Concept networks of students’ knowledge of relationships between physics concepts: finding key concepts and their epistemic support

Applied Network Science

Table 4 Key concepts as they appear in the collated and 12 individual concept networks

log β		I: (12-10)	II: (9-7)	III: (6)	COLLATED
-2	IN	–	120,113, *112*,	117,93, 82,	85, 109, 91, 100, 86, 83,
			109,100, 91,	69, 51, 41,	117, 113, 82, 71, 87,120,
			87, 85, *54, 44*		76, 69, 98, 34, 103, 116
	OUT	8, 28,	1, 2, 57, 66,	7, 76	66, 57, 71, 63, 55, 83,
			66, 71, 83, 90		82, 59, 65, 77, 72, 90,
					76, 9, 91, 2, 68, 27
0	IN	109	120, 117, 113,	87, 85, 83,	91, 109, 85, 100, 113, 83,
			*112*, 100, 91,	71, 54, 22	117, 82, 120, 86, 87, 71,
			86		116, 76, 33, 69, 34, 98
	OUT	2, 8, 28	1, 57, 63, 66	*33, 38*, 55,	57, 66, 2, 55, 28, 71,
			71, 83, 90	72, *109*	63, 72, 59, 83, 70, 62,
					91, 74, 9, 65, 8, 22
2	IN	–	*120, 117*, 113,	83, 87	100, 82, 63, 91, 38, 113,
			109, 100, 91,		109, 27, 71, 82, 74, 33,
			86, 71		86, 44, 69, 47, 85, 76
	OUT	2, 28	1, 33, 38,	16, 69, 71,	28, 2, 57, 66, 83, 71
			47, 57, 63,	72, *76, 95*	72, 33, 109, 14, 91, 63,
			66, 83, 90		55, 69, 20, 47, 27, 90

The columns from I to III show 18 key concepts selected from the 25 highest ranking concepts common to all 12 networks. Column I shows the concepts that appear in at least 10 networks; in II the concepts that appear in at least 7 but at the most 9 networks, and in III the concepts that appear in exactly 6 networks only. The column COLLATED shows concepts in the collated network in order of their ranking based on the communicability. The results in I-III and COLLATED are given for epistemic weights Logβ=−2,0 and 2, and for in-coming (IN) and out-going (OUT) links. In the COLLATED, the five highest ranking concepts for Logβ=−2 are shown in boldface. In Columns I-III the concepts not contained in the key concepts in COLLATED for the epistemic weight β are given in slanted font. If the concept is not among any of the 18 key concepts for collated, it is in slanted boldface