The problems that secondary school students have being faced with the Feynman´s Sum of all Paths

FANARO, MARIA DE LOS ANGELES; ELGUE, MARIANA; ARLEGO, MARCELO; OTERO, MARIA RITA

Congreso; 2nd World Conference on Physics Education; 2016

GIREP-MPTL

In this work we analyze part of the implementation of a didactic sequence [1,2], to teach different aspects of light in a unified non traditional framework. The goal of the sequence was to propose the quantum theory of light as a universal framework to describe different phenomena observed. The sequence was carried out in four courses of two secondary schools, with N=83 students aged 15-16, during 23 school hours approximately. The data analysis, based on all the students? productions, aims to understand the process of student´s conceptualization [4] of Feynman?s viewpoint of quantum mechanics. The results allow to make a preliminary assessment of the viability of the sequence based on this viewpoint and the changes necessary for future implementations. In particular, an adaptation of Feynman´s ?Sum of all Paths? approach (SAP) of quantum mechanics for the case of the light, was proposed as model to describe the light reflection and refraction, and the double slit experience. Graphical representations and basic operations with vectors capturing the essential aspects of the theory were used. Simulations made with the software GeoGebra(R) were created to help students visualize the SAP technique results [3]. Regarding the use of the SAP technique during the implementations, the results indicate that many students (n=43) were able to establish the adequate relationship between light paths and their associated vector angles. A good number of students (n=30) interpreted adequately that the vector angle is proportional to the light travel time. This is important because it is the previous step to build the concept of the dominant role of the minimum time path. Instead, some students (n=10) confused the vector concept with the light path, providing characteristics of a real physical object to the vector, which made the conceptualization extremely difficult. In relation to the vector sum to find the probability amplitude in the simple case of emission and detection of light, n=33 students conceptualized appropriately that the path of minimum length (i.e. the minimum time) and those that are around it contribute ?in phase? to the sum, while the other paths tend to cancel each other, because their directions are very different. The interpretation of this result was very important for the students. A similar number of students (n=27) considered that the most probable light path is the one that takes less time. In that case they were close to the adequate concept. Finally for n=23 students it was difficult to establish the relationship between the sum and the probability, because they still considered that the vector sum is the light path.We can conclude it is possible to teach basic quantum concepts from Feynman?s approach to the secondary school students although some changes are necessary in the SAP technique introduction and in the simulations used to prevent the identified obstacles in the conceptualization.