Developing interactive mathematical talk: investigating student perceptions and accounts of mathematical reasoning in a changing classroom context

Acknowledging the importance of mathematical reasoning in mathematics teaching, the present study analyzes middle school mathematics teachers’ understanding of reasoning. In line with the purpose, the study was performed using a phenomenological design, which is one of the qualitative research methods. The study was carried out with a total of 16 middle school mathematics teachers serving in different state schools in the 2016-2017 school year. The study employed an interview form consisting of four open-ended questions to determine the teachers’ theoretical and practical understanding of mathematical reasoning. Drawing on qualitative data, this study employed content analysis method for data analysis. As a result, it is understood that the middle school mathematics teachers do not have a comprehensive and adequate knowledge and view about mathematical reasoning when it is considered how they define, exemplify and support mathematical reasoning. Because it is appeared that mathematical reasoning means only making explanations, justifications and producing different solutions for a problem according to them. It is important that the teachers should broaden their view about mathematical reasoning to support their students’ reasoning better. Article visualizations:

The development of mathematical problem solving and logical-mathematical thinking is a core component of the basic education curriculum; however, traditional instructional approaches continue to show limitations in fostering deep and sustained learning in these competencies. In this context, the aim of this study was to analyze the impact of integrating active methodologies mediated by technological platforms on the development of mathematical problem solving and logical-mathematical thinking in basic education students. The study adopted a mixed-methods approach with a quasi-experimental design, including an experimental group and a control group. The sample consisted of 78 students aged between 9 and 11 years from a public educational institution. The pedagogical intervention lasted eight weeks and integrated problem-based learning strategies, gamified activities, and the use of interactive technological platforms, including mathematical visualization tools such as GeoGebra. Data were collected through standardized tests assessing mathematical problem solving and logical-mathematical reasoning, as well as classroom observations and semi-structured interviews. Quantitative data were analyzed using inferential statistical techniques, including ANCOVA, while qualitative data were examined through thematic analysis. The results revealed statistically significant improvements in mathematical problem solving and logical-mathematical thinking in the experimental group, with large effect sizes. A significant increase in academic motivation and engagement was also observed, along with positive associations between motivational variables and mathematical performance. In conclusion, the pedagogically intentional integration of active methodologies and technological platforms represents an effective approach to strengthening mathematics learning in basic education, provided that it is supported by sound instructional design and adequate teacher training.

The purpose of this research is to examine the mathematical reasoning competencies of mathematics teachers. As part of the research, mathematics teachers received in-service training in mathematical literacy. Following the training, classroom practices were conducted by these teachers using course modules designed in alignment with the training content. Due to the COVID-19 pandemic, the in-service training and training practices were conducted via online meeting platforms as distance education. In this research, conducted using the case study method, data were collected through open-ended reasoning tests and a mathematical reasoning basic concepts test. As a result of the research, it was found that the in-service teacher training and training practices delivered through distance education in the field of mathematical literacy had a positive impact on the mathematical reasoning competence of mathematics teachers. While most of the teachers showed a decrease in their scores on the reasoning test administered after in-service training, they achieved their highest score after training practices they implemented in their own classes. The mathematical reasoning basic concepts test conducted after the training practices indicated that the teachers’ perceptions of mathematical reasoning reached a high level.

This JiM project set out to research the current state of understanding of mathematical justification by both Singapore secondary school students and Mathematics teachers across the different content strands in the Singapore secondary Mathematics curriculum. This timely and relevant project was started to complement the current goal of the Ministry of Education (MOE) on fostering reasoning in the learning of Mathematics in schools. While MOE focuses on the reasoning process, our study examined the outcomes of this reasoning process. For many years, mathematical reasoning and communication have been two key process skills in the Singapore Mathematics Framework under the Processes component. Thus, mathematical reasoning and justification are essential components of any mathematical activity that students should be familiar with. Yet from our personal communications with secondary school mathematics teachers between 2013 and 2016 and evidence from GCE O and N Level examiners' reports, we obtained the impression that many students, as well as mathematics teachers, struggled to navigate mathematical justification successfully. Mathematics teachers seemed to point students' difficulties in justification to several student-related factors. Other than those factors, we, however, speculated that there might be other potential obstacles, which contribute to students' poor performance in justification tasks. Therefore, this JiM project was undertaken to explore the quality of written justifications constructed by secondary school students and their mathematics teachers, with the aim of proposing a professional development (PD) programme that would allow the teachers to better engage their students in mathematical reasoning and justification more effectively, thereby improving the quality of written justifications provided by their students.

Using classroom observation and video recording methods, we performed a comparative study on the forms and content of dialogues in the classrooms between expert and novice teachers. Of the 55 lessons surveyed, it was found that expert teachers tend to use analytical and comparative questions more frequently to detect students’ mathematical reasoning. Students and teachers work together to determine the answer to a question and the dialogue in the classroom takes place in a way that students present an answer, the teacher and the other students question the answer, and then the students explain the answer. On the other hand, a novice teacher often tends to give students hints, or utilize simple questions to jog the memory. The novice teacher recognizes students’ logic but does not incorporate them into his/her teaching. In this case, the teacher becomes the sole judge for the appropriateness of the answers and the typical dialogue in the classroom occurs in a way that the teacher asks a question, students answer, and the teacher comments.

Hybrid approaches in game-based mathematical literacy environments are increasingly recognized for providing varied, interactive, and adaptive learning experiences, yet games used in schools remain predominantly either digital or analog and are rarely supported by systematic teacher professional development. Consequently, the potential of culturally contextualized games to foster mathematical literacy and higher-order thinking has not been fully realized. This study develops and evaluates a hybrid teacher professional development environment designed to support teachers in facilitating a classroom-based role-playing game (RPG) contextualized in Cirebon’s religious tourism. Drawing on a design research approach adapted from Van den Akker and Guskey’s five-level evaluation framework, the study involved five mathematics teachers and their seventh-grade students. Data were collected through classroom observations, teacher reflections, questionnaires, interviews, and post-learning assessments. The findings indicate that the hybrid environment was valid and practical, with teachers reporting clearer guidance, feasible classroom integration, and greater confidence in facilitating RPG-based lessons. Evidence across Guskey’s levels suggests potential positive effects on teacher learning, instructional practice, and student engagement, while also indicating that students’ mathematical reasoning still requires further support. This study proposes a novel model that links hybrid professional development, cultural context, and game-based learning to strengthen teacher facilitation of mathematical literacy. Limitations include the small number of participating schools, the focus on Grade 7, and the short implementation duration, indicating the need for future research on longer-term effects, teacher involvement in RPG co-design, extension to other grade levels, and alternative assessment approaches.

Different teaching practices, such as autonomy support and structure, provide students with a positive learning context supporting their engagement, which can operate through their underlying motivation, including sense of competence and task value. This study aims at investigating the best configuration (unique or synergistic) between autonomy support and structure to support student behavioural engagement, including compliance, participation, and misbehaviour, and reading achievement. A second objective is to assess students' sense of competence and task value as mediators linking teaching practices to student engagement and achievement. The samples included 1,666 7th-grade students and their 85 teachers. Students answered questionnaires and tests at the beginning and the end of the school year. Students' perceptions of the use of autonomy support and structure by their Language Arts teacher were aggregated at the classroom level. Students rated their sense of competence and task value in Language Arts class. Twice during the school year, they also reported three facets of their behavioural engagement (compliance, participation, and misbehaviour) and answered a reading comprehension test. Multilevel path analyses using Mplus7 allowed accounting for the nested structure of data. Student sense of competence mediated the association of student classroom-aggregated perceptions of teacher structure and autonomy support with self-reported participation in the classroom. Task value mediated the association between both teaching practices and student misbehaviour and compliance, as reported by students. Sense of competence was directly associated with later reading achievement, but the indirect effect of teaching practices was not significant. We foundnosignificant interaction (synergistic effect) between teacher autonomy support and structure. Student classroom-aggregated perception of teacher autonomy support and structure is important to nurture behavioural engagement. However, we found no extra benefit of combining these two dimensions of teaching practices. The processes linking these teaching practices to the three facets of student behavioural engagement were different. As such, to support the various aspects of student engagement, the actions of teachers, as reported by their students, should tap into the mechanisms that are most strongly related to each type of behaviour.

This chapter looks at symbolizing and mathematical learning from a social constructivist perspective that is motivated by an interest in instructional design. The central theme is that of a concem for the way students actually use tools and symbols. Point of departure are analyses treat people’s activity with symbols as an integral aspect of their mathematical reasoning rather than as external aids to it. As a consequence, the process of learning to use symbols in general, and conventional mathematical symbols in particular, is cast in terms of participation. Symbol use is then seen not so much as something to be mastered, but as a constituent part of the mathematical practices in which students come to participate. This view corresponds with the author’s instructional design perspective, according to which it is essential to account for the mathematical learning not merely of individual students but of the classroom community taken as a unit of analysis in its own right. To account for this collective learning, the theoretical construct of a classroom mathematical practice is introduced, which involves taken-as-shared ways of symbolizing negotiated by the teacher and students.

This study aimed to investigate the effect of a training program based on the trends in international mathematics and science study (TIMSS) on developing the habits of mind and mathematical reasoning skills among pre-service math teachers in Oman. The study sample consisted of 24 female pre-service math teachers divided into two equal groups: experimental and control. The study data was collected by sued the mathematical reasoning test and questionnaire that measured the level of habits of mind after appropriate validity and reliability. The study results showed statistically significant differences between the two study groups in favor of the experimental group in the mathematical reasoning test and the habits of mind scale. The study recommended that the need for pre-service math teachers to use programs based on international studies such as TIMSS, PISA, PIRLS, and TAILS; this was done to prove their effectiveness in developing the levels of habits of mind and mathematical reasoning skills by subjecting them to training programs, courses, and workshops with the aim of training teachers to implement the training programs effectively.

The first year of primary school aims to be closely connected with early childhood education, yet this is often invisible in the curriculum of specific subjects. This paper sets out an approach that uses mathematical practices as a curriculum tool that reconceptualises school mathematics. Using the early childhood mathematics framework of Te Kākano, the strands of mathematical practices are important descriptors of mathematical activity for children. We describe examples of mathematical learning from both early childhood and the first year of school, and make a case for using mathematical practices as a conceptual tool for designing a mathematics curriculum in the first years of school.

ABSTRACTThis paper discusses the development and results of a new tool used for measuring shifts in students' perceptions of earth and ocean sciences called the Student Perceptions about Earth Sciences Survey (SPESS). The survey measures where students lie on the novice–expert continuum, and how their perceptions change after taking one or more earth and ocean science course(s). The survey is composed of 29 statements that have been validated with expert responses and student interviews. Factor analysis was used to group statements into seven categories, which provide instructors with valuable information to guide pedagogical change in their classes. Overall student perceptions in earth and ocean sciences show little change over the course of the term, in contrast to novice shifts in perceptions seen in other science disciplines. Students in earth and ocean sciences also do not display any gender differences, unlike those seen in these other disciplines. However, differences are seen between face-to-face and distance education versions of a course, between earth and ocean science majors and nonmajors, and between a community college and a large research institution. The former of each pair are more expert-like.

The state of modern mathematical practice called for a modern philosopher of mathematics to answer two interrelated questions. Given that mathematical ontology includes quantifiable empirical objects, how to explain the paradigmatic features of pure mathematical reasoning: universality, certainty, necessity. And, without giving up the special status of pure mathematical reasoning, how to explain the ability of pure mathematics to come into contact with and describe the empirically accessible natural world. The first question comes to a demand for apriority: a viable philosophical account of early modern mathematics must explain the apriority of mathematical reasoning. The second question comes to a demand for applicability: a viable philosophical account of early modern mathematics must explain the applicability of mathematical reasoning. This article begins by providing a brief account of a relevant aspect of early modern mathematical practice, in order to situate philosophers in their historical and mathematical context.

This study compares formative assessment practices in primary mathematics classrooms in Guangzhou, Hong Kong and Melbourne. Nine schools (three in each research location) were studied to examine the similarities in and differences between formative assessment practices for mathematics, and to identity underlying factors that may account for these similarities and differences. Videotaped classroom observations and face-to-face semi-structured teacher interview were the main data collection methods employed.
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\nThe study identifies several similarities and differences in formative assessment practices by reviewing a total of 1140minutes of videotaped classroom observations (380 minutes from each city). Four similarities were noted: (a)a common structure of formative assessment practice; (b) providing feedback on what students had done well and what they needed to improve; (c) encouraging students to engage actively in the feedback process; and, (d) infrequent use of practical assessments. In addition, six differences were found: (a) interpreting, judging and suggesting on students’ work; (b) forms of assessment (including self and peer assessment); (c) assessment items; (d) effective feedback;(e) specific format for presenting mathematics; and, (f) ways of receiving feedback.
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\nThree key factors have been suggested to account for the similarities in and differences between formative assessment practices in primary mathematics classrooms in the three research locations: (a) cultural influences on mathematics learning and examinations; (b) assessment reform initiatives; and, (c) teachers’ conceptions about formative assessment. This study contributes to the understanding of formative assessment practices in the classrooms by proposing a theoretical framework for comparing formative assessment practices that takes into account cultural, social, school and classroom factors. Potential directions for future research are suggested, including further comparisons of mathematics formative assessment practices at other schools in Guangzhou, Hong Kong and Melbourne, and in other countries with similar cultural backgrounds.

This exploratory study investigates the influence of teachers’ perception of students’ socio economic position (SEP) on the disciplinary practices they adopt in classrooms. Qualitative data were collected using classroom observations and interviews with students, their parents and teachers. Findings highlight differentiated disciplinary practices based on students perceived SEPs. Significant differences were evident in classroom observations and students’ description of their disciplinary experiences. Differences were also manifested in parents’ description of teachers’ interactions with both students and parents. Findings also indicate that teachers’ social class has no bearing on parents’ perceptions of teachers’ attitudes towards them. However, from the parents’ viewpoint, their SEP may explain teachers’ varied interactions towards parents and students from diverse backgrounds. Findings further indicate the implicit play of hierarchy and power within classroom settings was not lost on students who in turn engaged in the same manner during peer interactions.

This study aims to compare the effectiveness of the Deep Learning and Differentiated Instruction models in improving junior high school students’ mathematical problem-solving and reasoning abilities. The background of this research stems from the low level of mathematical literacy among Indonesian students, which demands innovative and reflective learning approaches. A quasi-experimental method was used with a Nonequivalent Control Group Design. The sample consisted of two eighth-grade classes at SMP Negeri Satu Atap 01 Ciseeng, each receiving different instructional treatments: one class was taught using the Deep Learning approach, and the other using the Differentiated Instruction approach. The instruments employed included mathematical problem-solving tests, observation sheets, and student perception questionnaires. The data analysis results indicated that the class taught with the Deep Learning model experienced a more significant improvement in mathematical reasoning ability compared to the class using Differentiated Instruction. These findings suggest that Deep Learning-based instruction is more effective in promoting students’ higher-order thinking skills. It encourages deeper engagement with mathematical concepts, fosters critical and analytical thinking, and allows students to construct knowledge through meaningful learning experiences. However, Differentiated Instruction remains relevant in providing learning comfort and addressing diverse student needs, making it beneficial in inclusive classroom settings. The theoretical and practical implications of this research highlight the importance of integrating both depth of thinking (Deep Learning) and flexibility in learning (Differentiation) within mathematics instruction. Such integration could offer a balanced learning environment that supports both cognitive development and emotional engagement, leading to more effective and equitable mathematics education. In conclusion, this study recommends educators and curriculum developers to consider incorporating Deep Learning strategies to enhance students’ mathematical reasoning while maintaining the adaptive and student-centered principles of Differentiated Instruction. Future research could explore hybrid learning models that combine the strengths of both approaches to maximize student outcomes in mathematics learning.