Table 3.

Open Equation Items with their a priori Levels on the Construct Map, and Accuracies

Item Number	Item	Construct Map Level	Mean Accuracy	SD
1	2 + __ = 8	1	0.77	0.42
2	__ − 4 = 3	1	0.44	0.50
7	9 −__ = 6	1	0.62	0.49
8	5 + __ = 11	1	0.74	0.44
12	14 − __ = 6	1	0.47	0.50
13	__ + 6 = 13	1	0.55	0.50
16	__ + 3 = 7	1	0.60	0.49
19	4 + 5 = __	1	0.76	0.43
23	__ − 6 = 4	1	0.18	0.38
30	8 − 3 = __	1	0.52	0.50
	Mean Accuracy Level 1		.57	.28
3	__ = 4	2	0.23	0.42
4	6 = 2 + __	2	0.50	0.50
5	9 = 14 − __	2	0.34	0.47
6	15 = __ + 7	2	0.47	0.50
10	5 = 9 − __	2	0.39	0.49
15	12 = 7 + __	2	0.38	0.49
18	__ = 6 + 5	2	0.43	0.50
21	6 = __ − 8	2	0.05	0.21
22	7 = __ − 2	2	0.15	0.36
25	__ = 7 − 4	2	0.35	0.48
26	7 = __	2	0.20	0.40
27	8 − 3 = __	2	0.36	0.48
	Mean Accuracy Level 2		.32	.25
9	11 − __ = 9 − 5	3	0.03	0.16
11	12 − 5 = __ − 3	3	0.05	0.21
14	7 + 4 = __ + 6	3	0.04	0.19
17	6 + __ = 2 + 8	3	0.10	0.31
20	__ + 4 = 5 + 2	3	0.08	0.27
24	3 + 5 = 4 + __	3	0.07	0.26
28	__ − 3 = 7 − 2	3	0.04	0.20
29	9 − 6 = 7 − __	3	0.07	0.25
	Mean Accuracy Level 3		.06	.15

Note: Items in gray yielded accuracies that were significantly lower than others in the same hypothesized level of the construct map. Each of these three took the form X = _ − Y