Principles for designing mathematical tasks that enhance imitative and creative reasoning

Principles for designing mathematical tasks that enhance imitative and creative reasoning

Imitative Reasoning

Taylor and Francis SEP_A_437580.sgm 10.1080/02691720903374026 Social Epistemology 0269-1728 (pri t)/1464-5297 (online) Original Article 2 0 & Francis 3 3/4 000July-December 200 Professor M amThalos m.th os@gm il.com On the classical instrumental view, practical reason is an all-things-considered enterprise, concerned not merely with identifying and evaluating appropriate means to the realizatio...

Designing Tasks for Visualization and Reasoning in Dynamic Geometry Environment

One of the important aims of the Hong Kong Secondary Mathematics Curriculum is to develop students’ ability to conceptualize, inquire, reason and communicate (Curriculum Development Council, 1999, p.4). Hence the terms “explore” and “justify” appear in the learning objectives of many topics. For example, it is expected that students could “explore the formula for the area of circles” (ibid., p....

Designing Toys That Come Alive: Curious Robots for Creative Play

Creative thinking requires imagination, creativity, play, sharing and reflection. This paper presents an architecture for a curious, reconfigurable robot that encourages creative design thinking by permitting designed structures to learn behaviours. These behaviours encourage designers to play with different structures, reflect on the relationship between structure and behaviour and imagine new...

Designing Object-oriented Representations for Reasoning from First-principles

Modeling expert knowledge using "situation-action" rules is not always feasible in knowledge intensive domains involving volatile knowledge (e.g., trading). The explosive search space involved in such domains and its dynamic nature make it extremely difficult to setup a rule base and keep it accurate. An alternative approach suggests that in some domains many of the rules expert use can be deri...