Differential relationships between mathematics self-efficacy and national test performance according to perceived task difficulty

Figures & data

Figure 1. Theoretical model.

Table 1. Item descriptives SEGD (Street et al., 2017).

	Item	n	missing	M	SD	Range	Skew	Kurt
1	No. of problems_easy	92	3 (3%)	10.93	.36	3	−6.83*	52.06*
2	No. of problems _easy2	92	3 (3%)	10.60	.94	5	−2.78	8.32
3	No. of problems _med	93	2 (2%)	9.22	2.09	7	−.86	−.52
4	No. of problems _hard	93	2 (2%)	6.71	2.55	9	−.07	−1.07
5	No. of problems _hard2	91	4 (4%)	3.41	2.61	9	1.03	.08
6	Solve tasks_easy	92	3 (3%)	10.17	1.19	5	−2.02	4.49
7	Solve tasks_med	93	2 (2%)	7.88	1.83	10	−.45	.68
8	Solve tasks_hard	92	3 (3%)	5.10	2.17	8	.06	−1.03
9	Concentrate _easy	92	3 (3%)	10.61	1.45	10	−4.69*	24.71*
10	Concentrate _med	92	3 (3%)	9.76	1.70	6	−1.24	.38
11	Concentrate _hard	93	2 (2%)	7.40	2.83	10	−.52	−.62
12	Not give up _easy	92	3 (3%)	10.05	1.65	10	−2.77	10.15*
13	Not give up _med	93	2 (2%)	8.62	1.92	7	−.38	−.77
14	Not give up _hard	92	3 (3%)	7.17	2.45	9	.06	−1.05
15	National test score	95	0	30.61	11.18	48.00	−.03	−.85
16	No. of problems_easy	89	6 (7%)	10.85	.61	4	−4.75*	23.69*
17	No. of problems _easy2	89	6 (7%)	10.39	1.40	7	−2.82	8.13
18	No. of problems _med	89	6 (7%)	9.11	2.24	9	−1.09	.39
19	No. of problems _hard	89	6 (7%)	6.40	2.67	10	−.10	−.92
20	No. of problems _hard2	89	6 (7%)	3.34	2.68	10	1.10	.18
21	Solve tasks_easy	89	6 (7%)	10.18	1.34	5	−2.12	4.12
22	Solve tasks_med	89	6 (7%)	8.01	2.08	10	−.72	1.24
23	Solve tasks_hard	89	6 (7%)	5.03	2.61	9	.14	−.91
24	Concentrate _easy	89	6 (7%)	10.56	1.22	7	−3.53*	13.37*
25	Concentrate _med	89	6 (7%)	9.57	2.06	7	−1.27	.36
26	Concentrate _hard	89	6 (7%)	7.25	3.10	10	−.45	−1.14
27	Not give up _easy	89	6 (7%)	9.87	1.87	10	−2.11	5.25
28	Not give up _med	89	6 (7%)	8.53	2.17	10	−.65	.13
29	Not give up _hard	89	6 (7%)	6.73	3.04	10	−.19	−1.14
30	National test score	93	2 (2%)	35.69	11.03	47.00	−.58	−.46

*Absolute value higher than recommended cut-off (Kline, 2011, p. 63)

Skewness /kurtosis z-score is larger than 1.65 for all estimates, except those in bold

Items 1–15 are from grade 8, while items 16–30 are from grade 9.

Figure 2. Factor structure of the Self-Efficacy Gradations of Difficulty questionnaire.

Figure 3. Reciprocal effects model with equality constraints (Model 1).

Table 2. Correlation matrix of latent SE level constructs and national test scores.

	1	2	3	4	5	6	7
1 Grade 8 SE easy
2 Grade 8 SE medium	.59**
3 Grade 8 SE hard	.23*	.70**
4 Grade 8 NT score	.22*	.46**	.34**
5 Grade 9 SE easy	.13	.26*	.14	.21
6 Grade 9 SE medium	.22*	.45**	.37**	.34**	.68**
7 Grade 9 SE hard	.23*	.40**	.45**	.31**	.36**	.80**
8 Grade 9 NT score	.24*	.44**	.32**	.87**	.26*	.44**	.39**

* Correlation is significant at the p < .05 level (2-tailed).

** Correlation is significant at the p < .01 level (2-tailed).

SE easy, medium, and hard = self-efficacy for easy, medium difficulty, and hard tasks.

NT score = national test score.

Variables 1–4 are measured in grade 8; variables 5–8 are measured in grade 9.

Figure 4. Best fit model (Model 2).

Table 3. Fit indices from structural equation models.

		Fit indices					Model comparison*
Model		x^2	p	RMSEA	CFI	SRMR	ΔCFI	Δx^2(Δdf)	p
0	All structural paths freely estimated	x^2(6) = 5.34	p = .501	0.00	1.00	0.05
		x^2/df = 0.89
1	Paths associated with SE level constructs constrained as equal	x^2(16) = 38.49	p = .001	0.12	0.93	0.16
		x^2/df = 2.41
2	Best fit model	x^2(12) = 6.53	p = .89	0.00	1.00	0.06	0.07	Δx^2(4) = 31.96	p < .05
		x^2/df = 0.54

* Model 2 was compared against the more parsimonious model, Model 1.

In Model 1 all autoregressive paths as well as all associations between SE level constructs and performance were constrained as equal across all SE level constructs. In Model 2 the associations between performance and SE for easy tasks were not constrained as equal to the associations between performance and SE for medium difficulty and hard tasks.

Street, K. E. S., Malmberg, L.-E., & Stylianides, G. J. (2017). Level, strength, and facet-specific self-efficacy in mathematics test performance. ZDM - Mathematics Education, 49(3), 379–395. https://doi.org/10.1007/s11858-017-0833-0

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Kline, R. B. (2011). Principles and practice of Structural Equation Modeling (3rd ed.). The Guildford Press.

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