Debugging an Artifact, Instrumenting a Bug: Dialectics of Instrumentation and Design in Technology-Rich Learning Environments

This article explores ways of conceptualizing the design of innovative learning tools as emergent from dialectics between designers and learner-users of those tools. More specifically, I focus on the reciprocities between a designer’s objectives for student learning and a user’s situated activity in a learning environment, as these interact and co-develop in cycles of design-based research. Recent investigations of technology-supported mathematics learning conducted from an ‘instrumental’ perspective provide a powerful framework for analyzing the process through which classroom artifacts become conceptual tools, simultaneously characterizing the ways students come to both implement and understand a device in the context of a task. Similarly, design-based approaches to investigating instructional activity offer epistemological grounds for treating the process of designing artifacts to support learning as unfolding in concert with rather than concluding prior to situated student use. Drawing on each of these perspectives, I describe the design and initial implementation of a set of software artifacts intended to support students’ collaborative problem solving through locally networked handheld computers. Through detailed analyses of three classroom episodes, I report on the ways one student group’s innovative and unexpected use of these tools served as an opportunity to both examine student learning in the context of that novelty and to refine the software design. This account provides an empirical example through which to consider the potential for instrumental genesis to inform design, and for design research epistemology to broaden the scope of instrumental theory.

Classification of Hadamard matrices of order 44 with automorphisms of order 7

The Hadamard matrices of order 44 possessing automorphisms of order 7 are classified. The number of their equivalence classes is 384. The order of their full automorphism group is calculated. These Hadamard matrices yield 1683 nonisomorphic 3-(44,22,10) designs, 57932 nonisomorphic 2-(43,21,10) designs, and two inequivalent extremal binary self-dual doubly even codes of length 88 (one of them being new).     

Effective collaboration in the productive failure process

Productive failure is a learning design that encompasses problem solving prior to instruction and the learning that occurs during and after this process. In the mathematics education literature, there is a need for analyses of students’ interactions that occur as they collaborate during the productive failure process. In this paper, we contribute to this area by taking a closer look at students’ interactions that characterize an effective productive failure process. In analyzing video footage of two different groups of students working on invention tasks in a flipped mathematics classroom, we observed that the productive failure process seemed to work best in groups of students among whom the instructional design evoked students’ intellectual need and curiosity. These students also developed a set routine for solving problems whose solutions are difficult to find without prior direct instruction on the topic, which proved valuable on follow-up in-class and posttest problems.     

Stochastic structural analysis and lifetime oriented optimization

A stochastic structural anal sis for lifetime oriented ontimization is presented. The covariance analysis and a shaping filter-realized with singular value decomposition -enables a simultaneous formulation of load process and structure in an overall state space equation. A numerical example - industrial structure and wind load-illustrates the efficiency of the algorithm to estimate the probability density of stress ranges. The algorithm is used in lifetime oriented structural optimization     

The effectiveness of manufacturer vs. retailer rebates within a newsvendor framework

This paper studies the impact of direct rebates to the end customer from the manufacturer and/or from the retailer upon the profitability and effectiveness of the policies of both channels. Effectiveness is measured by the ratio of the retailer’s to the manufacturer’s profits and by the sum of the profits for the two parties across scenarios wherein at least one of the parties offers a rebate. The main result is to prove analytically the conditions under which either all three scenarios are equally profitable or the retailer-only rebate policy is dominant. Another important result is to illustrate the likelihood that the manufacturer is able to coordinate the supply chain, by the appropriate choice of its pricing and rebate policies, thereby inducing the retailer to do likewise with its associated best pricing, ordering and rebate policies. Finally, numerical examples highlight the main features of the paper.     

Profiling effects in industrial data mining by non-parametric DOE methods: An application on screening checkweighing systems in packaging operations

There is a growing interest in applying robust techniques for profiling complex processes in industry. In this work, we present an approach for analyzing fractional-factorial data by building distribution-free models suitable for dealing with replicated trials in search of non-linear effects. The technique outlined in this article is synthesized by implementing four key elements: (1) the data collection efficiency of non-linear fractional factorial designs, (2) the data compression capabilities of rank-sums for repetitive sampling schemes, (3) the rank-ordering as a means to transform data, and (4) the non-parametric screening for prominent effects where the normality and sparsity assumptions are waived. The technique is tested on four controlling factors for profiling the packaging weighing operations of a pharmaceutical enterprise. The robust data mining of repeated trials based on an L₉(3⁴) orthogonal array scheme with embedded uncontrolled noise is discussed extensively. The technique has been subjected to quality control as it is tested with well-defined artificial data. Concluding remarks involve contrasting this new technique with mainstream competing schemes.     

A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis

Sustainable product design has been considered as one of the most important practices for achieving sustainability. To improve the environmental performances of a product through product design, however, a firm often needs to deal with some difficult technical trade-offs between traditional and environmental attributes which require new design concepts and engineering specifications. In this paper, we propose a novel use of the two-stage network Data Envelopment Analysis (DEA) to evaluate sustainable product design performances. We conceptualize “design efficiency” as a key measurement of design performance in terms of how well multiple product specifications and attributes are combined in a product design that leads to lower environmental impacts or better environmental performances. A two-stage network DEA model is developed for sustainable design performance evaluation with an “industrial design module” and a “bio design module.” To demonstrate the applications of our DEA-based methodology, we use data of key engineering specifications, product attributes, and emissions performances in the vehicle emissions testing database published by the US EPA to evaluate the sustainable design performances of different automobile manufacturers. Our test results show that sustainable design does not need to mean compromise between traditional and environmental attributes. Through addressing the interrelatedness of subsystems in product design, a firm can find the most efficient way to combine product specifications and attributes which leads to lower environmental impacts or better environmental performances. This paper contributes to the existing literature by developing a new research framework for evaluating sustainable design performances as well as by proposing an innovative application of the two-stage network DEA for finding the most eco-efficient way to achieve better environmental performances through product design.     

Understanding multidigit whole numbers: The role of knowledge components,connections, and context in understanding regrouping 3+-digit numbers

This case study of a PST's understanding of regrouping with multidigit whole numbers in base-10 and non-base-10 contexts shows that although she seems to have all the knowledge elements necessary to give a conceptually based explanation of regrouping in the context of 3-digit numbers, she is unable to do so. This inability may be due to a lack of connections among various knowledge components (conceptual knowledge) or a lack of connections between knowledge components and context (strategic knowledge). Although she exhibited both conceptual and strategic knowledge of numbers while regrouping 2-digit numbers, her struggles in explaining regrouping 3-digit numbers in the context of the standard algorithms indicate that explaining regrouping with 3-digit is not a mere extension of doing so for 2-digit numbers. She also accepts an overgeneralization of the standard algorithms for subtraction to a time (mixed-base) context, indicating a lack of recognition of the connections between the base-10 contexts and the standard algorithms. Implications for instruction are discussed.     

Analyticity and the Analysis Relation

Quine famously argued that analyticity is indefinable, since there is no good account of analyticity in terms of synonymy, and intensions are of no help since there are no intensions. Yet if there are intensions, the question still remains as to the right account of analyticity in terms of them. On the assumption that intensions must be admitted, the present paper considers two such accounts. The first analyzes analyticity in terms of concept identity, and the second analyzes analyticity in terms of the analysis relation. The first fails in light of possible counterexamples. The second is defended, both by considering test cases of intuitively clear analyticities, and by developing the account in light of possible counterexamples.