Mathematical Practice Research Articles

REMOTE: First insights into assessing and evaluating remote learning practices in STEM

The rapid transition to remote learning practices in Science, Technology, Engineering, and Mathematics (STEM) education necessitates a comprehensive assessment and evaluation of their effectiveness. This article presents the first findings of the UE funded project REMOTE “Assessing and evaluating remote learning practices in STEM” (ref: 2022-1-ES01-KA220-HED-000085829) project: a literature review focused on assessing and evaluating remote learning practices in STEM. Drawing on a wide range of scholarly articles, reports, and studies, this article review examines various dimensions of remote learning, including instructional design, student engagement, assessment methods, and instructor-student interaction associated with remote STEM learning in Higher Education Institutions (HEIs). The set of academic contributions detected can be classified into four major typologies according to the area in which they are focused: students, teaching methodologies, teaching staff and technologies. In consequence, the review carried out, summarized in a categorization of the research developed so far, allows a broad and critical view of the state of the art. The findings of this article contribute to the broader conversation surrounding remote learning and serve as a valuable resource for stakeholders involved in STEM education.

Academic Resilience Among Post Graduate Students in the Universities of Islamabad: A Comprehensive Assessment

Introduction: Mathematics plays a crucial role in the development of science and technology, and its importance is recognized at all educational levels. This study investigates the availability and utilization of mathematics facilities for the improvement and development of prospective teachers. Methodology: This quantitative study targeted students from four universities in Islamabad and Rawalpindi. A questionnaire was distributed to 300 respondents, with 175 completed responses collected through proportionate random sampling. The questionnaire was validated by experts and its reliability confirmed using Cronbach’s Alpha. Data analysis was conducted using the Statistical Package for Social Sciences (SPSS). Results/Findings: The findings revealed that most respondents strongly agreed that mathematical content knowledge significantly impacts the learning and understanding of prospective teachers. Additionally, the study highlighted the importance of practice in learning mathematics and emphasized the need for curriculum-based instruction that extends beyond exam preparation. Future Direction: The study recommends developing a framework to address identified challenges, enhance mathematical content, improve pedagogical approaches, and ensure the availability of up-to-date facilities for prospective teachers.

Classroom Supports for Generalizing

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This article proposes Classroom Supports for Generalizing (CSGs), investigating how multiple elements—such as tasks, teacher moves, student interactions, and representations—interact to meaningfully foster student generalizing. Drawing on class video data from a middle school teacher and two high school teachers, we present the CSG Framework, which identifies three categories of supports: Interactions for Generalizing, Structures for Generalizing, and Routines for Generalizing.

Research on the Personalized Correction Practice of Intelligent Problem Sets from the Perspective of Deep Learning—Reflections on the Personalized Generation of Primary School Mathematics Practice Problems under the Background of “Double Reduction”

Research on the Personalized Correction Practice of Intelligent Problem Sets from the Perspective of Deep Learning—Reflections on the Personalized Generation of Primary School Mathematics Practice Problems under the Background of “Double Reduction”

Mathematics Learning through the Lens of Neuroplasticity: A Researcher’s Perspective

This paper synthesizes key findings in neuroplasticity research to debunk the myth of a “fixed” mathematical ability, suggesting that cognitive capabilities in mathematics are not preordained but can be significantly improved through focused practice and tailored educational methods. Through an examination of selected research studies, this article demonstrate that consistent mathematical practice not only leads to improved problem-solving skills but also induces significant neural changes in brain regions associated with numerical processing. Furthermore, the paper delves into the critical role of focused attention and cognitive control in effective learning and proposes actionable strategies for educators to leverage these insights. This paper underscores the transformative implications of neuroplasticity for curriculum development, teaching strategies, and broader societal attitudes towards mathematical learning.

Exploring Challenges Towards Learning Mathematics Among Secondary School Students in Nepal

Mathematicians had been concerned with everyday problems. However, today's students are uninterested in learning mathematics. The main objective of this research is to identify students' challenges to learning mathematics. Employing an interpretative research paradigm, the study utilizes a narrative research design involving eight students from public and private schools in the Kaski district. To achieve the research objective, in-depth interviews were conducted with research participants. I had narrated views about challenges towards learning mathematics from my participants. After analysis and interpretation of data, challenges towards learning mathematics were difficulties in learning mathematics, negative perception and external pressure, disruption in learning environment and foundation, changing teacher and lack of support, enjoyment in mathematics practice and fear of teacher, barriers in conceptual clarity and guidance, obstacles in effective mathematics teaching and disinterest, unclear teaching and insufficient support respectively. Moreover, Students face a multitude of challenges in learning mathematics, including issues related to teacher behavior, lack of motivation, the current curriculum, low parental socio-economic status, ineffective teaching strategies, poor home environments, low academic achievements, math anxiety, impractical curricula, and traditional teaching methods.

Best Practices in STEM Education for Preschool Children: A Case Study in Malaysia

Previous research has demonstrated that since 1967, the Malaysian government has set a target percentage rate of 60:40 for student involvement in the science stream compared to literature. This ratio policy has been followed throughout the national school system ever since. However, such a ratio appears to be impossible to maintain year after year. Therefore, the empowerment of science education needs to be explored from an earlier. This study was conducted to (i) explore best practices in Early Science in relation to the implementation of STEM activity in preschool; (ii) explore best practices in Early Mathematics in relation to the implementation of STEM activity in preschool; (iii) explore technology-assisted teaching tools in relation to the implementation of STEM activity in preschool; and (iv) explore engineering activity in relation to the implementation of STEM activity in preschool. This qualitative study employed a case study approach, with data triangulation based on interviews, observations, and document analysis serving as the exploratory method. This study was conducted independently in three Malaysian preschools in Perak and Selangor respectively, with four teachers and 39 children participating as study participants. ATLAS.ti version 8 software was used to generate, arrange, and organise the themes from the three research instruments described utilizing descriptive analysis with the flow of coding processes. The results show that there are nine STEM education best practices, with play-based learning being identified by participants the most frequently. Thus, this study's most significant contribution is the potential to bridge the gap between the Ministry of Education Malaysia's goals to advance STEM education globally, starting in the early years.

Exploring School Improvement Opportunities through Distributed Leadership Practices for Science and Mathematics in South African Schools

School leadership practices are significant in addressing learner-attainment gaps in school subjects such as science and mathematics. This paper uses an exploratory qualitative case-study approach with four purposely selected high schools to explore how distributed leadership (DL) improves opportunities for teaching and learning in science and mathematics. The four schools constituted two suburban and two township schools prioritizing science and mathematics on school improvement agendas. Principals, deputy principals, heads of department, and teachers of science and mathematics participated in semi-structured interviews. Thematic content analysis in which the emerging themes were compared to the DL tenets was used to make sense of the gathered data. The findings indicate that DL practices influence the teaching and learning of science and mathematics, irrespective of a school’s socioeconomic status. The participating schools developed useful mechanisms for school improvement through science and mathematics that were compatible with the DL setups existing in their schools. The study recommends that DL should be promoted in schools by being one of the topics for professional development made available to science and mathematics teachers.

Primary Student Teachers’ Views on Scientific Measurement and Uncertainty: A Pilot Research

The paper presents primary student teachers’ views on the basic concepts related to scientific measurement and uncertainty. A pilot study was conducted, and a qualitative content analysis method was used, by distributing an open-ended questionnaire in a convenient sample including 24 primary student teachers. The first findings revealed that student teachers have some general idea about the importance of scientific measurement, they recognize uncertainty as human error or instrument failure, but they lack the deepest conceptualization of uncertainty as an aspect of the nature of scientific measurement. The above-mentioned views are discussed in the context of their influence in teaching practices of science and mathematics in primary education and their epistemological perspectives.

Introducing Students to the Role of Assumptions in Mathematical Activity

Assumptions play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in mathematical activity, with particular attention to the following two learning goals: recognize that (1) a conclusion depends on the assumption(s) underlying the argument that led to it; and (2) making the underlying assumption(s) explicit is crucial to reaching consensus on the conclusion. In the context of a 3-year design research study, we first used existing literature to construct an initial version of task design principles which we then empirically tested and refined by designing and implementing two tasks in Japanese school classrooms. One of the tasks was in the area of functions at the secondary level and the other in the area of geometry at the elementary level. We analyze two classroom episodes to discuss the promise and evolution of our proposed task design principles. In addition, our analysis sheds light on the role of the teacher’s instructional moves and the students’ mathematical knowledge during the implementation of the designed tasks.

How Teachers Make Decisions in Response to Professional Learning: A Study on Grade 3 Differentiation in Mathematics

This study used a mixed-methods design to examine teachers’ responses to professional learning on mathematics differentiation. Grade 3 classroom teachers ( N = 28) attended four 2-h professional learning sessions and an additional 2 h individually on differentiation and completed pre- and post-surveys with quantitative and short response items assessing their experiences. Although teachers did not report changes in overall differentiation rates, implementation of less extensive practices (i.e., talk moves and mathematical practices) increased. Changes did not appear to be driven by teachers’ valuation of differentiation, which was high across surveys. Rather, a thematic analysis indicated that teachers simultaneously weighed benefits, challenges, and alignment with existing practices when making decisions about whether to implement differentiation strategies.

Facilitating effective mathematical teaching practices in preschool

Initial seeds for mathematics literacy are planted during early childhood. Children benefit when they are exposed to and provided with opportunities for math experiences that emphasize their holistic development and not just mathematics proficiency in isolation. This way of viewing and presenting mathematics to young children requires teachers who are equipped with strong mathematics teaching skills. This study examined a 21-hour professional development series for public school preschool teachers on early numeracy, geometry, mathematical reasoning, and teaching pedagogies. This professional development series aimed to help preschool teachers incorporate effective mathematical practices and increase their comfort level in teaching mathematics. Participants noted this professional development series impacted their ability to foster children’s early numeracy development, engage in math talkpose questions that helped children process early numeracy, and contextualize early numeracy through stories and/or word problems. The study demonstrates change takes time, and the impact of this professional development series is dependent on preschool teachers’ readiness and their perception of their teaching context needs.

싱가포르 중학교 수학교과서에서의 빅 아이디어 접근 구현 사례 연구

Big Ideas approach is gaining attention as a design and implementation perspective for curriculum that intends connected and coherent mathematics learning. This study conducted quantitative and qualitative analysis on horizontal connections between mathematical content in middle school mathematics textbooks of Singapore where Big Ideas approach was applied. The quantitative analysis revealed the strength of horizontal connections within strands and within topics by Big Ideas. Among the eight Big Ideas in Singapore mathematics curriculum, “diagrams” and “notations” aided generally high level of horizontal connections, while “functions,” “invariance,” and “models” promoted generally lower level. The qualitative analysis distinguished between process-oriented and concept-oriented Big Ideas. Horizontal connections by process-oriented Big Ideas were further classified into “connections by conventional mathematical practices” and “connections through non-routine mathematical reasoning”, while horizontal connections by concept-oriented Big Ideas were classified as “deductive connections based on definitions” and “inductive connections based on awareness of structure”. Results are discussed and implications for the implementation of Big Ideas approach in the 2022 revised mathematics curriculum are suggested.

Epistemological and Ethical Philosophy of Mathematics In 21st Century Mathematics Learning Practices

21st century mathematics education has made use of science and technology while maintaining the philosophy of mathematics from an ethical and epistemological standpoint. This paper examines the goals of the philosophy of mathematics from an epistemological and ethical perspective. It also investigates the relationship between these perspectives and the practice of studying mathematics in the twenty-first century. This article was written using the Publish or Perish software and a systematic literature review approach. 41 initial articles were found by inputting keywords. Following review, fifteen articles were found to be in agreement. This study reveals that the goal of mathematics philosophy is to understand truth, meaning, certainty, and the nature and sources of mathematical knowledge, as well as how to interpret mathematics, from an epistemological perspective. Analyze and reflect on the ethical implications of mathematical practices. Its epistemological application in 21st century learning practices guides the way concepts are positioned, logical arguments are made, and mathematical problems are solved. Next, ethical considerations include maintaining student privacy, establishing learning agreements in every class, and avoiding creating group distinctions. by utilizing an interactive, student-centered learning paradigm like PBL, inquiry, contextual learning, use of technology, STEM, and others. Such behaviors will subsequently cultivate the values of critical, communicative, creative, and cooperative character. Therefore, we must uphold the fundamentals of learning in the 21st century, both in terms of epistemology and ethics.

Transformative Assessment Practices in Mathematics Classes: Lesson from Schools in Jimma, Ethiopia

AbstractTransformative assessment is a classroom assessment aimed at changing both how teachers teach and students learn a lesson. Nowadays, this kind of assessment needs to be practiced to encourage teachers to be creative and flexible when designing their assessments and for students to be reflective and take responsibility for their learning. Hence, this qualitative study aimed to examine mathematics teachers’ practices of transformative assessment and the associated challenges. Data collected from eight teachers using semi-structured interviews and lesson observations were analysed thematically. It was found that teachers did, in fact, not provide evidence of practicing transformative assessment in their teaching. There was an attempt to align assessment to learning outcomes even though the assessment practice utilized remained traditional. Teachers’ assessment practices focused on fast-learners while leaving behind the majority, lacking balance and equity. Teacher, student, and school-related factors were the main challenges facing the teachers during assessment practices. The study presents possible strategies by which transformative assessment practices in mathematics teaching can be developed, implemented, and sustained to improve students’ learning.

Weaving in: shifts in youth mathematical engagement through weaving

Despite recent efforts to support learners from traditionally minoritized backgrounds in mathematics, inequities in math achievement and participation still exist, particularly for women and people of color. Additionally, much of how math is taught in schools aligns with a particular epistemology that comes from western mathematicians and philosophers. While a strong link between weaving and mathematics has been established, fewer studies explore the possibilities of this link for supporting youth’s pluralistic engagement with mathematics in educational settings. Thus, we ask: In a making-focused intervention designed to expose youth to the mathematical practices inherent in weaving, how do student-created artifacts showcase learning? In this paper, four cases demonstrate how middle-school youth learning to weave and learning through weaving experimented or leveled up their planned or implemented designs. Their learning processes showcase engagement with mathematics that mirrors that of more experienced weavers. Making visible the mathematical engagement that youth undertake through weaving may be a step toward building frameworks and classroom activities through making that work to combat these disciplinary issues.

Technology maker practices in mathematics learning in STEM contexts: a case in Brazil and two cases in Canada

Technology maker practices in mathematics learning in STEM contexts: a case in Brazil and two cases in Canada

Reconnecting with the mathematical thought of the Mesoamerican numbers in Ixil: an onto-epistemological dialogue

AbstractNumbers and languages are present around the world. While mathematics is deemed as universal, communities around the world have developed mathematical practices that align with their specific context and needs. Rooted in an Indigenous epistemological framework, this manuscript presents a dialogue among four co-researchers and teachers retelling their experiences teaching and learning Mesoamerican numbers in both monolingual (Spanish) and bilingual (Ixil and Spanish) contexts. With a strong desire to learn about and reconnect with the forces of Indigenous mathematical thought and language that move within the teaching and learning of these numbers, the authors collectively reflected on their “tellings” of prior work. It is worthy of note that these reflections on teaching and learning processes of naming Mesoamerican numbers, their symbols, and numerical values help realize that these concepts are more fully animated when presented in contexts that are onto-epistemologically relevant.

Interpreting prospective teachers' responses to inequities in a written vignette: A plan for action

AbstractTo develop an equity‐centered orientation in teacher education programs, it is essential teacher educators recognize what prospective teachers attend to in classroom events and how they relate these events to mathematics instruction. In this study, we conceptualize the Equity Noticing Framework and use it as an analytic tool to examine what prospective teachers notice in a classroom vignette focused on cultural and racial biases. The Equity Noticing Framework focuses on understanding what prospective teachers recognize—or overlook—as bias, oppression, and privilege that permeate educational systems, analyze those events that contribute to inequities, and support prospective teachers in becoming change agents who implement strategies that can eradicate systemic barriers. The results from this study reinforce the importance of devoting time to supporting prospective teachers to become more cognizant of their own beliefs about equity and equitable mathematical practices and providing opportunities to analyze these beliefs through research‐proven attitudes and practices.

Teaching Mathematics in Kindergarten: How Does Instruction Differ by Classroom Ability?

Background/Context: Kindergarten mathematics instruction is critical for students’ future academic success. The nature and quality of this instruction may vary depending on classroom characteristics. However, little empirical work has examined how mathematics instruction in kindergarten might differ based on classroom performance levels. Purpose, Objective, Research Question, or Focus of Study: This study focuses on whether kindergarten teachers’ mathematics instructional practices differ based on reported performance levels of students in the classroom. In particular, we focused on whether mathematics instructional time, as well as the extent to which teachers use traditional versus ambitious mathematics practices, differed based on teaching a higher proportion of children performing below grade level. Research Design: This study used a nationally representative dataset of approximately 2,900 kindergarten teachers from the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11. With these data, the study utilized a model that compared teachers to each other within the same school (i.e., school fixed effects). Conclusions or Recommendations: This study found that mathematics instructional time did not differ based on the proportion of children reported to be below grade level in the classroom. However, how teachers taught mathematics differed: teachers who reported having a greater percentage of students performing below grade level used ambitious practices less frequently. These findings were not moderated by measures of teacher background or teachers’ reported expectations of their students.