Towards quality and equitable education in South Africa: Unpacking the relationship between teacher factors, students’ socioeconomic background and mathematics achievements

Figures & data

Table 1. Descriptive statistics of the dependent variable “BSMMAT01 to BSMMAT05”

Plausible Values	Variables Labels	N	Mean (M)	Standard Deviation (SD)
BSMMAT01	1st Plausible Value Mathematics	12,514	371.42	81.73
BSMMAT02	2nd Plausible Value Mathematics	12,514	370.90	82.13
BSMMAT03	3rd Plausible Value Mathematics	12,514	369.67	82.89
BSMMAT04	4th Plausible Value Mathematics	12,514	369.24	82.56
BSMMAT05	5th Plausible Value Mathematics	12,514	369.88	83.10

Table 2. Descriptive statistics for student-estimated number of books in the home, the number of home study support, and parents’ highest education level

Indicator/ item	Question/ Variable labels	Mean	Standard Deviation
BOOK	About how many books are there in your home? (Do not count magazines, newspapers, or your school books)	1.89	.99
HSS	Number of Home Study Supports	1.22	.73
PEDU	Parents’ Highest Education Level	3.18	1.69

Table 3. Descriptive Statistics for number of years of teacher experience, teacher degree, and teacher major (manifest variables)

Indicator	Question/ Variable labels	Response categories	M	SD
BTBG01	Number of years of experience	Reported in whole number	13.73	9.77
BTBG04	Level of formal education completed/ Teacher degree	Did not complete upper secondary, upper secondary, post-secondary, non-tertiary, short-cycle tertiary, bachelor’s or equivalent, master’s or equivalent, Doctor or equivalent	4.67	.68
BTDM05	Major	Focus on either mathematics major OR mathematics education	3.84	1.04

Table 4. Descriptive Statistics for Teacher Confidence in Mathematics

Indicator/ item	Question/ Variable labels	Response categories	M	SD
BTBM17A_R	Inspiring students to learn mathematics	Very high, high, medium, low	3.52	.596
BTBM17B_R	Showing students a variety of problem solving strategies		3.40	.596
BTBM17C_R	Providing challenging tasks for the highest achieving students		3.01	.804
BTBM17D_R	Adapting my teaching to engage students’ interest		3.25	.656
BTBM17E_R	Helping students appreciate the value of learning mathematics		3.41	.649
BTBM17F_R	Assessing student comprehension of mathematics		3.20	.686
BTBM17G_R	Improving the understanding of struggling students		3.04	.722
BTBM17H_R	Making mathematics relevant to students		3.26	.641
BTBM17I_R	Developing students’ higher-order thinking skills		3.10	.726

Table 5. Descriptive statistics for instructional quality as assessed by teachers

Indicator/ item	Question/ Variable labels	Response categories	M	SD
BTBG14A_R	Relate the lesson to students’ daily lives	Every or almost every lesson, about half the lessons, some lessons, never	3.12	.842
BTBG14B_R	Ask students to explain their answers		3.30	.800
BTBG14C_R	Ask students to complete challenging exercises that require them to go beyond the instruction		2.90	.864
BTBG14D_R	Encourage classroom discussions among students		3.14	.843
BTBG14E_R	Link new content to students’ prior knowledge		3.62	.593
BTBG14F_R	Ask students to decide their own problem-solving procedures		2.97	.836
BTBG14G_R	Encourage students to express their ideas in class		3.35	.758

Table 6. The reliability coefficient for instructional quality (InQua) and teacher confidence in mathematics (TCM)

Scale	Indicators	Cronbach’s alpha
InQua	BTBG14A_R, BTBG14B_R, BTBG14C_R, BTBG14D_R, BTBG14E_R, BTBG14F_R, BTBG14G_R	.80
TCM	BTBM17A_R, BTBM17B_R, BTBM17C_R, BTBM17D_R, BTBM17E_R, BTBM17F_R, BTBM17G_R, BTBM17H_R, BTBM17I_R	.91

Table 7. The model fit indices of teacher instructional quality (InQua) and teacher confidence in teaching mathematics (TCM)

Parameters	χ2	df	CFI	TLI	RMSEA	SRMR
InQua	22.865	14	0.980	0.970	0.044	0.029
TCM	57.826	27	0.969	0.959	0.060	0.035

Figure 1. The measurement model of teacher instructional quality (InQua).

Figure 2. The measurement model of teacher confidence in mathematics (TCM).

Figure 3. The hypothetical model with the relations between three teacher qualification and characteristics (TCM), instructional quality (InQua), student and classroom SES composition, and mathematics achievement (M_ACH).

Table 8. Model fit indices for the final structure model (two-level model)

Fit Indices			Mean	Standard deviation
Chi-square (χ2)			347.576	6.295
df	215		-	-
CFI			0.930	0.003
RMSEA			0.007	0.000
SRMR			0.013 (Within-level)	0.003 (Within-level)
			0.058 (Between-level)	0.000 (Between)

Table 9. Estimated Intraclass correlation coefficients of the latent variable indicators

CLUSTER	AVERAGE CLUSTER SIZE	BSMMAT	PEDU	BOOKS	HSS
326	38.172	0.623	0.094	0.158	0.162

Table 10. Standardized direct effects in the final model

Parameter Estimate	Factor loading	Standard Error* (S.E.)	P-value
Within level
SESW effect on BSMMAT	0.073	0.030	0.014
Between level
Teacher qualification effects on mathematics achievement
BTBG01 effect on BSMMAT	0.032	0.047	0.498
BTBG04 effect on BSMMAT	0.076	0.045	0.093
BTDM05 effect on BSMMAT	0.006	0.044	0.895
Teacher qualification effects on instructional quality
BTBG01 effect on INQUA	−0.148	0.070	0.034
BTBG04 effect on INQUA	−0.026	0.064	0.690
BTDM05 effect on INQUA	0.018	0.072	0.802
Classroom student’s SES composition effect on class-level factors
SESB effect on BSMMAT	0.874	0.032	0.000
SESB effect on INQUA	0.014	0.079	0.862
SESB effect on TCM	0.022	0.079	0.778
SESB effect on BTBG01	0.007	0.085	0.935
SESB effect on BTBG04	0.098	0.059	0.096
SESB effect on BTDM05	−0.019	0.080	0.809
Interrelationship among teacher-related factors and mathematics achievement
INQUA effect on BSMMAT	−0.085	0.077	0.267
TCM effect on BSMMAT	0.018	0.081	0.825
TCM effect on INQUA	0.713	0.051	0.000
Correlation among teacher-related factors
BTBG01 correlates with TCM	0.014	0.086	0.871
BTBG04 correlates with TCM	−0.067	0.061	0.274
BTDM05 correlates with TCM	0.051	0.077	0.508
BTBG04 correlates with BTBG01	−0.158	0.080	0.048
BTDM05 correlates with BTBG01	0.038	0.099	0.701
BTDM05 correlates with BTBG04	0.220	0.108	0.041

Table 11. Standardized total and specific indirect effects estimated in the structural model

Relations	Total Indirect effects (Z-effects)*	**P-value
Total indirect effect of SESB on mathematics
BSMMAT—SESB	0.006 (0.587)	0.557
The specific indirect effect of SESB on mathematics via teacher-related factors
BSMMAT—BTBG01—SESB	0.000 (0.003)	0.935
BSMMAT—BTBG04—SESB	0.007 (0.006)	0.192
BSMMAT—BTDM05—SESB	0.000 (0.001)	0.918
BSMMAT—INQUA—SESB	−0.001 (0.007)	0.870
BSMMAT—TCM—SESB	0.000 (0.002)	0.859
BSMMAT—INQUA—BTBG01—SESB	0.000 (0.001)	0.936
BSMMAT—INQUA—BTBG04—SESB	0.000 (0.001)	0.731
BSMMAT—INQUA—BTDM05—SESB	0.000 (0.000)	0.851
BSMMAT—INQUA—TCM—SESB	−0.001 (0.005)	0.786

*Z-effect is the ratio of the estimate or regression coefficient and standard error, (i.e. Z_value = estimate/ standard error) and when is 1.96, then the effect is significant. The estimates reflect the regression weight or the strength of the relationship between variables.

** P-value is significant at .05.