Publication Date

5-2018

Date of Final Oral Examination (Defense)

12-13-2017

Type of Culminating Activity

Dissertation

Degree Title

Doctor of Education in Curriculum and Instruction

Department

Curriculum, Instruction, and Foundational Studies

Supervisory Committee Chair

Jonathan Brendefur, Ph.D.

Supervisory Committee Member

Keith W. Thiede, Ph.D.

Supervisory Committee Member

Evelyn Johnson, Ed.D.

Supervisory Committee Member

Gwyneth R. Hughes, Ph.D.

Abstract

The equal sign is prevalent at all levels of mathematics however many students misunderstand the meaning of the equal sign and consider it an operational symbol for the completion of an algorithm (Baroody & Ginsburg, 1983; Rittle-Johnson & Alibali, 1999). Three constructs were studied through the lens of the Developing Mathematical Thinking (Brendefur, 2008), Relational Thinking, Spatial Reasoning and Modes of Representation. A review of literature was conducted to examine the effects of mathematics instruction on the development of students’ conceptual understanding of equivalence through the integration of spatial reasoning and relational thinking. The Developing Mathematical Thinking (DMT) curricular resources integrate Bruner’s enactive, iconic, and symbolic modes of representations (1966), using tasks designed to strengthen students’ spatial reasoning and relational thinking to develop mathematical equivalence. The research question “What is the effect of integrating iconic teaching methodology into mathematics instruction on first grade students’ relational thinking and spatial reasoning performance?” was analyzed to determine whether there was a significant difference in pre-and posttest scores for the two groups. Students were found to have a better opportunity to develop conceptual understanding of mathematics in their early years of school when taught with the progression of EIS, relational thinking and spatial reasoning.

DOI

10.18122/td/1416/boisestate

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