lecturer and a pedagogical developer at the Staff Development Centre at the Royal Institute of Technology in Stockholm, Sweden (KTH). He has worked for fifteen years with pedagogical courses for different types of teachers and is also responsible for the Research Supervision course that more than five hundred supervisors have taken. He has published in the areas of teaching and learning and supervision. His current field of interest is postgraduate supervision and the learning and teaching of mathematics in engineering education. Contextualizing Calculus with Everyday Examples to Enhance Conceptual Learning AbstractMany engineering students in Sweden have difficulty passing the initial mathematics courses. Teachers complain that students are ill-prepared in pre-calculus and even the best students can only solve standard problems using standard procedures. The aim of teaching in mathematics at university is to develop deep understanding of the subject and to produce conceptually trained students who can then creatively solve unforeseen problems. But how should we educate such students' We hypothesize that the root of the problem lies in decontextualized abstract teaching. The approach adopted in this study is to introduce contextualized teaching of mathematics through concrete examples and to focus students' attention on the role of definitions in mathematics in order to scaffold their development of conceptual understanding. The general idea is to start from the most concrete, everyday examples and work towards more abstract mathematics. By everyday examples, we mean those that can instantly be understood by the students with reference solely to their life experience. Each new concept in the course is introduced verbally, numerically, graphically, and algebraically when applicable. Everyday examples are introduced in the verbal phase of the sequence. Application examples are also used to boost the students' motivation. Quantitative data were gathered from both a diagnostic test and the exam, and qualitative data come from a student questionnaire. The exam results show that the students in the intervention group succeeded better than the control groups. They also became more motivated and had a better grasp of abstract thinking in mathematics.
The Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology is designing a portfolio assessment system to assess students' achievement of program outcomes. In the past three years, the undergraduate aerospace engineering program has embarked upon major curriculum reform initiatives centered on 16 program outcomes detailed in its CDIO Syllabus. Portfolios will be organized into categories reflecting these outcomes. (The 16 CDIO skills, or program outcomes, are also the cornerstone of the program's self-study report for ABET accreditation.) This paper addresses the planning and development of portfolios for assessing students' achievement at the end of their programs in aerospace engineering at MIT. BackgroundIn its strategic plan of 1998, the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology (MIT) committed to major reform of its curriculum, teaching and learning methods, and laboratory environments. To achieve its goals, the department framed its curriculum to model a product system life cycle. The four phases in the curriculum are referred to as Conceive-Design-Implement-Operate (CDIO). The Conceive stage includes defining the need and technology, considering the enterprise strategy and regulations, developing the concept, architecture, and business case. The second stage, Design, focuses on creating the design, i.e., the plans, drawings, and algorithms that describe what will be implemented. Implement refers to the transformation of the design into the product, including manufacturing, coding, test and validation. The final stage, Operate, uses the implemented product to deliver the intended value, including maintaining, evolving and retiring the system.Curriculum reform efforts centered on a set of 16 key learning outcomes deemed essential for new engineers. (See Table 1) These outcomes, categorized as technical, personal, interpersonal, and CDIO system skills, were validated in surveys of faculty, students, alumni, and industrial representatives, both in the United States and in Sweden. They serve as the program outcomes of MIT's two aerospace education programs accredited by ABET under its new evaluation criteria and policies. 1 The more detailed list of outcomes, called the CDIO Syllabus, is available at the CDIO Web-site. 2 Here, the 16 program outcomes are outlined in two additional levels of detail.
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