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## Revista Lusófona de Educação

*versão impressa* ISSN 1645-7250

#### Resumo

FERNANDES, Susana e CONCEICAO, Ana C.. **Precalculus and the education of pre-service teachers of Mathematics Worrying results of a diagnostic test**.* Rev. Lusófona de Educação* [online]. 2013, n.25, pp.135-155.
ISSN 1645-7250.

Adapting graduate degrees to the Bologna process reduced its duration to three scholar years. This promoted the creation of Masters in Teaching, the required degree to become an accredited teacher. Existing literature on training future teachers indicates the need for focusing on the mathematical (content) knowledge for teaching the subject matters of the curricula that will be taught, while not disregarding the acquisition of all teaching abilities. In this article we present data which reveals the lack of a strong scientific knowledge regarding the mathematical field of precalculus, of pre-service teachers attending a master degree in teaching Mathematics in junior high and high school levels. A diagnostic test was designed to measure the content knowledge in precalculus of these master students. They answered the same diagnostic test questions before and after the contents were addressed in the classroom. This paper presents different kinds of problems in their answers, exposing the mathematical weaknesses of these pre-service teachers in this field. These weaknesses are evident in solving equations and inequations and also in solving limits. We choose to present the two questions of the diagnostic test that illustrate these facts. There are three kinds of errors in the answers to the question of solving equations: the misuse of the Ruffini’s rule; the inability to find the correct domain of the expressions and the misuse of disjunctions/conjunctions symbols. Only 29% of the pre-service teachers solved correctly this test question before attending the precalculus classes. After attending classes the percentage of correct answers was 50%. There are three kinds of errors in the answers to the question of solving limits: basic errors, like misusing the distributive property of the multiplication operation over the addition operation or failing to solve simple derivatives; not knowing the module function and the inability to deal with indeterminations. Before attending the precalculus classes none of the pre-service teachers gave a correct answer to this diagnostic test question. The same happened one year after they attended the classes. All the answers to both questions revealed a strong lack of vocabulary knowledge and an unacceptable inability to use terms and notation correctly. This document concludes by stressing the need for the existence of graduate courses which specifically address mathematical knowledge for teaching; a crucial factor for a successful practice of pre-service teachers.

**Palavras-chave
:
**Education of pre-service teachers; Teachers of Mathematics; Post- Bologna degrees; Precalculus; Wolfram|Alpha.