Abstract
Paul was a common octopus living in a public aquarium in Germany. It became internationally known during the World Cup in 2010 when it was used to “predict” the results of football games. Paul correctly predicted all the outcomes. What animal best of octopus, with its eight tentacles-tips, lends itself to introduce non-deterministic phenomena? In the text, teachers who want to develop the theme “Data and forecasts” will find eight ideas. These ideas are supported by the use of artifacts, digital tools and Web resources.
TopIntroduction
Paul was a common octopus living (January 2008, October 2010) in a public aquarium at the marine life center in Oberhausen, Germany. Paul experienced some international notoriety during the 2010 World Cup when it was used to “predict” the results of football matches in which the German national football team was involved and the final (that was not played by Germany). Paul's predictions were all correct.
The octopus belongs to Octopodidae family and has eight tentacles, therefore we imagine that each of these gives us an indication as to which are the best strategies to analyze resources and obstacles of teaching probability and statistics.
Mathematical artifacts shown in the figures are the basis of a project that could be called educational gaming. The collection of materials found, purchased, and constructed is the result of many years of research work (Drivet, 2013). They are taken from https://sites.google.com/site/oggettimatematici/home site. Currently there are 210 objects and, of these, 40 relate to the mentioned subject (Figure 1).
Figure 1. Data and Forecasts Objects
TopEight Tips
First Idea: The Different Registers
The following quote makes it perfectly clear the key concept.
“For example, if you throw an ideal dice cube and one wonders what is the probability of getting either 1 or 6, it can be answered in different ways, using different registers or different representations within the same register. In the register of native language: “There are two possibilities on six.” By conversion to the fractional register “the probability is 2 /6” or by treatment within the fractional register the probability is 1/3, by conversion to the decimal register “the probability is 0.3”, or yet by conversion to the proportion register “the probability is 33.3%”. (Arrigo, 2010).
If you start with the dice (Figure 2) it is useful to show these different registers by using, for example, the different types of format available in a spreadsheet (Table 1).
Table 1. Register and Representations
| Registers | Representations |
| Linguistic | 2 of 6 |
| Fractional | 1/3 |
| Decimal | 0.33 |
| Percentage | 33.3% |
The example of the dice may seem trivial and indeed it is, if it is limited to standardized exercises. In reality, the problem is more complex and we can agree with the following quote: “Studying the patterns that occur in purely random behavior (such as dice rolls and card selections) helps us to understand the patterns that occur in real-life data sets (such as lists of patients’ pulse rates or baseball players’ batting averages)”(Pfenning, 1998).
Key Terms in this Chapter
Stochastic Modelling: A model that depends on random variables.
Statistic: Discipline that has as its goal the study of quantity and quality of a phenomenon.
Artifacts: Sometimes indicates an object in a digital environment.
Dynamic Statistic: The use of dynamic graphics for the representation of statistical data.
Combinatorics: A branch of math concerning the study of finite or countable discrete structures.
Predictive Modelling: Use of statistics to predict outcomes.
Information Technology: The use of a device to store, retrieve, transmit and manipulate data.
Big Data: A term for data sets that are so large or complex that traditional data processing applications are inadequate.