Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

The development of a conceptual framework for a district 4-Year Pavement Management Plan, implementation of network-level project screening process

The Texas Department of Transportation (TxDOT) is concerned about the widening gap between preservation needs and available funding. Funding levels are not adequate to meet the preservation needs of the roadway network; therefore projects listed in the 4-Year Pavement Management Plan must be ranked to determine which projects should be funded now and which can be postponed until a later year. Currently, each district uses locally developed methods to prioritize projects. These ranking methods have relied on less formal qualitative assessments based on engineers’ subjective judgment. It is important for TxDOT to have a 4-Year Pavement Management Plan that uses a transparent, rational project ranking process. The objective of this study is to develop a conceptual framework that describes the development of the 4-Year Pavement Management Plan. It can be largely divided into three Steps; 1) Network-Level project screening process, 2) Project-Level project ranking process, and 3) Economic Analysis. A rational pavement management procedure and a project ranking method accepted by districts and the TxDOT administration will maximize efficiency in budget allocations and will potentially help improve pavement condition. As a part of the implementation of the 4-Year Pavement Management Plan, the Network-Level Project Screening (NLPS) tool including the candidate project identification algorithm and the preliminary project ranking matrix was developed. The NLPS has been used by the Austin District Pavement Engineer (DPE) to evaluate PMIS (Pavement Management Information System) data and to prepare a preliminary list of candidate projects for further evaluation.

Understanding graphicacy : students’ making sense of graphics in mathematics assessment tasks

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed: 1) factors which contribute to success or hinder performance on tasks with various graphical representations; and 2) how the literacy and graphical demands of tasks influence the mathematical sense making of students. The outcomes of this study highlight the changing nature of assessment in school mathematics and identify the function and influence of graphics in the design of assessment tasks.

3D reconstruction of long bones utilising magnetic resonance imaging (MRI)

The design of pre-contoured fracture fixation implants (plates and nails) that correctly fit the anatomy of a patient utilises 3D models of long bones with accurate geometric representation. 3D data is usually available from computed tomography (CT) scans of human cadavers that generally represent the above 60 year old age group. Thus, despite the fact that half of the seriously injured population comes from the 30 year age group and below, virtually no data exists from these younger age groups to inform the design of implants that optimally fit patients from these groups. Hence, relevant bone data from these age groups is required. The current gold standard for acquiring such data–CT–involves ionising radiation and cannot be used to scan healthy human volunteers. Magnetic resonance imaging (MRI) has been shown to be a potential alternative in the previous studies conducted using small bones (tarsal bones) and parts of the long bones. However, in order to use MRI effectively for 3D reconstruction of human long bones, further validations using long bones and appropriate reference standards are required. Accurate reconstruction of 3D models from CT or MRI data sets requires an accurate image segmentation method. Currently available sophisticated segmentation methods involve complex programming and mathematics that researchers are not trained to perform. Therefore, an accurate but relatively simple segmentation method is required for segmentation of CT and MRI data. Furthermore, some of the limitations of 1.5T MRI such as very long scanning times and poor contrast in articular regions can potentially be reduced by using higher field 3T MRI imaging. However, a quantification of the signal to noise ratio (SNR) gain at the bone - soft tissue interface should be performed; this is not reported in the literature. As MRI scanning of long bones has very long scanning times, the acquired images are more prone to motion artefacts due to random movements of the subject‟s limbs. One of the artefacts observed is the step artefact that is believed to occur from the random movements of the volunteer during a scan. This needs to be corrected before the models can be used for implant design. As the first aim, this study investigated two segmentation methods: intensity thresholding and Canny edge detection as accurate but simple segmentation methods for segmentation of MRI and CT data. The second aim was to investigate the usability of MRI as a radiation free imaging alternative to CT for reconstruction of 3D models of long bones. The third aim was to use 3T MRI to improve the poor contrast in articular regions and long scanning times of current MRI. The fourth and final aim was to minimise the step artefact using 3D modelling techniques. The segmentation methods were investigated using CT scans of five ovine femora. The single level thresholding was performed using a visually selected threshold level to segment the complete femur. For multilevel thresholding, multiple threshold levels calculated from the threshold selection method were used for the proximal, diaphyseal and distal regions of the femur. Canny edge detection was used by delineating the outer and inner contour of 2D images and then combining them to generate the 3D model. Models generated from these methods were compared to the reference standard generated using the mechanical contact scans of the denuded bone. The second aim was achieved using CT and MRI scans of five ovine femora and segmenting them using the multilevel threshold method. A surface geometric comparison was conducted between CT based, MRI based and reference models. To quantitatively compare the 1.5T images to the 3T MRI images, the right lower limbs of five healthy volunteers were scanned using scanners from the same manufacturer. The images obtained using the identical protocols were compared by means of SNR and contrast to noise ratio (CNR) of muscle, bone marrow and bone. In order to correct the step artefact in the final 3D models, the step was simulated in five ovine femora scanned with a 3T MRI scanner. The step was corrected using the iterative closest point (ICP) algorithm based aligning method. The present study demonstrated that the multi-threshold approach in combination with the threshold selection method can generate 3D models from long bones with an average deviation of 0.18 mm. The same was 0.24 mm of the single threshold method. There was a significant statistical difference between the accuracy of models generated by the two methods. In comparison, the Canny edge detection method generated average deviation of 0.20 mm. MRI based models exhibited 0.23 mm average deviation in comparison to the 0.18 mm average deviation of CT based models. The differences were not statistically significant. 3T MRI improved the contrast in the bone–muscle interfaces of most anatomical regions of femora and tibiae, potentially improving the inaccuracies conferred by poor contrast of the articular regions. Using the robust ICP algorithm to align the 3D surfaces, the step artefact that occurred by the volunteer moving the leg was corrected, generating errors of 0.32 ± 0.02 mm when compared with the reference standard. The study concludes that magnetic resonance imaging, together with simple multilevel thresholding segmentation, is able to produce 3D models of long bones with accurate geometric representations. The method is, therefore, a potential alternative to the current gold standard CT imaging.

Family-level relationships among the Australasian marsupial “herbivores” (Diprotodontia: Koala, wombats, kangaroos and possums)

The marsupial order Diprotodontia includes 10 extant families, which occupy all terrestrial habitats across Australia and New Guinea and have evolved remarkable dietary and locomotory diversity. Despite considerable attention, the interrelations of these families have for the most part remained elusive. In this study, we separately model mitochondrial RNA and protein-coding sequences in addition to nuclear protein-coding sequences to provide near-complete resolution of diprotodontian family-level phylogeny. We show that alternative topologies inferred in some previous studies are likely to be artifactual, resulting from branch-length and compositional biases. Subordinal groupings resolved herein include Vombatiformes (wombats and koala) and Phalangerida, which in turn comprises Petauroidea (petaurid gliders and striped, feathertail, ringtail and honey possums) and a clade whose plesiomorphic members possess blade-like premolars (phalangerid possums, kangaroos and their allies and most likely, pygmy possums). The topology resolved reveals ecological niche structuring among diprotodontians that has likely been maintained for more than 40 million years.

Mathematics funds of knowledge : sotmaute and sermaute fish in a Torres Strait Islander community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

Multi-method, multi-theoretical, multi-level research in the learning sciences

We examine methodologies and methods that apply to multi-level research in the learning sciences. In so doing we describe how multiple theoretical frameworks informs the use of different methods that apply to social levels involving space-time relationships that are not accessible consciously as social life is enacted. Most of the methods involve analyses of video and audio files. Within a framework of interpretive research we present a methodology of event-oriented social science, which employs video ethnography, narrative, conversation analysis, prosody analysis, and facial expression analysis. We illustrate multi-method research in an examination of the role of emotions in teaching and learning. Conversation and prosody analyses augment facial expression analysis and ethnography. We conclude with an exploration of ways in which multi-level studies can be complemented with neural level analyses.

Adoption of low-cost rail level crossing warning devices : an Australian case study

The objective of this chapter is to provide rail practitioners with a practical approach for determining safety requirements of low-cost level crossing warning devices (LCLCWDs) on an Australian railway by way of a case study. LCLCWDs, in theory, allow railway operators to improve the safety of passively controlled crossing by upgrading a larger number of level crossings with the same budget that would otherwise be used to upgrade these using the conventional active level crossing control technologies, e.g. track circuit initiated flashing light systems. The chapter discusses the experience and obstacles of adopting LCLCWDs in Australia, and demonstrates how the risk-based approach may be used to make the case for LCLCWDs.

Drivers’ inability to assess their level of alertness on monotonous highways

Decline of alertness constitutes a normal physiological phenomenon but could be aggravated when drivers operate in monotonous environments, even in rested individuals. Driving performance is impaired and this increases crash risk due to inattention. This paper aims to show that road characteristics - namely road design (road geometry) and road side variability (signage and buildings) – influence subjective assessment of alertness by drivers. This study used a driving simulator to investigate the drivers’ ability to subjectively detect periods of time when their alertness is importantly reduced by varying road geometry and road environment. Driver’s EEG activity is recorded as a reference to evaluate objectively driver's alertness and is compared to self-reported alertness by participants. Twenty-five participants drove on four different scenarios (varying road design and road environment monotony) for forty minutes. It was observed that participants were significantly more accurate in their assessment before the driving task as compared to after (90% versus 60%). Errors in assessment were largely underestimations of their real alertness rather than over-estimations. The ability to detect low alertness as assessed with an EEG was highly dependent on the road monotony. Scenarios with low roadside variability resulted in high overestimation of the real alertness, which was not observed on monotonous road design. The findings have consequences for road safety and suggest that countermeasures to lapses of alertness cannot rely solely on self-assessment from drivers and road design should reduce environments with low variability.