## Poster Session #2

Poster

Matthew Roscoe

#### Faculty Mentor’s Department

Mathematical Sciences

#### Abstract / Artist's Statement

The understanding of ratio and the ability to use proportional reasoning are essential to a middle school student’s future success in the fields of math and science. For a student to achieve proficiency in this domain, they must be introduced to a variety of interpretations of rational number concepts. It was my objective in this research to help understand if students can learn these concepts through the investigation of gears as a model for proportional relationships. This research attempted to answer two primary questions through an intervention. Does structured investigation of gear-pairs lead to students’ ability to abstract ratio settings? Does unstructured investigation of gear-pairing possibilities show evidence supporting students’ ability to analyze ratio settings in pursuit of a “best solution?” I used structured and unstructured activities in a real seventh-grade classroom to facilitate this investigation. During the initial investigation of gears, students used manipulatives to complete a guided worksheet exploring the relationships of how different gear pairs interact. This initial investigation of gears was completed over two days. Then the students were given an open-ended problem designed to test their understanding of ratio in a gear pair context. Students were asked to analyze a variety of different combinations of bicycle front chainrings and rear cassettes using tables, equations, and graphs. Based on their analysis, students were then asked to recommend a new drivetrain using qualitative proportional reasoning while citing quantitative contextual factors. After the intervention, an analysis was made of the classroom artifacts created by students during both stages of the gears investigation. The students demonstrated a strong preference for tabular and arithmetic presentations of data, and an overwhelming lack of graphical representations. The results of this research show that with specific modifications to the original task, this proportional context can help inform future classroom instruction on the topics of ratio and proportion.

Humanities

#### Share

COinS

Apr 17th, 3:00 PM Apr 17th, 4:00 PM

Developing Proportional Reasoning Through Gears Investigation

UC South Ballroom

The understanding of ratio and the ability to use proportional reasoning are essential to a middle school student’s future success in the fields of math and science. For a student to achieve proficiency in this domain, they must be introduced to a variety of interpretations of rational number concepts. It was my objective in this research to help understand if students can learn these concepts through the investigation of gears as a model for proportional relationships. This research attempted to answer two primary questions through an intervention. Does structured investigation of gear-pairs lead to students’ ability to abstract ratio settings? Does unstructured investigation of gear-pairing possibilities show evidence supporting students’ ability to analyze ratio settings in pursuit of a “best solution?” I used structured and unstructured activities in a real seventh-grade classroom to facilitate this investigation. During the initial investigation of gears, students used manipulatives to complete a guided worksheet exploring the relationships of how different gear pairs interact. This initial investigation of gears was completed over two days. Then the students were given an open-ended problem designed to test their understanding of ratio in a gear pair context. Students were asked to analyze a variety of different combinations of bicycle front chainrings and rear cassettes using tables, equations, and graphs. Based on their analysis, students were then asked to recommend a new drivetrain using qualitative proportional reasoning while citing quantitative contextual factors. After the intervention, an analysis was made of the classroom artifacts created by students during both stages of the gears investigation. The students demonstrated a strong preference for tabular and arithmetic presentations of data, and an overwhelming lack of graphical representations. The results of this research show that with specific modifications to the original task, this proportional context can help inform future classroom instruction on the topics of ratio and proportion.