Abstract:

The study of median appears for the first time in the Spanish curriculum in the first and second years of Compulsory Secondary Education (12-13 year-olds students) and is included in the topic of central position measures. Its study continues in subsequent courses and educational levels, where this concept is located within the family of order statistics. This implies the use of equivalent terminologies to refer to this concept: median, 50th percentile, second quartile and fifth decile, which students often confuse. The median is used in the methodological development of numerous statistical tools. On the one hand, within descriptive statistics and exploratory data analysis, we can use the median to summarize information and even to compare different distributions of data. In addition, the median has a very important property: it is a robust statistics, which is not much affected by extreme values. Consequently, its use is more appropriate than that of the arithmetic mean in asymmetric distributions or in the presence of outliers. This measure also appears in the study of random variables and two-dimensional distributions in high school. On the other hand, non-parametric methods take on a large role in advanced statistics courses, and many of them are based on the median. Consequently, a misunderstanding of this concept can affect both the summary of the information in the secondary or high school courses and the development of understanding different methods in more advanced statistical courses at university level.

Numerous investigations describe errors and difficulties that students present in relation to the understanding of the median, in all its different elements of meaning (recognition of problem fields, language, definitions, associated properties and procedures). Some relevant results indicate that due to the variety of algorithms there are difficulties in their calculation, some students are not sure when they have to use one or another method. They also confuse when to employ the mean or the median and do not see the different notations of median as equivalent. Moreover, they attribute inexistent properties to the median (such as associativity). Basing on this research, the aim of our research was to compile free access teaching resources that we can find on the Internet and that can be used both by the teacher during the class and by the students independently to reinforce the study of the median. These resources will allow the students to deepen their understanding of the definition, properties and fields of application, because the calculation procedures can be carried out by statistical software or even by the spreadsheet. Using the ontosemiotic approach to mathematical knowledge and instruction, we present the detailed analysis of one of these resources, including its description, the identification of the mathematical objects required to work with the resource, the description of possible difficulties of the students and the study of the different components of didactic suitability of the resource. We complement the analysis with a list of other resources available on Internet, The selected resources present different degrees of semiotic complexity and is the teacher's function to analyze its usefulness and applicability for the classroom. Finally, 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 resources, semiotic analysis.