Teaching Huygens in the rue Huygens: Introducing the history of 17th-century mathematics in a junior secondary school

This article gives an account of the teaching of some aspects of 17th-century mathematics in a French junior high school. The mathematics was taught in the context of interdisciplinary, or thematic, studies focusing the attention of all students in different subjects upon a specific period in French history. Extracts of original works by Leibniz and Huygens were read; connections between mathematics and technology were made; some historical puzzles were investigated; and a variety of mathematical problems arising out of the texts were worded upon. Class reactions were uniformly enthusiastic.This paper was originally presented in French to ICME 6 (International Congress on Mathematics Education) in Budapest during 1988. It was translated by Chris Weeks and was first published in 1990 in a publication of the British Mathematical Association — History in the Mathematics Classroom, John Fauvel (ed.).     

Differences between students’ and teachers’ perceptions of education: profiles to describe congruence and friction

Teachers and students have their own perceptions of education. Congruent perceptions contribute to optimal teaching–learning processes and help achieving best learning outcomes. This study investigated patterns in differences between students’ and teachers’ perceptions of their learning environment. Student profiles were identified taking into account the degree of congruence/friction with teachers’ perceptions. Teacher profiles were identified based on their differences in perceptions to students. Profiles were validated with regard to learning-related student characteristics and approaches to teaching. Tenth graders (N = 994) of four secondary schools filled out the Inventory of Perceived Study Environment-Extended (IPSEE) and the Inventory of Learning Styles. Their teachers (N = 136) filled out the teacher version of the IPSEE and the Approaches to Teaching Inventory. Latent class analyses were conducted to define profiles with respect to the magnitude of differences in perceptions. Results showed three student profiles: Closest match profile (30 %), intermediate profile (59 %), and distal profile (11 %). While closest match students had desirable learning-related characteristics, others did not and are at risk for destructive friction. Two teacher profiles described idealistic teachers (70 %) and adaptive teachers (30 %), which related to approaches to teaching. Subgroups of students and teachers provide a comprehensive picture of those who are at risk because of too large differences in perceptions. This study stresses that differences in perceptions deserve detailed attention for optimising learning environments. Involving both students and teachers in the instructional design process could be a way to better account for perceptions of both stakeholders.     

A model for optimizing step size of learning tasks in competency-based multimedia practicals

Learners are often overwhelmed by the complexity of realistic learning tasks, but reducing this complexity through traditional Instructional Design (ID) methods jeopardizes the authenticity of the learning experience. To solve this apparent paradox, a two-phase ID model is presented. Phase 1 consists of cognitive task analysis, where a systematic approach to problem solving (SAP) is identified in conjunction with skill decomposition and determination of task complexity. In the subsequent design phase, inductive micro-level sequencing based on the four-component ID model (van Merriënboer, 1997) is applied where worked-out examples and problems accompanied by process worksheets assure the necessary variability of practice. Step size in a multiple-step whole-task approach—needed for the process worksheets—is determined on the basis of estimated part-task complexity. A developmental study of the model is illustrated with examples from the domain of law.