Probability and Statistics in Mathematics Education


It is intended to adjust the student’s prior knowledge of mathematics to the didactic teaching practice requirements of the Secondary Education. The recent reforms in the curriculum point to a pedagogical practice grounded in the scientific rigor. Thus, it is required, from the future mathematical teachers, a greater mathematical fluency. Accordingly, at the end of this course, the students should have acquired the following knowledge’s and capabilities:

- teach with confidence the topics of Probability and Statistics presented in the Mathematics Program;

- distinguish valid didactic approaches from those that do not fulfill the objectives listed in the Mathematics Program;

- being able use the calculator and the computer on the implementation of different statistical techniques.


General characterization





Responsible teacher

Inês Jorge da Silva Sequeira


Weekly - 5

Total - 42

Teaching language



Good knowledge of the mathematical analysis concepts, in particular of the topics: functions of several variables, series and calculation of primitives and integrals.


  1. Guimarães e Cabral (1997). Estatística. McGraw-Hill.
  2. Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley.
  3. Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
  4. Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2ª edição. McGraw-Hill
  5. Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora.
  6. Pestana, D. e Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian, Lisboa.
  7. Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley.
  8. Tiago de Oliveira (1990). Probabilidades e Estatística: Conceitos, Métodos e Aplicações, vol. I, II. McGraw-Hill.

Teaching method

Theoretical and practical lectures with oral exposition of the different topics complemented with examples and resolution of problems. In particular the discussion and reflection of the different topics will be promoted in order to create bases and critical capacity; fundamental features so that students, in the future, are able to transmit in a rigorous and motivating way the concepts in the program of Mathematics for Secondary Education. Calculators and computers will be used as supporting tools for the consolidation and exploration of the different concepts.

Evaluation method

Evaluation Method defined under the



All students are admitted to evaluation.



The continuous assessment will be made through two theoretical and practical written work and respective presentation (T1 and T2), one test (Te) and an element (P) corresponding to the level of participation and proficiency obtained in the proposed skills during the semester.

Final Grade = 0.25 T1 + 0.25 T2 + 0.3 Te + 0.2 P, with Te >= 8 values.

The student who obtains a final grade greater than or equal to 18.5 must take an oral defense of grade (on a date to be agreed). If the student does not attend the oral exam, the final grade will be 18 points.

The student obtains approval to UC if Final Grade is greater than or equal to 9.5 values.



The evaluation of Season 2 is made by Exam (E), being valid both for grade improvement and for approval to UC.

Resource Final Grade = 0.5 E + 0.25 (T1+T2) , com E >= 8 valores

The student obtains approval to the UC if Resource Final Grade is greater than or equal to 9.5 values.

The student who obtains a Resource Final Grade greater than or equal to 18.5 must take an oral defense of grade (on a date to be agreed). If the student does not attend the oral exam, the final grade will be 18 points.




Students who intend to take the appeal exam, with a view to improving their grades, must, in advance, request this improvement from academic services.

The works cannot be improved.

Subject matter

1. Descriptive Statistics in Secondary Education

2. Problems solving in combinatorial analysis in the Secondary Education

3. Theory of probability and probability distributions in Secondary Education.

4. A didactic approach to Statistical Inference

5. Linear regression in the Secondary Education


Programs where the course is taught: