
06243025
j
2014a.00605
Hilton, Annette
Hilton, Geoff
Dole, Shelley
Goos, Merrilyn
Development and application of a twotier diagnostic instrument to assess middleyears students' proportional reasoning.
Math. Educ. Res. J. 25, No. 4, 523545 (2013).
2013
Springer Netherlands, Dordrecht; Mathematics Education Research Group of Australasia (MERGA), Wahroonga, New South Wales, Australia
EN
F83
E53
D23
proportional reasoning
middleschool mathematics
diagnostic testing
twotier testing
doi:10.1007/s1339401300836
Summary: 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 nonproportional 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 twotier 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 middleyears 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.