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 Showing 601 - 538 of 538 Journals sorted alphabetically Results in Mathematics Results in Nonlinear Analysis Review of Symbolic Logic       (Followers: 2) Reviews in Mathematical Physics       (Followers: 1) Revista Baiana de Educação Matemática Revista Bases de la Ciencia Revista BoEM - Boletim online de Educação Matemática Revista Colombiana de Matemáticas       (Followers: 1) Revista de Ciencias Revista de Educación Matemática Revista de la Escuela de Perfeccionamiento en Investigación Operativa Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Revista de Matemática : Teoría y Aplicaciones       (Followers: 1) Revista Digital: Matemática, Educación e Internet Revista Electrónica de Conocimientos, Saberes y Prácticas Revista Integración : Temas de Matemáticas Revista Internacional de Sistemas Revista Latinoamericana de Etnomatemática Revista Latinoamericana de Investigación en Matemática Educativa Revista Matemática Complutense Revista REAMEC : Rede Amazônica de Educação em Ciências e Matemática Revista SIGMA Ricerche di Matematica RMS : Research in Mathematics & Statistics Royal Society Open Science       (Followers: 7) Russian Journal of Mathematical Physics Russian Mathematics Sahand Communications in Mathematical Analysis Sampling Theory, Signal Processing, and Data Analysis São Paulo Journal of Mathematical Sciences Science China Mathematics       (Followers: 1) Science Progress       (Followers: 1) Sciences & Technologie A : sciences exactes Selecta Mathematica       (Followers: 1) SeMA Journal Semigroup Forum       (Followers: 1) Set-Valued and Variational Analysis SIAM Journal on Applied Mathematics       (Followers: 11) SIAM Journal on Computing       (Followers: 11) SIAM Journal on Control and Optimization       (Followers: 18) SIAM Journal on Discrete Mathematics       (Followers: 8) SIAM Journal on Financial Mathematics       (Followers: 3) SIAM Journal on Mathematics of Data Science       (Followers: 1) SIAM Journal on Matrix Analysis and Applications       (Followers: 3) SIAM Journal on Optimization       (Followers: 12) Siberian Advances in Mathematics Siberian Mathematical Journal Sigmae SILICON SN Partial Differential Equations and Applications Soft Computing       (Followers: 7) Statistics and Computing       (Followers: 13) Stochastic Analysis and Applications       (Followers: 2) Stochastic Partial Differential Equations : Analysis and Computations       (Followers: 1) Stochastic Processes and their Applications       (Followers: 5) Stochastics and Dynamics Studia Scientiarum Mathematicarum Hungarica       (Followers: 1) Studia Universitatis Babeș-Bolyai Informatica Studies In Applied Mathematics       (Followers: 1) Studies in Mathematical Sciences       (Followers: 1) Superficies y vacio Suska Journal of Mathematics Education       (Followers: 1) Swiss Journal of Geosciences       (Followers: 1) Synthesis Lectures on Algorithms and Software in Engineering       (Followers: 2) Synthesis Lectures on Mathematics and Statistics       (Followers: 1) Tamkang Journal of Mathematics Tatra Mountains Mathematical Publications Teaching Mathematics       (Followers: 10) Teaching Mathematics and its Applications: An International Journal of the IMA       (Followers: 4) Teaching Statistics       (Followers: 8) Technometrics       (Followers: 8) The Journal of Supercomputing       (Followers: 1) The Mathematica journal The Mathematical Gazette       (Followers: 1) The Mathematical Intelligencer The Ramanujan Journal The VLDB Journal       (Followers: 2) Theoretical and Mathematical Physics       (Followers: 7) Theory and Applications of Graphs Topological Methods in Nonlinear Analysis Transactions of the London Mathematical Society       (Followers: 1) Transformation Groups Turkish Journal of Mathematics Ukrainian Mathematical Journal Uniciencia Uniform Distribution Theory Unisda Journal of Mathematics and Computer Science Unnes Journal of Mathematics       (Followers: 2) Unnes Journal of Mathematics Education       (Followers: 2) Unnes Journal of Mathematics Education Research       (Followers: 1) Ural Mathematical Journal Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Vestnik St. Petersburg University: Mathematics VFAST Transactions on Mathematics       (Followers: 1) Vietnam Journal of Mathematics Vinculum Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics       (Followers: 1) Water SA       (Followers: 2) Water Waves Zamm-Zeitschrift Fuer Angewandte Mathematik Und Mechanik       (Followers: 1) ZDM       (Followers: 2) Zeitschrift für angewandte Mathematik und Physik       (Followers: 2) Zeitschrift fur Energiewirtschaft Zetetike

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 ZDMJournal Prestige (SJR): 0.781 Citation Impact (citeScore): 1Number of Followers: 2      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1863-9704 - ISSN (Online) 1863-9690 Published by Springer-Verlag  [2469 journals]
• Characteristics of Chinese high-quality mathematics lessons from a lesson
structure perspective

Abstract: Abstract In this study we aimed to capture the characteristics of Chinese high-quality lessons from a lesson structure perspective, specifically addressing the elements of teaching activity and their sequence. Sixteen videotaped middle school mathematics lessons were selected from 224 daily lessons collected from urban districts in five cities located in the east, north, west, south, and center of China, approved by three independent parties (based on the scores of an instruction quality assessment and ratings by two experts). We found the following five common features among most mathematics lessons: (a) most lessons began with a review; (b) pure learning of mathematical knowledge was emphasized; (c) recurrent teaching activities related to mathematics problems ran throughout the lesson; (d) highlighting and summarizing important points during the lesson and summarizing the entire lesson at the end of the class were frequently used; and (e) teaching activities were dense and large in volume. The research findings paint a broad picture of high quality instruction (deepening our understanding of high-quality teaching in different cultures) and provide multiple choices for teachers.
PubDate: 2022-05-17

• The trajectory of Chinese mathematics textbook development for supporting
students’ interest within the curriculum reform: a grade eight example

Abstract: Abstract Interest is vital for students’ learning in mathematics. Over the course of the Chinese mathematics curriculum reform in the past 30 years, cultivating students’ positive emotions, attitudes, and values has gained growing attention. In the current study we examined the trajectory of Chinese mathematics textbook development by analyzing textbook content that stimulated students’ mathematics learning interest through the curriculum reform in the past three decades. First, we selected textbooks that represent each phase of the curriculum reform (the Incubation Phase, the Reform Phase, and the Conditioning Phase). Then, taking eighth grade as an example, we used Hidi and Renninger’s model to identify content that focus on stimulating students’ learning interest. Finally, we explored the trajectory of textbook development in this aspect within the scope of curriculum reform. Results show that attention to strategies developing positive emotions and values towards mathematics has been emerging in recent times. Interest-stimulating strategies directed toward the triggering and maintaining of situational interest have been integrated more frequently into textbooks since the Reform Phase, while text content employing strategies that may lead to rote memorization is generally decreasing. Using Chinese curriculum reform as a context, this study demonstrates how mathematics textbooks have been revisioned and revised with a focus on stimulating students’ learning interest. The reform of mathematics education has been successfully implemented in more than thirty provinces in China, despite significant differences in geographical, cultural, and economic development. It is hoped that this study can provide practical evidence of interest stimulation in mathematics for the international education community.
PubDate: 2022-05-14

• Mathematical metacognitive characteristics of Chinese middle school
students in efficient mathematics learning

Abstract: Abstract The purpose of this study was firstly to investigate the mathematical metacognitive characteristics of high-efficiency students by comparing high-efficiency and low-efficiency students. Secondly, the aim was to explore the pathways of mathematical metacognition of efficient mathematics learners in mathematics achievement. In this study, second-year Chinese middle school students were divided into a high-efficiency group (n = 297) and a low-efficiency group (n = 203) according to their learning efficiency in mathematics. The results indicated that the mathematical metacognitive knowledge and mathematical metacognitive monitoring of the students with high efficiency in mathematics learning were better than those of the other group. Their mathematical metacognitive characteristics were mainly reflected in the five dimensions of regulation, inspection, knowledge about individuals, knowledge about tasks, and knowledge about strategies. Furthermore, path analysis revealed that both mathematical metacognitive monitoring and mathematical metacognitive experience directly affected the mathematics achievement of students in the highly effective group. Mathematical metacognitive knowledge had an indirect effect on mathematics achievement. The findings imply that teachers should focus on the guidance of mathematical metacognition in mathematics instruction.
PubDate: 2022-05-12

• Exploring students’ mathematical discussions in a multi-level hybrid
learning environment

Abstract: Abstract The research described in this paper focused on the issue of describing and understanding how mathematical discussion develops in a hybrid learning environment, and how students participate in it. The experimental plan involved several classes working in parallel, with pupils and teachers interacting both in their real classrooms and in a digital environment with other pupils and teachers. The research was based on a rich set of data collected from the M@t.abel 2020 project, which was developed in Italy during the Covid health crisis. Based on Complementary Accounts Methodology, the data analysis presented in this paper involved specialists from the fields of mathematics education and inclusive education. In the study we considered the complexity of learning and the different elements that have an impact on students’ activity and participation, when they are engaged in mathematical discussions within the multilevel-digital environment that emerged due to the pandemic. These parallel analyses showed that ‘mathematical discussion in the classroom’ is a complex (and sometimes chaotic) phenomenon wherein different factors interweave. A complementary approach assists in developing a global vision for this dynamic phenomenon and in highlighting local episodes that are crucial in this interplay of factors. It is precisely in these episodes that the role of the teacher is fundamental: these episodes appear as catalysts for the different variables, with the teacher acting as mediator.
PubDate: 2022-05-05

• The Learner’s Perspective Study Methodology: a legacy for future
researchers

Abstract: Abstract David Clarke’s research has shifted the focus of classroom research in mathematics education from study of cultural patterns to study of patterns of participation and the learning that can result in highly complex social environments. His Complementary Accounts Methodology which informed the Learner’s Perspective Study design included multi-source data collection generated through the latest technological advances at that time. That research design enriched the author’s doctoral research which was situated within the Learner’s Perspective Study. One intention of this paper is to highlight ways in which Clarke’s methodology added to the richness of the study Williams undertook, in particular, the flexibility of Clarke’s methodology in enabling adaptation to support a theoretical framework that included but extended beyond social theories of learning. In doing so, this paper draws attention to an aspect of Clarke’s methodological legacy, the potential for his Complementary Accounts Methodology to contribute to support of researchers employing diverse theoretical frameworks.
PubDate: 2022-05-04

• Encouraging research on recursive thinking through the lens of a model of

Abstract: Abstract Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum’s later emphasis on calculus—the mathematics of change in continuous contexts—it is surprising that the curriculum seems to neglect recursive thinking after the early grades. Research shows that recursion supports the learning of algebra among younger students, but the lack of similar research with older students is concerning. In this paper we suggest possible affordances from teaching recursive modeling, including a basic model of the spread of contagious diseases. We also discuss different ways to present these models at various points in the curriculum that might develop connections between mathematics and the real world, and support students’ learning of mathematics. This leads to what we, as mathematicians, think would be interesting research questions for mathematical educators.
PubDate: 2022-05-03

• Chinese students’ access, use and perceptions of ICTs in learning

Abstract: Abstract Due to rapid social and economic development in China over the last three decades, information and communication technologies (ICTs) have become increasingly available in Chinese classrooms and families. However, there is a lack of research regarding Chinese students’ use of ICTs in mathematics learning. In this study, we examined how Chinese students access, use, and perceive ICTs in learning mathematics. To this end, a conceptual framework for ICTs and the role of ICTs in students’ learning of mathematics was established. Using a mixed-methods approach, we collected data from 223 students in four randomly selected secondary schools in Shanghai through a questionnaire survey, followed by classroom observations and interviews with students and teachers. The results revealed that various ICTs are widely accessible in Shanghai classrooms and students overall have a positive view about the role of ICTs in their mathematics learning, especially in problem solving and in learning geometry. When learning mathematics at home, students used handheld technological devices more frequently than non-portable devices. Furthermore, there were significant differences between different students in terms of school performance levels, grade levels, and genders in their use of ICTs in learning mathematics. In particular, students from high-performing schools had more access to various ICTs but used them less frequently than their peers from ordinary schools. Suggestions and implications of the findings are discussed at the end of the paper.
PubDate: 2022-04-29

• Investigating teacher noticing and learning in Australia, China, and
Germany: a tale of three teachers

Abstract: Abstract Teacher noticing can be an important element in improving teaching and students’ mathematical success. While the focus of the international project Learning from Lessons was on teacher learning, in this paper we report what mathematics teachers noticed and claimed to learn through the process of planning, teaching, and reflecting on their lessons. The study involved teachers and research teams from three countries (Australia, China and Germany) with different cultures, contexts and pedagogies. The explicit goal of the current study was to identify commonalities and differences with respect to those aspects that teachers noticed during their teaching. A multiple case study with three teachers, one from each of the three participating countries, was conducted using prompting questions to facilitate teacher reflection. The process of defining and refining categories for teacher noticing was implemented in the methodology. The findings suggest that there were many commonalities across the cases despite the different cultural and individual backgrounds of the teachers. The specific topic and individual lessons as well as the teachers’ expectations based on their lesson planning seemed to influence what the teachers noticed in their teaching process. The study highlights the importance of attending to the situational aspects of teacher noticing and learning.
PubDate: 2022-04-29

• What does it take to learn about teaching and learning in classrooms
across cultures'

Abstract: Abstract Beginning in the 1960s and early seventies, classroom research contributed to understandings and insights concerning the complexities and diversities of teaching. In the late 1990s, classroom research began to also include student voices in the classroom. Socio-cultural theory turned the empirical focus toward student interaction, and methodological development made new insights possible. The impact of this paradigmatic change is still in progress. At the same time, a rapid growth in international comparative classroom studies emerged, where the two most recognized comparative classroom research initiatives have been the TIMSS Video Studies, the first one initiated in 1995 at the University of California, Los Angeles, and the Learner’s Perspective Study (LPS), initiated in 1999, at the University of Melbourne’s International Center for Classroom Research (ICCR). In this paper, we ask what it takes to carry out successful international classroom research, using the LPS as an example. The analysis shows that the LPS project design made it possible for research groups from different countries and cultures to participate in building a sustainable community of research practice specialized in working with the complexities in the study of teaching and learning in classrooms. Of particular importance was the intense and sustained collaborative work on data, where researchers of varying seniority and experience met and carried out scholarly work in relation to a shared dataset. While also having disadvantages, the heavy emphasis on data was crucial for creating and sustaining a reflexive international research community.
PubDate: 2022-04-27

• The interplay between history of Mathematics and Digital Technologies: a
review

Abstract: Abstract This article is a review of the literature on the use of history of mathematics in combination with use of digital technologies in the teaching and learning of mathematics. The review identifies 33 peer-reviewed publications (book chapters, journal articles, and papers in conference proceedings) that address an actual interplay between use of history and digital technologies. Of these, 24 concern the use of primary historical source material, i.e., mathematical texts produced by past (historical) mathematicians. Besides asking the questions of which publications actually incorporate this interplay and what purposes the use of history and digital technology serve, we also address the question of the role of mathematics education theoretical perspectives (or the lack thereof) in the identified publications. A reading of the identified publications shows that the ones involving use of primary historical source material often have a clearer connection to theoretical constructs from mathematics education research (outside the area of History and Pedagogy of Mathematics, or HPM). Still, only a small number of the identified publications make use of mathematics education theoretical constructs specifically addressing the use of digital technology.
PubDate: 2022-04-26

• Using combinatorics problems to support secondary teachers understanding
of algebraic structure

Abstract: This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers’ combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of polynomials. The data in this paper examines the learning that occurred as one teacher transitioned from making a generalization from a sequence of contextualized combinatorics problems to applying her combinatorial reasoning to symbolic problems common in algebra curricula. The findings from the study include the identification of three planes of learning that can be used to differentiate among ways that combinatorial reasoning can be used to engage in binomial expansion. The highest plane involved constructing a combinatorial scheme for binomial expansion, a scheme that supported the teacher to produce the equivalence, $$\left(x+a\right)\left(x+b\right)\left(x+c\right)={x}^{3}+\left(a+b+c\right){x}^{2}+\left(ab+ac+bc\right)x+abc$$ ), and to see important algebraic structure in it. The contributions of the study include: (a) expanding earlier arguments about the ways that combinatorics can be integrated into goals of extant curricula (e.g., Maher et al. in Combinatorics and reasoning: Representing, justifying and building isomorphisms. Springer, 2011); and (b) proposing how reflecting abstraction can be used to study the transition between generalizations learners make from contextualized problem situations to operating with and on generalizations expressed with  conventional algebraic symbols. This second contribution is an under-researched area in the algebra literature (Dörfler in ZDM - Int J Math Educ 40(1):143–160, 2008), and points to an important role that combinatorial reasoning can play in algebra learning.
PubDate: 2022-04-25

• Teachers’ learning in lesson study: insights provided by a modified
version of the interconnected model of teacher professional growth

Abstract: Abstract In the research reported in this paper, using a modified version of the interconnected model of teacher professional growth (IMTPG) proposed by Clarke and Hollingsworth (Teaching Teacher Educ 18:947–967, 2002), we aimed to understand the learning dynamics in a lesson study of a group of five teachers of grades 5–6, during their work around mathematical tasks and in the elaboration and analysis of a diagnostic test of students’ knowledge. We draw on examples from a lesson study that took place in a school in Lisbon, involving five teachers that constituted the whole mathematics group of the school. The main feature of our adaptation is the consideration of a Group Domain instead of the Personal Domain of the original model. In the original model, the Domain of Practice had a broad definition but usually it was restricted to classroom experimentation. In the research reported in this paper, the lesson study sessions were taken as part of the Domain of Practice. For data collection, there was audio and video recording of the lesson study sessions and of the research lesson and the writing of a research journal. Data analysis was done using the modified IMTPG. The results suggest that this model is helpful in understanding the processes that make lesson study a valuable professional development setting, contributing to responding to the question of ‘how lesson study works’ (Lewis et al., Theory and practices of lesson study in mathematics: an international perspective, Springer, New York, 2019). In addition, the use of this model showed that the lesson study promoted the teachers’ development regarding knowledge of didactics, especially knowledge of students and their learning processes and of teaching practice.
PubDate: 2022-04-23

• Exploring Shanghai students’ mathematics learning as related to content
presentation in textbooks: the case of the commutative property of

Abstract: Abstract Properties of arithmetic operations are important in mathematics and play a significant role in elementary school students’ learning of mathematics. At the same time, it is quite challenging to help students learn arithmetic operational properties beyond memorization, so that they know when and how to use a specific arithmetic property. This paper reports a study containing two parts to explore students’ learning of the Commutative Property of Addition (CPA) as related to the content presentation in textbooks. Part one is to assess selected students’ performance on CPA at the end of Grade two, and part two is to explore possible contributions of textbooks to students’ performance in Shanghai. Firstly, we evaluated the performance of 41 second-graders on CPA by collecting data through a paper-and-pencil test, which was followed up with individual interviews. Through analyzing how textbooks present and organize this topic, we sought to better understand from a curriculum standpoint how students’ performance on CPA is impacted by textbooks. Results revealed that Shanghai textbooks make a positive contribution to students’ learning performance. The findings from this study help to shed light on how those textbooks aid student learning, and provide an example for further reflection on student learning of arithmetic operational properties in different curricula.
PubDate: 2022-04-20

• The impact of illustrations on solving mathematical word problems for
Chinese primary school students: evidence for a split attention effect on
eye-movement research

Abstract: Abstract To analyze the impact of illustrations on solving mathematical word problems for primary school students, in this study we investigated systematically the functions of illustrations in terms of various presentations of texts and illustrations, and the difficulties associated with various learning materials. The characteristics of eye movement were studied with regard to the effect of split attention by using eye trackers. The results revealed the following: the presentation format of integrated texts and illustrations worked the best for problem solving under the condition of mathematical word problems with illustrations; the difficulty of the problem affected the role of illustrations; a high frequency of attention switching between texts and illustrations and longer fixation durations on the required picture provided evidence for the split attention effect using an eye-movement index. Based on these results, using more visual and verbal representations helps students solve mathematical word problems.
PubDate: 2022-04-19

• Contradiction and its solutions in the mathematics teacher–researcher
partnership: an activity theory perspective

Abstract: Abstract As an essential community of practice which could facilitate teachers’ professional development and enrich research in teacher education, the teacher–researcher partnership (TRP) has not been sufficiently investigated in China. As reported in this paper, we conducted an empirical study on TRPs between secondary school mathematics teachers and university researchers by applying activity theory to investigate their collaboration and contradictions, through the process of co-designing lesson studies. We found four levels of contradictions, namely, primary, secondary, tertiary, and quaternary, within which the fourth one occurs less frequently compared to the other three. To ameliorate or even resolve the contradictions, it requires both sides to (1) achieve agreement on understanding the objects, (2) promote equality in communication and mutual respect, (3) facilitate transformation in identity, and (4) construct a united community. In addition, the investigation provided a depiction of how teachers learn and grow in the TRP as well as how teachers and researchers interact in the partnership, which in turn enriches both teacher education and activity theory.
PubDate: 2022-04-16

• Mathematicians’, mathematics educators’, and mathematics teachers’
professional conceptions of the school learning of mathematical modelling
in China

Abstract: Abstract Mathematical modelling has been included in many mathematics curricula worldwide, and China’s curricula are no exception. The development of modelling competencies has recently been listed among the Chinese mathematics curriculum’s six key objectives. However, the manner in which nationwide learning and teaching of modelling should be conducted presents a key challenge to China’s schools, most of which are wholly lacking in experience of this practice. In this study we present a thematic analysis of the conceptions of four mathematicians, five mathematics educators and seven mathematics teachers, with regard to the learning and teaching of modelling. The results show that the participants’ views of modelling can be categorised and linked to the following theoretical perspectives of modelling: applied, epistemological, educational, pedagogical and conceptual perspectives. Interestingly, the mathematicians and mathematics educators tended towards the atomistic approach to the learning and teaching of modelling, while the mathematics teachers placed greater emphasis on the holistic approach. The mathematicians and mathematics educators stressed student autonomy, while the teachers emphasised teacher demonstration. All participants considered group work to be an appropriate means of conducting modelling learning and teaching. Additionally, some teachers were concerned that modelling could not be incorporated into mathematical teaching and learning if it could not be included in high-stakes examinations. The paper concludes with a discussion on the rationale behind the existence of the various conceptions and the potential insights that may be drawn from these conceptions.
PubDate: 2022-04-15

• Coordinating invisible and visible sameness within equivalence
transformations of numerical equalities by 10- to 12-year-olds in their
movement from computational to structural approaches

Abstract: Abstract “They are the same” is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this' The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to 12-year-olds) was presented with tasks that required transforming the given numerical equalities in such a way as to show their truth-value. The students initially indicated this by calculating and demonstrating that the total was the same on both sides. When asked not to calculate, their approaches evolved into more structural transformations involving decomposition so as to arrive at an equality with the same expression on each side. Students used the language of sameness—both visible and invisible—to describe the truth-value of their transformed expressions and equalities. The visible sameness referred to the resulting identical form of each side of the equality and the invisible sameness to the top–down equivalences that they had generated by their decomposing transformations—both types of sameness being characterized by their hidden numerical values. These findings suggest implications for transitioning to the algebraic domain of equations with their similarly hidden values.
PubDate: 2022-04-09

• Two students’ mathematical thinking and activity across representational
registers in a combinatorial setting

Abstract: Abstract In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students’ combinatorial reasoning. In this paper, we contribute to research that explores effective ways to foster students’ combinatorial reasoning by highlighting the role that shifts in representational registers can play in supporting students’ combinatorial reasoning and activity. In particular, we present a case in which two students, aged 12 and 14, reasoned about, and developed a formula for, binomial coefficients. This occurred in a teaching experiment designed to examine their generalizing activity. In these interviews, the students first solved problems about determining the volume of a cube and then shifted to a combinatorial interpretation of this task, leveraging binomial coefficients as a way to consider growth in higher dimensions. The students demonstrated sophisticated reasoning about combinatorial tasks and were ultimately able to generate and understand a formula for binomial coefficients. In framing this case, we focus on the students’ use of different representations, highlighting the power of being able to transition between representational registers as a way of supporting students’ combinatorial reasoning. In this way, our case demonstrates the value of representational registers specifically as a mechanism by which to potentially improve the teaching and learning of combinatorics.
PubDate: 2022-04-08

• Mathematical competitions in Africa: their prevalence and relevance to
students and teachers

Abstract: Abstract Mathematical competitions feature in most developed countries as a part of the secondary school experience, but to a lesser extent in developing countries. In this paper we investigate how widespread these competitions are in Africa, both historically as well as currently, focussing both on national Olympiads and on the participation of African countries in competitions beyond their borders, such as the continent-wide Pan African Mathematical Olympiad and the global International Mathematical Olympiad. Since we could not find a consolidated source of information on African competitions, we include many details and links, hoping that this paper will serve as a valuable starting point for future investigators. Next, we present some survey findings on the attitudes towards and experiences of mathematical competitions, both from the perspective of teachers in secondary schools as well as from secondary school students, and whether these experiences have served to improve or degrade their perceptions of mathematics in general. Among other results, we find that teachers view their students’ participation in mathematics competitions as being important, with the biggest barrier to participation being that there are not enough competitions at appropriate levels available, and that students enjoy mathematics competitions and are more likely to pursue a STEM career because of them. Finally, we present some suggestions on how this research may be taken further, and on how the state of mathematical competition culture in Africa may be improved.
PubDate: 2022-04-07

• Profiles of Chinese mathematics teachers’ teaching beliefs and their
effects on students’ achievement

Abstract: Abstract Mathematics teachers’ teaching beliefs play an important role in instructional practices and students’ achievement. In China, transmissive teaching beliefs were prevalent before 2001. Since then, a student-centered concept has been advocated in the national curriculum reform; however, few studies have assessed contemporary Chinese mathematics teachers’ teaching beliefs during the 20 years since the reform. In the current study, we elucidated the teaching beliefs Chinese teachers hold and their effects on instructional practices and students’ mathematics achievement. A total of 1463 mathematics teachers and 12,437 students in grade 4 were recruited from Beijing, Shanghai, Jiangsu, and Zhejiang in Eastern China. Based on self-reported teaching beliefs using a short revised version of the Teacher Education and Development Study in Mathematics (TEDS-M), the study identified that contemporary Chinese teachers usually hold constructive teaching beliefs. In comparison, transmissive teaching beliefs showed significantly higher scores for teachers with more than 20 years of teaching experience. Moreover, male teachers and those with more teaching experience were more transmissive, but the effect of gender was small. The indirect effect of teachers’ teaching beliefs on students’ mathematics achievement through perceived constructive instructional practices was revealed using a multilevel structural equation model. This study illustrates the teaching beliefs of Chinese mathematics teachers and their effects, using evidence collected from a more general perspective.
PubDate: 2022-04-05

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