Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Identity Verification Using Speech and Face Information

This article first provides an review of important concepts in the field of information fusion, followed by a review of important milestones in audio–visual person identification and verification. Several recent adaptive and nonadaptive techniques for reaching the verification decision (i.e., to accept or reject the claimant), based on speech and face information, are then evaluated in clean and noisy audio conditions on a common database; it is shown that in clean conditions most of the nonadaptive approaches provide similar performance and in noisy conditions most exhibit a severe deterioration in performance; it is also shown that current adaptive approaches are either inadequate or utilize restrictive assumptions. A new category of classifiers is then introduced, where the decision boundary is fixed but constructed to take into account how the distributions of opinions are likely to change due to noisy conditions; compared to a previously proposed adaptive approach, the proposed classifiers do not make a direct assumption about the type of noise that causes the mismatch between training and testing conditions

Fundamentals of college algebra, 5th.ed./ Swokowski

x, 383 hal.: ill.; 24 cm

Calculus

XX, 1051 tr.; 26 cm

Fundamentals of trigonometry

viii, 211 p.; 23 cm

Algebra and Trigonometry with Analytic Geometry Ed. 7

xii, 651 hlm.; Ind.; 24 c