Journal article
Development and application of a two-tier diagnostic instrument to assess middle-years students’ proportional reasoning
Mathematics Education Research Journal, Vol.25(4), pp.523-545
2013
Abstract
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.
Details
- Title
- Development and application of a two-tier diagnostic instrument to assess middle-years students’ proportional reasoning
- Authors
- Annette Hilton (Author) - Aarhus UniversityGeoff Hilton (Author) - University of QueenslandShelley Dole (Author) - University of QueenslandMerrilyn Goos (Author) - University of Queensland
- Publication details
- Mathematics Education Research Journal, Vol.25(4), pp.523-545
- Publisher
- Springer Netherlands
- DOI
- 10.1007/s13394-013-0083-6
- ISSN
- 2211-050X
- Organisation Unit
- Indigenous and Transcultural Research Centre; University of the Sunshine Coast, Queensland; School of Education and Tertiary Access
- Language
- English
- Record Identifier
- 99554406002621
- Output Type
- Journal article
Metrics
55 Record Views
InCites Highlights
These are selected metrics from InCites Benchmarking & Analytics tool, related to this output
- Collaboration types
- Domestic collaboration
- International collaboration
- Web Of Science research areas
- Education, Scientific Disciplines
UN Sustainable Development Goals (SDGs)
This output has contributed to the advancement of the following goals:
Source: InCites