Valérie Munier

Interdisciplinary Mathematics–Physics Approaches to Teaching the Concept of Angle in Elementary School

The present study takes an interdisciplinary mathematics–physics approach to the acquisition of the concept of angle by children in Grades 3–5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics‐based teaching sequences tested in three classrooms. We showed that at the end of each teaching sequence the pupils had a good grasp of the concept of angle, they had truly appropriated the physics knowledge at play, and many pupils are enable to successfully grasp new physics situations in which the angle plays a highly meaningful role. Using a physics framework to introduce angles in problem situations is then pertinent: by interrelating different spaces, pupils were able to acquire skills in the domains of mathematics, physics, and modelling. In conclusion, we discuss the respective merits of each problem situation proposed.

Teaching Scientific Measurement and Uncertainty in Elementary School.

The concept of measurement is fundamental in science. In order to be meaningful, the value of a measurement must be given with a certain level of uncertainty. In this paper we try to identify and develop the reasoning of young French pupils about measurement variability. In France, official instructions for elementary school thus argue for having students do activities of measurement, followed by treatments and analysis of the data. The notion of measurement ‘uncertainty’ appears in fourth and fifth grades. A similar approach is proposed in the USA. We present a teaching sequence divided into two parts: the first part in grade 4, the second one in grade 5, the following year, with the same students. The main sources of data were field notes, videotapes, as well as the intermediate written traces produced, individual written tests given each year and clinical interview. We showed that the pupils were capable of entertaining all three possible causes of uncertainty (the quantity being measured, the measuring instrument, and the measurer). Concerning data organization and handling, we found that after teaching, most of them were able to construct a frequency table and a bar chart from a list of N measures of the same quantity. When interpreting this type of chart, some of them were able to argue in terms of a confidence interval. We have also shown that the proposed instructional units allowed pupils to become aware of the need to repeat measurements.

Grandeurs et mesures en électrocinétique des courants variables

Pupils tend to apply the same logic to variable electric-current readings as to those of direct current. This is often attributed to insufficient knowledge or a poor understanding of mathematics though this does not in itself fully explain the problem. This article is based on the hypothesis that certain measuring methods and their use, both of which are taught in elementary school as well as certain knowledge taught about direct current, can in fact be both a scientific and didactic obstacle later on. A study of the syllabus and textbooks suggests that theory and the use of measuring instruments remain independent activities, a fact which leaves students to their own devices when learning about the specifics of measuring variable currents. Students must understand by themselves that the laws of addition do not apply to effective values concerning potential differences. A questionnaire answered by pupils enrolled in a technical school shows that while they are capable of correctly associating magnitude and the measuring instrument, they encounter difficulties when trying to understand the notion of effective values.