This paper reports on an experiment comparing students’ results on image-rich numeracy problems and on equivalent word problems. Given the well reported problematic nature of word problems, the hypothesis is that students score better on image-rich numeracy problems than on comparable word problems. To test the hypothesis a randomized controlled trial was conducted with 31,842 students from primary, secondary, and vocational education. The trial consisted of 21 numeracy problems in two versions: word problems and image-rich problems. The hypothesis was confirmed for the problems used in this experiment. With the insights gained we intend to improve the assessment of students’ abilities in solving quantitative problems from daily life. Numeracy, word problem, image-rich problem, randomized controlled trial, assessment
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The aim of this study is to contribute to the body of knowledge on the use of contextual mathematical problems. Word problems are a predominant genre in mathematics classrooms in assessing students’ ability to solve problems from everyday life. Research on word problems, however, reveals a range of difficulties in their use in mathematics education. In our research we took an alternative approach: we designed image-rich numeracy problems as alternatives for word problems. A set of word problems was modified by systematically replacing the descriptive representation of the problem situation by a more depictive representation and an instrument was designed to measure the effect of this modification on students’ performance. The instrument can measure the effect of this alternative approach in a randomized controlled trial. In order to use the instrument at scale, we made this instrument also usable as a diagnostic test for an upcoming nationwide examination on numeracy. In this article we explain and discuss the design of the instrument and the validation of its intended uses.
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Presentation at the ALM28 Conference: Numeracy and Vulnerability, 5-7 july, Universität Hamburg, Germany.
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Technology, data use, and digitisation are based on mathematical structures, and this permeates many aspects of our daily lives: apps, online activities, and all kinds of communication. Equipping people to deal with this mathematisation of society is a big challenge. Which competences are needed, which skills must be mastered? Which dispositions are helpful? These are the questions that matter in the development of adult education. The concept of numeracy is mentioned already for many years as a possible useful approach to equip adults with the necessary skills. In this paper we will argue that is only true when numeracy is defined as a multifaceted concept which combines knowledges, skills, higher order skills, context and dispositions.
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This paper is a summary paper of the Thematic Working Group (TWG) on Adult Mathematics Education (AME). As the only thematic working group that focuses on adults’ lived experiences of mathematics, the research makes an important contribution to the field of Mathematics Education. The main themes in this group identify that adult numerical behaviour goes beyond the mathematics skills, knowledge, and procedures taught in formal education It is multifaceted, requiring the use of higher order skills of analysis and judgement, applied within a broad array of life’s contexts, experienced through a range of emotions. The research in this group points to the need to raise the profile of research that shows the benefits to adults of learning mathematics but also the long term economic disbenefits in the neglect of teaching and teacher training for this group.
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Proceedings of the 24th International Conference of Adults Learning Mathematics – A Research Forum (ALM).
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Citizens regularly search the Web to make informed decisions on daily life questions, like online purchases, but how they reason with the results is unknown. This reasoning involves engaging with data in ways that require statistical literacy, which is crucial for navigating contemporary data. However, many adults struggle to critically evaluate and interpret such data and make data-informed decisions. Existing literature provides limited insight into how citizens engage with web-sourced information. We investigated: How do adults reason statistically with web-search results to answer daily life questions? In this case study, we observed and interviewed three vocationally educated adults searching for products or mortgages. Unlike data producers, consumers handle pre-existing, often ambiguous data with unclear populations and no single dataset. Participants encountered unstructured (web links) and structured data (prices). We analysed their reasoning and the process of preparing data, which is part of data-ing. Key data-ing actions included judging relevance and trustworthiness of the data and using proxy variables when relevant data were missing (e.g., price for product quality). Participants’ statistical reasoning was mainly informal. For example, they reasoned about association but did not calculate a measure of it, nor assess underlying distributions. This study theoretically contributes to understanding data-ing and why contemporary data may necessitate updating the investigative cycle. As current education focuses mainly on producers’ tasks, we advocate including consumers’ tasks by using authentic contexts (e.g., music, environment, deferred payment) to promote data exploration, informal statistical reasoning, and critical web-search skills—including selecting and filtering information, identifying bias, and evaluating sources.
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In March 2020 schools in The Netherlands closed to contain the spread of Covid-19 virus. Shortly after, schools took to online education. The condensed setting of the Covid-19 situation provided a background to study which learning activities and tools teachers choose in online education and how they use them to promote interaction. Interaction is quintessential to learning but in online education it is not easy to provide room for interaction. Our central research question therefore is how interaction within online education activities change over time. An online longitudinal survey amongst teachers was conducted. The first four rounds took place in the early stages of the lockdowns and shortly after. In total 179 different secondary school teachers participated of whom 16 responded three rounds or more. Most teachers use tools in online education that can facilitate more interaction than necessary for the Instructional Design. This means that improving interaction in online education is more a pedagogical challenge than a technical one. It was also found that teachers who deploy Instructional Designs that require more interaction use more and different tools. However, only few of these tools seem to facilitate the interactive quality the teachers pursued. Over time we saw the interactive quality of Instructional Design and tools converge. We are in awe of the artful way in which some teachers manage to combine the possibilities of different tools to establish high interactive quality in the online learning processes they conduct.
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Background: The Turkish translation of the Dutch Talking Touch Screen Questionnaire (TTSQ) has been developed to help physical therapy patients with a Turkish background in the Netherlands to autonomously elucidate their health problems and impairments and set treatment goals, regardless of their level of health literacy. Objective: The aim of this study was to evaluate the usability of the Turkish TTSQ for physical therapy patients with a Turkish background with diverse levels of health literacy and experience in using mobile technology. Methods: The qualitative Three-Step Test-Interview method was carried out to gain insight into the usability of the Turkish TTSQ. A total of 10 physical therapy patients participated. The interview data were analyzed using a thematic content analysis approach aimed at determining the accuracy and completeness with which participants completed the questionnaire (effectiveness), the time it took participants to complete the questionnaire (efficiency), and the extent to which the participants were satisfied with the ease of use of the questionnaire (satisfaction). The problems encountered by the participants in this study were given a severity rating, which was used to provide a rough estimate of the need for additional usability improvements. Results: No participant in this study was able to complete the questionnaire without encountering at least one usability problem. A total of 17 different kinds of problems were found. On the basis of their severity score, 3 problems that should be addressed during future development of the tool were “Not using the navigation function of the photo gallery in Question 4 causing the participant to not see all presented response items;” “Touching the text underneath a photo in Question 4 to select an activity instead of touching the photo itself, causing the activity not to be selected;” and “Pushing too hard or tapping too softly on the touch screen causing the touch screen to not respond.” The data on efficiency within this study were not valid and are, therefore, not reported in this study. No participant was completely satisfied or dissatisfied with the overall ease of use of the Turkish TTSQ. Two participants with no prior experience of using tablet computers felt that, regardless of what kinds of improvement might be made, it would just be too difficult for them to learn to work with the device. Conclusions: As with the Dutch TTSQ, the Turkish TTSQ needs improvement before it can be released. The results of this study confirm the conclusion of the Dutch TTSQ study that participants with low levels of education and little experience in using mobile technology are less able to operate the TTSQ effectively. Using a Dutch speaking interviewer and Turkish interpreter has had a negative effect on data collection in this study.
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This article intends to focus on those critical issues arising from the Connect case study (Renshaw, 2005) that have wider applicability in contemporary professional practice in terms of lifelong learning. Special attention will be given to the following areas:• formal, non-formal and informal learning;• musical leadership;• quality;• self-assessment and reflective practice;• professional development of musicians.
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