Primary Mathematics Research Articles

Impact of programming on primary mathematics learning

The aim of this study is to investigate whether a programming activity might serve as a learning vehicle for mathematics acquisition in grades four and five. For this purpose, the effects of a programming activity, an essential component of computational thinking, were evaluated on learning outcomes of three mathematical notions: Euclidean division (N = 1,880), additive decomposition (N = 1,763) and fractions (N = 644). Classes were randomly assigned to the programming (with Scratch) and control conditions. Multilevel analyses indicate negative effects (effect size range −0.16 to −0.21) of the programming condition for the three mathematical notions. A potential explanation of these results is the difficulties in the transfer of learning from programming to mathematics.

Practical Research on Primary Mathematics Teaching Based on Deep Learning

With the rapid development of the knowledge economy, learning that stays at a shallow level is no longer able to meet the challenges of the times and deep learning has come into being. The key to deep learning is to develop students’ critical thinking, information integration, communication and collaboration, and constructive reflection skills, which can be cultivated in the process of problem solving. By exploring the theories of deep learning and problem solving, the basic elements of deep learning theory are incorporated into the design system of problem-solving teaching, and the problem-solving teaching model based on deep learning is proposed in conjunction with the content of elementary school mathematics, so that students can further develop their core literacy based on acquiring deep learning skills.

Teachers' learning from addressing the challenges of online teaching in a time of pandemic: a case in Shanghai.

Due to the COVID-19 pandemic in Shanghai, China, all school classes were delivered through an online environment from February 24 to May 22, 2020. To support this transition, the Shanghai Education Commission led expert teachers and specialists to develop a series of online video lessons based on the Shanghai unified curriculum, and suggested students watch the online video lessons individually from home, followed by an online synchronous lesson supported by class teachers. This study investigated what primary mathematics teachers learned from addressing these challenges through a case study. By following two purposefully selected teachers over 2 weeks during the transition, multiple data sets including online video lessons, online synchronous lessons, daily reflections, and post-online teacher interviews were collected. A fine-grained analysis of the data from the lens of the documentational approach to didactics found that teachers adaptively used online video lessons as important resources for their online synchronous lessons and virtual Teaching Research Groups as a teachers’ collaboration mechanism supported them to develop online video lessons and address various technological constraints. Finally, implications of this case study for mathematics education globally are discussed.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10649-022-10172-2.

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In this study, a technology-supported teaching module was designed to support the advancement of critical thinking as determined by Facione (1990). The lesson plans of the designed teaching module were applied to future mathematics teachers in primary schools. In the study, worksheets constitute teaching model applications lesson plans and it is aimed to evaluate the statements of the pre-service teachers on the worksheets regarding solutions, suggestions and results within the framework of critical thinking skills. During the fall term of the 2019-2020 educational year, we carried out the research study with fourth-graders enrolled at the Faculty of Education, Primary Mathematics Education of a state university in the Marmara Region in Turkey for one semester. This study utilized a case study design, also known as qualitative research. Worksheets that constitute the designed lesson plans served as instruments for collecting data. Using descriptive analysis and content analysis, we analyzed the answers provided by prospective teachers on the worksheets. The previous study concluded that the designed lesson plans were compatible with the critical thinking sub-skills determined by Facione, and contributed to the critical thinking skills of future teachers.

WORKING WITH GIFTED CHILDREN IN TEACHING MATHEMATICS IN PRIMARY GRADES

WORKING WITH GIFTED CHILDREN IN TEACHING MATHEMATICS IN PRIMARY GRADES

Online Mathematics Education during the COVID-19 Pandemic: Didactic Strategies, Educational Resources, and Educational Contexts

One of the impacts of the COVID-19 pandemic has been restrictions on mobility and thus the closure of schools. This has had consequences on the teaching strategies of primary mathematics educators who were not familiar with online education. Most schools in Chile have adopted virtual and hybrid classes to continue educational processes. From a quantitative approach with a sample of n = 105 primary school educators and through an online survey, we analyzed how educators implemented the mathematics curriculum during the pandemic using various didactic strategies and educational resources, as well as their respective contexts. The results show that there is a relationship between the level of technical knowledge of teachers, the years of experience, and the types of teaching strategies they use. Likewise, differences were found between educators in rural and urban sectors according to the use of teaching strategies and the types of educational resources used. Regarding the didactic strategies, it is shown that the emerging strategies most used are metaphorical and analogical, whereas in traditional strategies the automation of procedures is imposed. The implications for practice include suggestions and guidelines for improving the training and professional development of mathematics teachers including increasing and strengthening the number and quality of teachers’ didactic strategies and online pedagogical management skills and promoting metacognition through virtual forums. Finally, we discuss the context of the use of didactic strategies in mathematics during the pandemic, analyzing its challenges and opportunities.

Primary School Mathematics Teachers’ Beliefs About Teaching in Synchronous Virtual Classrooms: A Mixed Method Study

<p style="text-align:justify">This study was conducted following the initial stage of the transition to distance education necessitated by the onset of the COVID-19 pandemic and meeting the various challenges that came with it. At this point, countries and teachers have gained experience in preparing and delivering online education. Therefore, the study aimed to identify the beliefs of primary school mathematics teachers about teaching in synchronous virtual classrooms. It adopted a mixed methods approach, following a convergent parallel design. The overall study sample comprised 410 male and female teachers. A questionnaire was used to collect quantitative data across three dimensions (teaching efficiency, employing the philosophy of active learning, mathematical achievement). There were 31 items (verified for validity and reliability) comprising statements measured using a five-point Likert scale, together with open-ended options for further elaboration. In total, 130 teachers completed the questionnaire. Interviews were conducted with 10 teachers to collect qualitative data. The results show means in the range 3–5.75 for agreement with statements concerning the beliefs of mathematics teachers about teaching in virtual classrooms in the following order of importance: teaching competence; mathematical achievement; employing the philosophy of active learning. The study also found no statistically significant differences attributable to the variables of gender, qualification, or teaching experience, and also that many factors are considered to affect teaching in synchronous virtual classrooms related to the teacher, the family, and the student.</p>

Factors and Parameters Influencing Student Achievement in Mathematics: A Comparative Study between Israel and Finland

<p style="text-align: justify;">In all years of the Program for International Student Assessment (PISA) in primary mathematics education, Finland ranked in the lower places (44-61) in the dispersion index (the difference in scores between the 95th percentile and the 5th percentile), while Israel ranked in the upper places (1-3) in the same index. In the last PISA test, Israel ranked first (among the 78 participating countries) in grade differences, while Finland ranked 61st. The score for dispersion in Israel is 356 points, the highest among the countries and economic entities of the Organization for Economic Cooperation and Development (OECD). Based on these results, this comparative study between Israel and Finland was conducted to investigate the most important sociological factor in the Pisa test that influences most student achievements in mathematics in Finland and Israel, as well as the reasons for the differences in achievement between mathematics scores. The results of this study show that the differences in achievement in Israel are due to students' socio-economic status and the sector. In contrast, Finland's first sociological factor influencing student performance is socio-economic status. Nevertheless, it has a more negligible influence than in Israel. The second factor is student motivation.</p>

Growing research groves to visualize young students’ learning in small groups

This paper stems from calls for methodological advancement in two areas of research: primary mathematics education and dialogical education. We respond to these calls from the commognitive standpoint by introducing the Grove of Realizations as a tool for capturing and visualizing individual students’ learning through collaborative work in small groups. We focus on a group of four students from a New Zealand Year 4 class (aged 8 and 9 years old), as they classified odd and even numbers and reasoned about their sums. This data is used to present the analytical affordances of the tool for (i) visualizing gaps in communication between group members, (ii) mapping their discursive development, and (iii) showing whether and how gaps are bridged within a group. The paper concludes with the discussion of the tool’s affordances and directions for further development.

Primary School Teachers and Students’ Opinions of the First-Grade Mathematics Curriculum in a Turkish Context

This research was carried out to determine the opinions of teachers and students in-depth regarding the primary-school first-grade mathematics curriculum in a Turkish context. This study was designed in accordance with a mixed research method to achieve this goal and to examine the situation that emerged during the implementation of a curriculum. The data collection tools were the “Mathematics Curriculum Evaluation Scale,” semi-structured teacher and student interviews, and an observation form. The thoughts of teachers and students regarding the primary school mathematics curriculum were determined in-depth, and the situations that emerged during the implementation of the program were examined. The research population comprised first-grade teachers working in primary schools in central districts of Turkey. Descriptive statistics and content analyses were used for the data analysis. Based on the results, it was concluded that the general structure and objective of the mathematics curriculum were sufficient.

NEW INNOVATIVE IDEAS IN THE METHODS OF TEACHING MATHEMATICS IN PRIMARY SCHOOL AND METHODS OF TEACHING MATHEMATICS

NEW INNOVATIVE IDEAS IN THE METHODS OF TEACHING MATHEMATICS IN PRIMARY SCHOOL AND METHODS OF TEACHING MATHEMATICS

Integrating research into practice: The growth of collective pedagogical content knowledge for primary mathematics via lesson study

Teacher is the most important person in enhancing the students’ learning and lesson study (LS) has achieved international consensus as a vehicle for developing good lessons and enhancing teachers’ professional skills. The aim of this study is to explore how lesson study might act as a form of professional development in helping primary mathematics teachers to develop their collective pedagogical content knowledge in teaching mathematics for the topic of quadrilaterals in the fourth grade. The case study approach with a participant researcher was used. Adapting the sociocultural perspective, the teachers’ reflective practice in LS is linked to the teachers’ engagement with inquiry and research. The term “ Collective Pedagogical Content Knowledge” ( collective PCK) is used to describe the pedagogical content knowledge that is explicitly developed and shared by the LS teachers with evidence identified as “Seed Events” in the analysis. Seed Events are episodes identified in LS teacher meetings or research lessons, leading into deep reflection, consequently clarifying the conceptions of mathematics objects, enhancing the pedagogical strategies, and further enactment in subsequent research lessons. Finally, we further argue that LS is a wise investment of professional capital so that teachers can envision their professional growth with their industrious effort for something worthy.

Micro-lesson Embedded in Primary Mathematics Classrooms

Micro-lesson Embedded in Primary Mathematics Classrooms

Fostering Geometrical Measurement Skills to Enhance Geometrical Measurement Performance in Primary Schools

Geometrical measurement becomes one of the most critical topics in primary mathematics which require the understanding of the underlying concepts and not just focusing solely on formulas. Unfortunately, the teaching and learning of geometrical measurement is usually based on rules, procedures and formulas. Besides, research have also shown that the scarcity of the conceptual understanding significantly contributes to the poor geometrical measurement understanding. Thus, the focus of this study is to clarify the specific types of geometrical measurement skills that contribute to the geometrical measurement conceptual understanding. The research method was based on literature review search strategy through online database such as Google Scholar and Scopus. The results of this study indicate that in order to grasp the conceptual understanding of geometrical measurement, pupils need to be proficient in geometrical measurement skills. From the literature, it can be concluded that geometrical measurement skills involve the integration of spatial skills and numerical skills. Thus, the findings of this study led us to draw conclusions on the skills that guide primary-level pupils to grasp conceptual understanding in geometrical measurement. Subsequently, the findings may also provide guidance for potential researchers and teachers to evaluate the performance of pupils in geometrical measurement such as developing an alternative assessment tool.

Responsive Teaching: Differences in Primary Mathematics Teachers’ State of Awareness and Reflections on own Teaching

This paper contributes to research in responsive teaching in a context of collaborative discussion using video stimulated recall (VSR) techniques. The aim was to gain deeper understanding of the kinds of teachers’ reflective awareness that prompts changes (or lack of change) in responsive primary mathematics teaching. Using a case study methodology, I analysed the VSR interviews of two teachers who demonstrated different patterns of changes in responsive teaching. The findings revealed two distinct and complementary forms of evidence of states of awareness and reflections that support change in responsive teaching practices: (a) teachers acknowledging limitations of their practice; and (b) teachers expanding repertoires of tasks and example spaces. These two forms of evidence provide insights into ways of supporting primary mathematics teaching in the context of VSR techniques. The implication of these findings is that for effective use of VSR interviews, attention should be geared towards getting a teacher to acknowledge the limitations of her practice, and through reflection-oriented questions to encourage the teacher to expand task and example space to respond to the limitations noted within the teacher’s practice.

Comparing Two Frameworks for Exploring the Quality of Mathematics Teaching in a Malawian Primary Classroom

Over the years, several frameworks and lesson observation protocols have been developed to ensure objectivity and consistency when determining the quality of a mathematics lesson. Frequently, the frameworks do not agree on the benchmarks for assessing and describing the quality of a lesson. This puts mathematics education researchers in a dilemma when deciding the appropriate framework for analysing mathematics lessons. Instead of treating the frameworks as mutually exclusive, we are of the view that each framework has some unique aspects that contribute to the story about the quality of a mathematics lesson. In this paper, we examine how the Mathematical Quality of Instruction framework and the Mediating Primary Mathematics framework, as lenses, help us to see and describe various aspects of instructional quality from one episode of a mathematics lesson in Malawi. We notice that the two frameworks share some common criteria for describing the quality of a mathematics lesson, such as the focus on making mathematical connections and using multiple representations, but they also differ on other areas of emphasis, such as the use of artefacts in the Mediating Primary Mathematics framework, and the emphasis on errors in the Mathematical Quality of Instruction framework. As such, we conclude that both frameworks can be useful for discussing the quality of a lesson in a professional development setup.

Development of primary school fourth-grade students’ fraction calculation strategies through the argumentation method

One of the most fundamental subjects of primary school mathematics, the concept of fraction plays a key role in students' educational background. Students experience difficulties and misconceptions regarding this concept. Therefore, it is of great importance to understand this subject well and to use different teaching methods and techniques. Various methods can be used in learning mathematics, such as invention method, computer-assisted teaching, problem solving, creative drama and discussion. Argumentation method is a scientific discussion of a claim on a subject by providing data, warrant and backing, and by revealing the rebuttal and the invalidity of the claim. Students gain more skills by interacting with teachers or collaborating with their peers, and that they possess skills that have not been obtained before or that are too difficult to achieve on their own. Therefore, the argumentation method was chosen for its effect on the development of primary school students’ fraction calculation strategies. Having a case study design, this study was conducted with 28 primary school fourth-grade students and 10 open-ended questions prepared by the researchers were used during interviews. The results suggested that primary school students were able to develop fraction calculation strategies through the argumentation method. In general, inventing strategies, using representations, number sense, addition and subtraction, using unit fractions and proportional reasoning were used as fraction calculation strategies. It recommended to use the argumentation method in other critical subjects of mathematics as well.

Do There Any Higher Order Thinking Skills in the Cambridge Primary Mathematics Textbook?

The poor results of national and international assessments make the national curriculum get criticism. Meanwhile, the Cambridge curriculum gets popular because of its quality. Textbooks as curriculum manifestations affect student learning. This study describes Higher Order Thinking Skills (HOTS) and the dominance of its level in the Cambridge Primary Mathematics 4 textbooks which are Teacher's Resources and Learner's Book. This study uses a directed qualitative content analysis method. This research shows that all HOTS levels (analyze, evaluate, and create) are spread across four major themes (number, measure, data handling, and geometry) Teacher's Resource and Learner's Book. Theoretically, HOTS in the Teacher's Resource and Learner's Book can teach critical thinking, creativity, collaboration, and communication because the learning content of HOTS in this book uses a student-centered approach and the teacher actively provides scaffolding using open-ended questions, discussions, and group activities. HOTS level creating is dominant in Teacher's Resource and analysis is dominant in Learner's Book.
 Abstrak
 Hasil assesmen nasional dan internasional yang konsisten buruk membuat kurikulum nasional menuai kritik. Sementara itu, kurikulum Cambridge diminati sejumlah kalangan karena dianggap lebih berkualitas. Buku teks sebagai manifestasi kurikulum berpengaruh terhadap pembelajaran siswa. Tujuan penelitian ini yaitu mendeskripsikan Higher Order Thinking Skills (HOTS) dan dominasi levelnya dalam buku teks Cambridge Primary Mathematics 4 yang terdiri dari Teacher’s Resources dan Learner’s Book. Penelitian ini menggunakan metode analisis isi kualitatif terarah. Hasil penelitian ini menunjukkan bahwa ketiga level HOTS (menganalisis, mengevaluasi, dan mencipta) tersebar dalam keempat tema besar (number, measure, handling data, dan geometry) Teacher’s Resource dan Learner’s Book. Secara teoretis, HOTS dalam Teacher’s Resource dan Learner’s Book dapat membelajarkan critical thinking, creativity, collaboration, dan communication karena pembelajaran muatan HOTS dalam buku ini terpusat pada siswa dan guru aktif memberikan scaffolding menggunakan pertanyaan open-ended, diskusi, serta aktivitas berkelompok. HOTS dalam Teacher’s Resource didominasi oleh level mencipta, sedangkan Learner’s Book didominasi level menganalisis.

Noticing student thinking under pressure in primary mathematics and science lessons

Teacher noticing of student thinking represents a key aspect of teacher expertise as it informs teachers’ actions ‘on the fly’ during a lesson. In science and mathematics education, teacher noticing has been conceptualised as being driven by attending to and making sense of student thinking. A range of models of noticing developed in professional fields such as aviation posit that perceptual interaction is also a key driver of noticing. This paper presents an alternate, ecological model of teacher noticing that begins with the premise that teachers have limited capacity to make sense of noteworthy events mid-lesson. Multimodal data collected from a primary science and mathematics lesson, taught by the same teacher, is analysed using the ecological lens. The analysis draws research attention to aspects of teacher/classroom interaction such as attention deployment and the role that classroom environments play in facilitating mid-lesson noticing of student thinking. Differences in teacher noticing between the science and mathematics lesson can be accounted for in terms of variance in environmental structure rather than solely in terms of teacher cognition.

Problems and Optimization Strategies in Teaching Primary Mathematics

Problems and Optimization Strategies in Teaching Primary Mathematics