Search

The article focuses on the International Commission for Mathematical Instruction (ICMI) Study 21, which examines the relationship between language diversity and mathematics education. Topics discussed include the influence of historical multilingualism, migration, colonization, globalization, or other factors on mathematics classrooms, as well as learning through second or additional languages, minority or oppressed languages, and dominant languages.

Successful problem solving begins with constructing mental problem representations and the identification of problem characteristics to clarify the solution. The purpose of the current study is to examine the design principles of learning supports promoting mental problem representation in the math problem solving setting. We investigated the mental problem representations and problem solving performance influenced by the formats of the learning supports. Through the analysis of participants' visual attention and solution notations, the current study found that problem solvers' visual attention on symbolic learning support increases whereas their visual attention on iconic learning supports decreases during the problem representation stages. There is a significant difference in problem solvers' visual attention on iconic learning supports between the successful and unsuccessful problem-solving groups. Unsuccessful problem solvers tended to disregard critical elements in the math word problem. [ABSTRACT FROM AUTHOR]

In order to improve instruction, teachers need to make sense of and evaluate the critical events that have the potential to strengthen the understanding of students' mathematical thinking. Mathematics instruction has shifted toward inquiry teaching which leaves many teachers attempting to change their practices accordingly. While there are documents that help mathematics teachers understand inquiry practices, there is little guidance for teachers who teach in classroom settings in which students with special needs are included. Since mathematical reasoning and conceptual understanding have become as important to teach as procedures, it is imperative that co-teachers draw on each other's knowledge to incorporate inquiry co-teaching practices. A design-based research project was conducted to explore the co-teaching practices in an inquiry mathematics classroom setting. We document co-teaching practices that are effective for planning and implementing inquiry mathematics lessons. [ABSTRACT FROM AUTHOR]

Mathematics tutoring centres exist in varying forms at universities across the United States of America. Despite having similar goals, these centres vary a great deal in their practices, resources, and organizational structures. In this study, the researchers conducted a survey of mathematics tutoring centres in the United States in an effort to create a resource that can be used by administrators, faculty, and mathematics centre staff to make decisions regarding their centres. These results can also inform research into which attributes contribute to centres that effectively serve students. This study explores relationships between mathematics centres and departments, tutor training, types of tutoring, physical layout, tutoring capacity, human resources, data collection, courses serviced, evaluation methods, and mission statements. [ABSTRACT FROM AUTHOR]

The aim of this study was to reveal 5th class middle school students' determination skills on the truth value of mathematical propositions about multiplication and division. These skills were evaluated in the context of operation meanings preferred and arguments constructed by the students in the process. The research group consisted of 95 fifth-grade students studying at a state middle school in Turkey. The study an example of sequential explanatory from mixed research designs. The data of the study were collected in three stages. In the first and the second stage, quantitative data of the study were gathered with Awareness Questionnaire (AQ) and Proposition Evaluation Test (PET) developed by the researchers. In the third stage, semi-structured task-based interviews were conducted. As a result of the study, it was revealed that students had more difficulty in selecting false mathematical propositions. Most of the students used counterexample and deductive warrants for the falsity of the propositions, and inductive warrants for the truth of the propositions. These results showed that determining the false propositions was an important ability and students preferring operational meanings had disadvantages in this process. [ABSTRACT FROM AUTHOR]

Learners' perspectives on classroom teaching have been explored in various ways. Within the context of past research, the student voice approach has shown the potential of making teaching and learning more effective. This article reports on students' perceptions with the aim of revealing their predispositions in the sense of Bruner's perceptual set theory concerning mathematics lessons. By asking students about significant events in specific mathematics lessons they attended and their associated justifications, insights into students' predispositions (beliefs) about teaching and learning mathematics are gained. We were able to reconstruct a wide range of predispositions, which indicate both a view on mathematics education that is quite positive and as well a willingness to learn comprehensively. As a further result, we obtained information about which kinds of scenes are perceived as significant by students, which was then linked to their decisive predispositions. With our results in mind, teachers could react appropriately to the expectations of students related to these predispositions and thus avoid dissatisfaction and barriers to learning. [ABSTRACT FROM AUTHOR]

The following article deals with the possibility of discovering several parameters of the picture when using Google Maps images, e.g. time and date of taking the image. This is possible with all pictures in which buildings, trees, poles ('objects') can be seen with their shadows. In some cases, one can find – with a bit of luck – an aircraft shortly before landing or shortly after take-off at a big and busy airport. If one detects such a situation, the question arises whether it is possible to estimate reasonably the actual height over the ground of the aircraft. The answer is 'yes', and we will show several possibilities; in one of them, the concept of three-dimensional similarity will play an important role. [ABSTRACT FROM AUTHOR]

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the recurrence relations of the first or second order. To overcome this problem, in this paper, we propose a general combinatorial problem of path tiling with tiles of different sizes and colours. For especially selected tile sizes and for certain tile colours, the problem can be reduced to solving a recurrence relation of the third, fourth, or higher orders. Furthermore, through actual examples, we show that various cases can be derived from the roots of a characteristic equation: different real roots, different real and complex roots, and repeated real roots with different multiplicities. We hope that the presented problems will provide teachers with the opportunity to present this topic with better content. [ABSTRACT FROM AUTHOR]

The purpose of this study was to determine if the MathTwitterBlogosphere (MTBoS), an online community of practice, provides opportunities for mathematics educators to learn about the knowledge and conceptions that support the effective use of cognitively demanding tasks, including mathematical knowledge for teaching, visions of high-quality mathematics instruction, and views about how to support struggling students. A qualitative case study was used to explore how content within the MTBoS, and perceptions of the effects of participation in the MTBoS, related to learning specified knowledge and conceptions. Results suggest the MTBoS is a promising avenue for providing learning opportunities related to mathematical knowledge for teaching and visions of high-quality mathematics instruction, although it may provide fewer learning opportunities related to engaging struggling students. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the bibliometric analysis of number sense studies over the past 30 years and monitor the trend regarding the nomological network accordingly. All the published articles in Web of Science database, containing the term number sense between 1990 and 2019, constituted the focus of the study. In the analysis of 448 articles, the distance-based bibliometric maps and the clusters were created by VOSviewer so that they provide information about the existence of nomological networks and the occurrence of the number sense-related concepts. The results of the study indicated that the terms of number sense-related studies were clustered in four groups depending on the degree of the relationships among them. The groups were identified as recognition of number sense to define clearly (recognition), evaluating the number sense to support (evaluation), associating the number sense with other skills and abilities to increase the success (association) and promoting number sense to improve instruction (promotion). This study put forth evidence to list the interrelated terms, to show the close relationship among the terms, to emphasize the diversity, to reveal the intertwining and to show the richness of number sense. [ABSTRACT FROM AUTHOR]

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded against the eight categories of foundational number sense, which are the number-related competences literature has shown to be essential for the later mathematical success of year one learners. Two analyses were undertaken; the first was a frequency analysis of the tasks coded for a particular category, the second was a time-series analysis highlighting the temporal location of such opportunities. The frequency analyses identified statistically significant differences with respect to children's opportunities to acquire foundational number sense. Additionally, the time series showed substantial differences in the ways in which such tasks were located in the structure of the textbooks. Such differences, we argue, offer substantial didactical challenges to teachers trying to adapt their practices to the expectations of such imports. [ABSTRACT FROM AUTHOR]

Aiming to bring teachers' perspectives to research, teachers' (N = 12) discussions are explored in the context of a professional development program on teaching highly able pupils (HAPs) mathematics. The findings show that the teachers perceive they have the competence to recognize HAPs, for example through continuous assessment. However, they express that collaboration with colleagues is necessary and that they would like their principals' acknowledgement for their competence. They connect and verbalize their practical expertise with theories of teaching HAPs and demonstrate several criteria for teaching that successfully meet pupils' learning needs in heterogeneous classrooms. Thus, they feel confident in how to orchestrate teaching that is inclusive of HAPs in heterogeneous mathematics classrooms. [ABSTRACT FROM AUTHOR]

This article explains the rules history, and statistics for students, teachers, and other interested parties who have been using Mathe im Leben gGmbH in collaboration with DMV for years with great success. It will also help one discover how to get involved with minimum effort. It reports record numbers for the digital math challenges in the time of restricted school operations.

Background: Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. Aim: This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Sample(s): Thirty‐five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Methods: Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. Results: In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Conclusions: Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. [ABSTRACT FROM AUTHOR]

The article presents a puzzle If the rolled number equals 2 + 2, then it is equal to 5.

Recent literature has revealed underestimation effects in numerical judgments when adult participants are presented with emotional stimuli (as opposed to neutral). Whether these numerical biases emerge early in development however, or instead reflect overt, learned responses to emotional stimuli across development are unclear. Moreover, reported links between numerical acuity and mathematics achievement point to the importance of exploring how numerical approximation abilities in childhood may be influenced in real-world affective contexts. In this study, children (aged 6-10 years) and adults were presented with happy and neutral facial stimuli in the context of a numerical bisection task. Results reveal that children, like adults, underestimate number following emotional (i.e., happy) faces (relative to neutral). However, children’s, but not adult’s, responses were also significantly more precise following emotional stimuli. In a second experiment, adult judgments revealed a similar increase in precision following emotional stimuli when numerical discriminations were more challenging (involving larger sets). Together, results are the first to reveal children, like adults, underestimate number in the context of emotional stimuli and this underestimation bias is accompanied with enhanced response precision. [ABSTRACT FROM AUTHOR]

This article examines the use of a range of co‐teaching models when teaching mathematics. The approaches suggested have potential for all students, but in this instance their importance as a pedagogical approach with students with special educational needs (SEN) in inclusive classrooms is considered. The study was based in the first‐year mathematics classroom of an Irish, urban, mainstream, post‐primary, girls’ school. This article highlights the findings from the teacher's perspective and presents their reflections on a range of co‐teaching approaches. The potential and challenges of these are considered in the context of schools generally. [ABSTRACT FROM AUTHOR]

Classroom data modeling involves posing questions, identifying attributes of phenomena, measuring and structuring these attributes, and then composing, revising, and communicating the outcomes. Selecting attributes is a fundamental component of data modeling, and the considerations made when selecting attributes is the focus of this paper. A teaching experiment involving 2 teacher educators and 25 pre-service teachers (PSTs) was carried out with 24 young children (5–6-year-olds) as part of a 4-day data modeling investigation. Although perceptual features of the data influenced initial approaches to attribute selection, considerations of the problem situation influenced a shift from the perceptual and towards consideration of attributes such as taxonomy, habitat, behavior, and diet. Expertise in the data context (animal kingdom) and ability to collaborate and negotiate within groups supported children in their ability to switch attributes, attend to multiple situations presented by the problem, and modify and extend their categorizations of data. [ABSTRACT FROM AUTHOR]

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform –which was eventually itself replaced in the longer term – provides some keys to understanding the influence of mathematical theories on teaching and learning. The paper studies changes related to place value, a notion that was deeply impacted by the introduction of numeration bases other than ten in 1970, and their subsequent removal in the 1980s. What the author terms ‘numeration units’ (ones, tens, hundreds, thousands, etc.) and ‘powers-of-ten written in figures’ (1, 10, 100, 1000, etc.) are key tools for describing and understanding changes. The author identifies two theories that have formed the basis for place value teaching in the twentieth century, and examines some aspects of their influence. The paper also addresses epistemological issues in the relation between academic mathematics and school mathematics, and highlights the role of units in the teaching of basic arithmetic. [ABSTRACT FROM AUTHOR]

In our exploration of the order of operations we focus on the following claim: “In the conventional order of operations, division should be performed before multiplication.” This initially surprising claim is based on the acronym BEDMAS, a popular mnemonic used in Canada to assist students in remembering the order of operations. The claim was voiced by a teacher and then presented for consideration to a class of prospective elementary school teachers. We investigate the participants’ understanding of the order of operations, focusing on the operations of multiplication and division. We report on participants’ ways of resolving a cognitive conflict faced as a result of relying on memorized mnemonics. [ABSTRACT FROM AUTHOR]

Achieving fluency in important mathematical procedures is fundamental to students’ mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528 students aged 12–15. In each study, parallel classes were taught the same mathematical procedure before one class undertook traditional exercises while the other worked on a “mathematical etude” (Foster International Journal of Mathematical Education in Science and Technology, 44(5), 765–774, 2013b), designed to be a richer task involving extensive opportunities for practice of the relevant procedure. Bayesian t tests on the gain scores between pre- and post-tests in each study provided evidence of no difference between the two conditions. A Bayesian meta-analysis of the three studies gave a combined Bayes factor of 5.83, constituting “substantial” evidence (Jeffreys, 1961) in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data support the conclusion that the mathematical etudes trialled are comparable to traditional exercises in their effects on procedural fluency. This could make etudes a viable alternative to exercises, since they offer the possibility of richer, more creative problem-solving activity, with comparable effectiveness in developing procedural fluency. [ABSTRACT FROM AUTHOR]

In the viral New York Times essay \To Fall in Love with Anyone, Do This", Mandy Len Catron details an experience she and an acquaintance had as they shared responses to psychologist Arthur Aron's thirty-six questions intended to make participants fall in love. She notes that \we all have a narrative of ourselves that we over up to strangers and acquaintances, but Dr. Aron's questions make it impossible to rely on that narrative". In this paper, we claim that we also have narratives of our relationship to mathematics that we over up to ourselves and others. Following, we over a mathematical version on Aron's thirty-six questions, designed to break out of our personal mathematical narratives and foster intimacy with mathematics. [ABSTRACT FROM AUTHOR]

For almost three years, I have spent most of my Sunday afternoons doing math with my daughters and a group of their school friends. Below I detail why and how the math club is run. Unlike my day job, which is full of (statistical) learning objectives for my college students, my math club has only the objective that the kids I work with learn to associate mathematics with having fun. My math club has its challenges, but the motivation comes from love of mathematics, which makes it fun, and worth every minute. [ABSTRACT FROM AUTHOR]

The article presents examples of teachable moments that are based on mathematical teaching episodes. Topics covered include how teachers can capitalize on these opportunities to enhance students' learning, ways to provide students with opportunities to engage in mathematical discussions, and the importance for teachers to recognize these opportunities and respond to them effectively.

The article discusses the use of "Is it true?" tasks to encourage primary students to reason mathematically. Topics covered include the incorporation of reasoning to explore students' misconceptions, the rationale behind choosing the task and its development into a lesson with potential to assess reasoning, and a discussion of the examples of children's reasoning.

The purpose of this study was to investigate parents' attitudes toward mathematics, their students' attitude toward mathematics, and the influence of the parents' attitude on the students' attitude toward mathematics. Data analyses revealed statistically significant positive correlations between parents' and students' attitudes toward mathematics. Additionally, parents' mathematics attitude significantly predicted students' attitudes toward mathematics (n=146). By understanding the influence of parents' attitudes on students' attitudes toward mathematics, school efforts can be geared toward fostering favorable attitudes toward mathematics among parents. [ABSTRACT FROM AUTHOR]

Motivation: High throughput screening by fluorescence activated cell sorting (FACS) is a common task in protein engineering and directed evolution. It can also be a rate-limiting step if high false positive or negative rates necessitate multiple rounds of enrichment. Current FACS software requires the user to define sorting gates by intuition and is practically limited to two dimensions. In cases when multiple rounds of enrichment are required, the software cannot forecast the enrichment effort required. Results: We have developed CellSort, a support vector machine (SVM) algorithm that identifies optimal sorting gates based on machine learning using positive and negative control populations. CellSort can take advantage of more than two dimensions to enhance the ability to distinguish between populations. We also present a Bayesian approach to predict the number of sorting rounds required to enrich a population from a given library size. This Bayesian approach allowed us to determine strategies for biasing the sorting gates in order to reduce the required number of enrichment rounds. This algorithm should be generally useful for improve sorting outcomes and reducing effort when using FACS. [ABSTRACT FROM AUTHOR]

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of limit connect them. This paper examines the nature of connections made by students exposed to this fragmented curriculum. The study adopted a phenomenographic approach and used card sorting and comparison tasks to expose students to symbols representing these different types of limit. The findings suggest that, while some students treat limit cases as separate, some can draw connections, but often do so in ways which are at odds with the formal mathematics. In particular, while there are occasional, implicit uses of neighbourhood notions, no student in the study appeared to possess a unifying organisational framework for all three basic uses of limit. [ABSTRACT FROM AUTHOR]

In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations instruction were developed. Teachers' use of multiple representations within an example, attention to part-whole relations within examples, and relations between multiple examples were identified, with teachers' linking actions in speech or gestures pointing to connections between these. In this article, the coding framework is detailed and exemplified in the context of a structural approach to part-whole teaching in six South African grade 3 lessons. The coding framework enabled us to see fine-grained differences in teachers' handling of part-whole relations related to simultaneity of, and connections between, representations and examples as well as within examples. We went on to explore the associations between the simultaneity and connections seen through the coding framework in sections of teaching and students' responses on worksheets following each teaching section. [ABSTRACT FROM AUTHOR]

Mathematics coaching, which can be defined broadly as job-embedded learning for mathematics teachers with someone who can help, is being used in Canada to improve teaching practice and increase student achievement. Mathematics coaching research is quite new with little written on the components of effective coaching. The paper attempts to contribute to this research. Employing observations, interviews, archival data, and surveys, the study finds that time, trust, the coaches' backgrounds, and their courage in trying new initiatives may be elements of effective coaching. Effective coaching also required resources and was differentiated. Mathematics coaching improved teacher practices. [ABSTRACT FROM AUTHOR]

We discuss the pedagogical redesign of a liberal arts mathematics course that enrolls roughly 3000 students per year. Flipping the classroom is a prominent feature of the new pedagogical approach. We describe the nature of this redesign, course resources, and how students are assessed for both preparation and understanding. We also indicate how the course redesign was implemented, and we assess its success. The results thus far are encouraging. For example, an analysis of course grades indicates increased performance for students participating in the redesigned course, but we are cognizant of several confounding factors. [ABSTRACT FROM PUBLISHER]

This paper examines the literature on identity within mathematics education published in journals over the past two decades. It analyses the theoretical underpinnings, research methods and definitions of identity, providing a critique rather than a summary of the literature. A total of 188 articles from 85 different journals are reviewed in the sample. This review finds support for common complaints of this research area as lacking in definitions of the concept of identity and suggests that the writing in this topic is at times theoretically incompatible. Furthermore, the work in this field may be coming from two distinct paradigms. Identity may be seen as an action and fit within a sociological frame or it may be seen as an acquisition, fitting within a psychological framing. Defining identity as something we do, as an action, and in particular as performative is promoted in this paper. Finally, suggestions are made for future directions in identity research. [ABSTRACT FROM AUTHOR]