Primary Mathematics Classroom Research Articles

Computational thinking in primary mathematics classroom activities

The integration of computational thinking (CT) into primary education is often facilitated using one or more CT tools, such as block-based programming environments and educational robotics. A major concern is that these CT tools often are used to design mathematics classroom activities that focus on CT at the expense of mathematics. Hence, there is a need to investigate more closely how CT tools can be used in primary mathematics classroom activities in ways that enable a stronger focus on the learning of mathematics. Using information ecology as a theoretical lens, this study aims to understand how and why CT tools are integrated into primary mathematics classrooms, and how teachers value the possible contributions of such tools. We draw on multiple interviews with two primary teachers, recordings of planning sessions where classroom activities that include CT were designed, the classroom implementations themselves, and reflective conversations with the teachers after the CT tools were integrated in their mathematics classrooms. A deductive analytical approach to our data revealed that (1) CT tools, to varying degrees, facilitate the learning of mathematics; (2) some CT tools were valued by teachers as a better ‘fit’ than others; and (3) CT tools are primarily used to support the learning of geometry, excluding other mathematical domains. Based on these findings, we suggest that there is a need for more research on the use of different CT tools and their role in the learning of primary mathematics. Moreover, more research is needed to understand how CT tools can be used in topics other than geometry.

Non-Digital Games That Promote Mathematical Learning in Primary Years Students: A Systematic Review

Despite primary school teachers demonstrating strong preferences for using non-digital games over digital games to support mathematics instruction, much of the research review literature has focused on learning outcomes associated with digital mathematical games. To address this gap, the current systematic literature review focuses on non-digital, games-based, empirical studies in the primary mathematics classroom over the past two decades from 2003 to 2022. The Preferred Reporting Items for Systematic Reviews (PRISMA) statement was employed as a guideline for the data-collection process. The review presents an analysis and synthesis of 34 manuscripts, representing 32 distinct studies. Over three-quarters of manuscripts employed quantitative methodologies and around half qualitative methodologies, whilst studies focused exclusively on student, as opposed to teacher, outcomes. Despite Australia and Indonesia being comparatively overrepresented, the studies in scope were notable for both their geographic diversity and the eclectic range of game types and structures incorporated; although they did tend to disproportionately focus on number and operations, as opposed to other mathematical content areas. Moreover, the impact of mathematical games was generally positive across the broad range of outcomes considered, suggesting that mathematical games are potentially effective for both developing mathematical proficiencies, as well as improving dispositions towards mathematics. Future research directions are discussed.

Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies

STEM education has been promoted in schools worldwide to cultivate students’ 21st-century skills. Mathematical modelling is a valuable method for developing STEM education. However, in this respect, more attention is given to secondary level or above compared with kindergarten or primary level. Teaching mathematics at the primary level is closely related to authentic problems, which is a crucial characteristic of mathematical modelling activities. After screening 239 publications from various databases, we reviewed 10 empirical studies on mathematical modelling at the primary level. In this systematic review, we analysed the following three aspects: (1) the use of professional development intervention methods/strategies to enhance the intervention effects and the competencies of primary teachers to utilize mathematical modelling; (2) the effects of mathematical modelling on primary students and methods of improving their mathematical modelling skills; and (3) methods used to assess the modelling skills of primary school teachers and students. The results indicate that professional development interventions can enhance the teaching quality of mathematical modelling. The components of the interventions should include an introduction to the pedagogy of mathematical modelling, clarifying the role of the teacher and the student in mathematical modelling activities. Through mathematical modelling, students can generate mathematical ideas, explore mathematical theorems independently, develop critical thinking, and improve their metacognitive and communicative skills. The competency of mathematical modelling is often determined using formative assessments of teachers and students. Because limitations still exist in conducting primary-level modelling activities, schools should utilise more standardised assessment methods, provide universal teacher training, and grant more opportunities for primary school students to participate in mathematical modelling activities. The lack of research on cross-cultural contexts should draw the attention of future research.

Micro-lesson Embedded in Primary Mathematics Classrooms

Micro-lesson Embedded in Primary Mathematics Classrooms

Computational Thinking in the Primary Mathematics Classroom: a Systematic Review

Computational thinking (CT) has acquired the status of a necessary 21st-century skill and is currently being introduced in school curricula around the world, despite a lack of consensus about what it entails. The aims of this review are to provide an overview of the existing literature on CT activities in primary mathematics education, and to articulate how it is integrated into the teaching and learning of primary mathematics. This systematic review presents and analyses the findings of 10 empirical studies, revealing a recent increased focus on the inclusion of CT in primary mathematics classrooms, as most studies are published around 2020. Our findings indicate two categories of such activities, one focusing on skills (such as mainly sequencing, looping, conditionals, debugging, decomposition, and abstraction) and one on process-oriented activities (communication, creativity, exploration, and engagement). Furthermore, we found that, while there are studies reporting on mathematics being taught directly through CT activities (full integration), in most studies, the mathematics content was emphasised, with CT built in as a way for students to demonstrate their understanding of mathematics concepts (partial integration). This review identifies current gaps in the field and the need to investigate further such process-oriented activities, the use of these activities in accelerated mathematics, and the need for different methodological approaches in primary mathematics.

Early career teacher’s approach to fraction equivalence in Grade 4: A dialogic teaching perspective

The research presented in this article reports on the results of a case study examining the classroom practice of one early career Grade 4 teacher (Nox, pseudonym) as she teaches equivalent fractions. The goal was to explore the ways and extent to which her instruction reflected a dialogical teaching approach, defined as a pedagogical approach underpinned by five specific principles that can be enacted through a range of possible talk strategies to achieve sustained participation of learners and thus enhance meaningful learning. I provide a pedagogical activity to illustrate to teachers how, by instigating and developing classroom talk in the primary classes, a dialogic teaching sequence may be implemented. However, the majority of the existing literature on dialogic teaching stems from studies conducted in Asian, European, and North American countries, whereas systematic research on dialogic teaching across international contexts remains limited. Nox was interviewed after obtaining observational data to seek clarity on some of the observed instructional practices. Analysis of transcripts using the notion of dialogic teaching as a theoretical lens revealed that there was little evidence of Nox’s attempts to use talk to make learning of equivalent fractions a cumulative process. In addition, time constraint was the most significant factor in Nox’s teaching of equivalent fractions: she considered the curriculum too congested. Implications are drawn for evaluating dialogic teaching in primary mathematics classrooms. Future, larger studies may shed light on the extent of these results and, if need be, a significant investment on initial teacher training may be necessary to underscore the value of dialogic teaching in enhancing meaningful learning of, at least, equivalent fractions.

Constructing a design framework and design methodology from educational design research on real-world educational technology development

Educational design research (EDR) seeks to contribute to both practice and theory by developing solutions that improve educational practice and generating usable and generalisable knowledge. Most EDR researchers tend to focus on reporting their research contributions to educational practice. Therefore, there is a need for disseminating research that pays more attention to the theoretical contributions of EDR so that those outside a particular EDR project can benefit. This paper focuses on the theoretical contributions, particularly the design framework and design methodological knowledge, of a 6-year EDR enquiry that aimed to develop educational technologies that promote primary school mathematics learning and classroom practice. Informed by the literature and direct experiences of working in collaboration with teachers and various disciplines during this iterative study, a design framework for developing real-world educational technologies and guidelines for conducting EDR are proposed. The design framework highlights four essential aspects—content, pedagogy, practice, and technology—that should be considered when developing educational technologies to ensure their educational benefits, feasibility, and successful real-world utilisation and adoption. The proposed guidelines for conducting EDR, such as exploring design alternatives and employing appropriate design construction and evaluation methods, can assist other researchers, including a single doctoral student, in embracing opportunities and overcoming the challenges that may emerge.

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between ‘construction’ and ‘substantiation’ based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.

Current Changes in Primary Education: The issue of “different” in a primary school mathematics classroom

In the setting of the transformation of our societies to become multicultural ones, we intend in this paper to examine situations in a mathematics classroom where respect for, and exclusion of, the ‘different’ co-exist. Conducting an instrumental case study, we follow two Grade 4 groups while they are solving a mathematics generalization task. We examine how the interaction that took place between the members of the teams mirrors the two faces of the same coin (i.e. the culture of the classroom) and at the same time reflects the change in the primary classroom that necessitates openness and genuine respect for the ‘different’. On the one hand, we will demonstrate the dynamic of the harmony that was apparent between the members of one of the groups since the ‘different’ was not a barrier but a source of mathematical ideas that contributed to the solution. On the other hand, the lack of openness in the other group resulted in good opportunities for ‘doing mathematics’ being missed and put the self-confidence of one of its members at risk. Keywords: classroom diversity and conflict, multicultural mathematics classroom, collaborative problem-solving

A framework for designing mathematics instruction using comics at the primary school level

Developing primary school students’ interest in and getting them motivated to learn mathematics has been a perennial focus of educators. The use of comics for classroom instruction is an area gaining more attention from educators. In this paper, we review some existing education literature on the impact of comics on students’ cognitive and affective learning needs. We also propose a TSCT (Theme, Storyline, Character, Text) framework for educators to design instructional material using comics for mathematics instruction in the primary mathematics classroom. With the TSCT framework, we demonstrate the design of one comics mathematics lesson on the topic of Fraction.

Teachers’ Conceptions of Assessment for Learning: What are the Implications for Children?

Abstract This paper describes a multi-case study which linked conceptions and practices of assessment for learning to developing learner autonomy within UK primary mathematics classrooms. The project explored the use of assessment for learning in mathematics lessons with Year 5 (9–10 years old) children and their teachers. Four cases were studied in depth to understand how conceptions and practices impacted upon autonomy and control for teachers and learners. A typology of assessment for learning in mathematics is proposed, along with what this might mean for both teachers and learners in terms of the balance between control and autonomy. One case in particular, that of teacher Alex, is highlighted as it exemplified the expert teacher through the conceptions and use of assessment for learning, which led to the children becoming expert learners of mathematics. The class ethos was one of value for personal autonomy. Responsibility and control of learning was a shared endeavour within a community of learners. Community in this respect was broadened to include the environment and resources within the classroom and so demonstrated learners working within an expert classroom. This article was developed from a paper first presented at the ICME 13 conference (O’Shea, 2016).

An Exploratory Study of Game-Based Approaches in Primary Mathematics and Science Classrooms in Trinidad and Tobago

An Exploratory Study of Game-Based Approaches in Primary Mathematics and Science Classrooms in Trinidad and Tobago

Curriculum Alignment: Performance Types in the Intended, Enacted, and Assessed Curriculum in Primary Mathematics and Science Classrooms

This study examined the process of curricular alignment in primary school mathematics and science. Six performance type categories were used to define the cognitive-demand levels evident in the mandated curriculum and elicited through classroom practice. The purpose of this comparative case study is to understand how the intended goals of the mandated curriculum are interpreted for planning, instruction, and assessment purposes. The data includes video-recorded lessons, interviews, planning documents, and work samples from units of work. The results revealed that interpreting the intended goals of the mandated curriculum at the classroom level is a complex and dynamic process. The process is one of iterative interpretation at various levels of curriculum planning. The alignment of performance type expectations are influenced by the sources of authority that are accessed, such as standardized testing programs, textbooks, and curriculum consultants. The types of performances that were privileged in assessment practices were reflected in planning and instruction at the school level, indicating that, among other factors, assessment has a critical role in determining how the curriculum is enacted.

Pre-service and in-service teachers’ perceptions on the integration of children’s literature in mathematics teaching and learning in Ireland

The beneficial role that children’s literature plays in facilitating the meaningful integration and advancement of literacy and numeracy in the primary mathematics classroom has been well validated by research findings internationally. In Ireland, supporting the development of literacy and numeracy is a key educational priority. Consequently, a myriad of policy initiatives such as the Literacy and Numeracy for Learning and Life strategy have been introduced. All aim to address concerns about young people’s lack of basic literacy and numeracy skills and to consider new teaching and learning modalities to enhance same. Despite this, no official emphasis is given to incorporating literature in the Irish primary school mathematics curriculum. Therefore, it is pertinent and timely that this study seeks to ascertain pre-service and in-service teachers’ views on the use of literature to support mathematics teaching and learning and to investigate perceived barriers to and enablers for the integration of children’s literature in the mathematics classroom in Ireland. The analysis of the findings will be framed using Ajzen’s (Ajzen, Icek. 1991. “The Theory of Planned Behavior.” Organizational Behavior and Human Decision Processes 50 (2): 179–211) Theory of Planned Behavior (TPB) model. This research is part of a large international research collaboration (see www.mathsthroughstories.org), in which the beliefs of teachers with respect to children’s literature are investigated.

Personalised learning with mobile technologies in mathematics: An exploration of classroom practice

Personalised learning is generally understood to be of benefit to students’ learning. In addition, the flexible nature of mobile technologies (MTs) and the variety of available apps are seen to respond to the needs of individual students, and hence have the potential to support personalised learning. This paper reports on an aspect of a larger research project that investigated the use of mobile technologies in primary mathematics classrooms. Personalised learning was determined as one theme that emanated from the teachers’ and students’ use of MTs, and this paper aims to investigate how personalised learning was evidenced within the practice of three teachers. Video data of classroom practice were used to analyse the use of MTs within the theme of personalised learning. Four pathways to personalised learning emerged, enabling a more practical understanding of different types of personalisation afforded by MTs.

Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, “How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?” The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers’ progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

An examination of the roles of the teacher and students during a problem-based learning intervention: lessons learned from a study in a Taiwanese primary mathematics classroom

ABSTRACTThe benefits of problem-based learning (PBL) to student learning have prompted researchers to investigate this pedagogical approach over the past few decades. However, little research has examined how PBL can be applied to mathematics learning and teaching, especially in countries like Taiwan, where the majority of teachers are accustomed to lecture methods and students are used to this style of teaching. This study examines the actions of a teacher and her class of 35 fifth-grade students (10–11-year-olds) as they tried to take on and respond to the demands of their new roles as “facilitator” and “constructors”, respectively, during a one-year PBL intervention in a Taiwanese mathematics classroom. Our findings provide insights into classroom participants’ role transition, from a customary role to a new role, when engaging with PBL. We identify an interrelationship between the teacher and student roles and discuss implications for the implementation of PBL at the primary education level.

Using collective argumentation to engage students in a primary mathematics classroom

This article focuses on using sociocultural theory to support student engagement with mathematics. The sociocultural approach used, collective argumentation (CA), is based on interactive principles necessary for coordinating student engagement in the discourse of the classroom. A goal of the research was to explore the affordances and constraints of using CA to enrich student engagement with mathematics. The design of the research was based on a teaching experiment that sought to capture the influence of social and cultural processes on learning and development. Participants included primary and secondary school teachers and their mathematics classes. This article focuses on the practice of one female primary school teacher. Data sources included interview transcripts, report writings, journal entries and observational records. Data were analysed using a participation framework. Findings suggest that aspects of CA such as students explaining and justifying ideas and presenting ideas to the whole class can be used by teachers to promote student engagement with mathematics.

The implementation of problem-based learning in a Taiwanese primary mathematics classroom: lessons learned from the students’ side of the story

Research on problem-based learning (PBL) has tended to focus on the graduate level of education, paying less attention to the primary school level and to what is involved for students during the implementation of PBL. In this paper we take a step towards addressing this need for research by reporting findings from a descriptive, explanatory case study of a one-year PBL intervention in a fifth-grade (ages 10–11) mathematics classroom in Taiwan. We documented and analysed the students’ actions to reveal details in their part in the intervention. We compared the students’ performances on the five researcher-designed written tests, which were conducted at different points in time. Our findings cast light on the level of the students’ participation in PBL. The comparison between the test results shows improvements in students’ understanding of the concepts and supports the idea that PBL has positive effects on long-term knowledge retention.

Is Current Research Assisting the Implementation of Contemporary ICT in the Primary Mathematics Classroom?

The fast pace of development of ICT often results in primary teachers being expected to integrate new technologies effectively prior to the emergence of research findings that provide exemplars of best practice. This discussion paper explores contemporary research into ICT and primary school mathematics, and the issues that arise in relation to mobile technologies such as computer tablets in primary school classrooms. Although studies are beginning to emerge, this paper presents the argument that further research that would assist teachers in being prepared to teach mathematics with any technological tool would be more beneficial than working retrospectively to explore the use of specific devices that have already emerged in primary classrooms.