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Abstract: Abstract The first stage of a study in Québec enabled us to draw up a statistical portrait of probability teaching practices self-reported by 626 teachers at the elementary and secondary levels. For the second stage of the study, discussed here, we wanted to elaborate on some of the questionnaire answers and to discuss professional development avenues inspired by the teachers’ experience. We conducted 1-h individual interviews with eight teachers who had taken part in the first stage and whose self-reported teaching practices were considered to be exemplary. By means of a thematic analysis, we explore issues surrounding certain self-reported probability teaching practices through examples related to the social usefulness of probability, professional development associated with probability teaching, the use of the frequentist approach, the connection between probabilistic approaches, unusual tasks, manipulatives, and technological tools for teaching probability. PubDate: 2022-11-23

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Abstract: Abstract The objective of this qualitative research is to study the mathematical work when solving a mathematical task in the domain of probability presented by Chilean high school mathematics teachers in pre-service and in-service training. We consider as theoretical support the Mathematical Working Space model and methodological design of a collective case study, comprising of five teachers in pre-service training and eight teachers in in-service training. This research design allows us to analyze mathematical objects under semiotic, instrumental, and discursive dimensions, identifying privileged vertical planes, the paradigm applied, and the different strategies used by teachers. The task presented to the participants allows two different correct answers depending on the interpretation of the random experiment in question. Since the definition of the random experiment involved in the task is of utmost importance, according to our results, this notion was not evident in all the productions analyzed, which issue poses a challenge for the teaching and learning of probability. PubDate: 2022-11-09

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Abstract: Abstract To promote the development of young children’s probabilistic intuitions through experience, we focus on the dual nature of probability related to both belief (subjective notion) and frequency (objective notion). This paper reports on the responses of 7–8-year-olds on two tasks used to bridge subjective and objective notions of probability. We explore how these two conceptions interact in children’s estimations of the likelihood of outcomes from chance events as new information is obtained from data collected through physical experiments and computer simulations. Our findings suggest that even though children have not yet reached the desired level of quantitative reasoning, several used the data in a reasonable way to update their subjective probabilities based on their personal beliefs. These findings highlight the nascent potential of children to reason about probability when presented with a sequence of activities. These activities are used to support them to state their subjective probability estimations, using a contextually rich continuum, while at the same time recalibrate their estimations to more accurately reflect the theoretical probability. PubDate: 2022-11-04

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Abstract: Abstract In this commentary, I reflect on the relevant role that the education of teachers imply to assure a successful teaching of probability at school levels. Unfortunately, research on this issue is still scarce. In this sense, the four papers included in this section are welcome because they approach this research problem from different perspectives. I analyse these perspectives using the Didactic-Mathematics Knowledge and Competences Model (CCDM) developed at the University of Granada, Spain. PubDate: 2022-10-30

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Abstract: Abstract This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization by students. Considering schemas as a primitive form of algorithmic approaches, we observe interaction with mathematics. In class, students know how to use notion of frequency, but linking frequencies with probability appears to be a difficult issue. This absence of a statistical link leads us to identify entry points for probability teaching. We then decide to analyze primary school students when they have to explore a random experiment by using statistics. PubDate: 2022-10-14

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Abstract: Abstract As part of Springer, the edited book addresses innovative approaches and pedagogical strategies, the development of effective methods for assessing, and the innovative project in teaching and learning contemporary physics. This volume includes successful experimental and theoretical studies of QM teaching, which the experts or teachers can then adopt or modify the concept into practice in context. The 19 chapters, representing results of original study works dealing with Physics Education, are selected from the contributions in a conference on the teaching and learning of quantum physics. The goal of the book is to introduce contemporary physics to all level schools. Without a doubt, the book is recommended for high school teachers, instructional developers, and scientists to explore and develop the theories, approaches, and strategies in the book to advance teaching/learning of CP. PubDate: 2022-10-07

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Abstract: Abstract Using Mathematics to Understand the World: How Culture Promotes Children’s Mathematics provides a comprehensive overview of the importance of mathematical models and promotes quantitative reasoning. This book applies empirical and theoretical studies in mathematics for children, especially at the elementary level, by providing examples of mathematical models and explaining how to understand them. This essential text is for all students of mathematics education, developmental psychology, and cognitive psychology. PubDate: 2022-09-21

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Abstract: Abstract While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of Regina, I decided to bring one of those tasks, “to account for all possible three-tall towers using two colours” (pp. 567, 568), into the pedagogy and mathematics content courses that I was teaching. My goals were simple: to find out how the students thought about combinatorics using a situation that was most likely unique to them, and to inspire them to actually work with some of the plethora of manipulative materials in our “math lab.” The actual outcomes, however, went well beyond those goals, as problems related to common words used in relation to combinatorics, connections to Pascal’s triangle, and the development of the binomial expansion theorem also emerged during the pre-service teachers’ explorations of the two-coloured towers. As the task expanded into a suite of tasks and learnings over time, it also led the students and me to a new conundrum: “How did the permutations captured in the built towers change to combinations in the binomial expansion theorem'” This article reflects on the journey to an answer, while also leading to some questions about the existing literature related to the two-colour-tower tasks. PubDate: 2022-09-20

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Abstract: Abstract Preventive efforts are necessary to reduce the risk for problem gambling among adolescents, especially among more at-risk youth. However, only a small proportion of the preventive initiatives implemented in the field of adolescent problem gambling are based on robust theoretical models and have been evaluated in their efficacy. By referring to the dual-process model of human functioning, especially to the mindware concept, the goal of this study was to develop and evaluate a school-based preventive intervention based on teaching probabilistic reasoning ability and explaining biases in reasoning with probability. Indeed, research with adolescents found that poor probabilistic reasoning ability is associated with gambling-related cognitive distortions that, in turn, are a risk factor for problem gambling. The study aim was to reduce gambling-related distortions by working on the concept of randomness and probability. A pre- and post-test design was performed with 72 adolescents randomly assigned to a Training group and a No Training group. Results showed a significant reduction of cognitive distortions at the post-test only in the Training group. Findings suggest that teaching probability can serve to reduce the susceptibility to gambling-related distortions and should be pointed out in the training process of the intervention providers in the gambling field. PubDate: 2022-09-17

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Abstract: Abstract This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students’ combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo’s research to two groups of students with and without instruction on combinatorics in order to analyse the students’ performances and the strategies used in their solutions, as well as the effect of instruction on the same. We present the results obtained in two permutation and two combination problems (each in the distribution and selection models). Permutation problems were found easier than combination problems, selection problems were found easier after instruction, and the instruction group obtained better results. We found differences in the main strategies used in both groups: enumeration and dividing a problem in parts was more common in the no-instruction group. The instruction group frequently relied on the use of a formula and the product rule. PubDate: 2022-09-17

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Abstract: Abstract This study investigates the support provided using technology for learning the notion of normal distribution in high school students through the implementation of a teaching experiment. A strategy was designed and implemented using Fathom software as the main teaching resource. Data analysis focused on the role of the use of technology in student learning and the simulation process, considering the initial session. The conceptual framework was based on the documentational approach to didactics, whose perspective is to study the teacher’s use and design of resources in his teaching practice. Likewise, the results of the teaching experiment, whose objective was to introduce high school students to the notion of normal distribution by taking advantage of the repeated sampling resource using the Fathom software, are presented. The results show that the collaborative aspect of the lesson study methodology allowed professors to reflect and become aware of how they usually use the resources in their regular practice and thus contribute to improving their teaching activity. Evidence is provided on how students initiate a change in their reasoning to identify the probability of data collection from the simulation of problems with the software. PubDate: 2022-09-08 DOI: 10.1007/s42330-022-00226-1

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Abstract: Abstract This paper examines coin-toss comparison questions from two recent studies involving undergraduate students and high school teachers and connects to findings from two prior studies in the literature. Considering possible sample spaces employed by participants, this is a reflection on whether one sequence could be more likely depending on the interpretation of the question. To critique the choice of sequences and determine possible scenarios in which one sequence may be more likely than the other, three alternative sample spaces were explored. It was determined that different sample spaces can lead to one sequence being more likely to occur than the other. Further evaluation discusses whether alternative sample spaces may have been utilised by the participants in each of the studies, and hence, the paper concludes with an advocacy to enquire deeper into participants’ reasoning when investigating coin-toss questions. PubDate: 2022-09-01 DOI: 10.1007/s42330-022-00224-3

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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Financial Numeracy in Mathematics Education: Research and Practice is a book that brings unique and innovative ideas for using financial numeracy in learning mathematics in the classroom. The purpose of this book is to describe the different ways to integrate financial numeracy into mathematics classrooms. Empirical and conceptual studies related to the application of financial numeracy in learning are successfully discussed in this volume. This is perhaps the first book to comprehensively cover the theory and practice of financial numeracy in mathematics instruction. This book is ideal for instructors, lecturers, researchers, stakeholders, and anybody else interested in financial numeracy. PubDate: 2022-06-24 DOI: 10.1007/s42330-022-00215-4