Publication Date


Date of Final Oral Examination (Defense)


Type of Culminating Activity


Degree Title

Master of Arts in Education, Curriculum and Instruction


Curriculum, Instruction, and Foundational Studies

Major Advisor

Michele Carney, Ph.D.


Tatia Totorica, Ed.D.


Laurie Cavey, Ph.D.


The purpose of this study was twofold. First, a set of instructional materials surrounding proportional reasoning with ratios (particularly the understanding of the multiplicative relationship between the quantities within the ratio, referred to as functional reasoning throughout this thesis) were created using the free online tool, Desmos, with a goal of determining the impact of the lesson materials on student understanding. The second goal was to explore the impact of the order in which two instructional strategies, Explicit Attention to Concepts (EAC) and Students’ Opportunity to Struggle (SOS), had on student understanding. The lesson materials consisted of 5 lessons. These 5 lessons had two forms: EAC then SOS or SOS then EAC. In each of these instructional groups, all EAC and SOS sections were identical in each of the five lessons, the difference between materials in each of these groups was the order in which the EAC and SOS sections occurred. Students’ understanding was assessed anonymously, and answers were scored dichotomously (i.e. correct or incorrect). There was a total of 22 items on the full assessment with 8 items addressing functional reasoning specifically. The major findings of this study include that the lesson materials led to an increase in understanding for both overall understanding and the sub-area of functional reasoning, and the EAC then SOS instructional group’s understanding of functional reasoning was higher than that of the SOS then EAC instructional group.