Learning through teaching: the development of pedagogical content knowledge among novice mathematics teachers

Figures & data

Figure 1. A visual conceptual framework.

Table 1. Background characteristics of teachers in the present study.

Teacher background characteristic	Sample (%)
Gender
Female	84.1
Male	15.5
Ethnicity
White	70.1
Black	8.2
Hispanic	9.7
Other (e.g. Asian, multiracial, and other)	12.1
Professional background
Credential in mathematics	18.4
Credential in multiple subjects	69.6
Credential in other subjects (e.g. special education)	12.1
Route entering the profession
Traditional certification^a	72.0
Alternative certification^b	28.0

N = 207.

^aTo obtain traditional certification, an individual must first earn a bachelor’s degree and complete a teacher preparation programme before they can begin teaching.

^bAlternative certification allows individuals with a bachelor’s degree to teach without necessarily having completed a formal teacher preparation programme prior to teaching.

Figure 2. Growth of PCK among teachers with less and more robust mathematics content knowledge at the beginning of the study.

Note: The error bars indicate one standard deviation below and above the average.

Table 2. Estimates of the linear growth models for teachers’ PCK.

	Model
	1	2	3	4	5	6	7
Fixed effect
Intercept	24.51***	24.63***	24.45***	24.40***	25.75***	24.68***	24.06***
	(0.35)	(0.37)	(0.30)	(0.34)	(0.72)	(0.40)	(0.38)
Time (i.e. rate of change)	2.21***	2.09***	2.17***	2.22***	2.16***	2.27***	2.07***
	(0.21)	(0.34)	(0.20)	(0.21)	(0.43)	(0.24)	(0.23)
Formal support		0.01
		(0.67)
Formal support × Time		0.22
		(0.49)
Informal support		−0.96
		(0.56)
Informal support × Time		0.42
		(0.42)
Effect on intercept
Content knowledge			5.58***
			(0.58)
Content-specific noticing skills				1.52***
				(0.32)
Entry-level teaching experience					−1.45*
					(0.69)
Alternative certification						−0.62
						(0.85)
Math teaching credential							2.42*
							(0.96)
Effect on slope
Content knowledge			0.90*
			(0.36)
Content-specific noticing skills				−0.15
				(0.19)
Entry-level teaching experience					0.06
					(0.43)
Alternative certification						−0.24
						(0.48)
Math teaching credential							0.70
							(0.52)
Random effect (variance)
Intercept	18.59***	18.91***	11.59***	16.36***	18.05***	18.51***	17.73***
	(2.70)	(2.72)	(2.13)	(2.61)	(2.72)	(2.75)	(2.53)
Slope	3.07**	3.16***	2.81**	3.04**	3.07**	3.06**	3.00**
	(1.09)	(1.07)	(1.09)	(1.09)	(1.09)	(1.09)	(1.11)
Intercept and slope	1.13	1.01	0.04	1.36	1.16	1.11	0.82
	(1.39)	(1.39)	(1.25)	(1.34)	(1.41)	(1.39)	(1.34)
Residual	8.50***	8.20***	8.56***	8.50***	8.49***	8.49***	8.49***
	(1.06)	(1.04)	(1.07)	(1.06)	(1.06)	(1.06)	(1.06)

*p < .05; **p < .01; ***p < .001.