Ratio and Proportional Reasoning of Double-Accelerated Middle School Math Students
Open Access
- Author:
- Wynkoop, Donna
- Graduate Program:
- Curriculum and Instruction (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 22, 2022
- Committee Members:
- Andrea Mccloskey, Major Field Member
Elizabeth Hughes, Outside Unit & Field Member
Fran Arbaugh, Chair & Dissertation Advisor
Jane Wilburne, Special Member
Andrea Vujan Mccloskey, Professor in Charge/Director of Graduate Studies
Rachel Wolkenhauer, Major Field Member - Keywords:
- Ratio
Proportion
Proportional Reasoning
Accelerated
Double-accelerated
Schema-based Instruction
Gifted
Math Acceleration - Abstract:
- Ratio and proportional reasoning are critical concepts for students to understand to be successful in higher-level mathematics. In 1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum and Evaluation Standards for School Mathematics stating that the ability to reason proportionally is of “such great importance that it merits whatever time and effort that must be expended to assure its careful development” (NCTM, 1989, p. 82). According to the Common Core State Standards – Mathematics (CCSS-M), the development of these concepts begins in kindergarten and culminates in grades six and seven, where they are separate domains. The participants in this study took Pre-Algebra in the sixth grade and Algebra I in the seventh grade, rather than the district CCSS-M based math curriculum and are considered double-accelerated students. Because of this acceleration they did not receive instruction in the domain of Ratio and Proportional Reasoning as set forth in the CCSS-M. The NCTM 2016 Position Statement on Providing Opportunities for Students with Exceptional Mathematical Promise states, “When considering opportunities for acceleration in mathematics, care must be taken to ensure that opportunities are available to each and every prepared student and that no critical concepts are rushed or skipped ...” (page 1). The critical concept of Ratio and Proportional Reasoning may have been rushed or skipped for these participants. Therefore, this case study sought to characterize the conceptual and Essential Understandings of Ratio and Proportional Reasoning of these double-accelerated participants. Participants were a convenience sample of eighth-grade students enrolled in a suburban middle school in south-central Pennsylvania. Data was predominantly collected via written documentation including pretest, instructional response, post-test, and limited participant journals. Researcher notes were transcribed to capture participant discussion and interaction with the researcher. Pretest and post-data were then analyzed and coded using researcher-created codes based on NCTM’s Essential Understandings of Ratio and Proportional Reasoning Grades 6-8 and relevant conceptual understandings based on the literature. These double-accelerated participants demonstrated many of the same understandings as found in prior research conducted with on-grade level and lower-performing students. The implications of this study are that more care must be taken when accelerating students so that they develop deep, conceptual understandings in all areas of mathematics, but particularly in Ratio and Proportional Reasoning. The findings of this study call for more research into acceleration practices and curriculum development for accelerated students to ensure those students with exceptional mathematics promise have the understanding necessary to continue onto more advanced math topics.