Secondary Mathematics Classrooms Research Articles

Teacher emotions and in-the-moment decision making in the secondary mathematics classroom

Our study focuses on the interplay of two secondary school mathematics teachers’ emotions and decision-making in pivotal teaching moments. We highlight the interaction between teacher emotions and in-the-moment decision-making, and resources that coordinate this interplay, suggesting a theoretical and methodological way of addressing it. Our analyzed data comes from three teachers’ lessons and four semi-structured interviews. When analyzing pivotal moments where the teacher handles students’ errors, it appeared that teacher emotions and resources are interrelated elements of the decision-making. Findings show that: (1) teachers’ emotions, while handling students’ errors, are mostly negative, but differ in their kind and source; (2) the formation of teacher emotions and actions often seems to draw on the same resources (social-spatial, anticipatory-temporal, moral-ideological dimensions, and teacher’s responsibility about mathematics; (3)teachers’ actions, while handling students’ errors, differ in relation to the resources and the emotions that coordinate their formation.

Enabling collaborative lesson research

AbstractIn this paper, we interrogate and justify the design of a local project that used collaborative design research in a secondary school in England. As authors, we represent teachers and teacher educators engaged in design research, whereby we acknowledge the difficulties implicit to university and school collaborations within a performative culture. Our analysis recognises the struggle for research‐informed professional judgement in the decision‐making and actions of educators that are situated in schools. A professional learning project is analysed to position teachers and teacher educators as practitioner researchers. In this respect, Stenhouse's work provides an analytical framework that is both a lens through which to interpret the nature of collaborations, as well as a methodology that allows us to understand the way in which we navigate the gap between educators' aspirations and the curriculum design and teaching within the project. The collaborative design research project was stimulated by an aspiration to make trigonometry accessible to low prior attaining pupils in a secondary mathematics classroom. This provides a stimulus for understanding the conditions that enable collaborative lesson inquiry and to question whether it can provoke raised aspirations for young people in inclusive classrooms. This allows us to understand the work of teachers as researchers and research users in an increasingly messy teacher education context. We interrogate the potentially problematic connection between research and practice within collaborative inquiry, as we understand how we enable research that is “held accountable for its relevance to practice” because “that relevance can only be validated by practitioners” (Stenhouse, 1988, p. 49).

Effects of observation mode on ratings of teaching quality in secondary mathematics classrooms

AbstractIn educational research, teaching quality is extensively studied because of its role of a mediator between teacher characteristics and student learning. However, empirical evidence on differences between video and live scoring of teaching quality is rare. In the present study, thirty lessons from 15 secondary mathematics classrooms in a German metropolitan area were observed. Lessons were scored both live in the classroom and using video recordings. Live and video scoring was conducted by (different) trained observers. Ratings were obtained with a “hybrid” observational instrument that covers generic and subject-specific characteristics of teaching quality in mathematics classrooms. Generalizability analysis and paired t tests were performed to investigate mode effects. The findings showed that in live scoring, classroom management was rated lower, and cognitive activation was rated higher. Rankings of lessons or classrooms were very similar across modes, and reliabilities did not differ to a meaningful extent either, except for classroom management reaching better results for live ratings. This suggests that based on the present findings, classroom observation performed with our hybrid framework of teaching quality generalizes across observation mode only under certain circumstances. Further research is necessary to better understand the relation between observation mode and teaching quality ratings, as well as the impact of the scoring procedures. We discuss the implications of our findings for educational research and practice.

How do pre-service teachers view Galois theory? A questionnaire study

Abstract algebra is an important part of mathematics teacher education as it provides the rigorous mathematical foundations for many mathematics topics covered in school classrooms. Throughout their academic career, many secondary mathematics teachers even enroll in more advanced algebra courses, which often culminate in Galois theory. However, very little is known about educational aspects of Galois theory and respective mathematics education research is scarce. We contribute to closing this gap by reporting on the results of an exploratory questionnaire study with a sample of n=39 pre-service mathematics teachers, inquiring about the raison d’être of incorporating Galois theory into teacher education: Is Galois theory viewed as useful for their later profession and which connections are drawn to the secondary mathematics classroom? On the one hand, the results of our study indicate that a vast majority of pre-service teachers do not perceive studying Galois theory as meaningful and struggle to exemplify connections between Galois theory and secondary school mathematics. On the other hand, a small share of the participants experienced Galois theory as an important part of mathematics that elegantly connects a variety of algebraic and geometric notions.

Classroom interactional competence in an English medium instruction mathematics classroom: A creation of a technology-mediated translanguaging space

BackgroundSecond language classroom research has explored how teachers demonstrate their classroom interactional competence (CIC). CIC focuses on teachers’ ability to use appropriate language to mediate students’ learning and promote learning opportunities. Research on translanguaging has highlighted how teachers and students mobilise diverse multilingual, multimodal and spatial repertoires to collectively construct meaning in classroom interactions. Aims and samplesBased on a larger linguistic ethnographic project in a Hong Kong English-Medium-Instruction secondary mathematics classroom, this paper adopts a case study approach in order to examine how the teacher’s use of iPad expands his choice for using different multimodal repertoire to mediate and assist students’ learning of academic language and mathematical knowledge. MethodsMultimodal Conversation Analysis is deployed to analyse the classroom interaction data and it is triangulated with the video-stimulated-recall-interviews that are analysed using Interpretative Phenomenological Analysis. ResultsIt is evident in the findings that the construction of a technology-mediated space displays the English- Medium-Instruction teacher’s CIC, harnessing the available semiotic repertoires afforded by the iPad in order to achieve his pedagogical goals. ConclusionsI argue that the notion of CIC can be conceptualised through adopting translanguaging as an analytical perspective, which highlights the teacher’s ability in orchestrating technological affordances for creating an interactional space for student learning. Such a conceptualisation reinforces the need for teachers to draw on a wide range of available multilingual, multimodal, and technological repertoire to create a learning environment conductive to interaction and academic and language learning in English-Medium-Instruction classroom.

Concrete–Representational–Abstract (CRA) Instructional Approach in an Algebra I Inclusion Class: Knowledge Retention Versus Students’ Perception

Mathematical manipulatives and the concrete–representational–abstract (CRA) instructional approach are common in elementary classrooms, but their use declines significantly by high school. This paper describes a mixed methods study focused on knowledge retention and perceptions of students in a high school Algebra I inclusion class after a lesson on square roots using a novel algebra manipulative. Twenty-five students in a high school Algebra I inclusion class engaged in an interactive lesson on square roots paired with the manipulative to support their conceptual understanding. Participants completed a pretest, a post-treatment questionnaire, and a delayed post-test. The two-sample t test showed a significant difference in students’ pretest–post-test scores. However, conventional content analysis of the questionnaires showed that most students did not believe the CRA instructional approach supported their learning. Implications include increased use of manipulatives to teach abstract algebraic topics to support students’ conceptual understanding and destigmatizing the use of manipulatives in secondary mathematics classrooms.

Understanding Joint Exploration: the Epistemic Positioning Underlying Collaborative Activity in a Secondary Mathematics Classroom

Understanding Joint Exploration: the Epistemic Positioning Underlying Collaborative Activity in a Secondary Mathematics Classroom

Fostering a growth mindset in secondary mathematics classrooms in the Netherlands

ABSTRACT In a search for tools to support students to change towards growth mindsets, interventions were implemented by 17 teachers and their 512 students in 21 classes in 10 different secondary schools. The interventions consisted of classroom material explaining the theory of neuroplasticity and mindset to students, specific teaching methods, and student activities. Data were collected through a mindset questionnaire for students, interviews with students and teachers, and lesson observations. The change in average mindset scores of students showed a tendency to a more growth mindset after the interventions. More importantly, in the interviews and questionnaires right after the interventions, students and teachers indicated that their attitudes in the classroom with respect to mathematics changed, as became clear by their language use and their working with more trust and care. These findings indicate the importance of fostering growth mindsets to make mathematics accessible for all students.

Linking diversity in learning Geometry: Exploring tessellation in techno-based mathematical tasks

Nowadays, digital technologies are crucial in supporting students in geometry in secondary mathematics classrooms. However, in some cases, the role of visual function in technology was only utilized for seeing and conjecturing, not for experimenting, while to develop a relational understanding of geometry concepts, students should actively participate in the learning process. To address the issue, this study investigated how students learn geometry with digital technology assistance based on students' diversity in their mathematics abilities. A task with a dynamic geometry software called Techno-based Mathematical Tasks (TbMT) was designed to assist students in exploring geometrical activities and solving a problem through investigations on tessellation. This research employs educational design research and focuses on the preliminary design by conducting a pilot study on three students based on the diversity in their ability in mathematics classrooms, i.e., low, middle, and high. As part of data collection, we captured students' works to examine critical information in their responses based on their differences in abilities. We collected the data through online meetings and recorded the data. We analyzed students' work from the recording by capturing critical information. The results revealed that the TbMT might provide students with opportunities to learn by exploring tessellation activities that might contribute to students' understanding of geometry concepts. Due to the limited number of participants in this study, further research can be an opportunity to expand the number of participants to enhance the contribution to the literature with more comprehensive empirical evidence.

Geometry, groceries, and gardens: Learning mathematics and social justice through a nested, equity-directed instructional approach

We addressed the call for explorations of how BIPOC students’ “experiences in secondary mathematics classrooms might advance transformative, equity-focused, pedagogical models” (Joseph et al., 2019, p. 149) by exploring how a nested, equity-directed approach created different kinds of opportunities for students to take up, shift, or resist what it means to teach, learn, and do mathematics. Specifically, we looked at efforts to engage equity-directed dominant and critical approaches through a series of three mathematics projects aimed at investigating food insecurity as a social (in)justice issue using geometry. Our analysis focused on a subset of data generated during three projects from different times of the year. Findings revealed that the teacher more readily enacted critical equity-directed practices than dominant ones; that students more readily embraced those critical practices; and that students expected their use of mathematics and exploration of social issues to align with authentic, real-world situations.

Mathematics teachers’ professional noticing: Transfer of a video-based competence assessment instrument into teacher education for evaluation purposes

Teacher noticing has become widely accepted as a principal component of teacher competence; it is supported during university teacher education in many activities. However, only a few high-quality standardized measurement instruments exist that capture noticing and allow valid interpretations of how its development depends on factors within university teacher education. The present study is based on a video-based test instrument that has been developed to enable a standardized study of the noticing of practicing mathematics teachers—that is, their perception, interpretation, and decision-making skills—with respect to subject-specific and general pedagogical issues in secondary mathematics classrooms. This study examines how this instrument developed for in-service teachers can be used for pre-service teachers at the master’s degree level. Based on a sample of 313 pre-service mathematics teachers enrolled in six German universities, the study investigates (1) the instrument’s internal structure (scaling models based on item response theory) and (2) its association with relevant factors within university teacher education. The results reveal that a scaling model based on the three noticing facets (perception, interpretation, and decision-making) was superior to a one-dimensional scaling model. Opportunity to learn in mathematics education and average grades in final secondary school examinations were shown to be significant predictors of test performance. However, there was no effect for university-specific opportunity to learn in general pedagogy or pedagogical experiences outside teacher education. Overall, the results suggest that the measurement instrument can be used to assess pre-service mathematics teachers’ noticing in university teacher education.

Is Digital Game-Based Learning Possible in Mathematics Classrooms?

The literature reports that while digital educational games are used in the elementary classroom, they are rarely, if ever, used in the upper secondary mathematics classroom. In order to investigate this situation, a survey was conducted to determine what upper secondary school mathematics teachers think about digital games and what obstacles and limitations they perceive in using DGBL as a teaching approach. The results indicate that mathematics teachers view digital games as a useful teaching tool; however, the lack of knowledge about teaching with digital games and shortage of appropriate games for teaching upper secondary mathematics seems to discourage them from using them as a main teaching tool. These findings imply that professional development should be designed with a focus on teacher training. Furthermore, the development of constructionist-based games should be considered, where games are based on meaning-making rather than practicing mathematical content, as has previously been the case.

Improving Access to General Education via Co-Teaching in Secondary Mathematics Classrooms: An Evaluation of Utah’s Professional Development Initiative

Co-teaching may be a promising strategy to improve inclusive secondary mathematics education in rural schools. Professional development (PD) aids in special and general education teachers’ co-teaching implementation, yet little empirical research examines how to effectively train and support co-teachers. In this study, we describe one state’s PD model for secondary mathematics co-teaching, evaluate outcomes of the PD on co-teachers’ behaviors and beliefs, and examine the impact of co-teaching on students’ mathematics achievement. We examined data from observations, surveys, and students’ pre/post assessments across nine classes within seven school districts, including three rural school districts, over 3 years. We report data from a total of 19 teachers and 281 students in sixth through ninth grades. The PD participants implemented effective co-teaching strategies and reported positive viewpoints toward co-teaching. Additionally, students with and without disabilities improved their mathematics scores. We present key findings for rural schools to guide future implementation and research.

Embodied enactment of a hypothetical scenario in an English medium instruction secondary mathematics classroom: A translanguaging approach

Adopting a language other than the first as the medium of instruction in teaching mathematics can create significant problems for students’ mathematical learning. However, there is little research on the ways in which bi/multilingual mathematics teachers can make use of diverse multilingual and multimodal resources to keep students engaged in learning abstract mathematical knowledge. This article aims to explore how an English-medium-instruction (EMI) mathematics teacher creates different hypothetical scenarios through embodied enactments to enhance students’ mathematical understanding and motivate students’ interest in learning mathematics. The data of this study is obtained from a focused classroom observation in a Hong Kong EMI secondary mathematics classroom. Multimodal conversation analysis is employed to analyse the classroom interaction data, and the analysis is triangulated with video-stimulated-recall interviews which are analysed with interpretative phenomenological analysis. This article aims to extend the notion of embodied enactment as a form of translanguaging to facilitate mathematical learning and develop students’ motivation in learning mathematics in the EMI setting. Particularly, this article argues that embodied enactment creates a translanguaging space for the EMI teacher to achieve mathematical teaching.

Affective content knowledge as foundation for critical mathematics pedagogy

ABSTRACT Recent mathematics education research highlights the importance of developing rehumanising and critical mathematics pedagogies. The aim of this study is to develop a framework for affective content knowledge in mathematics and to apply that framework to instruction identified as supporting both mathematical learning (ML) and social emotional learning (SEL). Classroom observation and teacher interview data were collected in one primary and one secondary mathematics classroom in the United States and analysed qualitatively using case study methods. Two main findings are presented: 1) both teachers supported ML and SEL by modelling how to do and talk about mathematics with others; 2) both teachers leveraged affective content knowledge to provide instruction that supports ML and SEL. This study is significant because it describes how teachers in real classrooms are building affective content knowledge as part of a critical mathematics pedagogy that rehumanises the mathematics classroom.

Secondary school mathematics teacher-perceived factors involved in argumentation: an emerging framework

ABSTRACT Our research focuses on ways teachers envision argumentation in their secondary mathematics classrooms. Semi-structured interviews were conducted with 31 secondary school mathematics teachers in Israel. They were asked to envisage a hypothetical classroom dialogue focusing on mathematical tasks which would engage their students in some argumentative activity. Analysis of the teachers’ responses identified categories related to both structural and dialogic aspects associated with three dimensions of argumentation: (1) task characteristics, (2) teaching strategies, and (3) students’ characteristics. From a cross-analysis of the teachers’ statements certain categories appeared more frequently than others. We interpret our results from a theoretical and practical perspective and make recommendations for areas of future research.

Flipped Learning Method: Possible Antidote for Achieving Gender Equality in Mathematics in Secondary Schools in Cameroon and Nigeria

The purpose of the study was to compare the effectiveness of the flipped learning method in enhancing students’ achievements in mathematics, and also to determine the possibility of this method in minimizing gender inequality noticed in both Cameroonian and Nigerian secondary school mathematics classrooms. The study employed a pretest-posttest non-equivalent control group design. The population size was 5348 Form 3 students (2684 females and 2664 males) in Mezam Division – Cameroon and 5891 Junior Secondary (JS) 3 students (3236 females and 2655 males) in Awka South Local Government Area – Nigeria. A sample of 180 Form 3 and JS3 students from four schools (two from each country) were selected through a combination of simply random and purposive sampling techniques. A Mathematics Achievement Test (MAT) consisting of 20 items and validated by experts, was used in collecting data for the study. The Kudder-Richardson 20 (K-R 20) reliability of the MAT was found to be 0.79. Treatment lasted for six weeks. Mean was used to answer the research questions while the Analysis of Covariance (ANCOVA) was used to test the hypotheses at the 0.05 level of significance. The findings of this study revealed that the flipped learning method enhanced the achievement of students in mathematics no matter their gender or their country of origin. Furthermore, the flipped learning method enhanced the achievement of female students from both countries better than that of the males. It was recommended that curriculum planners and policy makers in education in Cameroon and Nigeria should consider effective alternative teaching-learning methods to be used in teaching mathematics, especially the flipped learning method considered in this study which did not only prove to be an effective enhancer of students’ achievement in mathematics but also provided activities which enabled the females to be as competent as or even more competent than the males.

The Peer-Enabled Restructured Classroom (PERC): Harnessing the Power of Urban Students to Achieve Success in STEM Classrooms

The Peer-Enabled Restructured Classroom (PERC) is an educational model for secondary school science and mathematics classrooms that was developed in New York City public schools under the auspices of a National Science Foundation-funded Math Science Partnership (MSP) between the City University of New York (CUNY) and the New York City Department of Education (NYC DOE). PERC successes demonstrate that middle-performing students in urban, often low-performing schools can be an integral resource to support academic reform and the success of all students. The origins, development, and implementation of PERC in multiple New York City public schools are reviewed in this retrospective. Research studies on the effects of PERC on the students, near-peer leaders, and teachers in the classrooms are presented. PERC demonstrates that restructuring classrooms to engage students deeply in peer instruction can empower students, including those from low-income, often under-resourced school communities, to become student leaders and achievers.

Narrative characteristics of captivating secondary mathematics lessons

Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like “intriguing,” “surprising”) with those the same students rated lowest with respect to their aesthetic affordances (e.g., “just ok,” “dull”). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we examine how some lessons can provoke curiosity or enable surprise. We identify eight characteristics that distinguish captivating lessons and show how some, such as the average number of questions under consideration at any point in the lesson, are strongly related to student aesthetic experiences. In addition, the lessons that students described as more interesting included more instances of misdirection, such as when students’ false assumptions provide opportunities for surprising results. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms.

Using vignettes to investigate mathematics teachers’ beliefs for promoting cognitive engagement in secondary mathematics classroom practice

Promoting engagement is crucial for encouraging student participation, interest, and learning in mathematics. Student engagement has been conceptualized as interrelated types comprising behavioural, emotional, and cognitive characteristics. Cognitive engagement, our focus in this paper, relates to students’ psychological investment in learning and practices used to enhance learning, such as self-regulatory strategies and metacognitive processes. Although crucial for students’ learning, research suggests that teachers’ practices for promoting students’ cognitive engagement are not well understood. In this qualitative study, we investigated the beliefs of 40 secondary mathematics teachers across eight English schools concerning promoting cognitive engagement in mathematics classrooms, and whether teachers with different cognitive engagement beliefs differ in the features of classroom practice they attend to in relation to promoting student self-regulation and metacognition. We developed a Cognitive Engagement Framework (CEF) for the following purposes: (1) to develop vignettes that described the practices of two contrasting teachers (Teacher A and Teacher B), who differed in their use of specific self-regulation and metacognitive processes; and (2) to use as a tool for analysis. 17 participants identified with Teacher A who favoured a controlling style towards student strategy use such as activating knowledge, planning, and enacting and regulating strategies, and a passive approach towards students’ use of self-reflection. 14 participants identified with Teacher B who favoured promoting student autonomy for planning and enacting and regulating strategies, self-reflection, and acknowledged affective elements. In addition to its findings, the paper makes a methodological contribution by using ‘vignettes’ as a new way of investigating teachers’ beliefs, and a theoretical contribution through the development of the CEF.