Zoekresultaten

Beware of chameleons – chameleons beware

Making IBSE durable through pre-service teacher education

How can we make Inquiry-Based Science and Mathematics Education (IBSME) durable? …. by incorporating it in the pre-service programs for elementary teachers! With pre-service students the training can be much more intensive than with inservice teachers. To have an impact in the classroom the minimum contact time in IBSME in-service and coaching has to be more than 90 hours (Supovitz & Turner, 2000). That number is hard to achieve in in-service but it is quite possible in preservice teacher education. From 9 – 11 January 2013 the Hogeschool van Amsterdam (HvA) hosted a field-visit sponsored by the EU Fibonacci project with a focus on pre-service teacher education. HvA developed two programs to strengthen IBSME in pre-service. One is an elective minor (30 ECTS) Science and Technology Education in the regularelementary teacher education program. The other is a pre-service program for academically talented students jointly developed by the University of Amsterdam and the Hogeschool of Amsterdam with inquiry as a major emphasis. The two programs are described in chapters 1 & 3 in this booklet. If you are still wondering what IBSE is, then read chapter 2 of Ana Blagotinsek of the University of Slovenia. She describes a neat example of an IBSE process with students in elementary teacher education. How do you start with a real worldquestion and initially little knowledge, and how do you investigate the question and eventually generate the knowledge needed to answer it? During the field-visit each participant presented one particularly successful approach in teacher training, for example, training teachers by ‘model teaching’ activities with these teachers’ own pupils. This method was used in different ways by 4 participants in different countries. They describe this in chapters 4 – 7. In chapter 8 colleague Frans Van Mulken describes the development of a lessonseries on graphs, rate of change, and speed using inquiry strategies inspired by the late mathematician and mathematics educator Hans Freudenthal. He also describes how pre-service students could be trained to teach the lesson series as inquiry. Simultaneously with this booklet, a Dutch booklet is published with overlapping contents but focused more on the Dutch context.

Creative Motor Actions As Emerging from Movement Variability

In cognitive science, creative ideas are defined as original and feasible solutions in response to problems. A common proposal is that creative ideas are generated across dedicated cognitive pathways. Only after creative ideas have emerged, they can be enacted to solve the problem. We present an alternative viewpoint, based upon the dynamic systems approach to perception and action, that creative solutions emerge in the act rather than before. Creative actions, thus, are as much a product of individual constraints as they are of the task and environment constraints. Accordingly, we understand creative motor actions as functional movement patterns that are new to the individual and/or group and adapted to satisfy the constraints on the motor problem at hand. We argue that creative motor actions are promoted by practice interventions that promote exploration by manipulating constraints. Exploration enhances variability of functional movement patterns in terms of either coordination or control solutions. At both levels, creative motor actions can emerge from finding new and degenerate adaptive motor solutions. Generally speaking, we anticipate that in most cases, when exposed to variation in constraints, people are not looking for creative motor actions, but discover them while doing an effort to satisfy constraints. For future research, this paper achieves two important aspects: it delineates how adaptive (movement) variability is at the heart of (motor) creativity, and it sets out methodologies toward stimulating adaptive variability.

Using machine learning to understand students' gaze patterns on graphing tasks

Graphs are ubiquitous. Many graphs, including histograms, bar charts, and stacked dotplots, have proven tricky to interpret. Students’ gaze data can indicate students’ interpretation strategies on these graphs. We therefore explore the question: In what way can machine learning quantify differences in students’ gaze data when interpreting two near-identical histograms with graph tasks in between? Our work provides evidence that using machine learning in conjunction with gaze data can provide insight into how students analyze and interpret graphs. This approach also sheds light on the ways in which students may better understand a graph after first being presented with other graph types, including dotplots. We conclude with a model that can accurately differentiate between the first and second time a student solved near-identical histogram tasks.

Interactive virtual math

An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions

Heuristic Coordination in Cooperative Multi-Agent Reinforcement Learning

Key to reinforcement learning in multi-agent systems is the ability to exploit the fact that agents only directly influence only a small subset of the other agents. Such loose couplings are often modelled using a graphical model: a coordination graph. Finding an (approximately) optimal joint action for a given coordination graph is therefore a central subroutine in cooperative multi-agent reinforcement learning (MARL). Much research in MARL focuses on how to gradually update the parameters of the coordination graph, whilst leaving the solving of the coordination graph up to a known typically exact and generic subroutine. However, exact methods { e.g., Variable Elimination { do not scale well, and generic methods do not exploit the MARL setting of gradually updating a coordination graph and recomputing the joint action to select. In this paper, we examine what happens if we use a heuristic method, i.e., local search, to select joint actions in MARL, and whether we can use outcome of this local search from a previous time-step to speed up and improve local search. We show empirically that by using local search, we can scale up to many agents and complex coordination graphs, and that by reusing joint actions from the previous time-step to initialise local search, we can both improve the quality of the joint actions found and the speed with which these joint actions are found.