The main results in chapter 4 indicated that AR students in schools that offered an online Algebra I course to broaden access to Algebra I in grade 8 were significantly more likely to follow an advanced mathematics course sequence in high school than AR students in control schools. This chapter examines two exploratory questions intended to further understand the main results regarding AR students’ coursetaking. It draws on data on AR students’ planned grade 9 mathematics classes and their actual grade 9 and grade 10 mathematics course sequences.
Exploratory Research Questions
Exploratory Research Question 1: How does access to online Algebra I in grade 8 affect the likelihood that AR students sign up for advanced courses in grade 9? This exploratory analysis examines the impact of access to online Algebra I in grade 8 on students’ planned grade 9
mathematics course enrollments, using data provided by schools at the end of grade 8. The outcome of interest is whether AR students in treatment schools are more likely than their counterparts in control schools to enroll in a course for grade 9 that if successfully completed, would place them on an advanced coursetaking trajectory.
Exploratory Research Question 2: How does access to online Algebra I in grade 8 affect the likelihood that AR students double up, or take more than one mathematics course a year, in grade 9 or 10? If access to online Algebra I in grade 8 enables students to enter high school farther along in the mathematics course progression, the intervention may decrease the probability that students double up on courses in grade 9 or 10. In addition to analyzing this question, researchers conducted a descriptive analysis of the coursetaking patterns that involve doubling up on mathematics courses. This analysis examined the different pathways by which students in treatment and control schools get on pace to complete Algebra II by the end of grade 10.
Results
Exploratory Research Question 1
To estimate the effect of having access to online Algebra I in grade 8 on the probability of enrolling in a course above Algebra I in grade 9, researchers employed the same two-level hierarchical generalized linear model used in the main analysis of high school coursetaking (see chapter 4).
The results of this analysis show that AR students in schools that offered the online Algebra I course were significantly more likely to register for an advanced grade 9 mathematics course than their AR counterparts in schools that did not offer the course (table 5-1). The average predicted probability of enrollment in an advanced mathematics course by AR students was 0.16 in control schools and 0.54 in treatment schools. The intervention thus yielded a difference in the probability of enrolling in a grade 9 course above Algebra I of 0.38, meaning that AR students in treatment schools were 3.38 times more likely than AR students in control schools to enroll in an advanced grade 9 course.
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Table 5-1. Predicted Probability of AR Students Enrolling in Advanced Mathematics Course in Grade 9
Difference in probability attributed
to intervention Treatment schools
(standard error) Control schools
(standard error) p-value
0.54 0.16 0.38* 0.005
(0.11) (0.07)
AR is algebra ready.
* No adjustments for multiple comparisons were applied for the secondary impact analyses, thus a p-value less than 0.05 is considered statistically significant.
Note: Sample includes 68 schools (35 treatment, 33 control) and 440 AR students (218 treatment, 222 control). Estimates were averaged across 10 multiply imputed datasets. Probabilities are the average model-predicted probabilities, controlling for all covariates specified for the model.
Source: Planned courses indicated by study students at end of Grade 8.
Exploratory Research Question 2
If access to online Algebra I in grade 8 enables students to enter high school farther along in the mathematics course progression, the intervention may affect the probability that students double up on full-year mathematics courses in grade 9 or 10. To address this question, researchers tested the impact of access to online Algebra I in grade 8 on the likelihood of taking two full-year mathematics courses in either grade 9 or grade 10 (that is, doubling up on mathematics coursework). The outcome for this analysis was a binary indicator of doubling up, where students were assigned a 1 if they doubled up in grade 9 or planned to do so in grade 10 and a 0 if they did neither. A total of 96 students—21% of the AR student sample across conditions—
were coded as doubling up.
The analytic model testing whether the intervention impacted whether AR students doubled up in grade 9 or 10 was a hierarchical generalized linear model that accounted for the nesting of
students within schools and included the same student- and school-level covariates as the impact models, with the exception of special education status.52 The results indicate that AR students from treatment schools were significantly less likely to double up on mathematics courses than AR students from control schools (table 5-2). Access to online Algebra I thus appeared to
decrease the likelihood that students take more than one full-year mathematics course in grade 9, grade 10, or both grades.
52 Special education status was removed from the analytic model because no students who were deemed eligible for special education services doubled up in mathematics courses in either grade 9 or 10, causing mathematical errors in the estimation of the treatment effect.
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Table 5-2. Predicted Probability of AR Students Doubling Up on Full-Year Mathematics Courses in Grade 9 or 10
Difference in probability attributed
to intervention Treatment schools
(standard error) Control schools
(standard error) p-value
0.10
(0.03) 0.23
(0.06) –0.13* 0.033
AR is algebra ready.
* No adjustments for multiple comparisons were applied for the secondary impact analyses, thus a p-value of less than 0.05 is considered statistically significant.
Note: Sample includes 68 schools (35 treatment, 33 control) and 440 AR students (218 treatment, 222 control). Estimates were averaged across 10 multiply imputed datasets. Probabilities are the average model-predicted probabilities, controlling for all covariates specified for the model.
Source: Coursetaking data collected from high schools study students attended in 2009/10.
Taken together with the results of the main analysis presented in chapter 4, this exploratory analysis indicates that in addition to affecting whether students appear positioned to complete an advanced course sequence by the end of high school at the end of grade 9, offering Algebra I as an online course in grade 8 may also affect how they do so. Students with access to online Algebra I in grade 8 were less likely to double up on mathematics courses in grades 9 or 10 than their counterparts in control schools who, by and large, did not have access to Algebra I in grade 8.
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