Secondary Mathematics Classrooms Research Articles

An Analysis of Questioning Strategies in Secondary Mathematics Classroom

An Analysis of Questioning Strategies in Secondary Mathematics Classroom

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.

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.

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.

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

In 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 U.S. 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 U.S. 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.

A framework for designing problem solving task for secondary school mathematics classroom

Although problem solving has been playing a critical role in the teaching and learning of mathematics in K-12 in many countries in the world, anecdotal evidence from mathematics classrooms shows that teachers are still facing challenges in designing mathematical tasks on problem solving for classroom instruction. Despite the effort of several existing research studies on enacting problem solving in the mathematics classroom, the guiding principles for designing problem solving tasks remain largely unexplored, thus teachers are left without being empowered to design their own problem solving tasks. The objective of this paper is to provide a comprehensive framework on designing problem solving tasks through a list of interrelated guiding principles. The proposed framework, which we name MIRACLE, foreground seven key considerations which mathematics educators should take into consideration when designing a task for a problem solving lesson: Mathematical content, method of Instruction, Required knowledge, Assessment, Complexity of problem, Learner’s profile, and Enactment of lesson. This paper also provides two exemplars on how the framework could be used to design mathematical tasks for problem solving through problem solving

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.