It has been argued that teachers need practical principled knowledge and that design research can help develop such knowledge. What has been underestimated, however, is how to make such know-how and know-why useful for teachers. To illustrate how principled knowledge can be “practicalized”, we draw on a design study in which we developed a professional development program for primary school teachers (N = 5) who learned to design language-oriented mathematics lessons. The principled knowledge we used in the program stemmed from the literature on genre pedagogy, scaffolding, and hypothetical learning trajectories. We show how shifting to a simple template focusing on “domain text” rather than genre, and “reasoning steps” rather than genre features made the principled knowledge more practical for the teachers.
LINK
The potential of software tools to support learning mathematics is widely acknowledged, but their use can be hindered for many reasons. When teaching future mathematics teachers, we observed that these students were unmotivated to use such tools. This lack of motivation was caused by two concerns held by the students. Firstly, expected difficulty with the software interface (`handling equations with computer interfaces is cumbersome') and secondly, having to do time-consuming exercises on top of the regular pen-and-paper material. To circumvent these concerns, we developed and deployed a set of exercises, categorized in seven different types, that required little effort in terms of equation `writing' with the computer interface but still covered the core mathematical principles taught in the lessons. To allow for sufficient training opportunities, the software automatically created new randomized versions of the same question type. In this paper, we present an exploratory study that discusses the potential of this approach and provides insight on the effectiveness of question types used.
DOCUMENT
Eighteen years after the introduction of the graphing calculator in national examinations in the Netherlands, much has been learned about the use of technology in education. One of the key lessons was that integrating ICT as a tool for learning math is a complex task, and this complexity is often underestimated. In this article we give a current view of the use of ICT in learner practice in the Netherlands and in particular in the discipline of mathematics. Some of the topics covered include the type of technologies and learning materials used and the curriculum guidelines for math and assessment. Reflecting on experiences and challenges of the last few years is given an idea of future priorities. Directions for improving the integration of technology in mathematics education include the need to understand their role in learning and developing students' mathematical knowledge and reasoning, an investment in teacher training, the quality of digital learning materials and in more forms evaluation
DOCUMENT
PURPOSE: This study examined the effect of a 16-wk ball skill intervention on the ball skills, executive functioning (in terms of problem solving and cognitive flexibility), and in how far improved executive functioning leads to improved reading and mathematics performance of children with learning disorders.METHODS: Ninety-one children with learning disorders (age 7-11 yr old) were recruited from six classes in a Dutch special-needs primary school. The six classes were assigned randomly either to the intervention or to the control group. The control group received the school's regular physical education lessons. In the intervention group, ball skills were practiced in relative static, simple settings as well as in more dynamic and cognitive demanding settings. Both groups received two 40-min lessons per week. Children's scores on the Test of Gross Motor Development-2 (ball skills), Tower of London (problem solving), Trail Making Test (cognitive flexibility), Dutch Analysis of Individual Word Forms (reading), and the Dutch World in Numbers test (mathematics) at pretest, posttest, and retention test were used to examine intervention effects.RESULTS: The results showed that the intervention group significantly improved their ball skills, whereas the control group did not. No intervention effects were found on the cognitive parameters. However, within the intervention group, a positive relationship (r = 0.41, P = 0.007) was found between the change in ball skill performance and the change in problem solving: the larger children's improvement in ball skills, the larger their improvement in problem solving.CONCLUSIONS: The present ball skill intervention is an effective instrument to improve the ball skills of children with learning disorders. Further research is needed to examine the effect of the ball skill intervention on the cognitive parameters in this population.
LINK
Over the past three years we have built a practice-oriented, bachelor level, educational programme for software engineers to specialize as AI engineers. The experience with this programme and the practical assignments our students execute in industry has given us valuable insights on the profession of AI engineer. In this paper we discuss our programme and the lessons learned for industry and research.
MULTIFILE
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.
LINK
Leerkrachten die hun leerlingen willen ontwikkelen tot reken-wiskundige probleemoplossers moeten zelf ook goede probleemoplossers zijn. Om toekomstige leraren basisonderwijs, aan dit doel te laten werken is het van belang dat ze non-routine reken-wiskundige problemen oplossen en bovendien daarbij reflecteren op hun rekenwerk.
DOCUMENT
Interactive Virtual Math (IVM) is a visualization tool to support secondary school students’ learning of graphs by dynamic events. In the prototype version students construct a graph and try to improve it themselves and with the feedback of the tool. In a small-scale experiment, which involved four classes at secondary and tertiary education and their mathematics teachers we investigated how the students used the tool in the classroom. In this study we focus on the students learning experience and the results are expected to provide knowledge and directions for further development of the tool. The corpus data consists of self-reported questionnaires and lessons observations. One main finding is that students, at different school levels, find the tool useful to construct or improve graphical representations and it can help to get a better understanding of the subject. The tool features that helped students most were the self-construction of the graphs and to get feedback about their own graph at the end. Other findings are that the students can work independently with the tool and we know more about the tool features that are attractive or need to be improved.
MULTIFILE
Computers are promising tools for providing educational experiences that meet individual learning needs. However, delivering this promise in practice is challenging, particularly when automated feedback is essential and the learning extends beyond using traditional methods such as writing and solving mathematics problems. We hypothesize that interactive knowledge representations can be deployed to address this challenge. Knowledge representations differ markedly from concept maps. Where the latter uses nodes (concepts) and arcs (links between concepts), a knowledge representation is based on an ontology that facilitates automated reasoning. By adjusting this reasoning towards interacting with learners for the benefit of learning, a new class of educational instruments emerges. In this contribution, we present three projects that use an interactive knowledge representation as their foundation. DynaLearn supports learners in acquiring system thinking skills. Minds-On helps learners to deepen their understanding of phenomena while performing experiments. Interactive Concept Cartoons engage learners in a science-based discussion about controversial topics. Each of these approaches has been developed iteratively in collaboration with teachers and tested in real classrooms, resulting in a suite of lessons available online. Evaluation studies involving pre-/post-tests and action-log data show that learners are easily capable of working with these educational instruments and that the instruments thus enable a semi-automated approach to constructive learning.
DOCUMENT
