Cognitive Skills, Math-Related Emotions, and Beliefs Explaining Response to Arithmetic Fluency Intervention

Figures & data

Table 1. Descriptive statistics on the study variables.

	Whole sample (N = 69)					Girls (N = 36)		Boys (N = 33)		t-Test
	Min/Max	Mean	SD	Skewness	Kurtosis	Mean	SD	Mean	SD	t (68), (sig.)
Gain score	−5.00/29.00	6.71	7.17	0.80	0.65	6.81	7.16	6.60	7.30	0.12 (ns.)
Initial arithmetic skills	9.00/30.00	19.68	5.26	−0.02	−0.61	20.34	5.30	19.00	5.20	1.05 (ns)
Initial reading skills^a	−2.45/2.27	−0.55	1.03	.046	−0.25	−0.53	1.03	−0.58	1.04	0.13 (ns)
Visuo-spatial skills^a	2.00/17.00	8.65	3.22	0.34	−0.13	8.58	2.71	8.73	3.80	−0.19 (ns.)
Vocabulary^a	1.00/15.00	7.90	2.75	−0.13	−0.02	7.72	2.42	8.10	3.13	−0.55 (ns.)
Working memory^a	3.00/14.00	8.06	2.36	0.31	0.12	8.53	2.21	7.50	2.45	1.79 (ns.)
Rapid automatized naming^b	−3.99/1.27	−0.65	1.14	−0.90	0.59	−0.57	1.06	–0.74	1.23	0.59 (ns.)
Math anxiety^b	−1.78/2.00	0.32	0.95	−0.04	−0.51	0.46	0.93	0.16	0.95	1.32 (ns.)
Math interest^b	−1,91/1.65	−0.24	1.05	0.06	−1.18	−0.27	1.04	−0.21	1.07	−0.21 (ns.)
Math SE^b	−3.50/.97	−0.53	1.05	−0.52	−0.22	−0.54	1.01	−0.52	1.12	−0.06 (ns.)

Note. ^aVariables are standardized (M = 10; SD = 3); ^bVariables are standardized (M = 0; SD = 1); i.e., p > 0.05. Math SE means math self-efficacy.

ns: non-significant

Table 2. Correlations of the study variables.

	1.	2.	3.	4.	5.	6.	7.	8.	9.	10.
1. Gain score	1.00	−0.01/0.05	−0.08/0.25	0.15/0.39*	−0.25/0.26	−0.02/0.57**	0.34*/0.53**	−0.36*/0.21	−0.09/−0.05	0.23/0.32
2. Initial arithmetic skills	0.02	1.00	0.20/–0.07	−0.22/–0.19	0.36*/–0.38	0.32/0.00	0.35*/–0.04	−0.05/–0.04	−0.11/0.10	0.03/0.04
3. Initial reading skills^a	0.08	0.07	1.00
4. Visuo-spatial skills^a	0.28*	−0.20	0.11	1.00
5. Vocabulary^a	0.02	−0.04	0.24	0.18	1.00
6. Working memory^a	0.26*	0.21	0.29*	0.19	0.33**	1.00
7. Rapid automatized naming^b	0.43**	0.16	0.28*	0.10	0.24	0.21	1.00
8. Math anxiety^b	−0.09	−0.03	−0.11	−0.29*	−0.06	−0.26	0.04	1.00
9. Math interest^b	−0.07	−0.02	−0.16	−0.29*	−0.06	−0.26*	0.04	−0.40**	1.00
10. Math SE^b	0.27*	0.04	0.07	−0.20	0.25	−0.08	0.14	−0.25*	0.16	1.00

Note. *p < 0.05, **p < 0.01. On the first and second rows, correlations of intervention gain and initial skill level with predictive variables are presented for girls/boys. ^aVariables are standardized (M = 10; SD = 3); ^bVariables are standardized (M = 0; SD = 1).

ns: non-significant

Table 3. Hierarchical regression models for predicting the gain score with cognitive variables.

	Total (N = 69)		Girls (N = 36)		Boys (N = 33)
	R^2/ΔR^2β	ΔF(df1;df2)	R^2/ΔR^2β	ΔF(df1;df2)	R^2/ΔR^2β	ΔF(df1;df2)
Step 1 Initial skill	0.00/0.00 0.02	0.17 (1;58)	0.00/0.00 −0.01	0.01 (1;32)	0.01/0.01 0.07	.011 (1;24)
Step 2 Initial skill BD/VOC	0.08/0.08 0.08 0.29*/−0.03	2.28 (2;56)	0.11/0.11 0.15 0.21/-0.32	1.83 (2;30)	0.22/0.21 0.26 0.35/0.28	2.98 (2;22)
Step 3 Initial skill BD/VOC WM	0.12/0.04 0.02 0.24/−0.10 0.22	2.47 (1;55)	0.11/0.00 0.15 0.21/−0.32 −0.02	0.01 (1;29)	0.37/0.16 0.14 0.23/0.05 0.47*	5.20 (1;21)*
Step 4 Initial skill BD/VOC WM RAN	0.29/0.18** −0.05 0.18/−0.18 0.19 0.44***	13.48 (1;54)**	0.24/0.13 0.02 0.19/−0.31 0.06 0.39*	4.69 (1;28)*	0.50/0.13 0.14 0.16/−0.04 0.35 0.41*	5.20 (1;20)*

Note. ***p < 0.001; **p < 0.01; *p < 0.05.

BD: WISC-IV Block Design; VOC: WISC-IV Vocabulary; WM: WISC-IV Digit Span; RAN: rapid automatized naming of object

Table 4. Hierarchical regression models for predicting the gain score with math-related emotions and beliefs.

	Total (N = 69)		Girls (N = 36)		Boys (N = 33)
	R^2/ΔR^2β	ΔF(df1;df2)	R^2/ΔR^2β	ΔF(df1;df2)	R^2/ΔR^2β	ΔF(df1;df2)
Step 1 Initial skill	0.01/0.01 0.07	0.25 (1;56)	0.00/0.00 −0.01	0.01 (1;32)	0.03/0.03 0.18	0.74 (1;22)
Step 2 Initial skill BD/VOC	0.05/0.05 0.10 0.22/−0.04	1.36 (2;54)	0.11/0.11 0.15 0.21/−0.32	1.83 (2;30)	0.19/0.16 0.34 0.23/0.33	1.97 (2;20)
Step 3 Initial skill BD/VOC Anxiety	0.09/0.04 0.09 0.27/−0.07 −0.20	2.15 (1;53)	0.26/0.15 0.14 0.28/-0.33 −0.40	6.06 (1;29)*	0.22/0.03 0.37 0.16/0.39 0.19	0.72 (1;19)
Step 4 Initial skill BD/VOC Anxiety Interest	0.9/0.03 0.09 0.26/−0.07 −0.22 −0.07	.020 (1;52)	0.32/0.05 0.12 0.19/−0.40* −0.46** −0.27	2.15 (1;28)	0.22/0.00 0.37 0.17/0.38 0.20 0.03	0.01 (1;18)
Step 5 Initial skill BD/VOC Anxiety Interest Self-efficacy	0.21/0.11 0.09 0.33*/−0.15 −0.18 −0.12 0.37*	7.20 (1;51)*	0.42/0.10 0.16 0.27/−0.50** −0.42* −0.310.35*	4.78 (1;27)*	0.36/0.14 0.35 0.25/0.29 0.24 −0.06 0.41	3.61 (1;17)

Note.  **p < 0.01; *p < 0.05.

BD: WISC-IV Block Design; VOC: WISC-IV Vocabulary; WM: WISC-IV Digit Span

Figure 1. Profiles of the cognitive predictive variables of the response and no-response Groups by gender.

Distribution information of each cognitive predictive variables for non-responding and responding girls and boys covering minimum, median and maximum value as well as outliers.

Figure 2. Profiles of the beliefs and emotions of the response and no-response groups by gender.

Distribution information of math-related emotions and beliefs for non-responding and responding girls and boys covering minimum, median and maximum value as well as outliers.

Figure A1. Scatterplots of relation between intervention gain and math anxiety presented separately for girls and boys and two intervention groups.