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Observing High-school Students' Mathematical Understanding and Mathematical Proficiency in the Context of Mathematical Modeling Open Access


Other title
Complexity Science
Mathematical Understanding
Mathematical Proficiency
Design-based Research
Mathematical Modeling
High-school Mathematics
Type of item
Degree grantor
University of Alberta
Author or creator
Dias Corrêa, Priscila M
Supervisor and department
Simmt, Elaine (Secondary Education)
Examining committee member and department
Glanfield, Florence (Secondary Education)
Nocente, Norma (Secondary Education)
De Vries, Gerda (Mathematics and Statistical Sciences)
McGarvey, Lynn (Elementary Education)
Department of Secondary Education

Date accepted
Graduation date
2017-06:Spring 2017
Doctor of Philosophy
Degree level
The use of mathematical modeling in education has been investigated for the last five decades. The benefits of bringing modeling into mathematics classes are well known and well accepted, and modeling is becoming more common and more appealing to mathematics teachers. However, there are still unanswered questions and conjectures to be explored, so as to aid and encourage mathematics teaching through modeling. The present study uses classroom-based research to explore the use of modeling tasks within high-school mathematics classes, in order to provide insight into the teaching of mathematics for understanding. In this study, participants' were engaged in mathematical modeling tasks in which they were required to develop models for mathematical situations, instead of using an already known mathematical model or a given one. This investigation intended to comprehend what forms of mathematical understanding and mathematical proficiency are observed and how they are expressed when high-school students are engaged in this mathematical modeling setting. The research methodology is founded on design-based research, since it combines theoretical research knowledge with practical experiences, yielding practical knowledge (The Design-Based Research Collective, 2003). The classroom design framework is based on complexity science underpinnings. This is due to the fact that mathematics classes are acknowledged as complex systems, in which students collectively act and interact in order to develop, construct and enhance their mathematical ideas. These actions and interactions are believed to be non-linear, spontaneous and self-organized, characterizing a complex system that allows mathematical understanding to emerge (Davis & Simmt, 2003). In order to investigate students' mathematical understanding and proficiency while engaged in mathematical modeling tasks, four different tasks were proposed to a high-school class taking grade 11 mathematics. The class was composed of 27 students. Although all of them participated in the tasks, data was collected from the 12 students who provided consent. Tasks were applied during a four-month Alberta mathematics course. Audio and video recordings, students' mathematics journals and researcher field notes were collected. Post class sessions, students were invited to participate in recall interviews. Assuming that students' mathematical understanding is encompassed by students‘ mathematical proficiency, data analysis was conducted using Kilpatrick, Swafford and Findell's (2001) model of mathematical proficiency, where mathematical proficiency is composed by five strands, namely: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. The basis of the research data analysis framework consists of identifying indicators of each of Kilpatrick et al.'s strands in students' work, and then investigating how students undergo these strands along the modeling tasks. This research study offers insight into the use of mathematics modeling by: 1) portraying how mathematical modeling tasks foster high-school students‘ mathematical understanding and proficiency; and 2) showing the feasibility of implementing this kind of task in mathematics classes with time and curriculum constraints. The study revealed that students demonstrate mathematical understanding and proficiency during the course of the modeling tasks, even when they do not come to full resolutions of problems. Research outcomes indicate that mathematical modeling tasks promote students‘ mathematical understanding and proficiency and can be an important approach in the task of teaching for understanding.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Corrêa, P. D. (2015). Teaching mathematics for understanding: Approaching and observing, Delta-k - Journal of the Mathematics Council of the Alberta Teachers’ Association, vol. 52, number 2, 37-43.

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