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The societal demand for inspiring and engaging science, technology, engineering, and mathematics (STEM) students and preparing our workforce for the emerging creative economy has necessitated developing students' self-efficacy and understanding of engineering design processes from as early as elementary school levels. Hands-on engineering design activities have shown the potential to promote middle school students' self-efficacy and understanding of engineering design processes. However, traditional classrooms often lack hands-on engineering design experiences, leaving students unprepared to solve real-world design problems. In this study, we introduce the framework of a toy design workshop and investigate the influence of the workshop activities on students' understanding of and self-efficacy beliefs in engineering design. Using a mixed method approach, we conducted quantitative analyses to show changes in students' engineering design self-efficacy and qualitative analyses to identify students' understanding of the engineering design processes. Findings show that among the 24 participants, there is a significant increase in students' self-efficacy beliefs after attending the workshop. We also identified major themes such as design goals and prototyping in students' understanding of engineering design processes. This research provides insights into the key elements of middle school students' engineering design learning and the benefits of engaging middle school students in hands-on toy design workshops.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.01.010 Byline: S. Kameshwaran (a), Y. Narahari (a), Charles H. Rosa (b), Devadatta M. Kulkarni (b), Jeffrey D. Tew (b) Keywords: Goal programming; e-Procurement; Multiattribute auctions; Multiple criteria optimization; Configurable bids; Business rules; Volume discount cost functions; Bid evaluation problem; Mixed integer linear program Abstract: One of the key challenges of current day electronic procurement systems is to enable procurement decisions transcend beyond a single attribute such as cost. Consequently, multiattribute procurement have emerged as an important research direction. In this paper, we develop a multiattribute e-procurement system for procuring large volume of a single item. Our system is motivated by an industrial procurement scenario for procuring raw material. The procurement scenario demands multiattribute bids, volume discount cost functions, inclusion of business constraints, and consideration of multiple criteria in bid evaluation. We develop a generic framework for an e-procurement system that meets the above requirements. The bid evaluation problem is formulated as a mixed linear integer multiple criteria optimization problem and goal programming is used as the solution technique. We present a case study for which we illustrate the proposed approach and a heuristic is proposed to handle the computational complexity arising out of the cost functions used in the bids. Author Affiliation: (a) Electronic Enterprises Laboratory, Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India (b) Manufacturing Systems Research Laboratory, General Motors Research and Development, Warren, MI, USA Article History: Received 30 October 2004; Accepted 8 January 2006

Auction-based mechanisms are extremely relevant in modern day electronic procurement systems since they enable a promising way of automating negotiations with suppliers and achieve the ideal goals of procurement efficiency and cost minimization. This paper surveys recent research and current art in the area of auction-based mechanisms for e-procurement. The survey delineates different representative scenarios in e-procurement where auctions can be deployed and describes the conceptual and mathematical aspects of different categories of procurement auctions. We discuss three broad categories: 1) single-item auctions: auctions for procuring a single unit or multiple units of a single homogeneous type of item; 2) multi-item auctions: auctions for procuring a single unit or multiple units of multiple items; and 3) multiattribute auctions where the procurement decisions are based not only on costs but also on attributes, such as lead times, maintenance contracts, quality, etc. In our review, we present the mathematical formulations under each of the above categories, bring out the game theoretic and computational issues involved in solving the problems, and summarize the current art. We also present a significant case study of auction based e-procurement at General Motors. [ABSTRACT FROM AUTHOR]

A path counting formula pivotal in the development of certain ladder determinantal ideals is revisited and recast in a probabilistic framework. Results from large-sample distribution theory are exploited to provide an approximate enumeration formula. The results in this note reside on the interface of statistics and combinatorics and hopefully stimulate further research in this direction. [ABSTRACT FROM AUTHOR]