Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

The role of timber plantations in U.K. investment portfolios

Although timber plantations and forests are classified as forms of agricultural production, the ownership of this land classification is not limited to rural producers. Timber plantations and forests are now regarded as a long-term investment with both institutional and absentee owners. While the NCREIF property indices have been the benchmarks for the measurement of the performance of the commercial property market in the UK, for many years the IPD timberland index has recently emerged as the U.K. forest and timberland performance indicator. The IPD Forest index incorporates 126 properties over five regions in the U.K. This paper will utilise the IPD Forestry Index to examine the performance of U.K. timber plantations and forests over the period 1981-2004. In particular, issues to be critically assessed include plantation and forest performance analysis, comparative investment analysis, and the role of plantations and forests in investment portfolios, the risk reduction and portfolio benefits of plantations and forests in mixed-asset portfolios and the strategic investment significance of U.K. timberlands.

Random Indexing K-tree

Random Indexing K-tree is the combination of two algorithms suited for large scale document clustering.

Vision-based topological mapping and localisation

Competent navigation in an environment is a major requirement for an autonomous mobile robot to accomplish its mission. Nowadays, many successful systems for navigating a mobile robot use an internal map which represents the environment in a detailed geometric manner. However, building, maintaining and using such environment maps for navigation is difficult because of perceptual aliasing and measurement noise. Moreover, geometric maps require the processing of huge amounts of data which is computationally expensive. This thesis addresses the problem of vision-based topological mapping and localisation for mobile robot navigation. Topological maps are concise and graphical representations of environments that are scalable and amenable to symbolic manipulation. Thus, they are well-suited for basic robot navigation applications, and also provide a representational basis for the procedural and semantic information needed for higher-level robotic tasks. In order to make vision-based topological navigation suitable for inexpensive mobile robots for the mass market we propose to characterise key places of the environment based on their visual appearance through colour histograms. The approach for representing places using visual appearance is based on the fact that colour histograms change slowly as the field of vision sweeps the scene when a robot moves through an environment. Hence, a place represents a region of the environment rather than a single position. We demonstrate in experiments using an indoor data set, that a topological map in which places are characterised using visual appearance augmented with metric clues provides sufficient information to perform continuous metric localisation which is robust to the kidnapped robot problem. Many topological mapping methods build a topological map by clustering visual observations to places. However, due to perceptual aliasing observations from different places may be mapped to the same place representative in the topological map. A main contribution of this thesis is a novel approach for dealing with the perceptual aliasing problem in topological mapping. We propose to incorporate neighbourhood relations for disambiguating places which otherwise are indistinguishable. We present a constraint based stochastic local search method which integrates the approach for place disambiguation in order to induce a topological map. Experiments show that the proposed method is capable of mapping environments with a high degree of perceptual aliasing, and that a small map is found quickly. Moreover, the method of using neighbourhood information for place disambiguation is integrated into a framework for topological off-line simultaneous localisation and mapping which does not require an initial categorisation of visual observations. Experiments on an indoor data set demonstrate the suitability of our method to reliably localise the robot while building a topological map.

Clustering with random indexing K-tree and XML structure

This paper describes the approach taken to the clustering task at INEX 2009 by a group at the Queensland University of Technology. The Random Indexing (RI) K-tree has been used with a representation that is based on the semantic markup available in the INEX 2009 Wikipedia collection. The RI K-tree is a scalable approach to clustering large document collections. This approach has produced quality clustering when evaluated using two different methodologies.

Perception of affordances in multi-scale dynamics as an alternative explanation for equivalence of analogical and inferential reasoning in animals and humans

Recent claims of equivalence of animal and human reasoning are evaluated and a study of avian cognition serves as an exemplar of weaknesses in these arguments. It is argued that current research into neurobiological cognition lacks theoretical breadth to substantiate comparative analyses of cognitive function. Evaluation of a greater range of theoretical explanations is needed to verify claims of equivalence in animal and human cognition. We conclude by exemplifying how the notion of affordances in multi-scale dynamics can capture behavior attributed to processes of analogical and inferential reasoning in animals and humans.

Application of K-tree to document clustering

Digital collections are growing exponentially in size as the information age takes a firm grip on all aspects of society. As a result Information Retrieval (IR) has become an increasingly important area of research. It promises to provide new and more effective ways for users to find information relevant to their search intentions. Document clustering is one of the many tools in the IR toolbox and is far from being perfected. It groups documents that share common features. This grouping allows a user to quickly identify relevant information. If these groups are misleading then valuable information can accidentally be ignored. There- fore, the study and analysis of the quality of document clustering is important. With more and more digital information available, the performance of these algorithms is also of interest. An algorithm with a time complexity of O(n2) can quickly become impractical when clustering a corpus containing millions of documents. Therefore, the investigation of algorithms and data structures to perform clustering in an efficient manner is vital to its success as an IR tool. Document classification is another tool frequently used in the IR field. It predicts categories of new documents based on an existing database of (doc- ument, category) pairs. Support Vector Machines (SVM) have been found to be effective when classifying text documents. As the algorithms for classifica- tion are both efficient and of high quality, the largest gains can be made from improvements to representation. Document representations are vital for both clustering and classification. Representations exploit the content and structure of documents. Dimensionality reduction can improve the effectiveness of existing representations in terms of quality and run-time performance. Research into these areas is another way to improve the efficiency and quality of clustering and classification results. Evaluating document clustering is a difficult task. Intrinsic measures of quality such as distortion only indicate how well an algorithm minimised a sim- ilarity function in a particular vector space. Intrinsic comparisons are inherently limited by the given representation and are not comparable between different representations. Extrinsic measures of quality compare a clustering solution to a “ground truth” solution. This allows comparison between different approaches. As the “ground truth” is created by humans it can suffer from the fact that not every human interprets a topic in the same manner. Whether a document belongs to a particular topic or not can be subjective.

Systematic variations in polymer gel dosimeter calibration due to container influence and deviations from water equivalence

There are a number of gel dosimeter calibration methods in contemporary usage. The present study is a detailed Monte Carlo investigation into the accuracy of several calibration techniques. Results show that for most arrangements the dose to gel accurately reflects the dose to water, with the most accurate method involving the use of a large diameter flask of gel into which multiple small fields of varying dose are directed. The least accurate method was found to be that of a long test tube in a water phantom, coaxial with the beam. The large flask method is also the most straightforward and least likely to introduce errors during setup, though, to its detriment, the volume of gel required is much more than other methods.

A comparative study of the effect of calibration conditions on the water equivalence of a range of gel dosimeters

Gel dosimeters are of increasing interest in the field of radiation oncology as the only truly three-dimensional integrating radiation dosimeter. There are a range of ferrous-sulphate and polymer gel dosimeters. To be of use, they must be water-equivalent. On their own, this relates to their radiological properties as determined by their composition. In the context of calibration of gel dosimeters, there is the added complexity of the calibration geometry; the presence of containment vessels may influence the dose absorbed. Five such methods of calibration are modelled here using the Monte Carlo method. It is found that the Fricke gel best matches water for most of the calibration methods, and that the best calibration method involves the use of a large tub into which multiple fields of different dose are directed. The least accurate calibration method involves the use of a long test tube along which a depth dose curve yields multiple calibration points.

A comparative study of the effect of calibration conditions on the water equivalence of a range of gel dosimeters

Gel dosimeters are of increasing interest in the field of radiation oncology as the only truly three-dimensional integrating radiation dosimeter. There are a range of ferrous-sulphate and polymer gel dosimeters. To be of use, they must be water-equivalent. On their own, this relates to their radiological properties as determined by their composition. In the context of calibration of gel dosimeters, there is the added complexity of the calibration geometry; the presence of containment vessels may influence the dose absorbed. Five such methods of calibration are modelled here using the Monte Carlo method. It is found that the Fricke gel best matches water for most of the calibration methods, and that the best calibration method involves the use of a large tub into which multiple fields of different dose are directed. The least accurate calibration method involves the use of a long test tube along which a depth dose curve yields multiple calibration points.

In-depth analysis of the J.A.C.K. model

The Texas Transportation Commission (“the Commission”) is responsible for planning and making policies for the location, construction, and maintenance of a comprehensive system of highways and public roads in Texas. In order for the Commission to carry out its legislative mandate, the Texas Constitution requires that most revenue generated by motor vehicle registration fees and motor fuel taxes be used for constructing and maintaining public roadways and other designated purposes. The Texas Department of Transportation (TxDOT) assists the Commission in executing state transportation policy. It is the responsibility of the legislature to appropriate money for TxDOT’s operation and maintenance expenses. All money authorized to be appropriated for TxDOT’s operations must come from the State Highway Fund (also known as Fund 6, Fund 006, or Fund 0006). The Commission can then use the balance in the fund to fulfill its responsibilities. However, the value of the revenue received in Fund 6 is not keeping pace with growing demand for transportation infrastructure in Texas. Additionally, diversion of revenue to nontransportation uses now exceeds $600 million per year. As shown in Figure 1.1, revenues and expenditures of the State Highway Fund per vehicle mile traveled (VMT) in Texas have remained almost flat since 1993. In the meantime, construction cost inflation has gone up more than 100%, effectively halving the value of expenditure.

Evaluation of TxDOT’s J.A.C.K. model for revenue and expenditure projections

This research report documents work conducted by the Center for Transportation (CTR) at The University of Texas at Austin in analyzing the Joint Analysis using the Combined Knowledge (J.A.C.K.) program. This program was developed by the Texas Department of Transportation (TxDOT) to make projections of revenues and expenditures. This research effort was to span from September 2008 to August 2009, but the bulk of the work was completed and presented by December 2008. J.A.C.K. was subsequently renamed TRENDS, but for consistency with the scope of work, the original name is used throughout this report.