Mathematics for the exploration of requirements

The exploration of requirements is as complex as it is important in ensuring a successful software production and software life cycle. Increasingly, tool-support is available for aiding such explorations. We use a toy example and a case study of modelling and analysing some requirements of the global assembly cache of .NET to illustrate the opportunities and challenges that mathematically founded exploration of requirements brings to the computer science and software engineering curricula

Fostering Inquiry and Creativity in Early Years STEM Education: Policy Recommendations from the <i>Creative Little Scientists</i> Project

Creative Little Scientists was a 30-month (2011-2014) EU/FP7-funded research project focusing on the synergies between early years science and mathematics education and the development of children’s creativity, in response to increasing interest in these areas in European educational policy. Using a variety of methods, including desk research, a teacher survey and classroom-based fieldwork, the research provided insights into whether and how children’s creativity is fostered and appropriate learning outcomes, including children’s interest, emerge. Based on these and ongoing collaboration and dialogue with participants and other stakeholders the project proposed recommendations for policy and teacher education. This paper presents these recommendations and the research on which they were based. Throughout the study, mixed methods were employed, combining quantitative approaches used in surveys of policy and teachers’ views based on a list of factors, alongside qualitative approaches employed in case studies of classroom practice. A strong conceptual framework developed at the start of the project guided data collection and analysis, as well as the presentation of findings and the development of policy recommendations, thus ensuring the latter’s strong and consistent relationship with the relevant theoretical knowledge, the comparative research, analysis of classroom practices and the production of guidelines for teacher education

The discipline of Natural Design

If we define design work as those cognitive and practical things to which designers give their valuable effort, then our Natural Design framework allows the recording and replaying of design work. Natural Design provides a meta-structural framework that has developed through our observations of engineering design in safety and mission critical industries, such as aircraft design. Our previous work has produced parametrisable models of design work for software intensive systems, and we now look to make an initial assessment of our natural design framework for its fit to the more creative design practices. In this paper we briefly sketch the framework and subsequently attempt to locate ‘creativity’ in it. We find that, although there are good strong hooks for what the designer does, we are forced to find a role for the community of the designer in the creative process in our framework, something that was only implicit in our previous work. Keywords: Natural design; Engineering design; Creativity</p

Learners' identity in mathematics

A dissertation submitted to the Faculty of Humanities, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Education. Johannesburg 2017The study reported in this dissertation sought to explore Grade 8 learners’ identities in mathematics. The study focused on examining learners’ interpretations of their relationships with the discipline of mathematics. The study drew on ideas from three different yet complementing theoretical perspectives as advocated by Gee (2001), Wenger (1998), and Sfard and Prusak (2005). However, Wenger’s (1998) broader social theory of learning was selected as a theoretical framework of this study to particularly connect the process of active engagement and participation in the practices of social communities and explain the construction of learners’ identity in mathematics. The study refuted a view that mathematics learners are born with special genes which drive them to succeed in doing the subject. This stance permitted the study to divert from discussing the role of models of abilities when doing mathematics or what Darragh (2016) described as a ‘performative identity’. Rather, the study was inclined to look at relationships between emotional and cognitive reactions that shift from time to time whenever mathematics is made accessible for learners through participatory pedagogy which encourages exploration, negotiation and ownership of knowledge. The study employed mixed methods research. The reasons for employing mixed methods research included the researcher’s beliefs and that the research questions were both exploratory and confirmatory type of questions. The research used a sequential mixed methods design. In the first phase, data sets were collected and analysed from an open-ended questionnaire (qualitative component). The results from the first phase were then used to develop a Likert-scale questionnaire (quantitative component) which informed the third phase (qualitative component). The third phase of the research design was semi-structured interviews. The interviews expanded the analyses of data from both initial qualitative and quantitative components. The reported findings indicated that the learners strongly needed teachers to clearly explain mathematics concepts. The learners required to understand mathematics in order to identify with the subject. The learners explained that if they understand mathematics, they become interested in learning the subject. Mathematics becomes their favourite subject. And if they do not understand, the learners expressed that they withdraw their participation in the classroom. In cases where learners shared incoherent views about how they are at learning mathematics, it was concluded from the analyses of the results that they needed to carefully listen to the teacher, ask for more examples to familiarise themselves with procedures, and then do their level best during assessments to pass the subject in order to align themselves with certain careers in the future.MT 201

Teaching and learning algebra word problems : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies in Mathematics, Massey University, Palmerston North, New Zealand

This study reports on a classroom design experiment into the teaching and learning of algebra word problems. The study was set in the mathematics department of a coeducational secondary school, and involved two teachers and 30 Year 12 students. The teachers and the researcher worked collaboratively to design and implement an intervention that focused explicitly on translation between word problems and algebra. Two issues were considered: the impact of the intervention on students, and the impact of the study on teachers. Students' responses to classroom activities, supported by individual student interviews, were used to examine their approaches to solving algebra word problems. Video-stimulated focus group interviews explored students' responses to classroom activities, and informed the ongoing planning and implementation of classroom activities. Data about the impact on teachers' understandings, beliefs and practices was gathered through individual interviews and classroom observations as well as the ongoing dialogue of the research team. The most significant impact on students related to their understandings of algebra as a tool. Some students were able to combine their new-found translation skills with algebraic manipulation skills to solve word problems algebraically. However, other students had difficulties at various stages of the translation process. Factors identified as supporting student learning included explicit objectives and clarity around what was to be learnt, the opportunity for students to engage in conversations about their thinking and to practise translating between verbal and symbolic forms, structured progression of learning tasks, time to consolidate understandings, and, a heuristic for problem solving. Participation in the project impacted on teachers in two ways: firstly, with regards to the immediate intervention of teaching algebra; and secondly, with regards to teaching strategies for mathematics in general. Translation activities provided a tool for teachers to engage students in mathematical discussion, enabling them to elicit and build on student thinking. As teachers developed new understandings about how their students approached word problems they gained insight into the importance of selecting problems for which students needed to use algebra. However, teachers experienced difficulty designing quality instructional activities, including algebra word problems, that pressed for algebraic thinking. The focus on translation within the study encouraged a shift in teacher practice away from a skills-focus toward a problem-focus. Whilst it was apparent that instructional focus on translation shifted teachers and students away from an emphasis on procedure, it was equally clear that translation alone is insufficient as an intervention. Students need both procedural and relational understandings to develop an understanding of the use of algebra as a tool to solve word problems. Students also need to develop fluency with a range of strategies, including algebra, in order to be able to select appropriate strategies to solve particular problems. This study affirmed for teachers that teaching with a focus on understanding can provide an effective and efficient method for increasing students' motivation, interest and success

Exploring grade 11 learner routines on function from a commognitive perspective

A thesis submitted to the Faculty of Humanities, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy September 2015This study explores the mathematical discourse of Grade 11 learners on the topic function through their routines. From a commognitive perspective, it describes routines in terms of exploration and ritual. Data was collected through in-depth interviews with 18 pairs of learners, from six South African secondary schools, capturing a landscape of public schooling, where poor performance in Mathematics predominates. The questions pursued became: why does poor performance persist and what might a commognitive lens bring into view? With the discursive turn in education research, commognition provides an alternate view of learning mathematics. With the emphasis on participation and not on constraints from inherited mental ability, the study explored the nature of learner discourse on the object, function. Function was chosen as it holds significant time and weight in the secondary school curriculum. Examining learners’ mathematical routines with the object was a way to look at their discourse development: what were the signifiers related to the object and what these made possible for learners to realise. Within learners’ routines, I was able to characterise these realisations, which were described and categorised. This enabled a description of learner thinking over three signifiers of function in school Mathematics: the algebraic expression, table and graph. In each school, Grade 11 learners were separated into three groups according to the levels at which they were performing, from summative scores of grade 11 assessments, so as to enable a description of discourse related to performance. Interviews were conducted in pairs, and designed to provoke discussion on aspects of function and its signifiers between learners in each pair. This communication between learners and with the interviewer provided data for description and analysis of rituals and explorations. Zooming in and out again on these routines made a characterisation of the discourse of failure possible, which is seldom done. It became apparent early in the study that learners talked of the object function, without a formal mathematical narrative, a definition in other words, of the object. The object was thus vested in its signifiers. The absence of an individualised formal narrative of the object impacts directly what is made possible for learners to realise, hence to learn. The study makes the following contributions: first, it describes learners’ discursive routines as they work with the object function. Second, it characterises the discourse of learners at different levels of performance. Third, it starts exploration of commognition as an alternate means to look at poor performance. The strengths and limitations of the theory as it pertains to this study, are discussed later in the concluding chapter. Keywords commognition, discourse, communication, participation, routines, exploration, ritual, learners, learning, narratives, endorsed narratives, visual mediators

A methodology for exploring emergence in learning communities

Learning communities are becoming increasingly complex in nature, often being used to drive multiple agendas. For example, there is an increasing move to develop learning cities which seek to draw on synergies to both improve citizen learning and skills as well as economic regeneration. Such synergy-driven learning communities, of which the learning cities are but one example, seek to utilise interaction to develop 'emergent products', be it at the individual level or the system-wide level, which could not be produced in isolation. Successfully enabling emergence is critical to their success. Designing for specific types of emergence is however difficult given the intrinsic unpredictability of complex systems. Insight into the intrinsic characteristics of these synergy-driven learning communities and how their interaction leads to emergence over time is required. This paper reports on the methodology developed to explore these highly complex learning communities. The approach adopted was to combine exploratory case studies which established the intrinsic characteristics of the learning communities with an exploration of emergence guided by a meta-level conceptual framework of emergence. This was augmented by secondary data to aid triangulation and provide rigour. As well as discussing the rationale for the adopted approach, implementation issues and the rich information set obtained are discussed using specific case examples. Findings from the investigations led to recommendations regarding future development of appropriate methods for seeding and managing such complex learning communities. The meta level framework means the approach may be readily adapted to other complex social system

EDIS 788 Mathematics/Science/Education Field Project as a Capstone Experience in Five Year BA/MT Teacher Education Program

As a culminating experience, students in the Elementary Education Program Area at the University of Virginia are expected to engage in a field project/thesis experience in the final semester of their program of study. This session will provide an overview of the Field Project/Thesis Experience as it currently exists and will discuss possible variations to encourage more math and science collaborations

Aerospace bibliography, fifth edition

Bibliography of references, periodicals, and educational materials related to space fligh