Mathematics Classroom Research Articles

Pedagogical responsiveness of mathematics instruction at inclusive secondary schools: A particularistic case study

This qualitative particularistic case study explores the perspectives and experiences of learners with visual and hearing impairments regarding the teaching of mathematics. Extreme-case sampling was employed to select four learners (three hearing impaired and one visually impaired) from the only two inclusive secondary schools in the northern part of Namibia. The study qualitative study utilised open-ended questionnaires and interviews. Verbatim quotes from the research participants were used as inferences to identify descriptors within the first-generation Cultural Historical Activity Theory, which served as a theoretical and analytical tool. The findings revealed that the activity system of learners with visual and hearing impairments exhibited tensions that negatively affected their performance in mathematics. Learners experienced marginal responsive pedagogy in mathematics classrooms due to teachers' lack of knowledge and pedagogical skills for delivering meaningful mathematical instruction. While learners without disabilities struggled with comprehension and effective communication skills, learners with visual and hearing impairments faced a lack of equipment to support the conceptualisation and visualisation of mathematical subject content. The authors emphasise the critical importance of addressing communication barriers and adapting teaching practices to support the learning and inclusion of visually and hearing-impaired learners in mathematics, with an emphasis on mathematical language that promotes a better understanding of mathematical concepts. Teacher training should also incorporate responsive pedagogy to enhance outcomes and foster a more inclusive learning environment that promotes academic success and positive social experiences for all learners. Recommendations at a policy level, including advocating for a decolonised curriculum were made.

Investigating students’ arguments with real-life functional situations throughout a sequence of collaborative activities

Recent years have seen increasing interest in providing students with opportunities for developing important argumentation skills in the mathematics classroom. Social interactions with peers to critique alternative ideas, justify arguments, and build consensus, have been found to promote deep thinking and meaningful development of concepts. In this study we explored 9<sup>th</sup>-grade students’ interactions during a sequence of specifically designed argumentation tasks on real-life functional situations to investigate the appropriateness of their arguments. Data were collected from the students’ written task responses, student reflections, small-group observations, individual interviews with the group members, and teacher interviews. Analysis of the level of appropriateness of the students’ individual and group written responses in each activity focused on three aspects: identifying variables, forming relations between them, and noticing contextual features of the real-life situation. We found evidence of students grappling with selecting two suitable variables and with conceptualizing the nature of their relation. It also appeared that aspects of the students’ social interactions played a role in students ignoring correct arguments and accepting incorrect arguments. We discuss implications for small-group argumentation and suggest avenues for future research.

Translanguaging for Linguistically Proud Mathematics Classrooms

Using translanguaging, we empower emergent bilinguals to express themselves and engage in rigorous mathematics. We highlight how translanguaging supports linguistic identities, creates inclusive environments, and enhances learning.

'Patterns in Mathematics Classroom Interaction' Jenni Ingram

Patterns in Mathematics Classroom InteractionJenni Ingram (Oxford University Press, 2021)

A Study on the Path of Improving the Quality of Mathematics Classroom Teaching in Vocational Universities

This study aims to explore the path of improving the quality of mathematics education in vocational colleges in order to meet the growing demand for high-quality applied talents in society and industry. It analyses the need to improve the quality of mathematics education and points out that mathematics education should not only focus on imparting theoretical knowledge, but also enhance students' practical application skills. To this end, six main paths were proposed, including clear career-oriented teaching objectives, innovative practice-oriented teaching models, flexible adaptation of course content, use of modern educational technology, diversified evaluation mechanisms and teacher training. Finally, it is recommended that vocational universities strengthen teacher training, increase investment in teaching resources, and deepen cooperation between schools and enterprises during the reform process, so as to ensure that mathematics education keeps pace with the needs of the economy, thereby cultivating applied talents with both a solid mathematical foundation and good professional qualities.

Science and Mathematics Teachers’ Integration of TPACK in STEM Subjects in Qatar: A Structural Equation Modeling Study

This study aimed to explore how secondary school science and mathematics teachers in Qatar integrate Technological Pedagogical Content Knowledge (TPACK) into their teaching practices. The study examined the relationships between the subcomponents of TPACK using structural equation modeling (SEM), complemented by an analysis of additional categorical variables. A total of 245 science and mathematics teachers from Qatar participated in the research. The model’s findings showed that the internal components—technological knowledge, pedagogical knowledge, and content knowledge—had a significant and positive direct effect on the external factors: technological pedagogical knowledge, technological content knowledge, and pedagogical content knowledge. However, these internal components did not directly impact TPACK itself. Together, these variables accounted for 77% of the variance in TPACK. Among the findings, Technological Content Knowledge (TCK) emerged as one of the most influential variables affecting TPACK, emphasizing its importance in teachers’ TPACK integration. On the other hand, it was found that Pedagogical Content Knowledge (PCK) did not have a direct and significant effect on TPACK. Categorical variables like certificates and postgraduate education significantly impact TPACK and its subcomponents, while gender, field of study, and teaching experience do not. This finding underscores the importance of structured training and postgraduate education in enhancing TPACK skills for science and mathematics teachers. Participation in technology-based certification programs and postgraduate studies in STEM is crucial for their TPACK development in teaching STEM subjects. Future studies could explore the long-term impact of structured, technology-based training programs on enhancing STEM teachers’ TPACK development and assess how this improvement influences student learning outcomes in science and mathematics classrooms. This would provide deeper insights into the effectiveness of such programs and their potential to transform teaching practices and student achievement in STEM education.

An Analysis of Questioning Strategies in Secondary Mathematics Classroom

An Analysis of Questioning Strategies in Secondary Mathematics Classroom

Teacher: Where are You? About a Scenario for Permanent Teacher Training in Which the Teaching of Geometry is Invited to Think Professionally

In this article we share the story of a proposal for permanent training for mathematics teachers who are in charge of the training of students between 12 and 18 years old. We present a task and the fundamentals that lead us to develop it in this training scenario, for the collective construction of specialized knowledge of those who teach topics related to metric geometry and its relationship with optical illusions. We comment on the planning of the scenario and the results achieved from the perspective of the Mathematics Teacher's Specialized Knowledge Model (MTSK Model), which we relate to studies on the use of technologies in mathematics classrooms. We conclude with an analysis of the strengths and weaknesses, opportunities and threats that may arise in scenarios such as the one described for the permanent training of teachers considered teaching professionals.

Teacher support of collective argumentation in mathematics classrooms: insights from an afterschool program

Teacher support of collective argumentation in mathematics classrooms: insights from an afterschool program

Investigating the Effects of Active Learning and Problem-based Learning Strategies on Students’ Poor Reasoning Skills in Understanding Mathematics Concepts across Four Different Schools’ Mathematics Classrooms in Kingston & St. Andrew, Jamaica

Investigating the Effects of Active Learning and Problem-based Learning Strategies on Students’ Poor Reasoning Skills in Understanding Mathematics Concepts across Four Different Schools’ Mathematics Classrooms in Kingston & St. Andrew, Jamaica

Centering students’ thinking with the rights of the learner to counter deficit narratives in mathematics

ABSTRACT This article explores the implementation of Olga Torres’s Rights of the Learner (Torres’s RotL) framework in a 100-level undergraduate mathematics course, particularly focusing on assessment practices. Torres’s RotL framework offers a means to center students’ voices, mathematical thinking, and humanity in the classroom. The article delves into the five rights outlined by Torres — the right (1) to be confused, (2) claim a mistake, (3) speak, listen and be heard, (4) write, do, and represent what makes sense to you, and (5) the right to feel safe and respected — and discusses their implications for assessment in the mathematics classroom. Drawing from sociopolitical perspectives in mathematics education, the article emphasizes the importance of rehumanizing the classroom environment and addressing power dynamics and identity issues. Through reflection and alignment with Torres’s RotL, various assessment practices are shared related to small group and individual classwork, whole class discussions, weekly homework, asynchronous choice activities, and exams, highlighting how each can honor students’ rights while fostering a supportive, inclusive learning environment.

The development of pre-service teachers’ competence to teach mental calculation strategies

Background: There is a concern in South Africa that pre-service teachers do not have the required knowledge to teach mathematics in primary school and to develop learners’ number sense. In this study, pre-service teachers taught the mental strategy of bridging through ten through a structured teaching sequence from the Mental Starters Assessment Project (MSAP) materials as a work-integrated learning opportunity.Aim: We ask the question: How do the MSAP materials support pre-service teachers in competently teaching mental mathematics?Setting: Thirty-eight Bachelor of Education (Foundation Phase) third-year preservice teachers from an Eastern Cape university participated in this study.Methods: Participants taught the strategy during their Teaching Practice, quantitatively analysed the results of their classes and reflected on the experience in a questionnaire and focus group interviews.Results: Results indicate that the teachers were relatively successful in their teaching of the strategy; however, all indicated that they taught the sequence for a more extended period than recommended. Qualitative responses provide evidence of the teachers’ development in their knowledge of learners and their characteristics, general pedagogical knowledge, pedagogical content knowledge and knowledge of educational contexts.Conclusion: This study offers evidence of the professional learning of pre-service teachers that resulted from taking an integrated approach to facilitating a mathematics teaching methodology course through requiring a work-integrated learning component.Contribution: We argue that such an approach is necessary for pre-service teachers to be adequately prepared for the challenges of teaching mathematics in the South African classroom.

Unplugged activities in the elementary school mathematics classroom: The effects on students’ computational thinking and mathematical creativity

The rapid development of artificial intelligence technology has led to the proliferation of computational thinking (CT) education. However, research on unplugged activities’ influence in elementary math classrooms is limited, despite some exploring programming's cognitive benefits. This study presents both qualitative and quantitative analyzes stemming from a ten-week quasi-experimental research endeavor, specifically tailored for third-grade students. The research devised a series of unplugged activities, encompassing mathematical games, hands-on construction of mathematical logic boards, and calculating shopping discounts. The overarching objective was to investigate the impact of these unplugged activities on students’ mathematical creativity and CT. Students participating in a mathematics curriculum based on unplugged activities (N = 47) were compared with students participating in a traditional lecture-based mathematics curriculum (N = 46). The results indicated that unplugged activities exhibited significant advantages in fostering students’ CT and mathematical creativity across three dimensions, namely, problem-posing creativity (t = 5.830, p < 0.01), problem-solving creativity (t = 6.633, p < 0.01), and creative self-efficacy (t = 7.554, p < 0.01). Furthermore, the study revealed a relationship between students’ mathematical creativity as a predictor of CT. The results of the quantitative analysis were supported by the teacher's and students’ interview data, and the students felt excited and interested in the unplugged activities, whereas some students using the lecture-based method reported boredom and lack of interactivity. This research offered valuable insights for mathematics and CT education practice, underscoring unplugged activity as an innovative instructional approach that brings forth new possibilities for traditional mathematics teaching, with potential applications in the K-12 curriculum.

Mathematical discussion in classrooms as a technologically-supported activity fostering participation and inclusion

AbstractWhole-class mathematical discussion in a problem-solving activity is recognized as a powerful pedagogical activity but also a challenge for teachers who must consider several difficulties that learners might face, particularly in terms of an overload of Working Memory and Executive Functions. This study investigates how the use of a digital platform (Padlet) can support participatory and inclusive mathematical classroom discussion. We proposed a teaching experiment based on graphical tasks anticipating integral calculus to grade 13 students, and we examined how the use of the digital platform plays a role in the construction and interpretation of new mathematical objects emerging from the activity. The use of Instrumental Genesis and Double Instrumental Genesis frameworks allowed us to make the affordances of the tool emerge. As a result, we got evidence of how mathematical discussion may develop as a network of interactions, feedback, and connection of input and discuss examples of how active participation and inclusion are enhanced by the tool affordances. Indeed, the digital platform allowed easy interaction, with many ways to represent and express the ongoing evolution of personal and shared meanings and the possibility to manage the time of the activity. This fostered students’ participation and students which did not participate in previous discussions were actively engaged in it.

Exploring mathematical wellbeing across cultures: insights from diverse students

AbstractAcross many countries, including New Zealand, diverse groups including indigenous, migrant, and marginalised communities, are under-represented in mathematics, as evidenced by achievement disparities and disengagement from higher-level mathematics. Both research and policy have focused on developing equitable education outcomes for all students. A key aspect of this is wellbeing, including within mathematics classrooms, which includes identifying classroom environments that enable wellbeing. This study examines mathematical wellbeing (MWB) across different ethnicities and genders, with a case study focus on students from Pacific heritages. Analysing qualitative responses from over 12,000 diverse students revealed that positive relationships in the mathematics classroom were most commonly associated with students’ MWB. Accomplishment and cognitive factors, including mathematical accuracy, learning new things, and understanding, were also identified as important. Minor gender differences emerged, with female students emphasising mathematical understanding, accuracy, and relationships more than male students. The Pacific student case study highlighted the importance of both cognitive aspects (learning new things and understanding) and relationships (peer and teacher support), uncovering an alignment between cultural values and MWB. This study empirically confirms seven universal values supporting student MWB, previously identified in Australian and Chinese contexts, suggesting that teachers internationally may align pedagogical practices with these values to support most students’ MWB. However, the instrumental values serving these universal values appear culturally unique. This research contributes novel insights to the field by examining wellbeing with a subject-specific focus through student-generated responses, offering implications for developing more equitable and culturally inclusive mathematics classrooms.

Responding to negative emotion in a pre-service mathematics classroom

AbstractEmotions associated with prior mathematics learning experiences endure for some pre-service teachers, leaching into their own teaching of mathematics. Taking a sociology of emotions framing, the naturalistic study used event-oriented social inquiry and employed multiple methods (classroom transcripts, interviews, email conversations and reflective notes). In the event selected for this paper, we identified the importance of teacher educators intentionally attending to emotions in pre-service mathematics classes to address a dominant cognitive emphasis in learning to teach mathematics. We found that collective empathy was central to an emotional climate in which responses to individual and collective emotions were considered. We argue that collectively creating an emotionally safe environment in pre-service teacher education can help disrupt cycles of negative emotion associated with mathematics.

Multimodal Resources and Approaches for Teaching Young Adolescents: A Review of the Literature

With an increased number of multimodal texts being read, viewed, or designed by young adolescents ages 10–15 years, classroom instruction requires a focus on current research related to multimodal pedagogy. This integrative literature review sought to determine how instruction based on multimodality has been implemented in middle school classrooms. Educational databases were searched to locate empirical quantitative and qualitative studies describing instruction focusing on reading, viewing, or designing multimodal texts. The authors reviewed 37 research studies published between 2013 and 2023 to update the MLER Research Agenda. An analysis of the studies revealed three themes related to multimodal pedagogy: promoting language and literacy development; enhancing content learning; and providing opportunities for empowerment, personal expression, and identity development. Three gaps in the literature were also noted: no studies were conducted in mathematics classrooms, few studies examined multimodal pedagogy and students with learning or language differences, and few studies investigated the impact of multimodal pedagogy on students’ learning. Based on our findings, we conclude with a series of questions for a research agenda.

Ground rules for talk – the use of conversation rules to increase productivity in mathematical conversations in the early years

ABSTRACT In recent years, social aspects of teaching and learning have gained increased recognition, prompting researchers to focus on conversations and language in mathematics classrooms. While prior studies have highlighted the importance of conversations in primary school teaching, a gap remains in understanding how they influence mathematics teaching and learning, especially among younger children (Muhonen et al. 2016; Patterson 2018). To address this gap, this study explores the implementation of ground rules for talk in two first-grade classrooms in Norway (ages 5–6 years). This educational design research study investigated the impact of conversation rules on enhancing mathematical reasoning and promoting productive communication in primary school. Findings indicate that implementing ground rules for talk can foster productivity by encouraging pupils to inquire about others’ reasoning and share their perspectives to foster a respectful discourse. However, it also emphasises the importance of teachers being mindful of their language to foster reasoning effectively.

Does the use of differentiated instruction through project-based learning in mathematics classroom settings facilitate the students’ collaborative skills?

This research aims to describe differentiated instruction through project-based learning on students' collaborative skills in solid geometry. This study is a case study type of research. Data collection techniques were carried out by observing and interviewing 32 students. The result of this research is that differentiated instruction begins with an assessment of student readiness and an assessment of student interest. The learning process continues with implementing three essential aspects of differentiated instruction: content, process, and product differentiation. Process differentiation begins with the implementation of project-based learning steps. In this case, differentiated teaching and project-based learning complement each other. The results of the collaborative skills show that the students in the forming category performed optimally. Pupils learn in groups voluntarily; pupils do not leave their groups, and they exchange ideas when completing their projects. However, in the other categories, i.e., students' functioning, formulating, and fermenting, they do not show maximum results.

The rights of undergraduate queer and trans* students of color as STEM majors

ABSTRACT STEM is an exclusionary space for queer and trans* students of color (QTSOCs). A critical site of justice-oriented transformation to enhance support for QTSOCs is mathematics education, which has significant impacts on access to STEM majors and positive identities in the sciences. This article proposes a set of rights for QTSOCs as STEM learners to guide pedagogy that affirms intersectionality of their experiences in and beyond mathematics classrooms. QTSOCs in STEM have the rights to: (i) feel confused and receive support; (ii) take risks in participation and identity expression; and (iii) have affirming representation of identity in knowledge production. To illustrate how these rights are denied and embraced through STEM pedagogy, I present 2 narrative cases from my research study about QTSOCs’ intersectionality of STEM experiences where mathematics played a central role. I conclude with implications for practice to cultivate rehumanizing STEM educational opportunities that QTSOCs deserve.