Mathematics Classroom Research Articles

Mathematics teachers and learners as collective agents of change

In this article, we report on findings from the Primary Maths and Social Justice research project, a recent collaboration between the three authors and six teacher researchers from two culturally diverse primary schools in London, UK. The project aimed to develop strategies for addressing issues of social justice in the mathematics classroom, and operationalising the recently developed theoretical concept of socio-mathematical agency, defined as learners’ capacity to apply mathematics in arguing collectively for social change. The teacher researchers’ experiences, as captured through audio recordings of research team meetings and interviews, form the basis of our data analysis. Our findings highlight the processes that enabled teachers to reflect critically on existing practice, prompting them to adopt more collaborative, discursive and inclusive problem-solving approaches that resulted in significantly higher levels of student engagement in mathematical activities. The teacher researchers found that cross-curricular projects provided more opportunities to apply mathematical knowledge in tackling social justice issues than the prescriptive and content-focused mastery-style mathematics schemes of work in place. They reported how students embraced opportunities to use mathematics in more meaningful contexts and in presenting arguments for change. We argue that a focus on developing socio-mathematical agency has the potential to enhance the role of teachers and learners as agents of change, an important element that is often underdeveloped in culturally responsive teaching.

Manipulatives in a Mathematics Classroom: The Case of Frankards

There are variety of ways on how to teach mathematics effectively. One of these effective strategies is the use of manipulatives in discussing abstract concepts of mathematics. In this short report, a discussion on the use of a manipulative in a mathematics classroom shall be presented and discussed through illustrative examples. Additionally, feedback from teachers and students about their perceptions and experiences with the manipulatives will also be presented. In general, this short report aims to provide a hands-on experience of teachers and students with manipulatives and how to use it effectively.

Considering Opportunities for Mathematical Magic

Mathematical magic, or experiences of beauty and creativity for K-12 mathematics students, can contribute to deepened content understanding. However, creating opportunities for mathematical magic. in mathematics classrooms has been a challenge for classroom practitioners. To support development of these experiences in classrooms, we deployed a bi-directional support program between a college-level mathematician and an early-career secondary teacher. Based on data collected from this project, we have identified four principles that will promote mathematical magic. We conclude that mathematicians and early career teachers can work together to a) leverage understandings of the nature of mathematics, b) apply meta-mathematical reasoning, c) share knowledge of content and students across contexts, and d) recognize students’ mathematical development to design learning experiences for mathematical magic.

Why ask why? An analysis of teachers’ why-questions in elementary and middle grade mathematics classrooms

Why ask why? An analysis of teachers’ why-questions in elementary and middle grade mathematics classrooms

Flipped Classroom Approach and Acquisition of Problem Solving Skills in Mathematics in Secondary Schools in Turkana County

In a flipped classroom, learners study structured mathematics content prior to the lesson via watching relevant videos outside the lesson. This study initiated the use of flipped classroom approach in mathematics classrooms in order to strengthen learners’ problem- solving skills and impact performance. Reviewed literature shows a positive correlation between using flipped classroom approach and problem solving. The study design is quasi-experimental. One group of participants was instructed via flipped classroom approach and the other conventional methods. A comparison of problem-solving ability between the groups was made. The form two students and their mathematics teachers were the target population. Data was collected by means of an achievement test and means calculated per group. The inferential statistic, t-test was used to determine if the difference in means between the experimental and control group in the achievement test was significant. The study found that where flipped classroom approach is used, learners performed better in mathematics problem-solving than their counterparts instructed via conventional methods.

Developing A Differentiated Learning Model Based on Artificial Intelligence : Implementation in The Mathematics Classroom

This study aims to produce a model that can meet the needs of Differentiated Learning based on AI. This method used research and development (R&D) with the Generic Desain Research Model (GDRM). The subject of this study was mathematics education experts and mathematics learning model experts. Instruments used in this study include quality validity assessment and feasibility assessment analysis. The data analysis techniques used were quantitative methods with learning model validity assessment criteria that use A Linkert Scale of 1-4. The test results of the AI-based Mathematics learning model show that (1) the Content Validity test resulted in an average of 3.47 which means the model is very valid, and (2) The average feasibility test is 3.43, which means it is also very valid. The results showed that the AI-based Mathematics learning model can be implemented in differentiated mathematics classes and train students to learn independently, think critically, provide solutions to problems, and have the courage to convey solutions.

What Mathematics Teachers’ Perceptions of The Integration of Educational Drama in Mathematics Instruction: A Mixed-Methods Study

This research aimed to explore mathematics teachers' perspectives on the integration of educational drama in mathematics instruction, specifically focusing on mathematical knowledge, classroom discourse and affective aspects. Using a mixed-methods approach and a sequential explanatory design, the study first employed a quantitative phase, applying a scale to gauge teachers’ views on incorporating educational drama into mathematics instruction. The questionnaire covered three key dimensions: the advancement of mathematical knowledge, facilitation of classroom discourse, and emotional elements. The framework was developed based on established theoretical models. Following this, interview protocols were designed, based on the quantitative outcomes, to explore the insights provided in greater depth. The results indicated a predominantly positive reception among mathematics educators for the use of drama in mathematics education, with consistent agreement observed across all aspects of the scale. The mean scores for the development of mathematical knowledge, classroom dialogue and emotional dimensions were notably high, reflecting substantial alignment among the participants. Qualitative analysis of the teacher interviews highlighted the beneficial aspects of employing drama in mathematics education. The teachers noted the role of drama in reinforcing concepts, enhancing specific mathematical skills and positively affecting student engagement. However, concerns were raised regarding the potential for students' focus to be diverted from core mathematical content. In terms of classroom discourse and emotional development, drama was acknowledged for its role in fostering interactive exchanges, refining students’ speaking abilities, and nurturing self-confidence and motivation. Nonetheless, there were caveats concerning the suitability of drama for all student cohorts, pointing to the need for tailored approaches.

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.

Examining the Mediating Role of Students’ Perception of Mathematics in the Relationship between Teacher Positioning and Mathematics Identity Among Senior High School Students

Mathematics learning involves not only acquiring mathematical concepts and skills but also developing an identity as a member of the mathematics classroom community. This study examined the relationship between teacher positioning and student mathematics identity and the mediating effect of students’ perceptions of mathematics. A survey was conducted among 508 senior high school students, and the research instrument was pilot-tested and validated on 340 students and 238 teachers. Structural equation modeling and mediation analysis were used to analyze the data. The findings revealed that teacher positioning had a direct impact on students’ mathematics identity even when students’ perception of mathematics was considered a mediator variable. Mediation analysis showed that students’ perception of mathematics partially mediated the relationship between teacher positioning and students’ mathematics identity, confirming that teacher positioning and students’ perceptions of mathematics are crucial components in the construction of students’ mathematics identity. This research demonstrates the role of teacher positioning and students’ perceptions of mathematics and highlights factors that contribute to the development of mathematics identity and their interactions with teacher positioning and students’ mathematics perception. Further research should investigate other factors that contribute to mathematics identity and their impact on student learning outcomes. Keywords: experience, identity construction, math teaching, position and role

Learning from errors in mathematics classrooms: Development over 2 years in dependence of perceived error climate.

Errors can provide informative feedback and exhibit a high potential for learning gains. Affective-motivational and action-related reactions to errors are two forms of error adaptivity that have been shown to enhance learning outcomes from errors. However, little is known regarding the development and contextual conditions of students' error reactions. A theoretically plausible facilitator to this end is the perceived error climate in the classroom. We investigated how students' dealing with errors develops over time and which role the classroom context in general, and the perceived error climate in particular, has for this development. A total of 1641 students participated in 69 mathematics classrooms in academic secondary schools. Perceived error climate alongside students' self-reported individual reactions to errors were assessed in a 2-year longitudinal study with five measurement points over the fifth and sixth grade. Growth-curve modelling indicated an, on average, negative development of students' individual reactions to errors. This development varied substantially between classrooms and systematically depended on perceived error climate. A more positive error climate was associated with a less negative development of error adaptivity. Taken together, our findings imply a strong need and considerable room for the teachers' support in developing and maintaining adaptive reactions to errors. They also allow for the conclusion that teachers can succeed here by means of realizing a positive error climate in class.

A model for investigating and developing mathematics teachers' noticing of argumentation

Drawing upon the imperative to foster argumentation within the mathematics classroom, this paper integrates two key areas of mathematics education research – argumentation and teachers' noticing. It proposes a model of mathematics teachers' noticing of argumentation that was designed and piloted in professional development courses for teachers in Israel dedicated to argumentation in mathematics teaching. The paper discusses the theoretical and empirical construction of the model and presents empirical evidence regarding the model's potential to foster and analyze teachers' noticing of argumentation. The paper concludes with a discussion of the model's contributions and limitations.

Noticing struggle during collaborative problem-solving in the middle-school mathematics classroom

Noticing struggle during collaborative problem-solving in the middle-school mathematics classroom

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.

Effects of a self-regulated-based gamified interactive e-books on primary students' learning performance and affection in a flipped mathematics classroom

Effects of a self-regulated-based gamified interactive e-books on primary students' learning performance and affection in a flipped mathematics classroom

Discussion on the Skillful Use of Mind Maps in High School Mathematics Teaching

With the continuous development of China’s education, the social requirements for high school teaching are constantly improving. The teaching of high school mathematics is a key point in the high school curriculum, but also a major difficulty. Due to the strong logic and abstraction of the content of high school mathematics, some students find it very difficult to learn. In order to solve this problem, high school mathematics teachers can make use of mind maps to teach, so that students can exercise their thinking ability, and realize the improvement of comprehensive ability in mathematics. This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms, so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.

Examining the elements of culturally relevant pedagogy captured and missed in a measure of high-quality mathematics instruction

Mathematics instruction is not race or culture neutral. For students who have been historically marginalized in mathematics classrooms, high-quality mathematics instruction, instruction that helps students build conceptual understanding, on its own might not be enough to disrupt inequities. These students might also need instruction that is culturally relevant, with teachers who demonstrate cultural competence, build critical consciousness, and support student learning. Our goal in this study was to understand which components of culturally relevant pedagogy (CRP) are captured and which are missed in a typical U.S. framework of high-quality mathematics instruction. To find the overlaps and gaps, we analyzed the mathematics lessons of three elementary teachers through both the lens of CRP and the Mathematics-Scan, a mathematics observation tool. We found the strongest overlap between the two frameworks in the patterns of strengths and weaknesses in the teachers’ lessons. When the teachers were delivering high-quality instruction, they were also often supporting students’ learning or showing cultural competence. When the teachers were delivering lower quality instruction, they were also often missing opportunities to enact CRP. At the same time, key elements of CRP including linguistic support for students, high expectations, critical consciousness, and nuances within cultural competence, were missed by the high-quality instruction framework. High-quality instruction was the foundation for CRP in the teachers’ classrooms, but CRP was more than just high-quality instruction. We conclude with recommendations for increasing the alignment between the frameworks and implications for international educators also grappling with equity in their own frameworks of mathematics instruction.

The modality of mathematics lesson observations: comparing the results of live and video-based coding

ABSTRACT Classroom observations are an integral part of qualitative educational research. Traditionally, classroom observations have been done in-person, with one or more researchers being physically present in a classroom to observe and take field notes. With the proliferation of video technology, researchers are now able to conduct classroom observations at a distance using a variety of technological tools. When deciding on whether to conduct live or video observations, researchers must consider how the observation modality may influence the data. We address this consideration by independently conducting both live and video observations of the same mathematics classroom lessons to identify similarities and differences in the resultant coding between the two modalities. Our findings suggest there are some dimensions of mathematics classroom instruction unaffected by the live or video modality (e.g. nature of discourse, student contribution length) and others that are affected (e.g. lesson connections, mathematical development). Thus, when making decisions about observation modality, it is important to consider the focus of one’s inquiry in addition to other factors such as cost, human capacity, geographical location, and more.

Norwegian teachers’ perspectives on inclusive practices in the mathematics classroom

ABSTRACT In this paper, we explore Norwegian teachers’ perspectives on inclusive teaching practices in the mathematics classroom, defined as practices which maximise every pupil’s potential regardless of prior attainment. As previous research suggests, both mathematics teachers’ perspectives in general and the conceptualisation of inclusion, inclusive education, and inclusive practices are culturally situated, varying significantly across countries and educational systems. We draw on data from a large project in Norway focusing on the use of grouping by attainment and its relation to policy and pedagogical practices around inclusion in mathematics. Participants were 13 primary and lower-secondary mathematics teachers from six schools in the Oslo area. Analysis of semi-structured interviews focusing on strategies for inclusion of all pupils in mathematics classrooms reveals the cultural particularities of mathematics teachers’ perspectives on inclusive practices, highlighting the value of similar investigations in other cultural contexts.

The Role of Translanguaging in Teaching Mathematics at Adult Correctional Centre Classrooms in South Africa

This paper sought to explore the use of the translanguaging strategy as the means for decolonising and advancing the teaching of mathematics procedural fluency. From the pragmatic epistemological stance, the study collected both qualitative and quantitative data from the group of fifty purposively sampled adult offenders. The intervention study inferred data from pre-tests, post-tests, and semi-structured interviews. The data, which was analysed using SPSS and the thematic analysis approach, through the conceptual framework of teaching adult offenders mathematics procedural fluency through the isiZulu-English translanguaging strategy, indicate that the use of the translanguaging strategy yields satisfactory performance in adult offenders’ mathematics procedural fluency. The study further discovered that the translanguaging strategy leads to the decolonization of the mathematics curriculum and the development of isiZulu and English languages in correctional centre classrooms. The researcher recommends the use of the translanguaging strategy and fluidity in the use of any repertoires in the teaching of mathematics procedural fluency, conceptual understanding, and factual knowledge within the context of correctional centre classrooms. The researcher further concludes that translanguaging is applicable, and resourceful in all mathematics educational contexts, and it leads to the decolonization of the mathematics curriculum for both children and adults, in all contexts. The paper contributed to the scholarship by exploring the mathematics learning, teaching and assessment processes and the role of translanguaging thereof in correctional centre classrooms. Keywords: Translanguaging, Correctional Centre, Mathematics Classroom, Mathematics Procedural Fluency, Adult Offenders, Educationists

Ubuntulisation of mathematics classroom for the enhancement of learner’s interest and achievement

Background: One of the primary challenges confronting African mathematics educators and students is the wholesale adoption of external methods, approaches, and ideas in the teaching and learning of mathematics. In response to this challenge, the concept of ethnomathematics has emerged, although it remains largely unadopted across many African countries. Recently, Social Justice Mathematics has been developed, a concept closely aligned with the principles of Ubuntu, which emphasizes equality and justice in all aspects of human life. Aim: This paper aims to highlight the ubuntulisation of mathematics classrooms. Instead of fully adopting Social Justice Mathematics as a contemporary solution to enhance students' interest and achievement in mathematics, this paper proposes an Africanized approach by integrating Ubuntu as a foundational element of ethnomathematics. This approach is posited to achieve greater success among learners. Methods: The study involves a comprehensive review of existing literature on ethnomathematics, Social Justice Mathematics, the benefits of Social Justice Mathematics in learning, Ubuntu pedagogy, and the ubuntulisation of mathematics classrooms.Results: The paper presents relevant examples that emphasize the need for mathematics educators to incorporate African cultural contexts in the planning and teaching of mathematics.Conclusion: The study concludes by recommending the ubuntulisation of mathematics classrooms as an effective alternative to Social Justice Mathematics for enhancing students' interest and achievement in mathematics.