Middle school rational number knowledge

2007 2007

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Abstract (summary)

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 error 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 AEs performed significantly better than those students classified by errors. However, further analysis revealed hidden misconceptions and deficiencies for a number of AEs. Results point to the need to make teachers more aware of students' misconceptions and deficiencies because in many ways errors reflect the school experiences of students.

Indexing (details)

Mathematics education
0280: Mathematics education
Identifier / keyword
Education; Middle school; Rational number
Middle school rational number knowledge
Martinie, Sherri L.
Number of pages
Publication year
Degree date
School code
DAI-A 68/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Bay-Williams, Jennifer M.
Kansas State University
Department of Elementary Education
University location
United States -- Kansas
Source type
Dissertations & Theses
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
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