Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

Realism and control : problem-based learning programs as a data source for work-related research

Problem-based learning (PBL) is a pedagogical methodology that presents the learner with a problem to be solved to stimulate and situate learning. This paper presents key characteristics of a problem-based learning environment that determines its suitability as a data source for workrelated research studies. To date, little has been written about the availability and validity of PBL environments as a data source and its suitability for work-related research. We describe problembased learning and use a research project case study to illustrate the challenges associated with industry work samples. We then describe the PBL course used in our research case study and use this example to illustrate the key attributes of problem-based learning environments and show how the chosen PBL environment met the work-related research requirements of the research case study. We propose that the more realistic the PBL work context and work group composition, the better the PBL environment as a data source for a work-related research. The work context is more realistic when relevant and complex project-based problems are tackled in industry-like work conditions over longer time frames. Work group composition is more realistic when participants with industry-level education and experience enact specialized roles in different disciplines within a professional community.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.