Mathematical Discourse Research Articles

Supporting High-Level Tasks and Talk Through Lesson Study

A cross-grade level team participates in lesson study to develop skills in engaging students in deep mathematical thinking and high-level mathematical discourse.

The We All Speak Math Campaign for Meaningful Discourse

Improving mathematical discourse in high school classrooms through a statewide campaign draws on the images of high-quality instruction promoted in Principles to Actions. The High School Visions Design Team of the North Carolina Collaborative for Mathematics Learning

Traveling waves reflecting various processes represented by reaction–diffusion equations

The aim of this paper is to discover analytically the interactional responses of populations in a dynamic region where the reaction–diffusion process with forcing effects takes place through traveling wave solutions. An expansion method is considered here to properly capture the responses for the first time. In order to profoundly analyze the physical and mathematical discussions, some illustrative behavioral results are exhibited for various values of physical parameters. Especially for the different values of diffusion coefficients in the model under consideration, their effects on the behavior of the solitary wave are discussed and observationally supported by considering various illustrations. It is also seen that the solutions representing the diffusion seen to be in the form of the behavior of hexagonal Turing patterns in different time periods. The application of this study in mathematical biology is to analyze the relationship between the population density of certain species in any local region and the specific population density with invasion characteristics. In addition, the formation of the extinction vortex of the invading population, depending on the characteristics of the solutions presented, is also descriptively discussed.

Comprehensive Review Discussion of Science Technology Engineering and Mathematics (STEM) Learners in Operations of Integers: An Action Research

Based on perceived general observation, most Senior High School students tend to have difficulties in performing the four basic operations to the set of numbers called “integers”. An integer is a whole number that can be positive, negative, or zero. This study chose Grade 11 Science Technology Engineering and Mathematics (STEM) students as the targeted respondents for this particular action research. It aims to aid STEM students in their struggles on performing operations of integers. The study will use Review Discussion as the intervention and aid for the problem. Results and Interpretation are obtained by using various appropriate statistical formulas like t-test and standard deviation. The researchers conducted this action research to verify if review discussion will have a positive effect and impact on enhancing the skills of Grade 11 STEM students in operations of integers.

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.

Explaining technical, social, and discursive participation in online mathematical discussions

Participating in online mathematical discussions is a beneficial strategy to improve online math learning. Research has examined online mathematical discussions from various aspects, focusing on the content discussed, student interaction, and the technical tools facilitating student participation, but few studies have investigated the interplay among these aspects. This study draws on Communicative Ecology Theory (CET, Foth & Hearn, 2007), which conceptualizes the sustainability of online communities as influenced by discursive, social, and technical factors, to explore how students’ discursive, social, and technical participation behaviors on an online mathematical discussion board are interacted. Leveraging a dataset including more than 90,000 students and two million online discussion interactions, this study indicated that students’ engagement with technical functions, especially a communication tool and a motivation system, within the discussion board significantly facilitated their social interactions and enhanced their demonstration of mathematical knowledge, mathematical literacy, and affective control in the discussions. These findings provide insights for educators and designers of educational applications to enhance student participation in online discussions thereby improving the effectiveness of these discussions in online learning.

Number Talks as Access to Teaching Practices: Pre-Service teachers’ Attention to Mathematical Teaching Practices While Reflecting on Number Talks Enacted in a Field Placement

ABSTRACT Number Talks are increasingly used in classrooms to support student’s number sense. While Matney et al. (2020) documented little empirical evidence about the effectiveness of Number Talks in improving student outcomes, we considered the potential benefits of Number Talks for teachers and their practices. We ask to which of NCTM’s Mathematical Teaching Practices do pre-service teachers attend while reflecting on Number Talks implemented in a field placement and what was the nature of their attention? Using a constructivist lens, we analyzed the reflections of ten pre-service elementary teachers on three Number Talks in a field placement. As they implemented Number Talks, the participants in this study constructed their own understanding of both the process and purpose of a Number Talk. By doing so, we found that not only was it possible for pre-service teachers to attend to each of the Mathematical Teaching Practices, but three practices were regularly attended to by participants: posing purposeful questions, facilitating mathematical discourse, and supporting productive struggle. Thus, Number Talks may serve pre-service teachers as important vehicles for developing these practices.

Engaging primary mathematics teachers in two private schools in South Sudan: A case study on student-centred teaching in problem-solving and mathematical discourse

The teaching and learning of mathematics in sub-Saharan African countries is dominated by teacher-centred pedagogies rather than student-centred ones. Observations of mathematics teachers at two private schools in South Sudan confirmed such practices. This inspired the researchers to design an intervention to help six primary mathematics teachers shift their practices through problem-solving and mathematical discourse. Design-based research methods were implemented, and data were gathered using observations supported by video and audio recordings and field notes. The participants were selected using convenience sampling, and the data were analysed using Stephan’s checklist of student-centred teaching as a framework. The findings revealed that initially, teachers were using tasks from textbooks, and the teachers themselves were engaged in solving the tasks while their students reproduced their actions. Additionally, all the teachers dominated classroom discussions. After the intervention, the teachers began to select tasks that could enhance learning through problem-solving and mathematical discourse among the students, shifting the teacher’s role to facilitation as the students engaged in solving the tasks on their own. However, the shift in practice was highly dependent on the intervention, as the teachers’ tasks were adopted from the workshop.Contribution: This study contributes to the literature on student-centred mathematics teaching in sub-Saharan Africa by providing insights into the factors that enable or hinder teachers’ adoption of student-centred approaches, and by suggesting ways to support teachers’ professional development and learning within their own contexts.

Exploring the mediating role of teacher expectation on whole class participation

Teacher expectation mediates the interaction between teacher and students, and teachers tend to differentiate their interaction with their students based on their expectation. In this study, I explore the mediator role of teacher expectation to the participation of ongoing mathematical discussion. Academic interaction between an 8th grade mathematics teacher, and her students ( n = 20) academic interactions were recorded ( n = 20) and analyzed by using EQUIP during two grading periods. Results of this study reveal that the majority of academic interaction happens between a teacher and a small subset (high expected) of students. High expected students had much more opportunities than all the other students to participate to the ongoing mathematical discussion.

Elementary students' argumentative and explanatory mathematical writing about fractions

AbstractMathematical writing (MW) is an important yet underutilized form of mathematics discourse. Given the lack of attention to MW, there are few resources to support the implementation and assessment of MW. This study responds to the lack of resources by describing a MW unit focused on fractions that was implemented during a summer school program to support rising fourth grade students with explanatory and argumentative writing. Findings from the study revealed that students used different forms of reasoning about fractions to compose their mathematical argument and explanation. We also identified five categories that captured how students communicated a mathematical argument and explanation: writing organization, precise mathematical vocabulary, mathematics content, mathematical representation, and characteristics specific to a mathematical argument/explanation. The five categories led to the development of an analytic rubric for argumentative and explanatory writing.

Fostering preservice teachers’ mathematical discourse through virtual simulation teaching

Simulation, a new tool in teacher education programmes, requires further evidence as to its effectiveness in supporting the development of preservice teachers’ (PSTs’) mathematical discourse. The study explores the discourse of a group of preservice teachers while teaching the concept of volume in a simulation setting. Specifically, PSTs’ verbal interactions with virtual students (i.e. avatars) are examined using utterances as the basic unit of analysis. By applying mathematics discourse frameworks, the PSTs’ discourse was categorised, identified as different types and analysed both quantitatively and qualitatively. The findings reveal the dynamics of PSTs’ discourse and highlight how simulations provide an authentic classroom-like environment, with the potential to elicit PSTs’ mathematical discourse, including preparation for unexpected situations and fostering inclusive pedagogy. This article makes a contribution to the current literature by exploring the effectiveness of simulation-based teacher education programmes in developing preservice teachers’ (PSTs’) mathematical discourse skills. Specifically, the discussion offers valuable insights into the potential of simulations as a platform for preparing PSTs to become confident and competent educators capable of fostering inclusive learning communities.

Identifying queer discourses and navigational strategies in mathematics for undergraduate STEM students

IntroductionWhile research has explored racialized and gendered discourses in mathematics, there is a gap in understanding the experiences of Queer students and the discourses related to sexual identity in mathematics. This study aims to identify the discourses about mathematics that Queer STEM students describe in relation to their Queer identity and how they navigate these discourses.MethodsUsing phenomenology, individual interviews were conducted with 17 Queer STEM students at four universities in the United States. The interviews explored their life histories, experiences in mathematics, and responses to vignettes depicting mathematical scenarios. Grounded theory was leveraged to analyze the interviews to build a framework for Queer discourses and navigational strategies.ResultsSeven Queer discourses in mathematics were identified with underlying notions of exclusion and irrelevancy. The most prevalent discourses cast Queer identity as being irrelevant (erasure), unseen (heteronormative), or discriminated against (marginalized) in mathematics. At the same time there were some beliefs that Queer identity acceptance was unknown (ambiguous) was treated equally (normalized) or was accepted and even valued in math. Key findings from the study help theory build an exclusion-irrelevancy space to network together mathematical discourses and highlight how Queer marginalization is acted upon based on notions of rightful presence and not mathematical success.DiscussionThis study highlights the need to recognize and address the marginalization of Queer students in mathematics. By understanding the discourses and navigational strategies employed by these students, educators can create more inclusive and equitable STEM environments. It is critical to recognize and build upon the unique strengths of Queer students in mathematics, rather than focusing only on the challenges they face.

Proving routines in a lecturer’s mathematical discourse for proof teaching: a case of analysis lecturing

This study focuses on the characterisation of proof teaching in university lectures on mathematical analysis using the commognitive framework. The case is set around a lecturer with experience in teaching this course and a good reputation among university students. Six lectures of the course were analysed using discourse and thematic analysis. The analysis resulted in a range of characteristics of the mathematical discourse for proof teaching of a lecturer. Then, by exploring the proving routines within the characteristics, we produced a typology of teaching characteristics in the lecturer’s discourse; that typology gave us insights into a pattern of proving specific to our case study. The exploration of the proving routines in the lecturer’s discourse offered an in-depth understanding of teaching proof beyond the macro-level descriptions of lectures in the extant literature. We conclude the study with implications for research and education.

Cultural Transitions in Mathematical Discourse: Unveiling Mathematical Writing Hurdles during the Rite of Passage

This qualitative case study delves into the intricate landscape of mathematical writing challenges faced by first-year university students undergoing the critical transition from school-level to university-level mathematical discourse. Conducted at a prominent South African university, the research, employing a purposive sampling technique, engaged thirty first-year mathematics students. Guided by the community of practice theory by Lave and Wenger, alongside van Gennep’s rite of passage analytical lens, the study sought answers to the question: What are the mathematical writing challenges encountered by first-year university students during their rite of passage period? Thematic analysis, informed by Adu's (2019) coding framework, was utilized to systematically examine common themes and patterns within the qualitative data. The findings illuminated key hurdles during this transitional phase, prominently including the inconsistency in working with mathematical notations, erroneous use of universal and existential quantifiers, and a notable confusion between the acts of illustrating and proving in mathematical contexts. In response to these challenges, the study advocates for the explicit incorporation of mathematical writing instruction to scaffold students during this rite of passage. Furthermore, it recommends a shift in the emphasis of first-year mathematics courses—suggesting a redirection from a content-centric approach to one that prioritizes the cultivation of students' new identities. This entails focused attention on teaching the customs, traditions, and adept ways of constructing and articulating mathematical proofs in the university context. The implications of this study extend beyond the immediate challenges identified, offering actionable recommendations to enhance the pedagogical strategies employed in the crucial transition period for first-year mathematics students.

Experts’ intuitive mathematical discourses about integration in complex analysis

Experts’ intuitive mathematical discourses about integration in complex analysis

When Learner-Centered Teaching and Learning Goes Online: Zooming into Linear Algebra Tutorials During the Pandemic

AbstractThe COVID-19 pandemic shifted higher education online, drawing attention to synchronous learning and instruction on digital communication platforms. Learner-centered teaching practices in the tertiary level, such as mathematical discussions, have been shown to benefit student learning. The interactions involved in online synchronous mathematical discussions have been studied less. Most research taps into these aspects drawing on students’ academic outcomes and reflective interviews. This study explores instructional practices as they unfold online, with a focus on student-instructor and student-student interactions. We zoom-in to online synchronous teaching and learning processes on a popular communication platform by analyzing Linear Algebra tutorials in the first pandemic year. Using the commognitive framework, we characterize instructional interactions with the construct of a learning-teaching agreement. The analysis resulted in three interactional patterns, where in all cases, the tutorial transformed at some point to the one dominated by the instructor.

Supporting students’ participation in collective argumentation: Use of displays in a secondary mathematics classroom

ABSTRACT Thoughtful and purposeful displays can support students’ participation in argumentation. This report addresses how displays are used within collective argumentation. We examined a secondary mathematics teacher’s and her students’ use of displays during selected episodes of collective argumentation. From video classroom observations and interviews with the teacher, we extracted several kinds of displays according to their functions and then investigated how these displays supported collective argumentation as direct contributions to the argument or actions supporting the argumentation. Furthermore, we also considered actions by the teacher that supported her students to display. We found displays can be both part of the mathematical argument and supportive of the mathematical argumentation. This finding has direct implications for studying mathematical discussions because the literature has primarily focused on verbal contributions to the argument over nonverbal contributions such as displays.

Vedic Contributions to Geometry: Unveiling the Origins of Mathematics

The historical origins of foundational mathematical principles often lie obscured in the past. Among the luminaries in this nebulous landscape were Vedic mathematicians like Baudhāyana, Bhāṣkarācārya, Brahmagupta, Aryabhata, Pāṇini, Kātyāyana, and Āpastamba, eminent figures and sages of their time. Baudhāyana, in particular, is revered for his seminal contributions, prominently through the Baudhāyana Sulba Sūtra. This compendium of mathematical and ritualistic precepts predates the. The Baudhāyana Sulba Sūtra text belongs to the ritualistic ethos of Vedic Hinduism, yet it contains profound geometric theorems that expose the multifaceted genius of Baudhāyana. A scholarly endeavor has been an exegetical exercise on the mathematical corpus left by Baudhāyana, which throws new light on his pivotal role in shaping the contours of mathematical discourse within the antiquity of our civilization. This research helps us to enrich our knowledge about Vedic mathematical thinking and its intricate relationship with cultural and spiritual traditions.

Lagrange points and regionally conserved quantities

Lagrange points are the equilibrium points within a restricted three-body system, epitomized by the Trojan asteroids near the L4 and L5 points of the Sun–Jupiter system. They also play a crucial role in some space missions, including the James Webb Space Telescope which is located at the Sun–Earth L2 point. While the existence of five Lagrange points is a well-known feature of the restricted three-body problem, the equations describing the precise location of all five points are not extensively documented. This work presents a derivation of all Lagrange points using polar coordinates and a new normalization scheme that offers a simpler interpretation of solutions compared to prior analyses. A subtle issue concerning the treatment of angular momentum in the potential formulation of this problem is addressed and resolved. The supplementary material to this work contains additional mathematical details and discussion.

Pelatihan Pembuatan Media Math Game Berbasis Android

Most students consider mathematics as a difficult subject to understand, unpleasant and tends to be boring. Many students consider mathematics as a boring subject because all discussions of mathematics involve numbers and examples. This concept applies to all levels of education, both elementary, secondary and higher education. The purpose of this training is to explain methods that can increase students' interest in learning mathematics. The solution provided in this training is to help mathematics teachers in implementing mathematics learning using android games. The methods used in this community service are observation, planning, implementation and evaluation. Based on the results of this community service, it is concluded that the application of learning aids using a mathematics learning platform on an android game will increase students' interest in learning mathematics. This is evidenced by the increasing percentage of students who achieved the KKM above after the training. Before the training, the pre-test results showed that the proportion of students who scored above the KKM was only 20%. After guidance, the post-test results showed that the percentage of students who passed the KKM reached 85%. The benefit of this training is that it can increase students' interest in learning mathematics so that students do not view mathematics as a difficult and boring subject