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Investigating students' understandings of probability : a study of a grade 7 classroom

University of British Columbia

This research study probes students’ understandings of various aspects of probability in a 3-week Probability unit in a Grade 7 classroom. Informing this study are the perspectives of constructivism and sociocultural theory which underpin the contemporary reform in mathematics education as codified in the NCTM standards and orient much of the teaching and learning of mathematics in today’s classrooms. Elements of culturally responsive pedagogy were also adopted within the research design. The study was carried out in an urban school where I collaborated with the teacher and students as co-teacher and researcher. As the population of this school was predominantly Aboriginal, the lessons included discussion of the tradition and significance of Aboriginal games of chance and an activity based on one of these games. Data sources included the responses in the pre- and post-tests, fleidnotes of the lessons, and audiotapes of student interviews. The key findings of the study are that the students had some understanding of formal probability theory with strongly-held persistent alternative thinking, some of which did not fit the informal conceptions of probability noted in the literature such as the outcome approach and the gambler’s fallacy. This has led to the proposal of a Personal Probability model in which the determination of a probability or a probability decision is a weighting of components such as experience, intuition and judgment, some normative thinicing, and personal choice, beliefs and attitudes. Though the alternative understandings were explored in interviews and resolved to some degree, the study finds that the probability understandings of students in this study are still fragile and inconsistent. Students demonstrated marked interest in tasks that combined mathematics, culture and community. This study presents evidence that the current prescribed learning outcomes in the elementary grades are too ambitious and best left to the higher grades. The difficulties in the teaching and learning of the subject induced by the nuances and challenges of the subject as well as the dearth of time that is needed for an adequate treatment further direct that instructional resources at this level be focused on deepening and strengthening the basic ideas.

Thesis/Dissertation

application/pdf

2009-02-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/4073

Mathematics Education

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/