The use of function has been recognized as an important part of the design process over last two decades, especially at the conceptual design stage, due to its critical role in determining the final product’s functionality. Although there are now some general methodologies dealing with functions or reasoning about functions, virtually no commercial CAD system can support conceptual design process due to their focus on geometrical modeling but not functional modeling. This paper presents a functional modeling approach to guide conceptual die design through functional reasoning steps including functional decomposition, functional supportive synthesis and function-structure mapping. The formed functional model provides a good basis to generate various die structures at the conceptual design stage, because function is a higher level of abstraction than structure, and helps to capture the designer’s intent. The functional modeling process has been implemented in a computerized design environment to expedite the conceptual die design process. / Singapore-MIT Alliance (SMA)

Engineering changes are unavoidable and occur throughout the lifecycle of products. Due to the high interconnectivity of engineering products, a single change to one component usually has knock-on effects on other components causing further changes. This change propagation significantly affects the success of a product in the market by increasing development cost and time-to-market. As such engineering change management is essential to companies, but it is a complex task for managers and researchers alike. To address this challenge, the thesis at hand investigates the state-of-the-art of research in engineering change management and develops a method to support engineering change propagation analysis, termed FBS Linkage. This method integrates functional reasoning with change prediction. A product is modelled as a network of its functional, behavioural, and structural attributes. Change propagation is then described as spread between the elements along the links of this network. The FBS Linkage concept is designed based on a comprehensive set of requirements derived from both the literature and industry practices as well as a comparative assessment of existing change methods and functional reasoning schemes. A step-by-step technique of building and using an FBS Linkage model is demonstrated. The method’s potential benefits are discussed. Finally, the application of the method to two industrial case studies involving a diesel engine and a scanning electron microscope is presented. The method evaluation indicates that the benefits of the method outweigh its application effort and pinpoints areas for further refinement.

abstract: The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children. The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems. The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated. Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender. / Dissertation/Thesis / Doctoral Dissertation Curriculum and Instruction 2016

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)

Design is hard and needs to be supported by software. One of the ways software can support designers is by providing analogical reasoning. To make analogical reasoning work well, the software makers need to know how to create a knowledge representation that will facilitate the kind of analogies that the designers want. This thesis will inform software makers by experimenting with two kinds of knowledge representations, called device-centric (DC) and environment-centric (EC), and to try to determine the relative benefits of using either one of them for analogical matching. We performed computational experiments, using Structure Mapping Engine for matching, to determine the quantity and quality of analogical matches that are produced when the representation is varied. We conducted a limited human experiment, using questionnaires and repertory grids, to determine if any of the computational results were novel, and to determine if the human similarity ratings between devices correlated with the computer results. We show that design software should use DC representations to produce a few focused matches which have high average weight. It should use EC representations to produce many matches some of high weight and some of low weight. Based on our human experiment, design software can use either DC or EC representations to produce novel matches. Our experiments also show that human matches correlate most strongly with a combined DC and EC representation and that their similarity reasons are more EC than DC. This suggests that designers tend to think more in EC terms than in DC terms.

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)