Middle school rational number knowledge

Date

2007-04-27T19:27:38Z

Journal Title

Journal ISSN

Volume Title

Publisher

Kansas State University

Abstract

This study examined end-of-the-year seventh grade students’ rational number knowledge using comparison tasks and rational number subconstruct tasks. Comparison tasks included: comparing two decimals, comparing two fractions and comparing a fraction and a decimal. The subconstructs of rational number addressed in this research include: part-whole, measure, quotient, operator, and ratio. Between eighty-six and one-hundred-one students were assessed using a written instrument divided into three sections. Nine students were interviewed following the written instrument to probe for further understanding. Students were classified by error patterns using decimal comparison tasks. Students were initially to be classified into four groups according to the error pattern: whole number rule (WNR), zero rule (ZR), fraction rule (FR) or apparent expert (AE). However, two new patterns emerged: ignore zero rule (IZR) and money rule (MR). Students’ knowledge of the subconstructs of rational numbers was analyzed for the students as a whole, but also analyzed by classification to look for patterns within small groups of students and by individual students to create a thick, rich description of what students know about rational numbers. Students classified as WNR struggled across almost all of the tasks. ZR students performed in many ways similar to WNR but in other ways performed better. FR and MR students had more success across all tasks compared to WNR and ZR. On average apparent experts performed significantly better than those students classified by errors. However, further analysis revealed hidden misconceptions and deficiencies for a number of apparent experts. Results point to the need to make teachers more aware of the misconceptions and deficiencies because in many ways errors reflect the school experiences of students.

Description

Keywords

Rational number, Fractions, Decimals, Middle school, Order and comparison, Subconstructs

Graduation Month

May

Degree

Doctor of Philosophy

Department

Curriculum and Instruction Programs

Major Professor

Jennifer M. Bay-Williams

Date

2007

Type

Dissertation

Citation