Integrated Testlets and the Immediate Feedback Assessment Technique

The increased use of multiple-choice (MC) questions in introductory-level physics final exams is largely hindered by reservations about its ability to test the broad cognitive domain that is routinely accessed with typical constructed-response (CR) questions. Thus, there is a need to explore ways in which MC questions can be utilized pedagogically more like CR questions while maintaining their attendant procedural advantages. we describe how an answer-until-correct MC response format allows for the construction of multiple-choice examinations designed to operate much as a hybrid between standard MC and CR testing. With this tool - the immediate feedback assessment technique (IF-AT) - students gain complete knowledge of the correct answer for each question during the examination, and can use such information for solving subsequent test items. This feature allows for the creation of a new type of context-dependent item sets; the "integrated testlet". In an integrated testlet certain items are purposefully inter-dependent and are thus presented in a particular order. Such integrated testlets represent a proxy of typical CR questions, but with a straightforward and uniform marking scheme that also allows for granting partial credit for proximal knowledge. We present a case study of an IF-AT-scored midterm and final examination for an introductory physics course, and discuss specific testlets with varying degrees of integration. In total, the items are found to allow for excellent discrimination, with a mean item-total correlation measure for the combined 45 items of the two examinations of $\bar{r}'=0.41\pm 0.13$ (mean $\pm$ standard deviation) and a final examination test reliability of $\alpha=0.82$ ($n=25$ items). Furthermore, partial credit is shown to be allocated in a discriminating and valid manner in these examinations.Comment: 13 pages. 7 figures. Accepted to the American Journal of Physics (August 2013

History and scientific practice in the construction of an adequate philosophy of science: revisiting a Whewell/Mill debate

William Whewell raised a series of objections concerning John Stuart Mill’s philosophy of science which suggested that Mill’s views were not properly informed by the history of science or by adequate reflection on scientific practices. The aim of this paper is to revisit and evaluate this incisive Whewellian criticism of Mill’s views by assessing Mill’s account of Michael Faraday’s discovery of electrical induction. The historical evidence demonstrates that Mill’s reconstruction is an inadequate reconstruction of this historical episode and the scientific practices Faraday employed. But a study of Faraday’s research also raises some questions about Whewell’s characterization of this discovery. Thus, this example provides an opportunity to reconsider the debate between Whewell and Mill concerning the role of the sciences in the development of an adequate philosophy of scientific methodology.Keywords: Inductivism; Experiment; Theory; Methodology; Electromagnetism

Deformation spaces of Kleinian surface groups are not locally connected

For any closed surface $S$ of genus $g \geq 2$, we show that the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to $S$, $AH(S \times I)$, is not locally connected. This proves a conjecture of Bromberg who recently proved that the space of Kleinian punctured torus groups is not locally connected. Playing an essential role in our proof is a new version of the filling theorem that is based on the theory of cone-manifold deformations developed by Hodgson, Kerckhoff, and Bromberg