Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

Evaluation of the "reconceptualising early mathematics learning" project

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ assessment and a Pattern and Structure Assessment (PASA) interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a relatively short period of time.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

An English-translated parallel corpus for the CJK Wikipedia collections

In this paper, we describe a machine-translated parallel English corpus for the NTCIR Chinese, Japanese and Korean (CJK) Wikipedia collections. This document collection is named CJK2E Wikipedia XML corpus. The corpus could be used by the information retrieval research community and knowledge sharing in Wikipedia in many ways; for example, this corpus could be used for experimentations in cross-lingual information retrieval, cross-lingual link discovery, or omni-lingual information retrieval research. Furthermore, the translated CJK articles could be used to further expand the current coverage of the English Wikipedia.

Cross-Lingual knowledge discovery : Chinese-to-English article linking in Wikipedia

In this paper we examine automated Chinese to English link discovery in Wikipedia and the effects of Chinese segmentation and Chinese to English translation on the hyperlink recommendation. Our experimental results show that the implemented link discovery framework can effectively recommend Chinese-to-English cross-lingual links. The techniques described here can assist bi-lingual users where a particular topic is not covered in Chinese, is not equally covered in both languages, or is biased in one language; as well as for language learning.

Characterizing multi-agent team behavior from partial team tracings : evidence from the English Premier League

Real-world AI systems have been recently deployed which can automatically analyze the plan and tactics of tennis players. As the game-state is updated regularly at short intervals (i.e. point-level), a library of successful and unsuccessful plans of a player can be learnt over time. Given the relative strengths and weaknesses of a player’s plans, a set of proven plans or tactics from the library that characterize a player can be identified. For low-scoring, continuous team sports like soccer, such analysis for multi-agent teams does not exist as the game is not segmented into “discretized” plays (i.e. plans), making it difficult to obtain a library that characterizes a team’s behavior. Additionally, as player tracking data is costly and difficult to obtain, we only have partial team tracings in the form of ball actions which makes this problem even more difficult. In this paper, we propose a method to overcome these issues by representing team behavior via play-segments, which are spatio-temporal descriptions of ball movement over fixed windows of time. Using these representations we can characterize team behavior from entropy maps, which give a measure of predictability of team behaviors across the field. We show the efficacy and applicability of our method on the 2010-2011 English Premier League soccer data.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Link discovery for Chinese/English cross-language web information retrieval

Nowadays people heavily rely on the Internet for information and knowledge. Wikipedia is an online multilingual encyclopaedia that contains a very large number of detailed articles covering most written languages. It is often considered to be a treasury of human knowledge. It includes extensive hypertext links between documents of the same language for easy navigation. However, the pages in different languages are rarely cross-linked except for direct equivalent pages on the same subject in different languages. This could pose serious difficulties to users seeking information or knowledge from different lingual sources, or where there is no equivalent page in one language or another. In this thesis, a new information retrieval task—cross-lingual link discovery (CLLD) is proposed to tackle the problem of the lack of cross-lingual anchored links in a knowledge base such as Wikipedia. In contrast to traditional information retrieval tasks, cross language link discovery algorithms actively recommend a set of meaningful anchors in a source document and establish links to documents in an alternative language. In other words, cross-lingual link discovery is a way of automatically finding hypertext links between documents in different languages, which is particularly helpful for knowledge discovery in different language domains. This study is specifically focused on Chinese / English link discovery (C/ELD). Chinese / English link discovery is a special case of cross-lingual link discovery task. It involves tasks including natural language processing (NLP), cross-lingual information retrieval (CLIR) and cross-lingual link discovery. To justify the effectiveness of CLLD, a standard evaluation framework is also proposed. The evaluation framework includes topics, document collections, a gold standard dataset, evaluation metrics, and toolkits for run pooling, link assessment and system evaluation. With the evaluation framework, performance of CLLD approaches and systems can be quantified. This thesis contributes to the research on natural language processing and cross-lingual information retrieval in CLLD: 1) a new simple, but effective Chinese segmentation method, n-gram mutual information, is presented for determining the boundaries of Chinese text; 2) a voting mechanism of name entity translation is demonstrated for achieving a high precision of English / Chinese machine translation; 3) a link mining approach that mines the existing link structure for anchor probabilities achieves encouraging results in suggesting cross-lingual Chinese / English links in Wikipedia. This approach was examined in the experiments for better, automatic generation of cross-lingual links that were carried out as part of the study. The overall major contribution of this thesis is the provision of a standard evaluation framework for cross-lingual link discovery research. It is important in CLLD evaluation to have this framework which helps in benchmarking the performance of various CLLD systems and in identifying good CLLD realisation approaches. The evaluation methods and the evaluation framework described in this thesis have been utilised to quantify the system performance in the NTCIR-9 Crosslink task which is the first information retrieval track of this kind.

Studying in Cuba, returning home to work : experiences of graduates from the English-speaking Caribbean

Cuba’s higher education scholarship program has received little attention in the literature on education and development. In this chapter, I discuss themes that emerge from my interviews with graduates from English-speaking Caribbean countries who studied in Cuba, as well as Cuban educators, on the nature of their academic programs and their subsequent careers. This facilitates exploration of a number of questions, including the following: 1. How, in the perceptions of scholarship students and graduates, have they experienced the philosophy of combing study, practical work, and research in the tertiary education curriculum in Cuban universities? 2. What impact does studying in Cuba appear to have on graduates after they return to their home countries? 3. How does the experience of the graduates throw light on the relationship between tertiary education and national development?

"You help me improve my English, I'll teach you Physics!" Cuban teachers overseas

Lending teachers for two-year periods is one of the ways in which Cuba has been able to collaborate with other countries in their efforts to improve educational planning and practice. My field research in 2001 in Jamaica (March and November) and in Namibia (December) enabled me to obtain information about how Cuban teachers are being utilized, and about the educational implications of this project. In Jamaica, I interviewed 15 Cuban teachers in several schools and one in the vocational institute, as well as the Cuban project supervisor in charge of the 51 Cuban teachers. I also talked with officials at the Jamaican Ministry of Education to obtain an idea of the developmental needs in the various subjects that the Cubans had been asked to teach. In Namibia I interviewed personnel in the National Sports Directorate and the Cuban manager in charge of the sports education project. The chapter draws on these interviews to build a picture of how the program of collaboration is organized, and considers its postcolonial significance, in theory and in practice, as an example of South-South collaboration. The chapter contributes to a multilevel style of comparative education analysis based on microlevel qualitative fieldwork within a framework that compares cross-cultural issues and national policies. The discussion of the educational situation of the host countries suggests why Cuban teachers can contribute to meeting curricular needs, particularly in the areas of the sciences, mathematics, Spanish, and sports. The friendly and joking remark of one of the Cuban teachers to school students in Jamaica: “You help me improve my English, I’ll teach you Physics!” highlights the reciprocal potential of these cooperation projects, discussed in several chapters of this book.

Basic cognitive experiences and definitions in the Longman Dictionary of Contemporary English

This study applies theories of cognitive linguistics to the compilation of English learners’ dictionaries. Specifically, it employs the concepts of basic level categories and image schemas, two basic cognitive experiences, to examine the ‘definition proper’ of English dictionaries for foreign learners. In the study, the definition proper refers to the constituent part of a reference work that provides an explanation of the meanings of a word, phrase or term. This rationalization mainly consists of defining vocabulary, sense division and arrangement, as well as the means of defining (i.e. paraphrase, true definition, functional definition, and pictorial illustration). The aim of the study is to suggest ways of aligning the consultation and learning of definitions with dictionary users’ cognitive experiences. For this purpose, an analysis of the definition proper of the fourth edition of the Longman Dictionary of Contemporary English (LDOCE4) from the perspective of basic cognitive experiences has been undertaken. The study found that, generally, the lexicographic practices of LDOCE4 are consistent with theories of cognitive linguistics. However, there exist shortcomings that result from disregarding basic cognitive experiences.

Australian Aboriginal words in English : their origin and meaning [Second edition]

Australian Aboriginal Words in English records the Aboriginal contribution to Australian English and provides a fascinating insight into the contact between the first Australians and European settlers. The words are grouped according to subject, and for each one there is information on the Aboriginal language from which it derives, the date of its first written use in English, and its present meaning and pronunciation. This book brings them together and provides the fullest available information about their Aboriginal background and their Australian English History.