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The task of curvature estimation from discrete sampling points along a curve is investigated. A novel curvature estimation algorithm based on performing line integrals over an adaptive data window is proposed. The use of line integrals makes the proposed approach inherently robust to noise. Furthermore, the accuracy of curvature estimation is significantly improved by using wild bootstrapping to adaptively adjusting the data window for line integral. Compared to existing approaches, this new method promises enhanced performance, in terms of both robustness and accuracy, as well as low computation cost. A number of numerical examples using synthetic noisy and noiseless data clearly demonstrated the advantages of this proposed method over state-of-the-art curvature estimation algorithms.

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Background To enhance tutors’ teaching skills, tutor shadowing for novice tutors of problem-based learning (PBL) in addition to conventional faculty development (FD) was applied. This study aimed to develop a tutoring-skill scale (TS-scale) and evaluate the effect of shadowing on PBL tutors. Methods This study employed a before-and-after study design with three phases. In phase 1, a TS-scale was elaborated. A validity examination was performed in phase 2. Phase 3 was a study of the effectiveness using a TS-scale survey of novice PBL tutors before and after the FD course. The FD course for novice PBL tutors included an FD workshop and PBL shadowing activities. Results A TS-scale with a 32-item questionnaire of self-rated confidence for PBL tutors was identified in phase 1. In phase 2, 7 experienced specialists in medical education were invited to evaluate the content validity of the scale. The item content validity index (I-CVI) ranged from 0.86 to 1, and the scale-CVI (S-CVI) was 0.95. A total of 85 novice PBL tutors completed the TS-scale before the FD course, yielding a Cronbach’s alpha of 0.98. An exploratory factor analysis with varimax rotation was performed. The twenty-four items with significant loadings greater than 0.5 were incorporated into a new TS-scale and were grouped into three factors: student contact, medical expertise, and teaching expertise. In phase 3, 76 novice PBL tutors completed the 24-item TS-scale before (pretest) and after (posttest) the FD course. Their self-rated confidence improved significantly across the three factors after the FD course. The pretest and posttest scores did not differ according to the tutors’ gender, the grades they taught, or their specialty background. Conclusions Novice PBL tutors benefit from FD that incorporates tutor shadowing in the 3 key domains of tutoring competencies. The TS-scale developed in this study can be applied in future research on FD design.

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