Developing The Attitude And Creativity In Mathematics Education

The structures in a traditionally-organized classroom of mathematics teaching can usually be linked readily with the routine classroom activities of teacher-exposition and teacher-supervised desk work, teacher’s initiation, teacher’s direction and strongly teacher’s expectations of the outcome of student learning. If the teacher wants to develop appropriate attitude and creativities in mathematics teaching learning it needs for him to develop innovation in mathematics teaching. The teacher may face challenge to develop various style of teaching i.e. various and flexible method of teaching, discussion method, problem-based method, various style of classroom interaction, contextual and or realistic mathematics approach. To develop mathematical attitude and creativity in mathematics teaching learning processes, the teacher may understand the nature and have the highly skill of implementing the aspects of the following: mathematics teaching materials, teacher’s preparation, student’s motivation and apperception, various interactions, small-group discussions, student’s works sheet development, students’ presentations, teacher’s facilitations, students’ conclusions, and the scheme of cognitive development.In the broader sense of developing attitude and creativity of mathematics learning, the teacher may needs to in-depth understanding of the nature of school mathematics, the nature of students learn mathematics and the nature of constructivism in learning mathematics. Key Word: mathematical attitude, creativity in mathematics, innovation of mathematics teaching,school mathematics

Transitioning Applications to Semantic Web Services: An Automated Formal Approach

Semantic Web Services have been recognized as a promising technology that exhibits huge commercial potential, and attract significant attention from both industry and the research community. Despite expectations being high, the industrial take-up of Semantic Web Service technologies has been slower than expected. One of the main reasons is that many systems have been developed without considering the potential of the web in integrating services and sharing resources. Without a systematic methodology and proper tool support, the migration from legacy systems to Semantic Web Service-based systems can be a very tedious and expensive process, which carries a definite risk of failure. There is an urgent need to provide strategies which allow the migration of legacy systems to Semantic Web Services platforms, and also tools to support such a strategy. In this paper we propose a methodology for transitioning these applications to Semantic Web Services by taking the advantage of rigorous mathematical methods. Our methodology allows users to migrate their applications to Semantic Web Services platform automatically or semi-automatically

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

Formalism and judgement in assurance cases

This position paper deals with the tension between the desire for sound and auditable assurance cases and the current ubiquitous reliance on expert judgement. I believe that the use of expert judgement, though inevitable, needs to be much more cautious and disciplined than it usually is. The idea of assurance “cases ” owes its appeal to an awareness that all too often critical decisions are made in ways that are difficult to justify or even to explain, leaving the doubt (for the decision makers as well as other interested parties) that the decision may be unsound. By building a well-structured “case ” we would wish to allow proper scrutiny of the evidence and assumptions used, and of the arguments that link them to support a decision. A

Start Time and Duration Distribution Estimation in Semi-Structured Processes

Semi-structured processes are business workflows, where the execution of the workflow is not completely controlled by a workflow engine, i.e., an implementation of a formal workflow model. Examples are workflows where actors potentially have interaction with customers reporting the result of the interaction in a process aware information system. Building a performance model for resource management in these processes is difficult since the required information is only partially recorded. In this paper we propose a systematic approach for the creation of an event log that is suitable for available process mining tools. This event log is created by an incrementally cleansing of data. The proposed approach is evaluated in an experiment

Discovering predictive variables when evolving cognitive models

A non-dominated sorting genetic algorithm is used to evolve models of learning from different theories for multiple tasks. Correlation analysis is performed to identify parameters which affect performance on specific tasks; these are the predictive variables. Mutation is biased so that changes to parameter values tend to preserve values within the population's current range. Experimental results show that optimal models are evolved, and also that uncovering predictive variables is beneficial in improving the rate of convergence

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)

Applying multi-criteria optimisation to develop cognitive models

A scientific theory is developed by modelling empirical data in a range of domains. The goal of developing a theory is to optimise the fit of the theory to as many experimental settings as possible, whilst retaining some qualitative properties such as `parsimony' or `comprehensibility'. We formalise the task of developing theories of human cognition as a problem in multi-criteria optimisation. There are many challenges in this task, including the representation of competing theories, coordinating the fit with multiple experiments, and bringing together competing results to provide suitable theories. Experiments demonstrate the development of a theory of categorisation, using multiple optimisation criteria in genetic algorithms to locate pareto-optimal sets

Learning about the Energy of a Hurricane System through an Estimation Epistemic Game

As part of a study into students' problem solving behaviors, we asked upper-division physics students to solve estimation problems in clinical interviews. We use the Resources Framework and epistemic games to describe students' problem solving moves. We present a new epistemic game, the "estimation epistemic game". In the estimation epistemic game, students break the larger problem into a series of smaller, tractable problems. Within each sub-problem, they try to remember a method for solving the problem, and use estimation and reasoning abilities to justify their answers. We demonstrate how a single case study student plays the game to estimate the total energy in a hurricane. Finally, we discuss the implications of epistemic game analysis for other estimation problems.Comment: 4 pages. Submitted to Physics Education Research Conference 201