The textbook as classroom context variable

To explore the role of the textbook as a context variable in process—product relationships, data on teaching practices and learning outcomes from the IEA Classroom Environment Study in The Netherlands were used. The sample consisted of 50 secondary school mathematics classes and their teachers. Three textbooks were represented in the sample. Data collection included systematic observation of lessons and administration of tests and questionnaires to students and teachers. Nine teaching practices analogous to the distinguishing features of the textbooks were identified, and data relating to these practices were analysed. Four of the teaching practices occurred to different degrees in the three groups of textbook users. The correlations with two learning outcomes in different groups of textbook users were significantly different for 5 of the 18 cases. These results suggest that the textbook is an important context variable

Instructional strategies and tactics for the design of introductory computer programming courses in high school

This article offers an examination of instructional strategies and tactics for the design of introductory computer programming courses in high school. We distinguish the Expert, Spiral and Reading approach as groups of instructional strategies that mainly differ in their general design plan to control students' processing load. In order, they emphasize topdown program design, incremental learning, and program modification and amplification. In contrast, tactics are specific design plans that prescribe methods to reach desired learning outcomes under given circumstances. Based on ACT* (Anderson, 1983) and relevant research, we distinguish between declarative and procedural instruction and present six tactics which can be used both to design courses and to evaluate strategies. Three tactics for declarative instruction involve concrete computer models, programming plans and design diagrams; three tactics for procedural instruction involve worked-out examples, practice of basic cognitive skills and task variation. In our evaluation of groups of instructional strategies, the Reading approach has been found to be superior to the Expert and Spiral approaches

A note on the Lawrence-Krammer-Bigelow representation

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-24.abs.htm