What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.

A probability problem suitable for Problem-Based Learning

We propose a simple probability problem for undergraduate level. This problem involves different branches of Mathematics, such as Graph Theory, Linear Algebra or hypergeometric sums, hence it is quite suitable to be used as Problem-Based Learning. In addition, the problem allows several variations so that it may be proposed to different groups of students at the same time.

PEMBELAJARAN TEORI PROBABILITAS MENGGUNAKAN R

In learning probability theory, if a series of statistical experiments is carried out several times, identifying the possible samples produced is not an easy thing. If this happens, then a significant probability problem will arise. The objective of this study is how to learn probability theory using R software. Based on the simulation results it can be concluded that by combining the syntax in R can be used to solve probability problems such as identifying sample points from experiments, events, event operations, probabilities and conditional probabilities. This will help students learning in understanding of the probability theory material. The use of R will be very pronounced for experiments with a large enough scale that results in a large sample probability.

La Enseñanza determinista de la probabilidad

El presente trabajo analiza las respuestas de docentes en formación, que ya cursaron un curso sobre probabilidad y son estudiantes del Instituto Tecnológico de Costa Rica, en un test de situaciones problema de probabilidad con el fin de valorar el manejo que hacen de la aleatoriedad. En las respuestas se evidencia que algunos: no saben hacer explícito el espacio muestral ni la experiencia aleatoria, descuidan las hipótesis que se necesitan para utilizar la probabilidad como un modelo y dan respuestas deterministas a situaciones aleatorias, es decir piensan que hay una única respuesta correcta. ¿Será que se enseña la probabilidad de forma determinista? Abstract This paper analyzes the responses of teachers in training, who have already taken a course on probability and are students of the Technological Institute of Costa Rica, in a test of probability problem situations in order to assess the handling they make of randomness. The answers show that some do not know how to make explicit the sample space or the random experience, neglect the hypotheses that are needed to use probability as a model and give deterministic answers to random situations. Could it be that probability is taught in a deterministic way?