Exploring mechanisms of peer-effects in education: a frame-factor analysis of instruction

Figures & data

Figure 1. Paradigm of the Frame Factor model (Lundgren, 1972, p. 43).

Table 1. Descriptive statistics for gross and net sample in the study.

	Gross sample	Net sample
Schools	150	142
Teachers	200	174
Classes	206	179
Average class size	23.3	23.6
Pupils	4090	3761
of which
share of boys	52%	52%
mother tongue*	3.64	3.65
parental education**	3.69	3.71
TIMSS mean score (BSMMAT01)	502.6	504.2

*Speaks test language at home, 1 = never, 4 = always.

** 1 = don’t know, 6 = university or higher.

Table 2. Descriptive statistics for all variables in the analysis.

		N	M	SD
Within-class	Instruction According to Students (ST_INSTR)
	S_INSTR_EASYUNDERST	3 711	3.05	0.86
	S_INSTR_CLEARANSW	3 706	3.04	0.87
	S_INSTR_EXPLGOOD	3 678	3.20	0.88
	S_INSTR_VARYHELP	3 702	3.21	0.84
	S_INSTR_TELLBETT	3 703	3.11	0.87
	Cronbach α = 0.897
Between-class	Advanced Instruction
	T_INSTR2_CHALLEXC	3 738	2.56	0.72
	T_INSTR2_PROBSOLVE	3 738	2.93	0.77
	T_INSTR2_NOSOLU	3 761	2.09	0.51
	Cronbach α = 0.749
	Limitations of Instruction
	T_LIMIT_LACKKNOW	3 624	2.08	0.59
	T_LIMIT_LACKSLEEP	3 609	1.71	0.59
	T_LIMIT_DISRUPT	3 623	1.72	0.61
	T_LIMIT_UNINTREST	3 624	1.90	0.58
	Cronbach α = 0.756
	Teacher Responsibility for Content
	T_INSTR1_LECTCONT	3 742	3.30	0.76
	T_INSTR1_LECTSOLVE	3 736	3.17	0.83
	T_INSTR1_MEMO	3 761	2.40	0.78
	Cronbach α = 0.728
	Instruction According to Students (SC_INSTR)
	SC_INSTR_EASYUNDERST	3 761	3.05	0.41
	SC_INSTR_CLEARANSW	3 761	3.03	0.39
	SC_INSTR_EXPLGOOD	3 761	3.20	0.46
	SC_INSTR_VARYHELP	3 761	3.21	0.36
	SC_INSTR_TELLBETT	3 761	3.11	0.34
	Cronbach α = 0.968
Dependent & control variables	BOY (Sex)	3 728	0.52	0.50
	MT (Mother Tongue)	3 725	3.65	0.68
	HEDREC (Home Educational Resources)	3 709	2.22	0.48
	PARED (Parents’ Level of Education)	3 568	3.71	2.19
	TIMSS-score (BSMMAT01)	3 761	504.2	70.10
	Level of SCG (Steering Criterion Group)	3 761	445.5	44.14

Table 3. Results for all structural equation models (M1-4).

	M1			M2			M3			M4
	Std.est.	S.E.	P	Std.est.	S.E.	p	Std.est.	S.E.	p	Std.est.	S.E.	p
WITHIN-CLASS
Instruction According to Students (ST_INSTR)	0.18	0.02	0.00	0.18	0.02	0.00	0.17	0.03	0.00	0.17	0.03	0.00
Boy (S_SEX)	–	–	–	–	–	–	0.05	0.03	0.10	0.05	0.03	0.11
Mother tongue (S_MT)	–	–	–	–	–	–	0.07	0.02	0.01	0.07	0.03	0.00
Home educational resources (S_HMEDR)	–	–	–	–	–	–	0.23	0.02	0.00	0.23	0.02	0.00
Parents’ educational background (S_PARED)	–	–	–	–	–	–	0.12	0.02	0.00	0.12	0.02	0.00
R^2 (BSMATH01)	0.03	0.01	0.00	0.03	0.01	0.00	0.13	0.01	0.00	0.13	0.01	0.00
BETWEEN-CLASS
Teacher Responsibility for Content (T_INSTR)	−0.04	0.09	0.62	−0.04	0.08	0.68	−0.04	0.09	0.66	−0.04	0.09	0.67
Advanced Instruction (T_ADVAN)	0.10	0.12	0.37	0.08	0.10	0.41	0.10	0.10	0.34	0.10	0.12	0.38
Instruction According to Students (SC_INSTR)	−0.16	0.11	0.15	−0.12	0.09	0.19	−0.15	0.10	0.13	−0.17	0.10	0.10
Limitations of Instruction (LIMIT_INSTR)	−0.56	0.09	0.00	−0.55	0.08	0.00	−0.54	0.07	0.00	−0.43	0.12	0.00
Parents’ educational background (C_PARED)	–	–	–	–	–	–	–	–	–	0.28	0.08	0.00
R^2 (BSMATH01)	0.28	0.09	0.00	0.28	0.09	0.00	0.26	0.10	0.01	0.25	0.09	0.00
Mediation	No	–	–	Yes	–	–	Yes	–	–	Yes	–	–
Control variables	No	–	–	No	–	–	Within	–	–	All	–	–
ICC (BSMATH)	0.25	–	–	0.25	–	–	0.18	–	–	0.18	–	–
N (students)	3 761	–	–	3 761	–	–	3 530	–	–	3 530	–	–
N (classes)	179	–	–	179	–	–	179	–	–	179	–	–
χ^2 (mean) (st.dev.)	449.8 (5.11) (104)	–	–	457.8 (5.11) (107)	–	–	491.6 (4.36) (127)	–	–	514.3 (4.39) (141)	–	–
(df)
RMSEA (mean) (st.dev.)	0.03 (0.00)	–	–	0.03 (0.00)	–	–	0.03 (0.00)	–	–	0.03 (0.00)		–
CFI (mean) (st.dev.)	0.97 (0.00)	–	–	0.97 (0.00)	–	–	0.96 (0.00)	–	–	0.96 (0.00)		–
SRMR (within, mean) (st.dev.)	0.03 (0.00)	–	–	0.03 (0.00)	–	–	0.04 (0.00)	–	–	0.04 (0.00)		–
(between, mean) (st.dev.)	0.07 (0.00)	–	–	0.09 (0.00)	–	–	0.09 (0.00)	–	–	0.08 (0.00)		–

Figure 2. Results for the measurement model.

Figure 3. Final structural equation model (M4). * = non-significant effects (p > 0.05).

Lundgren, U. P. (1972). Frame factors and the teaching process. A contribution to curriculum theory and theory on teaching. Göteborgs universitet.

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