Mathematics Classroom Practices Research Articles

Students' Perceptions and Interpretations of Democratic Practices in Mathematics Classroom

This study aimed to find out students’ perceptions and interpretations of democratic practices in mathematics classrooms. A quantitative research strategy based on the positivist paradigm was used. In Kathmandu district's 20 public secondary schools, 200 respondents in the ninth grade—100 boys and 100 girls—were randomly selected for the sample. Data collection was carried out using a self-created questionnaire that had 25 statements and five Likert-type response alternatives. The self-developed questionnaire's validity was verified by the opinions of experts, and reliability was established by the Cronbach's alpha, 0.82. I prepared four factors according to loading components. The results of the research showed that teachers should use democratic practices to engage students in the learning process and prepare them for the needs of democratic values in classroom practices.

Promoting formative assessment practices in senior phase mathematics classrooms using meaning equivalence reusable learning objects

South African mathematics teachers in the Senior Phase (Grades 8 and 9) were introduced to the pedagogical tool, meaning equivalence reusable learning objects (MERLO), as a formative assessment (FA) strategy to promote and support teachers’ professional growth in using FA practices in the classroom. The cultural-historical activity theory (CHAT) and meta-didactical transposition (MDT) were used to frame the evolution process of teachers’ praxeologies. In this study we used qualitative participatory action research that encompassed 3 phases: pre-MERLO phase, MERLO workshop and post-MERLO phase. The study was conducted in the northeast of Pretoria in the Tshwane district in the Gauteng province, South Africa. Twelve Senior Phase mathematics teachers were purposively sampled in 6 public schools before the workshop training. During the workshop training, only 5 teachers participated due to the COVID-19 outbreak. The data collection techniques included pre- and post-interviews, workshop training sessions, classroom observations, field notes, teachers’ reflective journals, teachers’ lesson plans, learners’ workbooks and learners’ worksheets, and data were analysed using thematic analysis. The findings reveal that the teachers acquired adequate knowledge and skills to effectively structure and integrate the lesson plan of teachers’ didactical praxeologies as FA activities into their mathematics classrooms. The findings also reveal that the learners showed more interest and motivation, were actively involved, developed a deeper understanding of mathematics content, and showed increased autonomy in learning. Future research could involve implementing MERLO in all South African provinces and introducing MERLO to other emerging countries. However, the findings of this study are based on a limited sample of teachers and schools, and the recommendation is that, for future studies, more teachers should be involved in the MERLO professional development.

Storylines in Voices of Frustration: Implications for Mathematics Teacher Education in Changing Times

We have interviewed becoming mathematics teachers, in the last semester of their education, asking how they experience their time as teacher students with the focus on inclusive teaching. In their forthcoming daily work, they will be responsible for arranging for inclusive teaching that addresses all the learners’ needs in mathematics. We believe the voices of future teachers are important to include in conversations about how programs prepare future mathematics teachers for the work of teaching in today’s schools and classrooms. We used storylines as a theoretical construct to discuss the socio-political aspects of mathematics teacher education through the lens of two research questions: What storylines emerged in interviews with becoming mathematics teachers in their last semester of teacher education when they talked about teaching in diverse classrooms? What implications might these storylines have on mathematics teacher education? Our analysis made us aware of three important storylines: (1) storylines about the importance of language in mathematics education; (2) storylines about the importance of accepting diverse methods when doing mathematics; and (3) storylines about issues of invisibility at play in mathematics classrooms. In this paper, we discuss the importance of creating space for discussions in teacher education about issues that may challenge inclusive practices in mathematics classrooms.

Mathematics Teacher’s Autonomy in Students' Performance

This study aims to investigate the perceptions of mathematics teachers’ autonomy in students’ performance. I applied quantitative research design, and positivist paradigm. In Kathmandu district's 40 public secondary schools, 80 respondents in the basic level teachers, 40 male and 40 females-were randomly selected for the sample. Data collection was carried out using a self-created questionnaire that had 50 statements and five Likert-type response alternatives. The self-developed questionnaire's validity was verified by the opinions of experts, and reliability was established Cronbach's alpha, 0 .89. I prepared five factors according to loading components. According to research, teacher’s autonomous teaching makes high performance of students in mathematics classroom practices.

A scoping review of research into mathematics classroom practices and affect

Despite much research exploring affect within a mathematics context, poor student engagement in mathematics persists internationally. There is limited research examining mathematics classroom practice and students' affect, with the potential to inform teachers' practice. This scoping review analysed this limited literature. Of 250 papers analysed, only 26 papers adequately described classroom practices, considered students’ affective state in response to the practice, and considered mathematics learning outcomes. Collectively, these explore very few of the practices used in mathematics classrooms, highlighting the need for more and improved practice-focussed research to better inform efforts to improve student engagement in mathematics.

Improving middle school students' geometry problem solving ability through hands-on experience: An fNIRS study.

Hands-on learning is proposed as a prerequisite for mathematics learning in kindergarten and primary school. However, it remains unclear that whether hands-on experience aids understanding of geometry knowledge for middle school students. We also know little about the neural basis underlying the value of hands-on experience in math education. In this study, 40 right-handed Chinese students (20 boys and 20 girls) with different academic levels were selected from 126 seventh-grade students in the same school, who learnt "Axisymmetric of an Isosceles Triangle" in different learning style (hands-on operation vs. video observation). Half of them operated the concrete manipulatives while the other half watched the instructional videos. The learning-test paradigm and functional near-infrared spectroscopy (fNIRS) technique were used to compare the differences in geometry reasoning involved in solving well-structured problems and ill-structured problems. Behavioral results showed that hands-on experience promoted students' performances of geometry problem-solving. Students with lower academic level were more dependent on hands-on experience than those with higher academic level. The fNIRS results showed that meaningful hands-on experience with concrete manipulatives related to learning contents increased reactivation of the somatosensory association cortex during subsequent reasoning, which helped to improve the problem-solving performance. Hands-on experience also reduced students' cognitive load during the well-structured problem-solving process. These findings contribute to better understand the value of hands-on experience in geometry learning and the implications for future mathematics classroom practices.

Reframing translanguaging practices to shift mathematics teachers’ language ideologies

While dominant narratives about multilingual students position them as deficient, translanguaging theory has played a critical role in making space for the languaging practices of multilingual students in education. However, we know little about how to best support mathematics teachers’ learning about translanguaging. Working with a group of accomplished mathematics teachers taking part in professional development on culturally sustaining pedagogies, in this paper we use frame analysis to examine the ways language ideologies shape teacher sensemaking about translanguaging. We then investigate affordances of classroom video for reframing teachers’ conceptualizations of language. We find that although teachers initially framed students’ language as a barrier to their success, with the introduction of video clips from mathematics classrooms, teachers began to frame students’ language as a tool for productive disciplinary engagement. These findings suggest that video may serve as a valuable resource for reframing teachers’ conceptualizations of students’ languaging practices in mathematics classrooms.

Understanding the interplay between targeted motivation interventions and motivational teaching practices in mathematics classrooms

Prior research has shown that brief motivation interventions, such as interventions targeting students’ perceptions concerning relevance of the learning material, can have long-lasting effects on students’ motivation and performance. However, the educational contexts in which these interventions have been implemented have their own motivational affordances, such as the extent to which teachers support students’ perceptions of relevance in regular classes. According to the seed-and-soil hypothesis for the effectiveness of psychological interventions, such interventions can be seen like a “seed” that needs to be implemented in a supportive educational context (i.e., the “soil”) in order to work. Therefore, in this study we examined the interplay between a one-time relevance intervention implemented in mathematics classrooms and the mathematics teacher’s relevance support as perceived by the students before and after the intervention. Data stemmed from a cluster-randomized controlled trial with 79 ninth-grade mathematics classes (N = 1744 students) in which the intervention was implemented by the mathematics teacher or a master’s student, both trained for this purpose. Multilevel moderation models showed that both intervention conditions had larger effects when students perceived higher relevance support before or after the intervention, thus providing support for the seed-and-soil hypothesis. Furthermore, multilevel mediation models indicated a positive effect of the teacher condition on perceived relevance support at posttest compared with the control condition, which partly explained the positive effect of this intervention condition on utility value at follow-up. The results shed light on the contexts in which these interventions are most effective and the mechanisms through which they work.

The knowledge produced through student drawings.

Drawings have been extensively used as a research method to gather data from research participants including school students regarding their perceptions of mathematics and its teaching and learning. What is valued in drawing-based research in mathematics education, and what kind of knowledge is produced through student drawings, however, is not known. This study examines drawing-based research studies to understand these questions by applying a novel framework - the legitimation code theory (LCT). The study focuses on two cases: one of which looked at middle school students' images of mathematicians (draw a mathematician) and the other examined the same age group students' descriptions of mathematics classrooms (draw a mathematics classroom). Within both studies, greater emphases are on the students' perceptions relating to the discipline-related issues such as teaching and learning of mathematics, mathematics classroom experiences, and practices and tools of mathematicians. Students' perceptions of the mathematics discipline and their attitudes toward mathematics and perceptions of the attributes of mathematicians are also a focus. The study offers the LCT approach to critically analyze the drawing-based research in the mathematics education field to contribute to the production of significant and needed knowledge in the field.

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.

Primary school teachers’ conceptions and practices of assessment and their Relationships

While much is known about assessment, a study examining the conceptions that teachers hold and its relation with their practices in mathematics classrooms is crucial for educators and needs further investigation. This cross-sectional survey study examined teachers’ conceptions and practices of classroom assessment and the relationships between them. Data were collected using a questionnaire from 228 mathematics teachers who were randomly selected from 98 primary schools. The result revealed that teachers mostly agreed to accountability and improvement conceptions and slightly agreed to the irrelevance conception of assessment. They also practiced mixed and different assessment types though they were focused practicing more on the assessment of learning. The moderate and positive relationship found between teachers’ assessment conceptions and practices (subgroups) revealed that the conceptions that teachers have about classroom assessment influenced their practices and it can account for only 27.3% of the variation in their practices. The study suggests that teachers practiced assessment consistent with their conceptions.

Teacher-student interactions for enhanced learning in upper secondary mathematics classroom

<span>Interactive teaching practices in mathematics classrooms are encouraged to meet the learning potential. However, how it is applied in the classroom is still challenging. This paper uses evidence gathered from a large research project to contribute to the understanding of teacher-student interactions. It followed an interventional approach with two teachers and 82 students of two grade 11 classes from one school of Kayonza District in Rwanda. Data were collected through observations, video recordings, and field notes. Results revealed that there is a variety of ways to facilitate and keep interactive learning. These include asking purposeful questions and giving feedback. The quality of teacher facilitation (52%) and students' engagement (60%) were moderately high. However, there was little guidance from teachers in the problem-solving process and the classroom discourse. It is argued that the role of instructional language in communication hinders the quality of teacher-student interactions. This leads us to advise an exploration of language supportive pedagogy in the Rwandan context.</span>

Learning to measure the area of quadrilaterals through decomposition and recomposition

Measuring the area of quadrilaterals through decomposition and recomposition is seen as an important precursor to deriving and understanding area formulae but important questions remain about how students solve such tasks in classrooms. This article presents the results of a classroom teaching experiment in which students studying Year 8 Mathematics (n = 47) developed a repertoire of strategies that they used to measure the area of quadrilaterals through decomposition and recomposition. The classes then used a second repertoire of strategies to derive area formulae based on their solutions. The theory of strategy choice was used to analyze strategy choice from an emergent perspective, which revealed that strategy flexibility and adaptivity were classroom mathematical practices that supported the students’ strategy choices.

Patterns of instruction in Finnish and Norwegian lower secondary mathematics classrooms

This paper focuses on patterns of instructional practices in mathematics classrooms in two Nordic contexts, Finland and Norway. While sharing some key features in terms of ways of organizing schooling and education, these two contexts also exhibit interesting differences in instruction at the classroom level. In using a standardized coding manual to systematically analyze features of instruction in 16 classrooms, eight in Helsinki, and eight in Oslo, we found that whole-class instruction dominated in Oslo, and individual seatwork was the main instructional activity in Helsinki. Instruction in Helsinki showed more evidence of clear instructional explanations, connection of new knowledge to existing knowledge, and explicit learning goals; Oslo students had greater opportunities to participate in classroom discourse and peer discussions. This study contributes to the understanding of how similar contexts enact distinct instructional patterns in the classroom, and how these can be related to the aspects of instructional quality.

Unboxing mathematics: creating a culture of modeling as critic.

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a research method. Twenty-seven college algebra students engaged in a 3-week modeling project at a community college in the USA. Audio-recorded group discussions and written reflections were collected to determine how reflexive discussions were taking place. Analysis of students’ actions and reflexive discussions during the modeling project produced four concepts: voicing mathematics, personalizing mathematics, challenging mathematics, and negotiating mathematics. These concepts are integrated into an overall process for stimulating reflexive discussions and are conceptualized as unboxing mathematics. The overarching concept of unboxing mathematics represents one interpretation of how reflexive discussions may be constituted during modeling activities and identifies classroom mathematical practices specific to the socio-critical modeling context of this study.

Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms

Feedback is a prevalent teaching practice in mathematics classrooms, but few studies have documented how mathematics teachers enact feedback in classrooms. We investigated how 47 teachers provided feedback in 172 mathematics lessons in Norwegian lower secondary schools. We analyzed the quality of feedback, the quantity of feedback, and whether the feedback addressed students’ procedural skills, conceptual understanding, or engagement in mathematical practices. Teachers spent large amounts of time providing concrete and specific feedback, most of it addressing procedural skills while conceptual feedback was less common. The study highlights details of feedback relevant for both pre- and inservice mathematics teacher training.

Translanguaging as Inclusive Pedagogical Practices in English-Medium Instruction Science and Mathematics Classrooms for Linguistically and Culturally Diverse Students

AbstractIn English-medium instruction (EMI), English-as-a-second-language students will learn all/some subjects through English. Although there are a considerable number of studies which explore classroom interaction in Hong Kong (HK) secondary EMI schools, few studies have investigated EMI lessons which involve South Asian ethnic minorised students. These students share different linguistic and cultural backgrounds and they may not share a common first language with the teacher and other classmates. This study conducts a multimodal conversation analysis of science and mathematics lessons at a HK EMI secondary school, triangulated with interview data, in order to explore how the EMI teacher mobilises various resources to make discipline-specific knowledge accessible and cater for the different needs of all students in the classroom. This study argues that the process of enacting inclusive practices is a process of translanguaging which requires the EMI teacher to mobilise various available multilingual and semiotic resources and draw on what students know collectively for transcending cultural boundaries from the students’ everyday culture to cultures of school science and mathematics.

Shifting teachers’ practice in early mathematics classrooms in Ghana: A case study

Shifting teachers’ practice in early mathematics classrooms in Ghana: A case study

Constructing a design framework and design methodology from educational design research on real-world educational technology development

Educational design research (EDR) seeks to contribute to both practice and theory by developing solutions that improve educational practice and generating usable and generalisable knowledge. Most EDR researchers tend to focus on reporting their research contributions to educational practice. Therefore, there is a need for disseminating research that pays more attention to the theoretical contributions of EDR so that those outside a particular EDR project can benefit. This paper focuses on the theoretical contributions, particularly the design framework and design methodological knowledge, of a 6-year EDR enquiry that aimed to develop educational technologies that promote primary school mathematics learning and classroom practice. Informed by the literature and direct experiences of working in collaboration with teachers and various disciplines during this iterative study, a design framework for developing real-world educational technologies and guidelines for conducting EDR are proposed. The design framework highlights four essential aspects—content, pedagogy, practice, and technology—that should be considered when developing educational technologies to ensure their educational benefits, feasibility, and successful real-world utilisation and adoption. The proposed guidelines for conducting EDR, such as exploring design alternatives and employing appropriate design construction and evaluation methods, can assist other researchers, including a single doctoral student, in embracing opportunities and overcoming the challenges that may emerge.

Fifty ways to work with students’ diverse abilities? A video study on inclusive teaching practices in secondary mathematics classrooms

ABSTRACT Inclusive teaching practices can be characterized as recurrent ways how teachers work with their students’ diverse abilities, but how exactly are they enacted in subject matter classrooms? The paper proposes a conceptual framework to unpack inclusive practices according to the student ability to which they refer, in five typical jobs for teachers: (a) identifying the demands for the ability, (b) differentiating learning goals, (c) compensating for low abilities, (d) enhancing abilities, and (e) addressing the abilities in joint learning. The proposed job-ability framework for inclusive teaching practices is substantiated in a video study of 25 mathematics lessons on percentages with the same curriculum material. In total, rather than 50, 133 different inclusive teaching practices were identified in 3862 sequences and structured into 20 cells. They address four abilities (from most often to least often): (1) selective attention/working memory, (2) mathematical pre-knowledge, (3) language proficiency, and (4) metacognitive regulation. The large variance of enacted practices identified within and between lessons calls for professional development that elicits, leverages, and extends the repertoire of practices. While the reported frequencies are specific to the chosen teaching unit, the job-ability framework can be transferred to other subject-matter classrooms and used in professional development programs.