Framework
Alternative routes to teaching certification in the United States have grown in number and account for an ever-increasing portion of the new teachers in American public schools. The majority of these routes are early entry programs, in which new teachers begin teaching before satisfying the requirements for full licensure. Policy arguments supporting alternative routes presume that new teachers can develop the knowledge, skills, and dispositions needed for teaching competently while on the job. In this study, I focus on teaching mathematics in the domain of multiplicative reasoning (for example, including fractions, ratios, and proportions) because this content is often difficult for students and teachers and, although multiplicative reasoning is a primary concern in the middle grade curriculum, it also plays a significant role in elementary and high school mathematics.
Recent work on teacher knowledge builds on Shulman's (1986) idea of pedagogical content knowledge to define mathematical knowledge for teaching (MKT) as the mathematics entailed in the work of teaching (e.g., Ball, Thames, & Phelps, 2008). In the last decade, success in identifying and measuring MKT has enabled researchers to establish empirical relationships between MKT and student achievement (e.g., Hill, Rowan, & Ball, 2005; Baumert et al., 2010). In two separate national samples of middle and elementary teachers, Hill (2007, 2010) found teachers' grade level and years of teaching experience to be positively correlated with their MKT, and called for more research describing the content knowledge of alternatively certified teachers.
Moreover, in the study of elementary teachers, Hill (2010) found a disappointingly low correlation (0.25) between MKT and teachers' self-concept of mathematics. Hill observed this result is concerning because program evaluations employ teachers' reports of learning, but in addition, the finding calls into question the expected relationship between motivation beliefs and knowledge (e.g., Newton, 2009). Bandura (1977) proposed self-efficacy beliefs, a judgment of one's ability to succeed in some activity, as the root of motivation, governing effort and perseverance. Teaching self-efficacy beliefs, in which teaching is the activity in question, have been successfully measured and related empirically with a variety of student outcomes including achievement (see Tschannen-Moran, M. & Woolfolk-Hoy, A., 2001, for a review).
Methods
This quantitative study is descriptive; I seek to answer the following research questions: How are teaching self-efficacy beliefs related to teachers' content knowledge for teaching in the domain of multiplicative reasoning? How are the MKT and teaching self-efficacy beliefs of early entry teachers different than those of traditionally certified teachers? Regression analysis of cross-sectional data is used to answer these questions; I do not presume to address questions of causality.
Data
The measure of content knowledge uses 26 items developed for the Measures of Effective Teaching Project. Because self-efficacy beliefs are task and situation specific, I developed a measure of teaching self-efficacy beliefs tailored to the domain of multiplicative reasoning by adapting existing measures for science teaching self-efficacy (Enochs & Riggs, 1990; Roberts & Henson, 2000).
The sample is derived from an ongoing census of Texas mathematics teachers currently being conducted by researchers at Michigan State University (see http://usteds.msu.edu/project_overview.asp). Teachers who complete the initial survey are invited to take an additional survey. Data from the second survey are reported here. Because of the timeframe for data collection, the sample reported in this study is partial. To date, 122 of the approximately 700 teachers invited to take the second survey have agreed to take it, but only 35 answered more than 25% of the survey questions. Of those 35 teachers, 33 answered all or all but 1 of the survey questions. Over the next few months, surveys will be sent to almost all of the approximately 70,000 mathematics teachers in Texas.
Results
The low n of 35 in the partial sample reported here is insufficient to do the necessary psychometric reliability and validity work (including IRT score estimation and factor analyses) and leads to inflated standard errors so fewer estimates are statistically significant. However, even this small (but possibly biased) sample yields some interesting preliminary results under classical test theory.
Table 1. Correlations among predictors of MKT.
| Teaching Experience | Highest Grade Taught
| GTES
| MTSE
| |||
MKT | .19 | .45 **
| .13
| .41 *
| |||
Teaching Experience | | .26
| .06
| .39 *
| |||
Highest Grade Taught | |
| .15
| .56
| |||
GTES | |
|
| .01 ***
| |||
* p < .05 | ** p < .01
| *** p < .001
|
| ||||
Correlations among predictors of MKT (Table 1) suggest that
domain-specific self-efficacy beliefs are more correlated with MKT than scores
on the General Teaching Efficacy Scale (the GTES, see Hoy
& Woolfolk,1993) and that grade level is also moderately correlated
with MKT. The sample further suggests that teachers at different grade levels
have different scores for MKT in the multiplicative reasoning domain (Figure
1), but that early entry teachers were not found to have significantly
different MKT than traditional route teachers (Figure 2).
Figure 1. Significant (p = .012) differences exist among the
mean MKT scores of teachers with experience at different grade levels.
Figure 2. Differences between the mean MKT scores of early
entry and traditional route teachers are not significant (p = .29).
A series of regression equations (Table 2) suggests that
teaching self-efficacy beliefs account for 16% of the variance in MKT scores,
and by adding teachers' grade level to the model, the variance explained rises
to 24%. Only 14% of variance in MKT was accounted for in a regression model for
MKT with 14 predictors (Hill, 2010). The regression coefficients in this model
are not significant. However, a simulation increasing the sample size to 128
but preserving the observed distribution suggests that with a larger number of
observations the parameter estimates for mathematics teaching self-efficacy and
grade level would be significant.
Table 2. Regression models of MKT.
Model 1 (n = 32) Model 2 (n = 32) Model 3 (simulated n = 128 ) Intercept .01 (.17) .00 (.17) .00 (.08) MTSE .38 * (.17) .19 (.21) .19 * (.10) GTES .13 (.17) .09 (.17) .09 (.08) Highest Grade Taught .33 (.20) .33 *** (.10) R2 .16 .24 .24 * p < .05 ** p < .01 *** p < .001 Implications Clearly, these results are very tentative and
preliminary. Once the full sample
is obtained, and if models similar to those presented here fit the full data set,
these results would suggest that early entry teachers are not significantly
more knowledgeable than their traditional route counterparts, contrary to
policy arguments that favor alternative certification routes because they
ostensibly increase the number of mathematically knowledgeable teachers in
schools. Moreover, the domain-specific measure of teaching self-efficacy
appears to be orthogonal to a general measure of teaching self-efficacy, and
together these beliefs explain a large portion of the variance in teachers'
domain-specific MKT. If the relationship between self-efficacy beliefs and
content knowledge holds up in the larger data set, future research might
explore the role of self-efficacy beliefs in teacher development designed to
increase content knowledge (for example, in early entry certification routes).
References Ball, D., Thames,
M., & Phelps, G. (2008). Content knowledge for teaching: What makes it
special? Journal of Teacher Education, 59(5), 389–407.
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This study used regression analysis of cross-sectional data to characterize traditional and alternative-route teachers’ mathematical knowledge for teaching multiplicative reasoning (fractions, ratios, and proportions), using beliefs of teaching self-efficacy and controlling for teachers’ experience and grade level.
Session Type: Poster Session