Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Survey of Spring Oats for Barley Yellow Dwarf Viruses in Illinois

During the spring of 1987, 1,215 samples of spring oats (Avena sativa L.) were collected in Madison, Champaign, Woodford, Warren, and DeKalb counties, Illinois. At each site on each of three sampling dates, 45 samples were collected (regardless of symptoms) in a W pattern in I ha and tested for the PAY, MAV, RPV, and RMV serotypes of barley yellow dwarf virus (BYDV) by direct doubleantibody sandwich enzyme-linked immunosorbent assay (ELISA). RMV was not detected at any location. PAY and RPV were detected at all locations, as early as 17 April in Champaign County. The incidences of P A V and RPV from all plants sampled ranged from 2 to 64% and from 2 to 88%, respectively. Highest incidences of both strains were in May samples [rom Woodford County. MAV was detected in lower incidences (2-16%) only in samples from the central region of the state (Champaign, Woodford, and Warren counties). The presence of MA V serotypes was confirmed in triple-antibody sandwich ELISA with the MA V -specific MAFF2 monoclonal antibody from L. Torrance. In the last previous survey for BYDV in Illinois during 1967-1968 (1), about 75% of the isolates were PAY and about 20% were RPV; single isolates of RMV and MAV were found. Twenty years later, 55% were PAY, 39% were RPV, and 6% were MAV.

Unaided stereo vision based pose estimation

This paper presents the development of a low-cost sensor platform for use in ground-based visual pose estimation and scene mapping tasks. We seek to develop a technical solution using low-cost vision hardware that allows us to accurately estimate robot position for SLAM tasks. We present results from the application of a vision based pose estimation technique to simultaneously determine camera poses and scene structure. The results are generated from a dataset gathered traversing a local road at the St Lucia Campus of the University of Queensland. We show the accuracy of the pose estimation over a 1.6km trajectory in relation to GPS ground truth.

A robust structure and motion replacement for bundle adjustment

This paper demonstrates the application of a robust form of pose estimation and scene reconstruction using data from camera images. We demonstrate results that suggest the ability of the algorithm to rival methods of RANSAC based pose estimation polished by bundle adjustment in terms of solution robustness, speed and accuracy, even when given poor initialisations. Our simulated results show the behaviour of the algorithm in a number of novel simulated scenarios reflective of real world cases that show the ability of the algorithm to handle large observation noise and difficult reconstruction scenes. These results have a number of implications for the vision and robotics community, and show that the application of visual motion estimation on robotic platforms in an online fashion is approaching real-world feasibility.

Vision only pose estimation and scene reconstruction on airborne platforms

We aim to demonstrate unaided visual 3D pose estimation and map reconstruction using both monocular and stereo vision techniques. To date, our work has focused on collecting data from Unmanned Aerial Vehicles, which generates a number of significant issues specific to the application. Such issues include scene reconstruction degeneracy from planar data, poor structure initialisation for monocular schemes and difficult 3D reconstruction due to high feature covariance. Most modern Visual Odometry (VO) and related SLAM systems make use of a number of sensors to inform pose and map generation, including laser range-finders, radar, inertial units and vision [1]. By fusing sensor inputs, the advantages and deficiencies of each sensor type can be handled in an efficient manner. However, many of these sensors are costly and each adds to the complexity of such robotic systems. With continual advances in the abilities, small size, passivity and low cost of visual sensors along with the dense, information rich data that they provide our research focuses on the use of unaided vision to generate pose estimates and maps from robotic platforms. We propose that highly accurate (�5cm) dense 3D reconstructions of large scale environments can be obtained in addition to the localisation of the platform described in other work [2]. Using images taken from cameras, our algorithm simultaneously generates an initial visual odometry estimate and scene reconstruction from visible features, then passes this estimate to a bundle-adjustment routine to optimise the solution. From this optimised scene structure and the original images, we aim to create a detailed, textured reconstruction of the scene. By applying such techniques to a unique airborne scenario, we hope to expose new robotic applications of SLAM techniques. The ability to obtain highly accurate 3D measurements of an environment at a low cost is critical in a number of agricultural and urban monitoring situations. We focus on cameras as such sensors are small, cheap and light-weight and can therefore be deployed in smaller aerial vehicles. This, coupled with the ability of small aerial vehicles to fly near to the ground in a controlled fashion, will assist in increasing the effective resolution of the reconstructed maps.

Graphcut-based interactive segmentation using colour and depth cues

Segmentation of novel or dynamic objects in a scene, often referred to as background sub- traction or foreground segmentation, is critical for robust high level computer vision applica- tions such as object tracking, object classifca- tion and recognition. However, automatic real- time segmentation for robotics still poses chal- lenges including global illumination changes, shadows, inter-re ections, colour similarity of foreground to background, and cluttered back- grounds. This paper introduces depth cues provided by structure from motion (SFM) for interactive segmentation to alleviate some of these challenges. In this paper, two prevailing interactive segmentation algorithms are com- pared; Lazysnapping [Li et al., 2004] and Grab- cut [Rother et al., 2004], both based on graph- cut optimisation [Boykov and Jolly, 2001]. The algorithms are extended to include depth cues rather than colour only as in the original pa- pers. Results show interactive segmentation based on colour and depth cues enhances the performance of segmentation with a lower er- ror with respect to ground truth.

Re-engaging adolescent students in science : an experienced teachers' classroom

Adolescents are both aware of and have the impetuous to exploit aspects of Science, Technology, Engineering and Mathematics (STEM) within their personal lives. Whether they are surfing, cycling, skateboarding or shopping, STEM concepts impact their lives. However science, mathematics, engineering and technology are still treated in the classroom as separate fragmented entities in the educational environment where most classroom talk is seemingly incomprehensible to the adolescent senses. The aim of this study was to examine the experiences of young adolescents with the aim of transforming school learning at least of science into meaningful experiences that connected with their lives using a self-study approach. Over a 12-month period, the researcher, an experienced secondary-science teacher, designed, implemented and documented a range of pedagogical practices with his Year-7 secondary science class. Data for this case study included video recordings, journals, interviews and surveys of students. By setting an environment empathetic to adolescent needs and understandings, students were able to actively explore phenomena collaboratively through developmentally appropriate experiences. Providing a more contextually relevant environment fostered meta-cognitive practices, encouraged new learning through open dialogue, multi-modal representations and assessments that contributed to building upon, re-affirming, or challenging both the students' prior learning and the teacher’s pedagogical content knowledge. A significant outcome of this study was the transformative experiences of an insider, the teacher as researcher, whose reflections provided an authentic model for reforming pedagogy in STEM classes.

Marginalised students and insider knowledge

One of the claims made for valuing the voices of marginalised students is that an insider perspective can be revealed on student issues and the ways in which education policies and systems impact on them. This chapter examines the ways in which participants in an Australian ‘students-as-researchers’ (SaR) project were able to raise knowledge of and address, to some extent, long-standing issues of racism in their schools. The SaR project has operated in more than thirty schools for periods of one to five years. Based on a participatory action research model, groups of secondary school students from schools serving socio-economically disadvantaged communities have worked with nominated teachers and university researchers to identify and research local issues relating to low academic outcomes and to develop and enact responses to the identified concerns. The voices of marginalised students quoted in this chapter illustrate that important insider knowledge can be revealed through the SaR process. Where student views have been acknowledged and acted on by the schools, significant change to student-teacher relationships and school culture has been achieved; the participants have been personally empowered and academic improvements across the schools have been noted. For such change to occur, however, a culture of mutual respect must be created in which teachers and school administrators value students’ views and are open to the possibility of unfavourable criticism.

An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.