In this chapter, the focus is on arithmetic which for the Netherlands as a trading nation is a crucial part of the mathematics curriculum.The chapter goes back to the roots of arithmetic education in the sixteenth century and compares it with the current approach to teaching arithmetic. In the sixteenth century, in the Netherlands, the traditional arithmetic method using coins on a counting board was replaced by written arithmetic with Hindu–Arabic numbers. Many manuscripts and books written in the vernacular teach this new method to future merchants, money changers, bankers, bookkeepers, etcetera. These students wanted to learn recipes to solve the arithmetical problems of their future profession. The books offer standard algorithms and many practical exercises. Much attention was paid to memorising rules and recipes, tables of multiplication and other number relations. It seems likely that the sixteenth century craftsmen became skilful reckoners within their profession and that was sufficient. They did not need mathematical insight to solve new problems. Five centuries later we want to teach our students mathematical skills to survive in a computerised and globalised society. They also need knowledge about number relations and arithmetical rules, but they have to learn to apply this knowledge flexibly and meaningfully to solve new problems, to mathematise situations, and to evaluate, interpret and check output of computers and calculators. The twenty-first century needs problem solvers, but to acquire the skills of a good problem solver a firm knowledge base—comparable with that of the sixteenth century reckoner—is still necessary.
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Many students persistently misinterpret histograms. This calls for closer inspection of students’ strategies when interpreting histograms and case-value plots (which look similar but are diferent). Using students’ gaze data, we ask: How and how well do upper secondary pre-university school students estimate and compare arithmetic means of histograms and case-value plots? We designed four item types: two requiring mean estimation and two requiring means comparison. Analysis of gaze data of 50 students (15–19 years old) solving these items was triangulated with data from cued recall. We found five strategies. Two hypothesized most common strategies for estimating means were confirmed: a strategy associated with horizontal gazes and a strategy associated with vertical gazes. A third, new, count-and-compute strategy was found. Two more strategies emerged for comparing means that take specific features of the distribution into account. In about half of the histogram tasks, students used correct strategies. Surprisingly, when comparing two case-value plots, some students used distribution features that are only relevant for histograms, such as symmetry. As several incorrect strategies related to how and where the data and the distribution of these data are depicted in histograms, future interventions should aim at supporting students in understanding these concepts in histograms. A methodological advantage of eye-tracking data collection is that it reveals more details about students’ problem-solving processes than thinking-aloud protocols. We speculate that spatial gaze data can be re-used to substantiate ideas about the sensorimotor origin of learning mathematics.
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Conducting large calculations manually with pen and paper following prescribed procedures or algorithms has been diminishing in significance for some time. In most cultures, and for many years already, individuals employ digital instruments for such computational tasks, when confronted with them in daily life. Yet, a closer examination of prevalent practices in the teaching of basic numeracy skills in adult education reveals a persistent emphasis on mastering standardized manual calculation techniques, especially with abstract and decontextualized numbers. This emphasis predominantly stems from the belief that mastering these manual procedures forms the cornerstone of all numeracy abilities. Contrastingly, our research indicates that the numeracy skills most frequently utilized and required in contemporary professions and daily activities encompass higher-order capabilities (Hoogland and Stoker, 2021; Boels et al., 2022; Hoogland and Díez-Palomar, 2022). These include interpretation, reasoning, mathematizing, estimation, critical reflection on quantitative data, and the application of digital instruments for computation. It is imperative, therefore, that numeracy education for adults prioritizes these competencies to achieve efficacy.
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Within the Erasmus+ project Common European Numeracy Framework (CENF) (2018-2021) a framework was developed on numeracy in response to the challenges and needs of the 21st century.
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Introduction: The contemporary scientific literature indicates that numeracy is a multifaceted concept. The ongoing societal and technological transformations underscore the imperative to re-evaluate the attributes characterizing a numerate individual and the strategic initiatives that policymakers should devise and implement to ensure that individuals are not marginalized from participation in public and private domains due to their lack of numeracy proficiency. Numerous empirical investigations on numeracy consistently affirm its pivotal role in enabling individuals to engage autonomously across diverse contexts within their daily lives. However, numeracy’s fundamental role has often been neglected in our societies. The present study scrutinizes the overarching challenges associated with numeracy, particularly emphasizing the challenges regarding healthcare, finance, and the critical utilization and interpretation of data awareness. Methods: A two-phase research framework was adopted to address this inquiry. A comprehensive literature review was conducted to discern the prevalent challenges regarding numeracy awareness. Subsequently, two illustrative case studies were undertaken in Slovenia and Spain to contrast and deliberate upon the insights derived from the literature review. Qualitative research methods were employed to engage in a nuanced exploration of the gathered data. Results: This empirical analysis deduced guidelines aimed at enhancing awareness and ameliorating some of these challenges. Discussion and Conclusion: We conclude that making visible the awareness that adults already have about numeracy in aspects of their lives, such as finance, health, or the use and critical interpretation of data, can give policymakers and curriculum developers clues to design effective numeracy programs to address the multifaceted challenges confronting contemporary society, both in the immediate and foreseeable future.
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This paper is a summary paper of the Thematic Working Group (TWG) on Adult Mathematics Education (AME). The theme AME made its first appearance on CERME11 and in this paper we provide an overview of the growing and blossoming field of AME and the results of the working group. The main themes associated with AME are: the definition, scope, and assessment of numeracy, the role of language and dialogue, the role of affect, including motivation, and the role of societal power structures, including subthemes like equity, inclusion, vulnerable learners, agency and self-efficacy. We conclude with the opportunities and challenges for this theme from both scientific and societal perspective.
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The main objective of the study is to determine if non-specific physical symptoms (NSPS) in people with self-declared sensitivity to radiofrequency electromagnetic fields (RF EMF) can be explained (across subjects) by exposure to RF EMF. Furthermore, we pioneered whether analysis at the individual level or at the group level may lead to different conclusions. By our knowledge, this is the first longitudinal study exploring the data at the individual level. A group of 57 participants was equipped with a measurement set for five consecutive days. The measurement set consisted of a body worn exposimeter measuring the radiofrequency electromagnetic field in twelve frequency bands used for communication, a GPS logger, and an electronic diary giving cues at random intervals within a two to three hour interval. At every cue, a questionnaire on the most important health complaint and nine NSPS had to be filled out. We analysed the (time-lagged) associations between RF-EMF exposure in the included frequency bands and the total number of NSPS and self-rated severity of the most important health complaint. The manifestation of NSPS was studied during two different time lags - 0–1 h, and 1–4 h - after exposure and for different exposure metrics of RF EMF. The exposure was characterised by exposure metrics describing the central tendency and the intermittency of the signal, i.e. the time-weighted average exposure, the time above an exposure level or the rate of change metric. At group level, there was no statistically significant and relevant (fixed effect) association between the measured personal exposure to RF EMF and NSPS. At individual level, after correction for multiple testing and confounding, we found significant within-person associations between WiFi (the self-declared most important source) exposure metrics and the total NSPS score and severity of the most important complaint in one participant. However, it cannot be ruled out that this association is explained by residual confounding due to imperfect control for location or activities. Therefore, the outcomes have to be regarded very prudently. The significant associations were found for the short and the long time lag, but not always concurrently, so both provide complementary information. We also conclude that analyses at the individual level can lead to different findings when compared to an analysis at group level. https://doi.org/10.1016/j.envint.2019.104948 LinkedIn: https://www.linkedin.com/in/john-bolte-0856134/
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Numeracy and mathematics education in vocational education is under pressure to keep up with the rapid changes in the workplace due to developments in workplace mathematics and the ubiquitous availability of technological tools. Vocational education is a large stream in education for 12- to 20-years-olds in the Netherlands and the numeracy and mathematics curriculum is on the brink of a reform. To assess what is known from research on numeracy in vocational education, we are in the process of conducting a systematic review of the international scientific literature of the past five years to get an overview of the recent developments and to answer research questions on the developments in vocational educational practices. The work is still in progress. We will present preliminary and global results. We see vocational education from the perspective of (young) adults learning mathematics.
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This paper explores the contributions of research to the field of adults learning mathematics (ALM) in the last twenty years. The results of the review of the literature on ALM show that the most cited studies that have been published in the last twenty years tend to focus on the field of numeracy to understand health data (such as understanding how to dose a medicine in a medical treatment). However, we know little about key aspects of how adults learn mathematics, what obstacles they encounter, and how they overcome them. This paper identifies the main gaps that ALM research faces in the coming years.
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