This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems.
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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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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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In this chapter, I look back at the implementation of W12-16, a major reform of mathematics education in the lower grades of general secondary education and pre-vocational secondary education in the Netherlands including all students aged 12–16. The nationwide implementation of W12-16 started in 1990 and envisioned a major change in what and how mathematics was taught and learned. The content was broadened from algebra and geometry to algebra, geometry and measurement, numeracy, and data processing and statistics. The learning trajectories and the instruction theory were based on the ideas of Realistic Mathematics Education (RME): the primary processes used in the classroom were to be guided re-invention and problem solving. ‘Ensuring usability’ in the title of this chapter refers to the aim of the content being useful and understandable for all students, but also to the involvement of all relevant stakeholders in the implementation project, including teachers, students, parents, editors, curriculum and assessment developers, teacher educators, publishers, media and policy makers. Finally, I reflect on the current state of affairs more than 20 years after the nationwide introduction. The main questions to be asked are: Have the goals been reached? Was the implementation successful?
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Research on solving mathematical word problems suggests that students may perform better on problems with a close to real-life representation of the problem situation than on word problems. In this study we pursued real-life representation by a mainly depictive representation of the problem situation, mostly by photographs. The prediction that students perform better on problems with a depictive representation of the problem situation than on comparable word problems was tested in a randomised controlled trial with 31,842 students, aged 10–20 years, from primary and secondary education. The conclusion was that students scored significantly higher on problems with a depictive representation of the problem situation, but with a very small effect size of Cohen’s d = 0.09. The results of this research are likely to be relevant for evaluations of mathematics education where word problems are used to evaluate the mathematical capacity of students.
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Social robots have been introduced in different fields such as retail, health care and education. Primary education in the Netherlands (and elsewhere) recently faced new challenges because of the COVID-19 pandemic, lockdowns and quarantines including students falling behind and teachers burdened with high workloads. Together with two Dutch municipalities and nine primary schools we are exploring the long-term use of social robots to study how social robots might support teachers in primary education, with a focus on mathematics education. This paper presents an explorative study to define requirements for a social robot math tutor. Multiple focus groups were held with the two main stakeholders, namely teachers and students. During the focus groups the aim was 1) to understand the current situation of mathematics education in the upper primary school level, 2) to identify the problems that teachers and students encounter in mathematics education, and 3) to identify opportunities for deploying a social robot math tutor in primary education from the perspective of both the teachers and students. The results inform the development of social robots and opportunities for pedagogical methods used in math teaching, child-robot interaction and potential support for teachers in the classroom
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Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
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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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We are well into the 21st century now and the urgency for lifelong learning is growing especially regarding numeracy. There are major societal and policy pressures on education to prepare citizens for a complex and technologized society, in literature referred to as “21st century skills” (Voogt & ParejaRoblin, 2012), “global competences” (OECD, 2016a) or “the 4th industrial revolution” (Schwab, 2016). International research has demonstrated the economic and social value of literacy and numeracy knowledge and skills (Hanushek and Wöbmann, 2012; Grotlüschen, et al. 2016). With respect to numeracy (and/or mathematics) education, we explore the implications of these pressures to the mathematical demands at individuals living and working in modern life, and what is expected from numeracy education as society moves further into the 21st century. New means of communication and types of services have changed the way individuals interact with governments, institutions, services and each other, and social and economic transformations have in turn, changed the nature of the demand for skills as well.
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This study focuses on revealing and developing personal constructs regarding problem behaviour in classrooms. Twenty-nine teachers (initial and in-service students) took part in the project. The main idea is that teachers opinions about their pupils and themselves influence the way they act in their classrooms. Their thoughts and ideas about students - their personal constructs - are generally unconscious. To clarify and to develop teachers constructs, we used Kellys repertory grid technique and Garmans reflective approach. Both methods give a powerful impulse to the development of thinking and acting of teachers. They can use the experiences as an integral part of their own action research. & I am one of the teachers who took part in the constructs research.A personal set of fifteen constructs on twenty-eight pupils was collected. These constructs showed me what kinds of constructs I have (mainly social-emotional and cognitive ones) and made me reflect. They also made clear to me that I think less positively on problem children. Participation in this research includes coaching, theoretical orientation and continuous reflection, making me conscious of what (problem) behaviour I like or dislike and what I should change to get a professional, holistic view. Then problem behaviour will be more easily tolerated by me and I can teach my colleagues about my new insights in intercommunicative sessions and by personal counselling.
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