Learning progression toward a measurement concept of fractions

International Journal of STEM Education

Table 4 Percentage of students with indication of fraction schemes and associated mental actions by grade

	Grade 5^a (N = 44)	Grade 5^b (N = 45)	Grade 6^a (N = 40)	Grade 6^b (N = 31)	Grade 6^c (N = 66)	Grade 6^d (N = 49)	Grade 7^e (N = 56)	Grade 7^g (N = 49)	Grade 8^h (N = 58)
Scheme/action	%	%	%	%	%	%	%	%	%
Partitioning					88
Part-whole	58	80	78	100
Iterating					86
MSUF	52	67	70	81	61	59	61	65
Splitting	34	42	36	77	44	41	55	63	66
MSPF	14	16	18	19	(17)		13^f		19
Units coordination									26
GMSF	14		20						12

Percentage in parentheses represents only the composability component of the MSPF and does not include tasks testing for reversibility
^aFrom Norton and Wilkins 2009
^bFrom Norton et al. 2018
^cFrom Wilkins and Norton 2011
^dFrom Norton and Wilkins 2013, subset of children in Wilkins and Norton 2011
^eFrom Norton and Wilkins 2010
^fNot previously published, but associated with students in Norton and Wilkins 2010
^gFrom Norton and Wilkins 2013
^hFrom Norton and Wilkins 2012