There is increasing concern that student interest in learning mathematics and attitude towards mathematics were declining. This decline is being experienced worldwide and is most evident in the senior years of high school and at university. This study explores the role that inquiry-based learning has in positively influencing and reshaping students’ beliefs and attitudes towards mathematics. Ill-structured tasks have proven a valuable tool for initiating inquiry-based learning in mathematics.
Students in one senior high school mathematics class worked on an ill-structured task each semester for three consecutive semesters. Each ill-structured task took approximately 7 to 10 hours of learning time and targeted the content for a whole unit of work. Data were collected in a number of ways including surveys and ill-structured tasks both before and after implementation of the study, video recording of classes, audio recordings of post-task interviews with four pairs of students, extracts from students’ workbooks, and field notes.
Surveys and interview questions used in this study focused on students’ beliefs and attitudes towards mathematics. Three students were also identified for case study and their progress was monitored more closely throughout the inquiry lessons. Data from surveys and ill-structured tasks were analysed using descriptive and comparative methods. Video and audio data were analysed by mapping excerpts of relevant data to predefined belief categories. Comparisons of initial and final surveys indicated that students in this class did self-report significant, positive shifts in their beliefs about the usefulness of mathematics.
Comparisons of individual work on initial and final ill-structured tasks suggested that students became more able to select appropriate pathways for solution and provide justification for their selection. Students also appeared to be more able to overcome the impasses created by the ill-structured aspect of the problem towards the end of the study.
Analysis of the video and audio data led to the central thesis for this study; as students worked with ill-structured tasks they developed an inquiry attitude. The students became more likely to believe that mathematics was useful for their lives, came to understand that mathematics has complex, multilayered, open-ended, messy components that are best attempted collaboratively with other students in a group, and came to value the role of the teacher as a guide and expert mathematician while ceasing to rely on her as a source of truth. Students with an inquiry attitude actively explored multiple pathways for solution, justified their selected pathways, sought deep understanding of the task, took intellectual risks, and provided hypotheses. Results from case studies suggested students progressively developed this inquiry attitude through repeated engagement with the ill-structured tasks.
The findings of this study make a significant contribution to research within inquiry-based learning in mathematics as they present a senior high school example of the ways students initially adapt to inquiry learning environments. Results from this study also make a significant contribution to research within the affective domain of the classroom as they explore the ways in which learning opportunities influence and shape senior high school students’ mathematical beliefs and attitudes.