Diagnostic assessment of children’s proportional reasoning

By Christina Misailidou, J. Williams. 2003

101 citations recorded by the source corpus.

Abstract A proportional reasoning item bank was created from the relevant literature and tested in various forms. Rasch analyses of 303 pupils’ test results were used to calibrate the bank, and data from 84 pupils’ interviews was used to confirm our diagnostic interpretations. A number of sub-tests were scaled, including parallel ‘without models’ and ‘with models’ forms. We provide details of the 13-item ‘without models’ test which was formed from the ‘richest’ diagnostic items and verified on a further test sample ( N =212, ages 10–13). Two scales were constructed for this test, one that measures children’s ‘ratio attainment’ and one that measures their ‘tendency for additive strategy.’ Other significant errors — ‘incorrect build-up,’ ‘magical doubling/halving,’ ‘constant sum’ and ‘incomplete reasoning’ — were identified. Finally, an empirical hierarchy of pupils’ attainment of proportional reasoning was formed, incorporating the significant errors and the additive scale.

Subfields: Education, Experimental and Cognitive Psychology, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/31f6fc964468a9f017e19520e5afce9fc322d4f3

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In Education

1. W. Van Dooren
2. Lieven Verschaffel
3. Dirk De Bock
4. S. Llinares
5. Geoffrey Hilton
6. Shelley Dole
7. A. Hilton
8. M. Goos

In Experimental and Cognitive Psychology

1. W. Van Dooren
2. Lieven Verschaffel
3. Dirk De Bock
4. Geoffrey Hilton
5. Shelley Dole
6. A. Hilton
7. M. Goos

In Management Science and Operations Research

1. Geoffrey Hilton
2. W. Van Dooren
3. Shelley Dole
4. Lieven Verschaffel
5. A. Hilton
6. M. Goos

Citations in the corpus

• Development and application of a two-tier diagnostic instrument to assess middle-years students’ proportional reasoning (2013, methodology): “…2010); & a tendency to approach proportional situations additively instead of multiplicatively (Cramer and Post 1993; Lamon 1993; Lesh et al. 1988; Misailidou and Williams 2003; Tourniaire and Pulos 1985); & the use of multiplicative approaches unnecessarily, for example, when additive strategies…”
• Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers (2016, background): “…application of algorithms, such as cross multiplication; and incorrect patterning strategies (Cramer & Post, 1993; Lamon 1993; Lesh et al., 1988; Misailidou & Williams, 2003; Nabors, 2003; Tourniaire & Pulos, 1985; Van de Walle, Karp, & Bay-Williams, 2010; Van Dooren, De Bock, & Verschaffel,…”
• The development of students’ use of additive and proportional methods along primary and secondary school (2012, methodology): “Besides the use of proportional methods in additive situations, another and already older line of research has addressed the incorrect use of additive methods to proportional problems (Hart 1981; Karplus et al. 1983; Misailidou and Williams 2003; Tourniaire and Pulos 1985).”