A Multidimensional Analysis of Randomness Misconceptions: Triangulating Teachers' Concept Knowledge Flexibility, Opinions of the Concept of Randomness, and Use of Multisensory Learning

Randomness misconceptions impact our statistical literacy and can affect our understanding of related concepts, such as in the context of distributions. Misconceptions are particularly problematic if held by teachers since their heuristics and biases could be passed on to students. This thesis uses triangulation to consider New Zealand teachers’ concept knowledge flexibility, which is a novel approach to investigating the presence of randomness misconceptions. Within New Zealand, statistics education is a key focus of the curriculum, so the characteristics of randomness misconceptions held by New Zealand teachers may differ from those identified in international research. Multisensory learning is one feasible approach for attending to randomness misconceptions. As an engaging active learning approach, multisensory learning is beneficial for providing students with alternative experiences of concepts. This thesis also considers whether attending to randomness misconceptions using multisensory learning elements would be adopted in New Zealand statistics classrooms. This aims to identify perceived barriers than would need to be considered in the development of multisensory activities aiming to challenge perceptions of randomness. To carry out this research, a series of questionnaires were designed and sent to members of New Zealand mathematics and statistics associations. Mixed methods, involving thematic analysis and quantitative methods, were implemented to triangulate findings. Triangulation was used to cross-validate conclusions and provide a multidimensional analysis of responses. Consistent with international findings, this thesis identifies the presence of randomness misconceptions held by teachers. Participants exhibited inflexible concept knowledge and were challenged when asked to apply their knowledge of randomness to distribution-based examples. Triangulation allowed for the identification of some participants having only an instrumental understanding of randomness. In terms of adopting a multisensory learning approach to attend to these misconceptions, participants appeared open to this with the biggest barrier being a lack of current resources.

Name thesis:degree_name

PhD

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

ResearchSpace@Auckland

Year dc:date.issued

2022

Author dc:creator

• Renelle, Amy May

Advisors dc:contributor.advisor

• Budgett, Stephanie
• Jones, Rhys

Statement dc:rights

• Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Licence dc:rights.uri

• https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm

Handle dc:identifier.uri

https://hdl.handle.net/2292/64378

OAI identifier oai:identifier

oai:researchspace.auckland.ac.nz:2292/64378