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.
From the article: Abstract Adjustment and testing of a combination of stochastic and nonstochastic observations is applied to the deformation analysis of a time series of 3D coordinates. Nonstochastic observations are constant values that are treated as if they were observations. They are used to formulate constraints on the unknown parameters of the adjustment problem. Thus they describe deformation patterns. If deformation is absent, the epochs of the time series are supposed to be related via affine, similarity or congruence transformations. S-basis invariant testing of deformation patterns is treated. The model is experimentally validated by showing the procedure for a point set of 3D coordinates, determined from total station measurements during five epochs. The modelling of two patterns, the movement of just one point in several epochs, and of several points, is shown. Full, rank deficient covariance matrices of the 3D coordinates, resulting from free network adjustments of the total station measurements of each epoch, are used in the analysis.
MULTIFILE
Many students persistently misinterpret histograms. This calls for closer inspection of students’ strategies when interpreting histograms and case-value plots (which look similar but are diferent). Using students’ gaze data, we ask: How and how well do upper secondary pre-university school students estimate and compare arithmetic means of histograms and case-value plots? We designed four item types: two requiring mean estimation and two requiring means comparison. Analysis of gaze data of 50 students (15–19 years old) solving these items was triangulated with data from cued recall. We found five strategies. Two hypothesized most common strategies for estimating means were confirmed: a strategy associated with horizontal gazes and a strategy associated with vertical gazes. A third, new, count-and-compute strategy was found. Two more strategies emerged for comparing means that take specific features of the distribution into account. In about half of the histogram tasks, students used correct strategies. Surprisingly, when comparing two case-value plots, some students used distribution features that are only relevant for histograms, such as symmetry. As several incorrect strategies related to how and where the data and the distribution of these data are depicted in histograms, future interventions should aim at supporting students in understanding these concepts in histograms. A methodological advantage of eye-tracking data collection is that it reveals more details about students’ problem-solving processes than thinking-aloud protocols. We speculate that spatial gaze data can be re-used to substantiate ideas about the sensorimotor origin of learning mathematics.
LINK