CSMS ratio items

the CSMS (concepts in secondary maths and science) project was extensive (thousands of students) and longitudinal - looking across the three central years of secondary education in England

it was led by Kath Hart
whose thesis on this is available as a pdf
work was started in 1976/1977 and published in 1981

these are four of the eight diagnostic test items (they were questions 1, 3, 5 and 7) used to appraise cognitive growth

the work drew on the research of Piaget and the 'eel feeding' test was based on one of his experiments

this work has been repeated and built on recently by Jeremy Hodgen et al, for the ICCAMS project (first phase 2008 to 2012)
this project looks at two aspects: multiplicative reasoning and algebra, before and after interventions

'onion soup' and some wording is adapted

the main student error involved was the use of additive rather than multiplicative methods
students were more confident to use doubling and halving rather than additive methods - sometimes over using doubling

data for 'Mr Short' shows a propensity to use addition, difficult to dislodge
(Y8 = 12 to 13 years old, etc)