Abstract:

The median is a central tendency measure, which is preferable to the mean in asymmetric distributions or in presence of outliers. It is also an order statistics and the base of nonparametric statistics and data exploratory analysis. Its study begins in the first year of Compulsory Secondary Education and continues in subsequent courses and educational levels. Students frequently have problems in using the different terms such as median, 50th percentile, second quartile and fifth decile. Various investigations describe a misunderstanding of the different definitions of median; for example, some students consider the median as the centre of the non-ordered distribution or the geometrical centre of the data. The variety of algorithms also make that students employ an inadequate procedure when computing the median. Students also doubt when to use the mean or the median and attributed inexistent properties to the median (such as associativity).

In order to help overcome these didactical problems, teachers should use all the available resources and this is particularly relevant in the COVID period, when often students should work at a distance, due to periods of confinement. Fortunately, the Internet provides many useful resources that can complement the teacher and textbooks to help students progress in their knowledge.

Taking into account these ideas, our research aimed to compile a sample of free access videos that we can find on the Internet and that can be used both by the teacher during the class and by the students independently at home to reinforce the study of the median. We base as a theoretical framework on the ontosemiotic approach to mathematical knowledge and instruction, which assumes knowledge emerges from the practices made by students in solving problems. In this framework, different mathematical objects are described (problems, language, concepts, properties, procedures and arguments). In this presentation we describe in detail one of these videos, analyse the different mathematical objects implicit in the resource, and the possible difficulties of the students to understand the video. We also perform a study of the different components of didactic suitability of the resource. We complement the analysis with a list of other videos related to the median available on the Internet. We conclude that these videos are a complement to the student in the confinement situation, as well as in ordinary classrooms. Moreover, the analysis presented in this work can serve as a guide for the teacher to select the most suitable didactic resources at each moment of the teaching and learning process.

Keywords:

Median, Internet video, didactical analysis.