ASSESSING PROSPECTIVE HIGH SCHOOL TEACHERS' UNDERSTANDING OF STATISTICAL HYPOTHESES

In spite that statistical tests are widely used in research, its interpretation and application have been discussed in the past 50 years. An explanation of this paradox is that statistical tests are difficult, because performing these tests requires students to understand and be able to relate many abstract concepts such as those of parameter and statistics, sampling distribution, significance level, null and alternative hypotheses, and p - value. Most previous research on this topic deals with understanding the concepts of level of significance and p - value and has described many related misconceptions. However, there is also confusion between the roles of null and alternative hypotheses; other students state their hypotheses in terms of the sample statistics (for example, the sample mean) instead of using the parameter (the sample population), set non complementary hypotheses or else the hypotheses do not cover the parametric space. Statistical tests have been included in the Spanish high school curriculum periodically, as well as in the test that are compulsory for students to enter University (University Entrance Tests, UET). Moreover a basic knowledge of this topic as well as elementary competence in solving simple tests problems are important for high school teachers, since results of applying statistical tests often appear in educational research papers. Taking into account these considerations, the aim of this research was assessing prospective high school teachers' understanding of hypotheses in statistical tests. In this paper we describe the responses to an open-ended problem, similar to those proposed at the entrance to university tests for high school students in the past years. The sample consists of 73 students preparing to become secondary and high school mathematics teacher. The results show that, although the majority of students provided correct hypotheses, only part of them established the correct critical region consistently with the established hypotheses and correctly finished the whole procedure. Consequently, it is important to improve the preparation of prospective and in-service teachers in this topic.