Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Adaptive Bayesian compound designs for dose finding studies

We consider the problem of how to efficiently and safely design dose finding studies. Both current and novel utility functions are explored using Bayesian adaptive design methodology for the estimation of a maximum tolerated dose (MTD). In particular, we explore widely adopted approaches such as the continual reassessment method and minimizing the variance of the estimate of an MTD. New utility functions are constructed in the Bayesian framework and are evaluated against current approaches. To reduce computing time, importance sampling is implemented to re-weight posterior samples thus avoiding the need to draw samples using Markov chain Monte Carlo techniques. Further, as such studies are generally first-in-man, the safety of patients is paramount. We therefore explore methods for the incorporation of safety considerations into utility functions to ensure that only safe and well-predicted doses are administered. The amalgamation of Bayesian methodology, adaptive design and compound utility functions is termed adaptive Bayesian compound design (ABCD). The performance of this amalgamation of methodology is investigated via the simulation of dose finding studies. The paper concludes with a discussion of results and extensions that could be included into our approach.

Lesion selection by melanoma high-risk consumers during skin self-examination using mobile teledermoscopy

Mobile teledermatoscopy (MTD) for the early detection of skin cancer uses smartphones with dermatoscope attachments to magnify, capture, and transfer images remotely.1 Using the asymmetry–color variation (AC) rule, consumers achieve dermoscopy sensitivity of 92.9% to 94.0% and specificity of 62.0% to 64.2% for melanoma.2 This pilot randomized trial assessed lesions of concern selected by consumers at high risk of melanoma using MTD plus the AC rule (intervention, n = 10) or the AC rule alone (control, n = 12) during skin self-examination (SSE). Also measured were lesion location patterns, lesions overlooked by participants, provisional clinical diagnoses, likelihood of malignant tumor, and participant pressure to excise lesions.

Gemcitabine and paclitaxel associated pneumonitis in non-small cell lung cancer : report of a phase I/II dose-escalating study

The aim of this phase I/II dose escalating study was to establish the maximum tolerated dose (MTD) of gemcitabine and paclitaxel given in combination in non-small cell lung cancer (NSCLC). 12 patients with stage IIIB and IV NSCLC received paclitaxel administered intravenously over 1 h followed by gemcitabine given over 30 min on days 1, 8 and 15 every 28 days. Pneumonitis was the principal side-effect observed with 4 patients affected. Of these, 1 experienced grade 3 toxicity after one cycle of treatment and the others had grade 2 toxicity. All 4 cases responded to prednisolone. No other significant toxicities were observed. Of the 8 evaluable patients, 3 had a partial response and 2 had minor responses. The study was discontinued due to this dose-limiting toxicity. The combination of paclitaxel and gemcitabine shows promising antitumour activity in NSCLC, however, this treatment schedule may predispose to pneumonitis. (C) 2000 Elsevier Science Ltd.

An extension of the continual reassessment method using decision theory

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q*, of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q*, a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q*, that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q*, among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.