Secondary Mathematics Classrooms Research Articles

\u201cI am part of the group, the others listen to me\u201d: theorising productive listening in mathematical group work

Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students’ listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, “productive listening,” is described which focuses on observable features connected to students’ ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker’s contribution as being valuable and feeling that one’s own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others’ mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

Designing learning environments to promote academic literacy in mathematics in multilingual secondary mathematics classrooms

Emerging multilingual students can develop the dimensions of Academic Literacy in Mathematics (ALM) in classroom discussions. But, there is a need for empirically-validated principles for fostering such discussions. This research used ALM as a framework to create a unit of instruction on linear rates of change for ninth grade mathematics in which multilingual students benefit from discussions. Project-specific design principles are presented along with qualitative analysis of classroom discussions from each phase of the project. The results illustrate how discussions in the redesigned lessons contributed to developing the interrelated dimensions of ALM among multilingual learners. The work concludes with a discussion of how the project-specific design principles can serve as a framework for fostering discussions in other multilingual secondary mathematics learning environments.

Audience interrogator: constructing meaning about mathematical learning experience in filmed research

ABSTRACT This paper argues that an Arts-Based Research (ABR) methodology, drawing on the Ethnofiction work of filmmaker Jean Rouch, can facilitate new ways of researching mathematics, science and education more generally by: (i) making past learning experiences more accessible and (ii) considering the affective engagement of the audience as interrogator of research to open up myriad understandings of research data. Here, dissemination and impact are positioned as ‘inside’ the research process, rather than ‘informed by’ or directed by the outcome of research. The paper discusses the research film Performatics: Performing stories of mathematical identity through filmed drama Performatics https://vimeo.com/147449932, and a scene which shows Claire (a postgraduate student studying quantitative analysis), in a scene entitled ‘Sum Anxiety’, as she dramatizes an experience from the secondary school mathematics classroom. A moment, which Claire expresses as pivotal in negatively affecting her as a mathematics learner; an experience still viscerally felt.

Types of Humour Categories Used to Generate and Maintain Interest in Mathematics Among Secondary School Students in South Sudan’s Displaced and Re-settled Communities

While there has been appreciable consensus among humour researchers as well as classroom teachers that the use of humour in the classroom setting can be an effective teaching tool, there is still, however, a dearth of literature available that classroom practitioners could use as a guide in actual practice. Most of the literature currently available tends to address the potential use of classroom humour in general, and does not go into the specifics of exactly “what types of humour forms” are effective. This article addresses this question in the context of a secondary school mathematics classroom in South Sudan’s displaced and re-settled communities, where the lesson plans used in the intervention were infused and laced with instructional humour–humour related to the mathematics concepts being discussed–for the purpose of generating and maintaining student interest in mathematics. Using a researcher constructed observation sheet (RCOS) as the research instrument for capturing the desired qualitative data, five specific literature recommended humour types or categories (namely: mathematical jokes, puns, riddles, related stories and funny-multiple choice items) were used and identified as the ones that generated and maintained interest among the South Sudanese secondary school students. Classroom teachers who would like to use classroom humour for the purpose of motivating and inspiring their students may find the information contained in this article useful, as a practical-reference classroom guide.

The links between pedagogical competence, instructional quality, and mathematics achievement in the lower secondary classroom

It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students’ learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the secondary level, this study investigates the links between teachers’ pedagogical competence (i.e., cognitive pedagogical facets of their professional competence), instructional quality, and students’ mathematics achievement. The sample comprises mathematics teacher and student data from 59 classrooms in Germany. Student mathematics achievement was measured across two time points (grade 7 and 8). Teachers’ pedagogical competence was tested using two tests measuring their general pedagogical knowledge (GPK) and situation-specific classroom management expertise (CME). Instructional quality was measured using observational rating data from in vivo rating in mathematics classrooms. Research questions on the relation of teachers’ competence and students’ mathematics achievement were answered using multilevel models. Results from multilevel regression analyses indicate that both GPK and CME predict instructional quality. Direct statistical effects on students’ mathematical progress were identified, whereas no indirect statistical effects via instructional quality could be identified. Although teachers’ measured pedagogical competence is not subject-specific, it serves as a significant predictor for cognitive activation as an indispensable part of quality-oriented mathematical teaching and learning processes in the lower secondary mathematics classroom, and it contributes to students’ mathematical progress.

Relationships Between Teachers’ Interactions with Learner Errors and Learners’ Mathematical Identities

Engaging with learner errors in mathematics classrooms is an important aspect of teacher pedagogy which can support learner identification with mathematics. This study examined the opportunities that teachers provided for the construction of learner identities based on how the teachers spoke about and interacted with learner errors in two secondary school mathematics classrooms. Data were collected over two years in the form of videotaped lessons, field notes, photographed learner notebooks and audiotaped interviews with participants, and were analyzed qualitatively. Two ways in which teachers spoke about errors are discussed: errors are contagious and errors are lessons. How the teachers spoke about and interacted with errors were informed by their views of learners and their reasoning in mathematics, which shaped the identities they offered learners. We show that while learners’ experiences of their teachers’ approaches to errors informed their identification with mathematics to some extent, the learners also played a role in the construction of their mathematical identities.

Co-Learning in Hong Kong English medium instruction mathematics secondary classrooms: a translanguaging perspective

Recent studies on classroom discourse have challenged the traditional classroom role set and emphasised equal contributions from the participants and the emergence of knowledge through active participation. Co-learning emphasises the process in which teachers and students attempt to adapt to one another's behaviour and learn from each other in order to produce desirable learning outcomes. Current research has paid little attention to the ways in which content teachers and students jointly negotiate new knowledge in bi/multilingual classrooms. Based on data collected from a linguistic ethnography in Hong Kong English-Medium-Instruction secondary mathematics classrooms, this paper uses translanguaging as an analytical perspective to analyse how the EMI teacher and students co-learn in the classroom. The data are analysed using Multimodal Conversation Analysis and triangulated with the video-stimulated-recall-interviews which are analysed using Interpretative Phenomenological Analysis. The paper argues that translanguaging creates a safe space for co-learning that emphasises equity in knowledge construction and challenges the hierarchical relationship between the teacher and the learner.

Unpacking teacher challenges in understanding and implementing cognitively demanding tasks in secondary school mathematics classrooms

ABSTRACT Literature suggests that students need to be exposed to cognitively demanding tasks (CDT). In this qualitative study, we examined in-service secondary school teachers’ challenges in understanding (e.g. recognizing, solving, and designing) and implementing cognitively demanding tasks in mathematics classrooms. Purposive sampling consisted of eleven teachers who completed the cognitive demand survey. Qualitative data sources included semi-structured interviews and classroom observations. Data analysis consisted of open and focused coding based on which the following main challenges were reported: challenges related to students’ knowledge, challenges related to English language learners (ELL), challenges related to teachers’ knowledge, and challenges related to curriculum. The study results suggest that teachers may need a support system built to address the challenges and to assist in implementing CDT in their classrooms.

The Interaction of Gender and Pedagogy on Learning Motivations in a Secondary PBL Mathematics Classroom

The purpose of this study was to investigate the interactive effects of gender, learning motivations, and pedagogy (Project-Based Learning [PBL] and conventional) on secondary mathematics learning. In order to measure their academic achievement and learning motivations, 165 secondary students were given a state standardized mathematics test and the Motivated Strategies for Learning Questionnaire. Study results indicated that pedagogy and gender had no impact on academic achievement. Pedagogy played a stronger role in rehearsal, peer learning, and task value. Gender played a stronger role in test anxiety, organization, help seeking, and control of learning. PBL students seemed to value and actively engage in the mathematics more than did the conventional students.

An exploration of teacher and student perceptions of blended learning in four secondary mathematics classrooms

The COVID-19 pandemic forced many teachers around the world to make a sudden switch from face-to-face to online teaching. This shift in practice has provided an opportunity to reconsider how technology use in mathematics education can be utilised to improve student engagement. In this study, we explore four case studies of Australian secondary mathematics classrooms conducted prior to the COVID-19 pandemic to examine how teachers are using blended learning approaches and how their students perceive these pedagogical practices. Findings across all four sites indicate that technology use expands student opportunities to engage with mathematics learning through the provision of multiple pathways and methods of access. Specifically, we find evidence supporting the use of blended classroom teaching strategies to provide differentiation and personalised learning approaches; visualisation and dynamic manipulation of mathematics concepts; and alternative methods for teacher-student feedback and communication. We argue that the student learning experience in mathematics can be enhanced through a variety of blended learning approaches by allowing for diverse points of access to learning opportunities which are more closely aligned to individual learning needs and free from the temporal constraints of the classroom.

Productive Technology Use in Mathematics Explorations

We investigate different ways interactive diagrams can be used in secondary mathematics classrooms.

Examining Indonesian Secondary School Mathematics Teachers' Instructional Practice in the Integration of Technology

The Indonesian secondary school mathematics curriculum advocates the use of technology in teaching and learning of mathematics. The previous studies paid less attention to what type of digital tools that the teachers used and how they integrated them in the mathematics teaching. This study aimed at investigating Indonesian secondary school mathematics teachers' instructional practices in the integration of digital technology in classrooms and examined differences in teachers' instructional practice according to their background. It employed a quantitative approach whereby were collected through a questionnaire survey. The data were gathered from 341 mathematics teachers in 93 secondary schools. This study suggested that the integration of digital technology has emerged in Indonesian secondary school mathematics classrooms. However, it was also found that most of the teachers did not use the technology in constructive ways. The result also revealed that female teachers have better instructional practices in the use of digital technology than male teachers. In addition, teachers' levels of education play an important role on their instructional practices with digital technologies. This study suggests that it needs a radical improvement of the integration of technology in Indonesian secondary school mathematics classrooms in order to achieve the curriculum objective. Therefore, further research and development on this issue is needed in the country.

Implementation of STEM in Secondary Mathematics Classrooms: Identification of Teachers' Beliefs

The purpose of this study was to investigate teachers’ beliefs about the implementation of STEM (Science Technology Engineering and Mathematics) approach in secondary (6-12 grades) mathematics classes and identify intervening belief aspects. A questionnaire was developed regarding practicing secondary level mathematics teachers’ beliefs about the implementation of STEM in mathematics classes. An online form of the questionnaire was created and sent to all secondary math teachers in two counties in the state of Florida. Eighty-two were received back from teachers. The results of factor analysis confirmed that items were distributed under five major aspects. Finally, the results of the data analysis disclosed that although most teachers believe that the implementation of STEM education is necessary, some have concerns about the effectiveness of the implementation because of shortages of materials, resources, and equipment needed for implementation of STEM. Another important finding is that teachers don’t have appropriate and sufficient knowledge for the implementation of STEM activities.

Teaching to Listen, Question, and Ponder: An Investigation into Promoting an Enquiring Atmosphere in a Mathematics Classroom

This study reports on a classroom-based intervention that lasted eight lessons with the particular focus of exploring whether and how specific activities, strategies, and questions may promote an enquiring atmosphere in a mathematics classroom, i.e., a classroom environment in which students feel safe to investigate new mathematical ideas in order to produce, share, and test their conjectures in search for a proof. Although many researchers agree on the central role that conjectures and proofs should play in all students’ mathematical experiences, many students find it difficult to engage with conjecturing and proving. In this paper we argue that the classroom atmosphere has a crucial influence in helping students to overcome these difficulties and we focus our investigation on an English secondary mathematics classroom taught by the first author. Students’ responses to questionnaires, prompts, tasks, and interview questions were analysed in order to evaluate the impact of the intervention. The analysis suggests that specific activities, strategies, and questions can be used by teachers to facilitate an enquiring classroom atmosphere. However, for these to be effective, the teacher needs to explicitly teach students how to listen, question, and ponder in order to give students the tools to formulate conjectures and proofs.

Scrutinizing two Finnish teachers’ instructional rationales and perceived tensions in enacting student participation in mathematical discourse

This study employs interviews and observations to investigate instructional rationales of two purposefully sampled teachers with divergent classroom discourse practices in Swedish-speaking Finnish lower secondary mathematics classrooms. Studies on classroom discourse often point to beliefs and contextual factors shaping teachers’ discourse practices. Less is known about how tensions perceived by teachers can influence the instructional rationale in a context such as Finland, known for traditional and teacher-centered mathematics instruction. Findings of this study suggest that these Finnish teachers’ instructional rationales for differently enacted classroom-discourse practices are grounded in similar concerns of student needs, related to student learning, well-being, and equity. One of the teachers perceived a tension between these concerns and mathematics education literature’s ideals of classroom discourse and avoided engaging students in discussions other than in tightly teacher-led format. The other embraced the idea of discourse as facilitating learning and created methods for giving all students equal access to the perceived benefits of mathematical discussions. The identified tensions of student learning, well-being, and equity can be used as guiding principles in developing teachers’ discourse practices in professional development in Finland and beyond.

Research methodology in critical mathematics education

ABSTRACT This article examines research methodologies for classroom-based research in light of the complementary ideas of Freire and Habermas. After reflecting on classroom-based participatory action research in a secondary mathematics classroom, I discuss the suitability of critical participatory action research in critical mathematics education. Critical participatory action research resonates with central concerns of critical mathematics education as it allows researchers to consider emancipatory alternatives to existing situations.

Transforming mathematics classroom practice through participatory action research

This paper explores the potential of participatory action research to bring about significant changes in practice in a context in which more conventional approaches to research have had limited impact. It focuses on secondary mathematics classrooms where teaching approaches characterised by memorising and practising mathematical procedures, with little understanding of their application, purpose or underlying concepts, remain commonplace in many countries around the world and have proved highly resistant to change. The paper highlights the damage caused by such practices in terms of the alienation of large numbers of students and the inequitable outcomes they are associated with, including the strong correlation that persists between students’ socio-economic status and mathematical attainment. It reports on the case of one participatory action research project, involving the author and five teacher researchers, that demonstrated how a vision of mathematics education, involving a genuinely engaging and empowering curriculum, can be translated into classroom practice. The paper considers the extent to which this research project was conducted in a collaborative, systematic and rigorous way. It reflects on the research processes that facilitated critical reflection, enabled the teacher researchers to overcome constraints and generated trustworthy findings. The insights gained from this analysis are used to argue that a participatory action research methodology, which resonates with a critical mathematics pedagogy, has the potential to challenge prevailing discourses in mathematics education and hence lead to genuine transformations in classroom practice.

EXPLORING THE BARRIERS TO EFFECTIVE COOPERATIVE LEARNING IMPLEMENTATION IN SCHOOL MATHEMATICS CLASSROOMS

Literature is replete with research confirming the benefits of cooperative learning on students’ academic achievement and attitude towards mathematics. Despite these benefits, cooperative learning implementation in most Zambian secondary school mathematics classrooms has remained a challenge. An explanatory sequential mixed methods research design was employed to determine the causes of teacher-resistance to cooperative learning implementation in selected schools. A cluster random sampling method was used to select 62 teachers (43 male and 19 female) of mathematics from six public secondary schools in Ndola district of Zambia. A questionnaire was administered to all the 62 teachers followed by lesson observations in six randomly selected grade 11 mathematics classrooms, whose teachers later attended a focus group discussion. Research findings revealed that the majority of participants prefer expository teaching to cooperative learning. More than 64% of the participants indicated that they resisted implementing cooperative learning in their classrooms due to shortcomings in; assessing learners, ensuring a disciplined class environment, completing the already bulky syllabus, handling large classes, students’ low reasoning abilities and preparation time versus high teaching loads. These results provide evidence on the need for more attention to how the identified challenges could be addressed not only in Zambian mathematics classrooms but in other educational settings elsewhere. Keywords: cooperative learning, expository teaching, mathematics classrooms, mixed methods research.

Indonesian Teachers’ Knowledge of ICT and the Use of ICT in Secondary Mathematics Teaching

Indonesia, like many other countries, see Information and Communication Technology (ICT) as a potential tool for enhancing the quality of education. However, there is a lack of research examining Indonesian secondary mathematics teachers’ knowledge in the integration of ICT. In this study, we aimed to investigate Indonesian secondary teachers’ knowledge in the use of ICT in secondary mathematics classrooms. The study employed a quantitative method with a cross-sectional survey approach. It was conducted in one of Indonesia’s provinces where the data were collected from 341 secondary mathematics teachers through a questionnaire survey. The findings suggest that, to a large extent, Indonesian secondary mathematics teachers have a largely inadequate knowledge of ICT and knowledge of ICT use in teaching. Based on the findings, we argue that it is crucial to improve Indonesian teachers’ knowledge of both aspects, and more training courses for teachers’ knowledge development are needed.

Preparing pre-service mathematics teachers for STEM education: an analysis of lesson proposals

Based on an investigation of research literature on the role of mathematics within the context of STEM education and twenty-first century skills, this explorative study presents and analyses 19 pre-service teachers’ lesson proposals for innovative STEM activities in secondary mathematics classrooms. Drawing on a categorisation of twenty-first century skills and key concepts from Realistic Mathematics Education and Basil Bernstein’s writings, the analysis indicated a use of detailed instructions regarding what students should do but unspecified criteria for their expected knowledge productions. Rather than serving as a digital tool for problem solving, programming was used for the purpose of generalising students’ conceptual knowledge in mathematics. At the same time a focus on modelling and applications in the STEM activities tended to weaken the disciplinary character of mathematics. The learning of various twenty-first century skills was promoted to different extents. The study raises a discussion of affordances and constraints regarding students’ access to mathematical knowledge through different modes of integration of mathematics and other STEM subjects aiming to support the development of twenty-first century skills.