Developing the Mathematical Beliefs of Second-level Students: An Intervention Study

This study examined the effects of a learning environment (embodying many of De Corte et al.’s, (2004) CLIA-model components) on secondary students’ mathematical beliefs. Such mathematical beliefs have been of interest to the research community due to their expected impact on students’ willingness to engage in mathematical problem-solving. This research adopted an action research methodology using a quasi-experimental sequential explanatory mixed methods design. Data was collected using the Mathematics Related Beliefs Questionnaire (MRBQ) and a number of focus groups and individual interviews were undertaken. The sample selected (age 13-14) was from a population of convenience. There was one treatment class (N=22) and three control classes (N=45). The classroom intervention was of six months duration and was carried out by the researcher teacher in a secondary community school. Findings revealed no significant positive effects on students’ beliefs from the new learning environment about the teacher’s role in the classroom, their personal competence and the relevance to their lives and mathematics as an inaccessible subject. A more negative outcome for the fourth factor of the MRBQ scale, ‘mathematics as an inaccessible subject’, resulted for all participants (experimental and control combined) with a moderate effect of eta2=0.09. Findings from the qualitative data indicated the experimental participants found mathematics to be a difficult but useful subject. Findings, overall, revealed no significant differences between the experimental and control classes, indicating the new learning environment had not had a positive impact on the beliefs examined. Possible factors identified were the length of the intervention, the ages of participants and the socio-economic status of the majority taking part in this study. Qualitative data also indicated participants in the treatment class had found some of the activities used in the intervention to be interesting and enjoyable. Responses to the use of group work indicated participants were both willing and able to enter into communities of learners. Other results showed that participants with the highest achievement scores appeared to be the most confident learners of mathematics. Participants appeared to accept the need to have patience and perseverance when solving difficult problems but this was not translated into action in the classroom. The importance of understanding mathematics appeared to be accepted by participants. Implications for methodology, research and practice are discussed in light of these findings