Autobiographical Accounts of Students' Experiences Learning Mathematics: A Review

ABSTRACT

In this article, we review published literature that draws on autobiographical accounts of students' experiences learning mathematics. We summarize the main findings of the target literature and present recommendations for further research that will extend this field. Our review indicates that autobiographical and narrative methodological approaches have the potential to occasion important advances in our knowledge of students' experiences learning mathematics. However, relative to accounts of preservice teacher learning, there is a paucity of published research that documents the mathematics learning experiences of kindergarten to Grade 12 students.     

Discipline-based instruction to promote interdisciplinary design of wearable and pervasive computing products

This paper reports on a design experience for undergraduates in computer engineering, industrial design, and marketing that focuses on pervasive computing devices. Across a broad range of targeted application areas and user groups, many of the student designs have been wearable computers. Consequently, our course will be of interest to the wearable computing community, particularly in terms of our aim of bridging the gap between design and engineering. For the two most recent offerings of the course, we have utilized external observers and surveyed the students in order to validate the impact of aspects of our process and changes to it. This paper is based upon 5 years of experience and 2 years of analysis of our course, and it presents an overview of our process with both qualitative and quantitative results from these two most recent offerings.     

Invasive species detection in Hawaiian rainforests using airborne imaging spectroscopy and LiDAR

Remote sensing of invasive species is a critical component of conservation and management efforts, but reliable methods for the detection of invaders have not been widely established. In Hawaiian forests, we recently found that invasive trees often have hyperspectral signatures unique from that of native trees, but mapping based on spectral reflectance properties alone is confounded by issues of canopy senescence and mortality, intra- and inter-canopy gaps and shadowing, and terrain variability. We deployed a new hybrid airborne system combining the Carnegie Airborne Observatory (CAO) small-footprint light detection and ranging (LiDAR) system with the Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) to map the three-dimensional spectral and structural properties of Hawaiian forests. The CAO-AVIRIS systems and data were fully integrated using in-flight and post-flight fusion techniques, facilitating an analysis of forest canopy properties to determine the presence and abundance of three highly invasive tree species in Hawaiian rainforests.

The LiDAR sub-system was used to model forest canopy height and top-of-canopy surfaces; these structural data allowed for automated masking of forest gaps, intra- and inter-canopy shadows, and minimum vegetation height in the AVIRIS images. The remaining sunlit canopy spectra were analyzed using spatially-constrained spectral mixture analysis. The results of the combined LiDAR-spectroscopic analysis highlighted the location and fractional abundance of each invasive tree species throughout the rainforest sites. Field validation studies demonstrated < 6.8% and < 18.6% error rates in the detection of invasive tree species at  7 m² and  2 m² minimum canopy cover thresholds. Our results show that full integration of imaging spectroscopy and LiDAR measurements provides enormous flexibility and analytical potential for studies of terrestrial ecosystems and the species contained within them.     

Processing and interactive editing of huge point clouds from 3D scanners

This paper describes a new out-of-core multi-resolution data structure for real-time visualization, interactive editing and externally efficient processing of large point clouds. We describe an editing system that makes use of the novel data structure to provide interactive editing and preprocessing tools for large scanner data sets. Using the new data structure, we provide a complete tool chain for 3D scanner data processing, from data preprocessing and filtering to manual touch-up and real-time visualization. In particular, we describe an out-of-core outlier removal and bilateral geometry filtering algorithm, a toolset for interactive selection, painting, transformation, and filtering of huge out-of-core point-cloud data sets and a real-time rendering algorithm, which all use the same data structure as storage backend. The interactive tools work in real-time for small model modifications. For large scale editing operations, we employ a two-resolution approach where editing is planned in real-time and executed in an externally efficient offline computation afterwards. We evaluate our implementation on example data sets of sizes up to 63 GB, demonstrating that the proposed technique can be used effectively in real-world applications.     

Shape from defocus via diffusion

Defocus can be modeled as a diffusion process and represented mathematically using the heat equation, where image blur corresponds to the diffusion of heat. This analogy can be extended to non-planar scenes by allowing a space-varying diffusion coefficient. The inverse problem of reconstructing 3-D structure from blurred images corresponds to an "inverse diffusion" that is notoriously ill-posed. We show how to bypass this problem by using the notion of relative blur. Given two images, within each neighborhood, the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene. This can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image, using only forward diffusion.     

ICT integration in the classroom: Challenging the potential of a school policy

Despite the assumption that the integration of ICT influences the entire school system, research focusing on ICT in schools is generally limited to the study of variables at class level. In contrast to these studies, the present research explores ICT integration from a school improvement approach. More particularly, it examines the local school policy with respect to ICT integration from both the principal’s perspective and perceptions of teachers. Furthermore, it studies the relationship between school policies and the actual use of ICT in the classroom. To answer the research questions, a representative sample of 53 primary school principals was interviewed. In addition, the interview data were supplemented with survey data of 574 teachers from the same 53 schools. What emerged from the analyses was that school-related policies, such as an ICT plan, ICT support and ICT training have a significant effect on class use of ICT. In addition, the findings from the interviews indicate that school policies are often underdeveloped and underutilised. The discussion section focuses on challenges to improve the potential of an ICT school policy.     

Network invariants for real-time systems

We extend the approach of model checking parameterized networks of processes by means of network invariants to the setting of real-time systems. We introduce timed transition structures (which are similar in spirit to timed automata) and define a notion of abstraction that is safe with respect to linear temporal properties. We strengthen the notion of abstraction to allow a finite system, then called network invariant, to be an abstraction of networks of real-time systems. In general the problem of checking abstraction of real-time systems is undecidable. Hence, we provide sufficient criteria, which can be checked automatically, to conclude that one system is an abstraction of a concrete one. Our method is based on timed superposition and discretization of timed systems. We exemplify our approach by proving mutual exclusion of a simple protocol inspired by Fischer’s protocol, using the model checker TLV. Part of this work was done during O. Grinchtein’s stay at Weizmann Institute. This author was supported by the European Research Training Network “Games”.     

Batch process modelling with mixtures of Gaussian processes

In recent years Gaussian processes have attracted a significant amount of interest with the particular focus being that of process modelling. This has primarily been a consequence of their good predictive performance and inherent analytical properties. Gaussian processes are a member of the family of non-parametric Bayesian regression models and can be derived from the perspective of neural networks. Their behaviour is controlled through the structure of the covariance function. However, when applied to batch processes, whose data exhibits different variance structures throughout the duration of the batch, a single Gaussian process may not be appropriate for the accurate modelling of its behaviour. Furthermore there are issues with respect to the computational costs of Gaussian processes. The implementation of a Gaussian process model requires the repeated computation of a matrix inverse whose order is the cubic of the number of training data points. This renders the algorithm impractical when dealing with large data sets. To address these two issues, a mixture model of Gaussian processes is proposed. The resulting prediction is attained as a weighted sum of the outputs from each Gaussian process component, with the weights determined by a Gaussian kernel gating network. The model is implemented through a Bayesian approach utilising Markov chain Monte Carlo algorithms. The proposed methodology is applied to data from a bench-mark batch simulation polymerization process, methyl methacrylate (MMA), and the results are compared with those from a single Gaussian process to illustrate the advantages of the proposed mixture model approach.     

Stiction issues and actuation of RF LIGA-MEMS variable capacitors

High aspect ratio variable capacitors have been fabricated using deep X-ray lithography and electroplating. Stiction phenomena applicable to high aspect ratio devices are presented, including the conditions for stiction to occur and the critical dimensions of structures. Actuation tests at 3 GHz are also presented and show a maximum capacitance of 0.86 pF with no actuation voltage and a minimum capacitance of 0.70 pF with an actuation voltage of 20 V just before pull-in, which gives a tuning range of 1.23:1. Corresponding Q-factor values are 49.3 and 70.8 respectively. After pull-in, the measured capacitance is 0.61 pF, corresponding to a tuning range of 1.41:1, with a maximum Q-factor of 102.9.