Cultivating the Growth of Mathematical Images

Plosz, Jennifer A.

Cultivating the Growth of Mathematical Images

dc.contributor.advisor	Towers, Jo
dc.contributor.author	Plosz, Jennifer A.
dc.contributor.committeemember	Francis, Krista
dc.contributor.committeemember	Metz, Martina L.
dc.date	2019-11
dc.date.accessioned	2019-07-10T16:37:55Z
dc.date.available	2019-07-10T16:37:55Z
dc.date.issued	2019-07-05
dc.description.abstract	In this document, I present some of the findings of the study, Cultivating the Growth of Mathematical Images, in which I explore the role that spatial reasoning plays in the growth of mathematical images. This study involved Grade Five students labelled with learning disabilities and their teacher. This study was a microanalysis of a participatory action research study, as it looked at the beginning stages of exploration with students and the impact that a more spatial approach to fractions might have on their growth. Information was gathered from students’ psychoeducational assessment, an informal assessment of spatial reasoning ability, and a pre-assessment task that looked at their understanding of basic number and fractions. There were many layers of complexity surrounding each student’s psychoeducational profile, their performance in the classroom, and the pre-assessment task offered to the students. Certain aspects of these experiences seemed consistent with each other, others contradictory, and still others contained much variability, such as in the area of working memory. During the second week of the study, video data were collected while students engaged with a task that created an interplay between visualizing and building fractions. In analysis of the data, close attention was paid to what sort of offerings the students were given such as signitive (written and oral), imaginative (visualizing), and perceptual (sensory), which are somewhat modified from Husserl (1970). During this task, a pattern of growth began to emerge which is discussed and connected to the Pirie-Kieren (1994) Dynamical Theory for the Growth of Mathematical Understanding. Generally, with the introduction of the signitive only, there was No appearance of movement. Then as the student began either producing or receiving perceptual experiences they progressed into the Image Making phase. The continued engagement with perceptual experiences appeared to create the beginnings of the imaginative, Image Making emergent Image Having phase, and some students were even able to reach the point of being predominately in the Image Having phase. Each participant went through the various phases at varying speeds. Within these various phases, there was found to be much complexity in terms of contributing factors towards growth. The fact that some participants built more than others and therefore had more perceptual offerings seemed a strong contributing factor but other aspects such as their own personal commitment to sense-making as they built, their social interactions, and their own self-belief seemed to also impact growth.	en_US
dc.identifier.citation	Plosz, J. A. (2019). Cultivating the Growth of Mathematical Images (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.	en_US
dc.identifier.doi	http://dx.doi.org/10.11575/PRISM/36721
dc.identifier.uri	http://hdl.handle.net/1880/110606
dc.language.iso	eng	en_US
dc.publisher.faculty	Werklund School of Education	en_US
dc.publisher.institution	University of Calgary	en
dc.rights	University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.	en_US
dc.subject	visualization	en_US
dc.subject	images	en_US
dc.subject	embodied cognition	en_US
dc.subject	learning disabilities	en_US
dc.subject	dyslexia	en_US
dc.subject	mathematics education	en_US
dc.subject.classification	Education--Curriculum and Instruction	en_US
dc.subject.classification	Education--Elementary	en_US
dc.subject.classification	Education--Mathematics	en_US
dc.subject.classification	Neuroscience	en_US
dc.title	Cultivating the Growth of Mathematical Images	en_US
dc.type	master thesis	en_US
thesis.degree.discipline	Education Graduate Program – Educational Research	en_US
thesis.degree.grantor	University of Calgary	en_US
thesis.degree.name	Master of Science (MSc)	en_US
ucalgary.item.requestcopy	true	en_US