Stijn Vanhoof’s research while affiliated with KU Leuven and other places

In this paper we discuss the distinction between statistical literacy and mathematical literacy. The starting point of this discussion is the fact that within the Programme for International Student Assessment (PISA) statistical survey items are elaborated only from the mathematical literacy point of view. We first present theoretical elements on the differences between mathematics and statistics, between mathematical and statistical literacy and we elaborate on the growing interest in statistical literacy as a specific competence. Second we present results of an empirical analysis based on the PISA 2003 data. The analysis showed an extremely high correlation between mathematical and statistical literacy. In the conclusion we emphasise the necessity to reveal the notion of statistical literacy within the PISA results. RESUMO In this paper we discuss the distinction between statistical literacy and mathematical literacy. The starting point of this discussion is the fact that within the Programme for International Student Assessment (PISA) statistical survey items are elaborated only from the mathematical literacy point of view. We first present theoretical elements on the differences between mathematics and statistics, between mathematical and statistical literacy and we elaborate on the growing interest in statistical literacy as a specific competence. Second we present results of an empirical analysis based on the PISA 2003 data. The analysis showed an extremely high correlation between mathematical and statistical literacy. In the conclusion we emphasise the necessity to reveal the notion of statistical literacy within the PISA results.

Although a number of instruments for assessing attitudes toward statistics have been developed, several questions with regard to the structure and item functioning remain unresolved. In this study, the structure of the Survey of Attitudes Toward Statistics (SATS-36), a widely used questionnaire to measure six aspects of students' attitudes toward statistics, is investigated. This study addresses the previously unexplored issue of individual item functioning. Based on confirmatory factor analysis using individual items, the results suggest that the SATS-36 can be improved by removing some poorly functioning items and that depending on the goals of a specific study either six subscales could be used or three of them (Affect, Cognitive Competence, and Difficulty) can be combined into one subscale without losing much information. © International Association for Statistical Education (IASE/ISI), May, 2011.

The implementation of educational innovations is far more complex than the straightforward execution of policy prescriptions. Individual and collective processes of interpretation and sensemaking, as well as the actual working conditions in the school determine the (lack of) implementation practices. This article reports on an exploratory study of the perception and actual implementation of the new mathematics curriculum by secondary school teachers in Flanders (Belgium). Data from semi-structured interviews with twenty mathematics teachers show that the actual implementation strongly depends on the congruence between the innovation content and teachers' perceptions regarding their educational tasks. One striking finding was that a deep concern for the interests of the pupils for some teachers operated as an argument for and justification of dedicated implementation, whereas the same argument was used by others to resist the reform. Furthermore, the actual 'weight' of mathematics in the study programme of the student (number of course hours per week) turned out to be a crucial factor in understanding the (lack of) implementation.

Despite the relevance of correlational studies for most research domains, many students, teachers, and researchers alike hold misconceptions concerning the Pearson product-moment correlation coefficient. One of these, the transitivity misconception, has not yet been documented in a systematic way. This paper summarizes the first empirical study, using 279 university students, and examines the relationship between student-based and task-based factors and the appearance of this misconception. In particular, two task-based factors seemed to have a significant effect on its appearance. In addition, the respondents' level of confidence in their answer to the transitivity item was significantly lower than for most other times.

Both researchers and teachers of statistics have made considerable efforts during the last decades to re-conceptualize statistics courses in accordance with the general reform movement in mathematics education. However, students still hold misconceptions about statistical inference even after following a reformed course. The study presented in this paper addresses the need to further investigate misconceptions about hypothesis tests by (1) documenting which misconceptions are the most common among university students of introductory courses of statistics, and (2) concentrating on an aspect of research about misconceptions that has not yet received much attention thus far, namely the confidence that students have in their misconceptions. Data from 144 college students were collected by means of a questionnaire addressing the most common misconceptions found in the literature about the definitions of hypothesis test, p-value, and significance level. In this questionnaire, students were asked to select a level of confidence in their responses (from 0 to 10) for each item. A considerable number of participants seemed to hold misconceptions and lower levels of concept-specific self-perceived efficacy were found to be related to misconceptions more than to the correct answers. On average, students selected significantly lower levels of confidence for the question addressing the definition of the significance level than for the other two items. Suggestions for further research and practice that emerge from this study are proposed.

A solid understanding of inferential statistics is of major importance for designing and interpreting empirical results in any scientific discipline. However, students are prone to many misconceptions regarding this topic. This article structurally summarizes and describes these misconceptions by presenting a systematic review of publications that provide empirical evidence of them. This group of publications was found to be dispersed over a wide range of specialized journals and proceedings, and the methodology used in the empirical studies was very diverse. Three research needs rise from this review: (1) further empirical studies that identify the sources and possible solutions for misconceptions in order to complement the abundant theoretical and statistical discussion about them; (2) new insights into effective research designs and methodologies to perform this type of research; and (3) structured and systematic summaries of findings like the one presented here, concerning misconceptions in other areas of statistics, that might be of interest both for educational researchers and teachers of statistics.

This paper presents an empirical study that used the Attitudes Toward Statistics (ATS) scale (Wise, 1985) to investigate the relationship between attitudes toward statistics and short- and long-term exam results for Flemish university students taking statistics courses in a five year Educational Sciences curriculum. The aim was to examine whether the previously reported relationship between attitudes toward statistics and first year statistics exam results also exists for later statistics and general exam results. The results indicate that there indeed exists a relationship between attitudes toward statistics (at the beginning of the curriculum) and later statistics performance (indicated by the dissertation grade), but that this relation between attitudes and results is content-specific.