Effects of Teachers' Mathematical Knowledge for Teaching on - Apple

Student Background
Several student background measures were included in this study. Students’
rate <strong>of</strong> absence from mathematics instruction was generated by aggregating
log reports <strong>of</strong> daily student absences to the student level. Just over nine logs
were recorded <strong>for</strong> the average first grader and eight logs <strong>for</strong> the average
third grader, and the reliability <strong>of</strong> this aggregated estimate in discriminating
among students’ rate <strong>of</strong> absence was .41. Using these data, we created a
dummy variable representing students whose absence rate exceeded 20%
(the reference category being students with less than a 20% absence rate).
In<strong>for</strong>mation on students’ gender and minority status was collected from
teachers and other school personnel at the time <strong>of</strong> student sampling. In<strong>for</strong>mation
on family SES was collected via telephone interviews with the parents
or legal guardian <strong>of</strong> the study students. The composite SES variable
represented an average <strong>of</strong> father’s and mother’s education level, their occupation
level, and family income.
Teacher Background and Classroom Characteristics
The primary source <strong>of</strong> data on teacher background variables was the teacher
questionnaire, from which in<strong>for</strong>mation was used to construct measures <strong>of</strong>
teacher experience, certification, and undergraduate/graduate coursework.
These teacher background characteristics were straight<strong>for</strong>wardly represented
in our statistical models. For instance, teachers’ experience was reported as
number <strong>of</strong> years in service at Year 2 <strong>of</strong> the study. Although we had in<strong>for</strong>mation
on noncertified teachers’ credentials (e.g., provisional or emergency
certification), too few teachers existed in each such category to include them
independently in statistical analyses; thus, our credential variable simply represented
the presence (coded as 1) or absence (coded as 0) <strong>of</strong> certification.
Finally, teachers reported the total number <strong>of</strong> mathematics methods and
mathematics content courses taken as part <strong>of</strong> their preservice and postgraduate
higher education. Because reports <strong>of</strong> methods courses and reports
<strong>of</strong> content courses were highly correlated (r = .80), they led to multicollinearity
in regression models estimated during both the first and third
grades. As a result, we <strong>for</strong>med a single measure combining reports <strong>of</strong> mathematics
methods and content coursework. Un<strong>for</strong>tunately, this strategy did
not allow <strong>for</strong> an examination <strong>of</strong> the independent effects <strong>of</strong> methods and content
courses, as is standard practice in the educational production function
literature (e.g., Monk, 1994).
We included three classroom variables in our analyses. First, in<strong>for</strong>mation
on percentage <strong>of</strong> minority students was obtained by aggregating student characteristics
<strong>for</strong> each classroom. Second, to capture variation in the absolute
amount <strong>of</strong> mathematics instruction to which students were exposed, we developed
a measure <strong>of</strong> average classroom time spent on mathematics using data
from teachers’ mathematics logs. The time measure excluded days on which
the student or teacher was absent. Finally, rate <strong>of</strong> teacher absence from mathematics
lessons was calculated by aggregating logs to the teacher level.
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