ERIC Number: EJ1040895
Record Type: Journal
Publication Date: 2013-Dec
Pages: 23
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1033-2170
EISSN: N/A
Available Date: N/A
Development and Application of a Two-Tier Diagnostic Instrument to Assess Middle-Years Students' Proportional Reasoning
Hilton, Annette; Hilton, Geoff; Dole, Shelley; Goos, Merrilyn
Mathematics Education Research Journal, v25 n4 p523-545 Dec 2013
Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously apply both multiplicative and additive thinking. Further, students cannot always distinguish non-proportional situations from those that are proportional. Understanding the situations in which students mistakenly use additive or multiplicative thinking and the nature of the proportional reasoning that students apply to different problem types is important for teachers seeking to support their students to develop proportional reasoning in the classroom. This paper describes the development and use of a two-tier diagnostic instrument to identify situations in which students could and could not apply proportional reasoning and the types of reasoning they used. It presents data from an Australian study involving over 2000 middle-years students (Years 5 to 9) as a means of illustrating the use of the instrument for diagnosing students' reasoning in different situations. The findings showed that the instrument was useful for identifying problem types in which students of different ages were able to apply correct reasoning. It also allowed identification of the types of incorrect reasoning used by students. The paper also describes useful applications of the instrument, including its use as a diagnostic instrument by classroom teachers and its use in the design of classroom activities included in teacher professional learning workshops.
Descriptors: Diagnostic Tests, Thinking Skills, Psychometrics, Skill Analysis, Knowledge Level, Numeracy, Middle School Students, Identification, Test Reliability, Test Validity, Program Descriptions, Addition, Multiplication, Problem Solving, Cognitive Style, Mathematical Aptitude, Foreign Countries
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Publication Type: Journal Articles; Reports - Research
Education Level: Middle Schools; Secondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia
Grant or Contract Numbers: N/A
Author Affiliations: N/A