In the Netherlands there is discussion about the best way to teach mathematics, especially in the case of primary school students. Being able to identify and understand pupils’ multiple problem solving strategies is one of the pillars of pedagogy. However, it is very demanding for teachers, since it requires to notice and analyze pupils’ mathematical thinking and to understanding their actions. The skill to notice and analyze a student’s mathematical thinking is usually not emphasized in Dutch primary school teacher training. It is important to find ways to help teacher-students to analyze student mathematical reasoning, and to learn to recognize the importance of such analysis. Sherin and van Es used the concept of video clubs to help teachers in US schools to notice and analyze their students’ mathematical thinking. In such video clubs, students jointly discuss their filmed lessons. This leads to the following research question:How can video clubs be used to teach students who are learning to become primary school teachers to analyze their pupils’ mathematical thinking and to learn to recognize the importance of such analysis?This paper describes a study that monitors a video club with four participants.
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Naast mijn werk als lector bij Zuyd Hogeschool ben ik bij de Universiteit Maastricht en bij ouderenzorgorganisatie Sevagram werkzaam op het thema Innovatiemanagement. Omdat ik ondersteun bij het opzetten van innovatiebeleid woonde ik een cursus Design Thinking bij voor leden van het Innovatieplatform van Sevagram. Design Thinking staat enorm in de belangstelling in de hedendaagse zorg. Ook in het prachtige tv-programma ‘We gaan het maken’ zijn het designers die aan de slag gaan met het ontwerpen van producten voor mensen met een beperking. En ik ben fan.
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Torpedo is a digital learning environment for developing mathematical problem-solving ability through self-study for pre-service teachers in primary teacher education. To achieve this, Torpedo supports and challenges pre-service teachers’ reflection during and after solving non-routine mathematics problems. To investigate the feasibility of the Torpedo approach, 271 pre-service teachers used Torpedo during one month in a pilot study. They used and evaluated Torpedo’s reflective elements differently. The results varied from pre-service teachers who experienced that reflection really contributed to the development of their problem-solving ability, to pre-service teachers who hardly reflected. The last group consisted of those who found the problems too difficult to reflect upon and those who used Torpedo to prepare for the National Mathematics Test and preferred to do so by drill and practice. As a conclusion, the study provides clues for improving Torpedo so that it invites more reflective self-study behaviour. For pre-service teachers who consider reflection valueless, however, self-study in a digital learning environment may be insufficient to change this attitude.
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Studenten opleiden tot professionals die kunnen leven en werken in de huidige complexe en diverse samenleving. Kunnen acteren met mensen van verschillende achtergronden en de verhoudingen in de wereld kennen. Wereldburgers opleiden die zelfbewust zijn en met een kritische en empathische blik naar de wereld om hen heen kijken. Zodat ze na hun opleiding professionals zijn die begrijpen dat onderwerpen door henzelf en anderen vanuit verschillende invalshoeken kunnen worden aangevlogen. En in staat zijn om oplossingen te vinden voor ingewikkelde vraagstukken. Dat is een leven lang leren! Aan die ontwikkeling draag jij als onderwijsprofessional, op jouw manier, bij. Maar, dat vraagt ook van jou om steeds meer te acteren op het snijvlak van de interne leeromgeving van school en een externe (leer)omgeving, waarbij het cocreëren met verschillende stakeholders steeds belangrijker wordt voor het slim vormgeven van leerprocessen. De afgelopen periode onderschrijft des te meer dat we in een sneltreinvaart toe bewegen naar het ‘nieuwe normaal’, waarbij van ons wordt verwacht om anders te werken én te denken. Ingesleten denk- en werkpatronen volstaan niet meer in onze internationale samenleving die steeds complexer en onvoorspelbaarder wordt. Je ontkomt pas aan die patronen door opnieuw te gaan denken, te leren afstand nemen van vooropgestelde ideeën over wat er zou moeten zijn en ontstane situaties als kansen voor ontwikkeling te zien. Juist in deze tijd is flexibilisering van het onderwijs en cocreatie hard nodig om bij te dragen aan het ‘nieuwe normaal’. Design Thinking is een gedachtegoed, aanpak en onderwijsmethodiek die hierbij kan helpen. Het is een manier om vanuit een mens-perspectief te kunnen vernieuwen. In deze Design Thinking ‘proeverij’ hebben we gepoogd onze ervaringen met Design Thinking in living labs voor business en management studenten te bundelen met ervaringen van anderen en theorie. Daarvoor hebben we ervaringen van andere hogeschooldocenten die Design Thinking reeds toepas sen in hun onderwijsomgevingen en een praktische vertaling van de theorie over Design Thinking & Doing gebruikt. Met als doel dat jij voor jezelf kunt gaan ontdekken of Design Thinking (& Doing) iets is voor jou, en voor jouw studenten. Wie weet, misschien ontdek je zelfs dat je al een onbewust, bekwame Design Thinker bent.
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The implementation of the new mathematical knowledge base in Dutch teacher education institutes for primary education raises a need for curriculum development. Teacher educators have to raise student teachers’ subject matter knowledge to a higher level. In working on this aim teacher educators experience that student teachers often feel uncertain about their mathematical skills and are not very interested in formal and abstract mathematics. Student teachers prefer to focus on mathematical pedagogical content knowledge. This paper presents two design studies that try to tackle this problem. The first one targets the development of student teachers’ specialized content knowledge (SCK) and the second one focuses on their horizon content knowledge (HCK). Both studies target developing student teachers’ mathematical subject matter knowledge in the perspective of teaching mathematics in primary school. In the studies we established student teachers’ learning environments that kept them involved and motivated, even when they found the mathematics hard to do. Primarily, this attitude supported their mathematical growth, while it also developed their pedagogical skills and insight. INTRODUCTION
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A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathematical behaviour. Student teachers need to mathematize and generalize problems and problem approaches, and evaluate heuristics and problem solving processes. This demands self-confidence, motivation, cognition and metacognition. To what extent do student teachers show reflective behaviour during mathematical self-study and how can we explain their study behaviour? In this study 97 student teachers from seven different teacher education institutes worked on ten non-routine problems. They were motivated because the test-like problems gave them an impression of the test and enabled them to investigate whether they were already prepared well enough. This study also shows that student teachers preparing for the test were not focused on developing their mathematical problem solving ability. They did not know that this was the goal to strive for and how to aim for it. They lacked self-confidence and knowledge to mathematize problems and problem approaches, and to evaluate the problem solving process. These results indicate that student teachers do hardly develop their mathematical problem solving ability in self-study situations. This leaves a question for future research: What do student teachers need to improve their mathematical self-study behaviour? EAPRIL Proceedings, November 29 – December 1, 2017, Hämeenlinna, Finland
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Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11th grade students’ mathematical thinking and reasoning. The results show that the integral-as-accumulation-function has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.
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In recent decades, technology has influenced various aspects of assessment in mathematics education: (1) supporting the assessment of higher-order thinking skills in mathematics, (2) representing authentic problems from the world around us to use and apply mathematical knowledge and skills, and (3) making the delivery of tests and the analysis of results through psychometric analysis more sophisticated. We argue that these developments are not pushing mathematics education in the same direction, however, which creates tensions. Mathematics education—so essential for educating young people to be creative and problem solving agents in the twenty-first century—is at risk of focusing too much on assessment of lower order goals, such as the reproduction of procedural, calculation based, knowledge and skills. While there is an availability of an increasing amount of sophisticated technology, the related advances in measurement, creation and delivery of automated assessments of mathematics are however being based on sequences of atomised test items. In this article several aspects of the use of technology in the assessment of mathematics education are exemplified and discussed, including in relation to the aforementioned tension. A way forward is suggested by the introduction of a framework for the categorisation of mathematical problem situations with an increasing sophistication of representing the problem situation using various aspects of technology. The framework could be used to reflect on and discuss mathematical assessment tasks, especially in relation to twenty-first century skills.
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Paper presented at the 14th International Congress on Mathematical Education (ICME14), 11-18 July, Shanghai, China.
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Blended learning, a teaching format in which face-to-face and online learning is integrated, nowadays is an important development in education. Little is known, however, about its affordances for teacher education, and for domain specific didactical courses in particular. To investigate this topic, we carried out a design research project in which teacher educators engaged in a co-design process of developing and field-testing open online learning units for mathematics and science didactics. The preliminary results concern descriptions of the work processes by the design teams, of design heuristics, and of typical ways of collaborating. These findings are illustrated for the case of two of the designed online units on statistics didactics and mathematical thinking, respectively.
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