comprehensive usability survey, which included a range of Likert scale questions alongside an open-ended response. This survey was designed to evaluate the usability of the prototype, pinpointing its strengths and weaknesses from the students’ perspectives. The analysis of the survey results provided detailed insights into the most and least effective aspects of the prototype. Overall, the study contributes valuable insights into the effectiveness of adaptive e-learning platforms in enhancing and enriching students’ learning experiences in mathematics, and it lays the groundwork for future research in this evolving educational field.

The Effect of Improvised Computer-Based Software Package on Secondary School Students’ Achievement and Attitude Towards Mathematics

The study was conducted to determine the effect of improvised computer-based software on the achievement and attitude of senior secondary school students towards mathematics. Fifteen secondary school mathematics teachers were trained to produce a computer-based software package and use the package to teach ‘graphical solution to quadratic equations’ to senior secondary class one (SSCI) students. A total sample of 1487 SSCI students was used in the study: 745 students in the 15 secondary schools purposively selected on the rationale of their closeness to a computer center, used as the experimental group, and 742 students from the 15 schools randomly selected for use as the control group. Pre-test, post-test, and quasi-experimental research designs were used to conduct the study. Fifteen intact classes were simultaneously used for treatment in the experimental and control groups. The experimental groups were taught with computers using the computer-based software package on teaching graphical solutions to quadratics equations produced by their teacher, while the control groups were taught using the conventional strategy. The result reveals a significant difference in academic achievement between students taught with improvised computer-based software packages and those taught using the conventional strategy. The mean achievement score of 73% and standard deviation of 9% was obtained from the experimental group, while the control group had a mean achievement of 57% and standard deviation of 5%. Similarly, the experimental group had an attitude test score of 82% and a standard deviation of 6%, while the control group had a mean attitude test score of 59% and a standard deviation of 11%. This gave the calculated value of the t-test as t = 42.3 for achievement and t = 50.1 for attitude, showing a significant difference in achievement and attitude between the experimental and control groups. Thus, an improvised computer-based software package is more effective in teaching mathematics than the conventional strategy. Hence, improvising computer-based software for teaching and learning is highly recommended.

Enhancing learning outcomes in mathematics education through innovative assessment methods and timely feedback

This study explored the transformative impact of innovative assessment methods and timely feedback on learning outcomes in advanced public secondary mathematics schools within Gasabo District, Rwanda. A total of 139 students and seven teachers participated in a focus group discussion to investigate the efficacy of these pedagogical strategies. The findings indicated that the implementation of innovative assessment methods, such as formative assessments and project-based learning, coupled with a timely feedback approach, significantly enhances students’ comprehension, engagement, and overall performance. Teachers, as facilitators of this process, played a crucial role in creating a supportive learning environment. The study indicated the importance of adopting assessment practices and feedback mechanisms in improving educational outcomes, especially in the context of mathematics education in Rwanda. These insights held promise for teachers seeking to enhance learning outcomes in mathematics and other science, technology, engineering, and mathematics disciplines in the region.

AlgeoMath를 활용한 초등 도형 과제의 도구화 스킴 분석

Recently, there has been increasing interest in the use of Dynamic Geometry Environments (DGE) in elementary geometry learning. This study aims to analyze elementary geometry tasks utilizing DGE from an instrumental perspective and to identify the conceptual and technical difficulties that elementary students may encounter. To achieve this, we analyzed textbooks and previous studies to extract tasks that utilize the Korean DGE, AlgeoMath, and conducted practical exercises to analyze the instrumentation schemes for each task. The analysis revealed that some terms and symbols of the tools were not aligned with the elementary curriculum or contained mathematical errors, and that some schemes requiring an understanding of functional perspectives or basic constructions in secondary mathematics could present conceptual and procedural difficulties for elementary students. Furthermore, we found that precisely implemented transformation tools were not suitable for the informal and intuitive learning of elementary plane figure movements. Finally, it was confirmed that the inherent characteristics of DGE, such as the independence and dependence of objects and the hiding feature, as well as the functional limitations and errors of AlgeoMath, could pose challenges for students. Based on these findings, the study suggests pedagogical implications for elementary mathematics lessons using AlgeoMath and provides insights into the functional composition of DGE for elementary use.

Preservice secondary science and mathematics teachers' readiness to teach multilingual learners: An investigation across four teacher education programs

AbstractIn this mixed methods study, we analyzed survey and interview data from 100 preservice secondary science and mathematics teachers enrolled in four teacher education programs (TEPs) to investigate their readiness to teach multilingual learners. We defined readiness as preservice teachers' sense of preparedness to teach multilingual learners and their understanding of effective multilingual learner instruction. We examined participants' self‐reported levels of preparedness, their understanding of effective multilingual learner instruction, and sources contributing to and/or limiting their readiness. We found that participants' readiness to teach multilingual learners significantly increased between the beginning and end of their TEPs. We also found that participants' understanding of effective multilingual learner instruction was significantly associated with a higher sense of preparedness. Furthermore, we found that participants enrolled in graduate TEPs reported higher levels of preparedness than participants enrolled in an undergraduate TEP. Likewise, participants whose first language was other than or in addition to English reported higher levels of preparedness. Finally, participants identified field placement experiences, personal and professional background, and coursework as factors contributing to their readiness to teach multilingual learners. We close with recommendations for teacher educators intent on helping preservice teachers better understand and implement effective instruction for multilingual learners.

Gender and circadian preferences influence emotions and motivation in secondary mathematics classrooms

ABSTRACT Many studies have reported poor school achievement in evening persons and general circadian fluctuations in cognition. The aim of this study was to analyze circadian fluctuations in a cross-sectional design and examine the effects of chronotype on situational emotions and intrinsic motivation. A cross-sectional survey study was conducted in three Turkish secondary schools with a total sample of 599 students (283 females and 316 males). Data were collected at the end of specific math lessons of the same grade level and content, using a form combining three scales. We found no gender-related differences in intrinsic motivation, while there were some differences in situational motivation. In math classes, female students exhibited higher level of interest, while boys scored higher on boredom. In addition, students who scored high on morning affect reported higher levels of interest, well-being, and less boredom. Students with higher stability (and lower fluctuations in mood and cognition during the day) reported a higher degree of enjoyment, perceived competence, perceived choice, and less pressure/tension in their math lessons. A positive association was observed between distinctness, interest, and well-being, while negative correlations existed between distinctness and boredom. This suggests that students with higher diurnal stability reported a higher level of interest, well-being, and a lower level of boredom. Additionally, the results of the analyses showed that morningness, distinctness, and eveningness were significant predictors of intrinsic motivation. Conversely, gender, time of application, morningness, and distinctness emerged as predictors for situational emotions in mathematics classes.

High-quality use of representations in the mathematics classroom – a matter of the cultural perspective?

The teacher’s use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether the perspectives from Western literature, emphasizing the importance of explicit connections between symbolic and graphic representations, can be extended legitimately to the East Asian context. Using a situated approach, the study elicited norms of high-quality representation use from researchers in Germany and Taiwan. A total of 31 mathematics education professors from both countries evaluated the use of representations in three secondary mathematics classroom situations presented as text vignettes. The vignettes, designed by the German research team, each depicted a situation where from their perspective, a norm of high-quality representation use, specifically the explicit connection between symbolic and graphic representations, was violated. Qualitative analysis of the researchers' responses revealed that in each situation, at least half of the German researchers expected explicit connections between representations. Conversely, the majority of Taiwanese researchers only expected such connections in one situation, particularly when the graphic representation served as an independent learning objective rather than solely aiding conceptual understanding. These findings indicate easily unnoticed culture-specific differences regarding how a common aspect of instructional quality is expected to unfold in teaching.

The Mathematics Teacher Education Partnership: The Power of a Networked Improvement Community to Transform Secondary Mathematics Teacher Preparation: A Review

The Mathematics Teacher Education Partnership: The Power of a Networked Improvement Community to Transform Secondary Mathematics Teacher Preparation: A Review

Towards constructive ambiguity: changing views during secondary mathematics teacher education?

ABSTRACT Previous research on whether pre-service teachers change their views of mathematics and its teaching during their education has mixed results. We pursued a descriptive understanding of the effect of teacher education on the views of teacher education graduates, through using data from ten interviews with Swedish secondary mathematics pre-service teachers. The soon-to-be graduates’ views of mathematics had not changed substantially, and they rarely communicated clear views. The static and dynamic groupings of views coexisted, although dynamic views dominated. We further found indications of a communication view of mathematics. Respondents generally displayed a multifaceted view of mathematics teaching, to which teacher education had contributed. Their views corresponded more frequently with images of the desired teacher as knowledge-transforming and interested. We argue that a multifaceted view of teaching is a welcome outcome for teacher education.

Facilitating Productive Struggle in an Online Secondary Education Mathematics Methods Course: Experiences of Pre-Service Teachers

This research investigated preservice teachers’ (PSTs) experiences with productive struggle in an online environment, and how it influenced their pedagogical knowledge. This action research study reports on secondary mathematics pre-service teachers (PSTs) who completed mathematical tasks in weekly synchronous Zoom sessions to develop their understanding of productive struggle. Vygotsky’s (1978) Social Constructivist Theory and the growth mindset framework (Boaler, 2016; Dweck 2006; 2008) provided the lenses through which the research was designed and analyzed. Findings show that presenting opportunities for PSTs to experience productive struggle informs their pedagogical practice, and that providing this experience in an online environment is possible. PSTs gained an increased understanding of the importance of collaborative work, asking purposeful questions, and the alignment between productive struggle and improved mathematical understanding.

Blended Learning in Secondary Mathematics: Effects on Student Achievement and Knowledge Retention

This study explores the implementation of blended learning in high school mathematics education in Jordan. The primary objective is to develop a structured framework that integrates traditional classroom methods with digital learning tools to create a more dynamic and effective learning environment. Using a quasi-experimental design, this research evaluates the effectiveness of blended learning strategies in enhancing student understanding, engagement, and retention in mathematics. A sample of high school students from a single institution in Jordan was divided into experimental and control groups, with the former utilizing blended learning techniques and the latter following conventional teaching methods. The results demonstrate significant improvements in the mathematics achievement and retention rates of students in the blended learning group compared to the control group. The study also identifies key components and best practices for successful implementation, offering practical recommendations for educators and policymakers. These findings highlight the potential of blended learning to transform mathematics education by catering to diverse student needs and fostering a more engaging and personalized learning experience.

Design and practice of secondary mathematics teaching based on PAD class model

Design and practice of secondary mathematics teaching based on PAD class model

Evaluation of the nexus between student attitude, teacher teaching methods, and achievement in junior secondary school mathematics

This study investigated the relationship among students’ attitudes, teachers’ teaching methods, and mathematics achievement in Lagos State, Nigeria. The study employed a correlational research design. The population consisted of all the public junior secondary school students in Lagos State. The stratified sampling technique was used to select 30 junior secondary schools across the six education districts in the state, and the simple random sampling technique was used to select 900 students from the selected schools. Participants completed standardised instruments: the Student Attitude Questionnaire (α=0.77), the Teacher Teaching Methods Questionnaire (α=0.92), and the Mathematics Achievement Test (α=0.89). The data collected were analysed using frequency, percentage, Pearson product moment correlation, and multiple regression at α=0.05. The majority of the respondents (75 %) were between 12 and 15 years old, of which 341 were boys and 342 were girls. There is a low positive significant relationship between students’ attitudes and students’ mathematics achievement (r=0.24) and between teachers’ teaching methods and students’ mathematics achievement (r=0.17). The multiple correlation coefficients (R) of all the variables were 0.25. The adjusted R2, which estimates the variance of the dependent variable measured, was 0.06. This implies that all the independent variables students’ attitudes and teachers’ teaching methods—made a 6 % contribution to the variance in students’ achievement in mathematics (F=29.029). It is recommended that students be motivated to have the right attitude towards mathematics and that appropriate teaching methods be employed throughout the teaching-learning process.