Exploratory Problem Solving Research Articles

Problematizing Helps! A Classroom Study of Computer-Based Guidance for Invention Activities

A successful instructional method is to engage learners with exploratory problem-solving before providing explanations of the canonical solutions and foundational concepts. A key question is whether and what type of guidance will lead learners to explore more productively and how this guidance will affect subsequent learning and transfer. We investigate this question through the design and study of the Invention Coach, an adaptive, computer-based learning environment that problematizes students’ understanding as they invent fundamental physics equations. Problematizing guidance (Reiser Journal of the Learning Sciences, 13(3), 273–304, 2004), which encourages learners to grapple with domain complexity, is well-suited to the goals of Invention. However, there are few examples of technology-based learning environments that were explicitly designed to problematize and scant research on their efficacy. In an experimental study, 199 middle schoolers worked with either motivational, task + motivational, or problematizing + task + motivational guidance versions of the Coach while inventing. Students who engaged with the problematizing Coach were better able to transfer their knowledge to novel domains in the short term, and their transfer gains were comparable to those provoked by human tutors. While students in the problematizing condition were less likely to invent the correct solutions, they engaged in more targeted and efficient exploration of the solution space and were less likely to report experiences of difficulty. Findings suggest that problematizing guidance has the potential to effectively support exploratory problem-solving, when the goal is to facilitate productive exploration and transfer from subsequent instruction. The work also has implications for the design of problematizing guidance.

Multilevel Modeling for Data Mining of Downstream Bio-Industrial Processes

The throughput of a continuous ultrafiltration operation is limited by membrane fouling phenomena where the production capacity - monitored as flow through the membrane or flux - typically decreases as a function of run-time. Significant attention has been paid in both public research and industry to understanding why flux varies as these discrepancies clearly affect the production scheduling and hence economics. The potential of huge amounts of already collected full-scale processing data and its related performance history have however so far been under-employed in the production optimization efforts. The reason behind this is primarily a lack of methods capable of analyzing time series data generated during (semi-)continuous processes, characterized by widely varying operation times. The dataset examined in this investigation was compiled from records of conventional, univariate process sensors collected over several years of production of one intermediate enzyme product. Consequently, the dataset has a natural multilevel structure with level one being the process timestamps which are nested within the individual ultrafiltration runs, referred as level two. Multilevel Simultaneous Component Analysis with invariant Pattern (MSCA-P) is applied to explore this historical dataset in the context of flux decline. The unusual runs are easily identified in diagnostic plots of the between-model and the reason behind their outlying behavior becomes apparent in contribution plots. In this paper we build on the two-level idea and expand the model to a third level: processing recipe. MSCA-P offers a good overview during exploratory problem solving or data mining and helps optimization engineers to focus attention on suitable target areas. The extent of flux decline as well as higher overall mean flux value appears to be related to process temperatures and in particular increased feed temperature.

Distinguishing 'Crowded' Organizations from Groups and Communities: Is Three a Crowd?

In conventional wisdom on crowdsourcing, the number of people define the crowd and maximizing this number is often assumed to be the goal of any crowdsourcing exercise. However, we propose that there are structural characteristics of the crowd that might be more important than the sheer number of participants. These characteristics include (1) growth rate and its attractiveness to the members, (2) the equality among members, (3) the density within provisional boundaries, (4) the goal orientation of the crowd, and (5) the seriality of the interactions between members of the crowd. We then propose a typology that may allow managers to position their companies’ initiatives among four strategic types: crowd crystals, online communities, closed crowd, and open crowd driven innovation. We show that incumbent companies may prefer a closed and controlled access to the crowd, limiting the potential for gaining results and insights from fully open crowd-driven innovation initiatives. Consequently, we argue that the effects on industries and organizations by open crowds are still to be explored, possibly via the mechanisms of entrepreneurs exploiting open crowds as new entrants, but also for the configuration of industries such as, e.g., finance, pharmaceuticals, or even the public sector where the value created usually comes from interpretation issues and exploratory problem solving.

The problem with problems: Potential difficulties in implementing problem-based learning as the core method in primary school mathematics

This viewpoint paper presents the writer's opinion that while the use of problem solving as the core method for learning mathematics is valid and reasonable in secondary schools (where students generally possess the necessary prior skills and strategies) there are many obstacles to applying the same method in primary schools, particularly in the early years. In addition to acquiring a conceptual understanding of number, young learners – and older students with learning difficulties – need to develop automaticity in recalling basic number facts and in applying computational procedures. To do this they require both active experience with number relationships and direct teaching with guided and independent practice. There is no hard evidence that most students achieve adequate mastery of basic numeracy skills simply by engaging in exploratory problem solving. Drawing on the relevant literature the writer identifies and analyses the potential difficulties associated with using such an approach as a main method for teaching primary mathematics.