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The shift of contents in prototypical tasks used in education reforms
203-219Views:152The paper discusses the shift of contents in prototypical tasks provoked by the current educational reform in Austria. The paper starts with the educational backboard of the process of changes in particular with the out tting of the students' abilities in different taxonomies and its implementation in the competence models of Mathematics. A methodological didactical point of view on the process is given additionally. Examples out of a specific collection of math problems which arise from the educational reform are integrated and analysed in the context of educational principles and methods. The discussion ends with a short evaluation of the role of traditional approaches to tasks in the ongoing reform. A bundle of tasks as proof that they are still alive is presented finally.
Subject Classification: 97B50, 97D40, 97D50
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Promoting a meaningful learning of double integrals through routes of digital tasks
107-134Views:356Within a wider project aimed at innovating the teaching of mathematics for freshmen, in this study we describe the design and the implementation of two routes of digital tasks aimed at fostering students' approach to double integrals. The tasks are built on a formative assessment frame and classical works on problem solving. They provide facilitative and response-specific feedback and the possibility to request different hints. In this way, students may be guided to the development of well-connected knowledge, operative and decision-making skills. We investigated the effects of the interaction with the digital tasks on the learning of engineering freshmen, by comparing the behaviours of students who worked with the digital tasks (experimental group, N=19) and students who did not (control group, N=19). We detected that students in the experimental group showed more exibility of thinking and obtained better results in the final exam than students in the control group. The results confirmed the effectiveness of the experimental educational path and offered us interesting indications for further studies.
Subject Classification: 97D40, 97U70, 44A45
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Teaching puzzle-based learning: development of transferable skills
245-268Views:233While computer science and engineering students are trained to recognise familiar problems with known solutions, they may not be sufficiently prepared to address novel real-world problems. A successful computer science graduate does far more than just program and we must train our students to reach the required levels of analytical and computational thinking, rather than hoping that it will just 'develop'. As a step in this direction, we have created and experimented with a new first-year level course, Puzzle-based Learning (PBL), that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is increase students' mathematical awareness and general problem solving skills by employing puzzles, which are educational, engaging, and thought provoking. In this paper we continue sharing our experiences in teaching such a course. Whereas a brief discussion on our pedagogical objectives were covered in the first paper together with the material of the first of two lectures on pattern recognition, this follow-up paper presents the material of the second of two lectures, in which additional exercises are discussed to reinforce the lesson. Along the way we provide a glimpse of some foundational ideas of computer science such as incomputability and general system development strategies such as incremental and iterative reasoning. This paper discusses the outcomes of PBL courses, which include expected improvement in the overall results achieved by students who have undertaken PBL courses, compared to those students who have not. -
Teaching puzzle-based learning: development of basic concepts
183-204Views:301While computer science and engineering students are trained to recognise familiar problems with known solutions, they may not be sufficiently prepared to address novel real-world problems. A successful computer science graduate does far more than just program and we must train our students to reach the required levels of analytical and computational thinking, rather than hoping that it will just 'develop'. As a step in this direction, we have created and experimented with a new first-year level course, Puzzle-based Learning (PBL), that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is increase students' mathematical awareness and general problem solving skills by employing puzzles, which are educational, engaging, and thought provoking. We share our experiences in teaching such a course – apart from a brief discussion on our pedagogical objectives, we concentrate on discussing the presented material which covers (in two lectures) just one selected topic (pattern recognition). In this paper we present the ideas behind foundations for PBL and the material of the first of two lectures on pattern recognition, in which we address core concepts and provide students with sufficient exemplars to illustrate the main points. -
A role of geometry in the frame of competencies attainment
41-55Views:112We discuss aspects of the Education Reform from teaching to educational system. In this context we recognize some problems in recognition of some competencies that students need to achieve and we present how we have developed the measurement method of spatial abilities and problem solving competence. Especially, we investigate how students use spatial visualization abilities in solving various problems in other mathematical course. We have tested how students use their spatial abilities previously developed in geometry courses based on conceptual approach to solve a test based on procedural concept in Mathematical Analysis course.
