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Online self-paced high-school class size and student achievement

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In the traditional brick-and-mortar classroom, small classes are generally perceived as desirable, but the benefits associated with particular class sizes in online education have not yet received much scholarly attention. Using a dataset of 10,648 enrollment records generated during the 2013–2014 school year at a state virtual school in the Midwestern U.S., this study examined the relationship between class size and student learning outcomes. The results of hierarchical linear modeling with fractional polynomial analysis suggest a reverse-U-shaped relationship, in which increasing online class sizes had a positive impact on achievement until the number of students reached 45, but a negative one if numbers increased beyond that level. At the subject level, similar reverse-U-shaped patterns were observed in math, social science, and other subjects, but not in English, foreign languages, or science. © 2018 Association for Educational Communications and Technology
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Class Size in Online High-School Courses
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Suggested citation:
Lin, C.-H., Bae, J., & Zhang, Y. (2019). Online self-paced high-school class size and
student achievement. Educational Technology Research and Development, 67, 317-
336. doi: 10.1007/s11423-018-9614-x
Introduction
The number of enrollments in K-12 online courses in the United States tripled
from 1.5 million in 2009-2010 (Watson, Murin, Vashaw, Gemin, & Rapp, 2010) to 4.5
million in 2014-2015 (Watson, Pape, Murin, Gemin, & Vashaw, 2015). Schools are
continuing to expand their online course offerings, both to overcome school-level
challenges and to meet student needs. For instance, they have been deployed as
alternative courses to resolve scheduling conflicts; to offset shortages of highly qualified
teachers, especially in Advanced Placement; and to provide a wider range of electives
and other accelerated options for college-bound students (Watson et al., 2015).
The provision of online courses, however, creates another challenge. On the one
hand, offering them helps to improve educational access, expand curricular choices, and
increase high-quality learning opportunities (Barbour & Reeves, 2009; Berge & Clark,
2005; Cavanaugh & Blomeyer, 2007). On the other, such goals appear to be associated
with extreme class sizes. Miron and Gulosino (2016) found that 356 students were
enrolled in one virtual-school class, and that the average virtual-school class size was 35
– far above the U.S. averages for face-to-face class sizes, of 26.2 for primary schools,
25.5 for middle schools, and 24.2 for high schools (Coopersmith, 2009). At the other end
of the scale, Watson et al. (2015, p. 56) found some virtual-school classes so small that
their costs were “difficult to justify”; and of the online classes examined in the current
study, 47% had 10 students or fewer (see Figure 1).
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A meaningful answer to the question of whether the costs of small online classes
are justified requires careful evaluation of the relationship between class size and
students’ learning outcomes. Accordingly, the purpose of this study is to examine this
under-researched relationship between class size and online learners’ performance, using
data from a statewide virtual school. The main research questions are as follows:
1. What is the optimal class size (across all subjects) for self-paced courses at the
high-school level?
2. What are the optimal class sizes in each subject for self-paced courses at the high-
school level?
Effects of Class Size
Face-to-face Settings
A crucial indicator of classroom context, class size has been widely studied in
face-to-face K-12 settings (Konstantopoulos & Sun, 2014). In general, researchers have
favored smaller classes over larger ones when discussing class size’s impact on teaching
effectiveness, teacher-student interaction, and student achievement (Blatchford, Russell,
Bassett, Brown, & Martin, 2007; Burruss, Billings, Brownrigg, Skiba, & Connors, 2009;
Education Next, 2007; Ehrenberg, Brewer, Gamoran, & Willms, 2001; Hattie, 2005;
Kokkelenberg, Dillon, & Christy, 2008). For example, a synthesis of more than 500
meta-analyses of class size suggested that small classes in face-to-face K-12 settings were
usually perceived as desirable by both teachers and students, and as beneficial for
students’ learning (Hattie, 2005).
The literature has also consistently reported a relation between small class sizes
and students’ improvements in learning (for a review, see Kokkelenberg et al., 2008).
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Specifically, students in small classes have been found to experience higher rates of
teacher-student interaction than students in large classes do (Brühwiler & Blatchford,
2011; Zyngier, 2014). Students in smaller classrooms naturally gain more intense
individual attention from teachers (Blatchford, Bassett, & Brown, 2011; Blatchford et al.,
2007; Ehrenberg et al., 2001), which in turn improves their chances of learning
(Konstantopoulos & Sun, 2014), of engaging in active learning (Blatchford et al., 2011),
and of achieving high grades (Zyngier, 2014). In addition to fostering more active
teacher-student interaction, small class sizes have been found to correlate with decreases
in students’ misbehavior and increases in their positive learning behaviors in class
(Babcock & Betts, 2009; Bascia, 2010; Finn, Pannozzo, & Achilles, 2003).
From the perspective of teaching, reducing classroom sizes has been found to
result in positive changes in the effectiveness of teaching styles and strategies, e.g., more
individualization of teaching with the aim of increasing class engagement (Brühwiler &
Blatchford, 2011), better interaction patterns, use of humor, and classroom
organization/rule-setting (Harfitt, 2013), and increased teacher-parent interaction (Bascia,
2010). Perhaps unsurprisingly, K-12 teachers have consistently been found to strongly
prefer small class sizes. For example, 81% of one group of teachers reported that they
would prefer a reduction of class size over an increase in salary (Education Next, 2007).
Conversely, large class sizes have been identified as a major driver of teacher attrition
(Isenberg, 2010).
Despite the widely reported positive pedagogical effects of small classes in K-12
settings, researchers should be cautious about overemphasizing this positive impact, as
the relationship between class size and student learning is not linear (Borland, Howse &
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Trawick, 2005). Evaluations of optimal class size should take account of various factors
(Hattie, 2005) including, but not limited to, ethnicity (Krueger & Whitmore, 2001) and
grade level (Konstantopoulous & Sun, 2014). Additionally, it should be borne in mind
that factors other than pedagogy often affect administrative decisions regarding class size.
For instance, if instructors can teach larger classes without students’ learning outcomes
being adversely affected, it may be tempting to reduce overall educational costs through
economies of scale (Hattie, 2008).
Online Settings
No prior studies of the relationship between class size and learning behaviors or
outcomes in online K-12 settings appear to have been published, though the dearth of and
need for such studies have been pointed out by some researchers (Miron & Gulosino,
2016; Zhang, Liu, & Lin, 2018). The following review of the literature on class size in
online learning therefore contains only studies that were conducted in post-secondary
settings.
Looking for the Optimal Class Size in Online Learning
Like research on class size in face-to-face environments, scholarship on online
class size has suggested that it is not a stand-alone issue. Rather, it interacts with other
components of online learning, and decision-making regarding online class sizes should
therefore be context-dependent (Tomei, 2006; Zhang, Liu, & Lin, 2018). The existing
scholarly discourse on online class size reflects two conflicting assumptions, both drawn
from studies of higher education: namely, that small class sizes are better than large ones,
or vice versa.
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On the one hand, instructors have tended to argue – based on some combination
of teacher- and student-level considerations – that the online environment requires
smaller classes if it is to achieve desirable learning outcomes (Aragon, 2003; Arbaugh &
Benbunan-Fich, 2005; Arzt, 2011; Orellana, 2006; Qiu, Hewitt, & Brett, 2012; Sorensen,
2014; Taft, Perkowski, & Martin, 2011; Tomei, 2006). At the teacher level, small online
classes have been seen as keeping working loads at a reasonable level, and thus enabling
a sufficient quantity and quality of feedback and student-teacher interaction, as well as
adequate time for grading (Sorensen, 2015; Tomei, 2006). At the student level,
meanwhile, online instructors have argued that large classes impede active student-
student interactions as well as student-teacher ones (Arzt, 2011; Orellana, 2006; Taft et
al., 2011).
Studies aimed at identifying the optimal online class size in post-secondary
settings have recommended sizes in the range of 12 to 30 students. Tomei (2006), for
example, estimated the optimal class size for a graduate-level course based on specific
local conditions, including faculty teaching load (i.e., 85% of time to be spent on
teaching, 10% on service, and 5% on research, with a three-course assignment per
semester), and concluded that the ideal number of students would be 17 in a face-to-face
format, but 12 in an online format. Orellana (2006) surveyed 131 teachers of online
undergraduate or graduate courses, and found that while the respondents’ actual average
class size was 22.8, they perceived the optimal class size as 18.9 if their goal was to boost
the existing level of interaction, or 15.9 if it was to maximize interaction. More recently,
Qiu et al. (2012) asserted that 13 to 15 students was the optimal size for online classes,
based on their finding of a significant positive association between class size and
Class Size in Online High-School Courses
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information overload. Approaching the matter from a pedagogical perspective, however,
Arbaugh and Benbunan-Fitch (2005) concluded that the ideal online class size was
considerably larger: between 25 and 30. And based on an examination of the social
presence required for online courses, coupled with personal teaching experience, Argon
(2003) also argued that 25 students would be an optimal online class size in higher
education.
In contrast to instructors, administrators often favor the large classes that are
made possible by the online environment’s lack of physical-space limitations, as a means
of lowering teaching costs (Sorensen, 2014; Tomei, 2006), though many institutions
simply set online class sizes at the same level as their face-to-face counterparts (Mupinga
& Maughan, 2008). One of the few studies of class size in K-12 online settings, Miron
and Gulosino’s (2016) report on more than 400 virtual schools, found an overall average
class size of 35, but with a large variation in within-school average class size, from a
minimum of 1.3 to a maximum of 356.
Online Class Size and Learning Outcomes
Research on the relationship between online class sizes and learning outcomes is
scant. However, Qiu et al.’s (2012) study of graduate-level online courses found that
large class sizes caused information overload among students, which decreased their
engagement with learning and the quality of their note-taking and note-reading. Based on
those findings, the authors concluded that a class size of 15 would be optimal.
Online Class Size and Subject Effects
Although no research on the relationship between online class size and subject
matter in either secondary or post-secondary settings has yet been published, it is possible
Class Size in Online High-School Courses
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that the effect of class size varies across subjects in K-12 online learning environments
(Zhang et al., 2018). According to Cavanaugh, Gillan, Kromrey, Hess, and Blomeyer
(2004), math and science seem to be more difficult to learn in virtual schools than other
subjects are. Other researchers have also suggested that world languages can be
especially challenging for students to learn online (Lin & Warschauer, 2015; Lin, Zheng,
& Zhang, 2017); and this has been borne out empirically in K-12 virtual-school contexts,
where world-language students have been found to face more challenges and perform less
successfully than their face-to-face counterparts (Cavanaugh, 2001; Oliver, Kellogg, &
Patel, 2012).
In sum, there are three distinct gaps in the literature on class size in online
settings. First, because the above-noted optimal ranges of class size were all derived from
post-secondary online settings, it is unclear whether such numbers are also applicable to
K-12 online settings – especially given that online learning requires a high level of self-
regulation (Lin, Zhang, & Zheng, 2017; Lin, Zheng, et al., 2017) and students at the
secondary level are still developing such skills (Elliot, Dweck, & Yeager, 2017). Second,
none of the studies reviewed above looked directly at the relationship between online
class size and learning outcomes. As previously mentioned, it is problematic (but
commonplace) for schools to simply pre-set a size for their online classes without
considering contextual factors, including especially students’ learning achievement. And
third, all prior research on online class size has utilized small sample sizes and focused on
a narrow range of subjects in higher education, without considering possible differences
across subjects. Therefore, estimating the optimal online class sizes for secondary
Class Size in Online High-School Courses
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students is still uncharted territory, and doubly so if budgetary concerns and between-
subject differences are also taken into account.
Methods
Research Site
This study utilized a dataset covering all students enrolled during the 2013-14
school year at an accredited state-wide virtual school in the Midwestern U.S. Though
always officially referred to as a school, it in fact comprises a supplementary program of
a la carte online courses for students who are all enrolled elsewhere, either in physical or
cyber schools, mostly though not exclusively within the same state.
During the year in question, the virtual school’s courses used digital texts in
which learning was self-paced, and communications between and among teachers and
students were asynchronous. Online instructors in this school were not required to devise
curricula, but only to supplement fully designed online courses that were provided to
them. These courses, which were designed based on research on effective online teaching
and learning strategies, were reviewed and certified by a third-party quality assurance
program (Quality Matters) as well as by the virtual school for their compliance with its
own quality standards. All such courses followed the state’s and/or national curriculum
standards and were taught by state-certified teachers with endorsements for the relevant
content area and grade level. Representative instructional practices included guiding and
supporting students’ learning through communication with them, their parents/guardians,
and their mentors at their own respective schools; providing progress-monitoring,
informative feedback, and personalized supports throughout the term; and facilitating
specific student tasks and activities, especially class discussions. Instructional materials,
Class Size in Online High-School Courses
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tools and assignments included streaming audio and video, computer animations, email,
chat rooms, digital portfolios, individual and team projects, and discussion forums, and
shared the general aim of offering problem-based learning opportunities that would
enhance interaction and collaboration. However, the school’s administrators reported that
due to the nature of self-paced online learning, students’ interactions with their peers
were limited.
At the time of writing, none of the course providers had granted the research team
access to any of their courses; though problematic, this is commonplace in K-12 online
learning (Barbour, 2017). Thus, instructional approaches could not be evaluated.
Data
Initially, the data included 21,253 enrollment records from 12,445 students, but
students who withdrew from or dropped a course were excluded, as they did not receive
any grade. This yielded a sample size of 20,540 records relating to 12,032 students and
233 courses in six subjects, taught by 155 instructors. The enrollment data for each
individual student included the name(s) of the course(s) taken, the semester(s) in which
they were enrolled, their grades, and their instructors’ unique identifying numbers. The
dataset also included information about each student’s local school, including its name
and location; the name of the student’s local-school mentor; and the student’s gender and
self-reported reason for taking online courses.
Measures
For purposes of this study, course refers to the subject a student is enrolled in
(e.g., Algebra, Geometry, beginning Chinese), and class size as the number of students in
one course section. An online instructor might teach a course in multiple sections (e.g.,
Class Size in Online High-School Courses
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Algebra section I and section II). A given student could take one or more courses from
the school in one, two or all three semesters of the year (i.e., Fall, Spring and Summer).
Gender. Among the 12,032 students who completed at least one course during the
year, 5,324 (or 44.2%) were males and 6,708 (or 55.8%) were females.
Grade level. All courses offered in the virtual school were at high-school levels,
and the great majority of its student population was of high-school age. Some middle-
school students were enrolled subject to approval from their own schools, but their exact
numbers cannot be known. This was because the virtual school asked its students for their
demographic information, but did not require them to provide it; and their response rate
to the school’s question about their current grade level was below 30%. However, a
survey with a 29% response rate that two of the researchers conducted in the same virtual
school in spring 2014 found that the student body consisted of 9% middle schoolers, 15%
9th graders, 31% 10th graders, 26% 11th graders, and 20% 12th graders (Lin, Zheng, et al.,
2017).
Reasons for enrollment. The dataset included students’ reasons for enrollment in
online classes, based on a multiple-choice question with five possible answers: 1) the
course being unavailable at local schools, 2) credit recovery, 3) the learning preferences
of the student, 4) scheduling conflicts, and 5) other. By far the most common reason
given was the local unavailability of similar courses (46.7%; see Table 1). A further
15.2% responded that their enrollment was due to their personal learning preferences,
while 11.3% cited scheduling conflicts. Only 8.1% of students stated that their enrollment
was for credit recovery, and nearly one in five students (18.8%) did not provide any clear
Class Size in Online High-School Courses
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reason for why they enrolled, except to the extent that it did not fit into any of the other
four categories.
Learning outcomes. Learning outcomes were the course grades reported by the
virtual school to the students’ own schools at the end of each semester. All courses with
the same name shared the same assessment regime across their different sessions. In other
words, the design of the assessment was at the course level, not at the instructor- or class
level. As noted above, all the courses were certified by Quality Matters; and one aspect of
such certification involves standards of assessment and measurement. Specifically, each
course’s assessment strategy must be capable of evaluating the effectiveness of student
learning based on its stated learning outcomes
In all subjects, each course grade consisted of a mixture of the scores from auto-
graded and instructor-graded assignments, transformed into a percentage format. To a
certain extent, this dual grading system ensured the consistency of the assessment system.
Class size. The size of a class (i.e., section, in the case of courses with two or
more sections) was calculated as the sum of the students who had completed it, regardless
of whether they had passed or failed. However, as noted above, students who dropped a
class were not included when calculating its size.
The virtual school’s decisions regarding online class size were based on estimated
numbers of enrollments, and its administrative staff sought to ensure that the sections of
the same course were of roughly equal sizes. In some instances, classes ended up smaller
than the administrators had anticipated, but the school did not cancel any classes for this
reason alone.
Class Size in Online High-School Courses
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The sizes of the 1,380 class sections in which at least one of our student
participants was enrolled ranged from one student to 60 (see Figure 1). There were five or
fewer students in 29% of the online classes in our sample; six to 10 students in 18% of
the classes; 11 to 20 students in another 20%; and 21 or more in 33%. The average class
size was 14.88, with a standard deviation of 12.09.
Subjects. The virtual school’s administrators had divided the subjects taken by the
students in the dataset into the following categories: 1) English (making up 7.54% of all
enrollments); 2) foreign languages (21.51%); 3) science (11.73%); 4) math (14.51%); 5)
social science (19.03%); and 6) other subjects (25.68%; e.g., art, business, and physical
education).
Data Analysis
Stata 14 software was used to conduct all the quantitative analyses for this study.
Hierarchical linear modeling (HLM) with maximal likelihood estimates (Singer &
Willett, 2003) was employed to examine all of the research questions. HLM is a type of
regression model used to account for correlated errors in nested data structures. In this
case, students were nested in different class sections, which violates an assumption of
multiple regression: that individuals should be independent. As compared to multiple
regression, HLM provides a more accurate form of estimation that accounts more
rigorously for sources of statistical error.
A series of five two-level models were fit to answer the research questions
regarding class size. Level 1 consisted of students’ enrollment records, and level 2 of
each class section. In all models, the students’ final grades were entered as the dependent
variable. The majority (54%) of the students in the dataset took only one course during
Class Size in Online High-School Courses
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the school year in question, and in cases where a student had multiple enrollments, only
his/her first record was used, to ensure that no students’ learning outcomes were biased
upward due solely to their greater familiarity with the virtual-school environment.
However, all the enrollments of students who had multiple enrollments were still
included in calculations of class size. In addition, given that HLM requires a considerate
numbers of students in level 1 of each model (McNeish & Stapleton, 2016), classes with
fewer than 10 students were removed from HLM analysis. After these removal criteria
were applied, the final sample size was 10,648 students.
Model 1 was the unconditional model, essential for determining overall section-
related random effects. Model 2 added class size as a level-2 variable, which enabled
examination of the linear relationship between class size and learning outcomes.
However, since this relationship is not necessarily linear, Model 3 added a class-size
quadratic term and examined whether the relationship between class size and learning
outcomes was a parabolic curve. Likewise, Model 4 added a class-size cubic term to
examine whether the relationship between class size and learning outcomes was
nonlinear and nonparabolic.
To compare which model fit the data best, the researchers used the two types of
information criterion that are most frequently utilized in the HLM literature: Akaike’s
information criterion (AIC; Akaike, 1998) and the Bayesian information criterion (BIC;
Schwarz, 1978). Both are used comparatively, to evaluate which of two or more models
has the best combination of fit and complexity, with the model whose index value is
closest to zero being the best-fitting.
Class Size in Online High-School Courses
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The use of pre-determined shapes to describe the relationship between class size
and final grades, as in Models 2, 3 and 4, may not result in accurate descriptions of this
relationship. To overcome this issue, Model 5 used fractional polynomial (FP) analysis
with multilevel modeling. FP regression provides a flexible parametric method for
modeling non-linear relationships using the smallest possible number of parameters, and
allows the use of logarithms, non-integer powers, and repeated powers (Royston &
Altman, 1997). It was performed in Stata using the fp command.
After identifying the model that was best able to describe the relationship between
class size and student learning outcomes in general, we used that model to examine the
effects of class size on student learning outcomes for each subject.
Results
Optimal Class Size across All Subjects
The unconditional model, or Model 1, estimated the overall mean attainment
across classes as 71.59 points out of 100 (see Table 2). The between-class (level-2)
variance in attainment was estimated as 185.71, and the within-class/between-student
(level-1) variance in attainment as 617.77. The total variance was the sum of between-
class and within-class/between-student variance, i.e., 803.48. Intraclass correlation (i.e.,
between-class variance divided by total variance) was 0.231, indicating that 23.1% of the
observed variance in attainment was attributable to differences between classes. It should
be noted at this point that our dataset did not include entry scores, so the class effect was
not value-added.
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Model 2, which was used to examine a linear class-size effect, found that each
one-person increase in class size resulted in a 0.32-point increase in average final grade, p
< .001, and the effect size was 0.024. This linear relationship is illustrated in Figure 2.
In Model 3, the quadratic model, both class size (B = 1.10, p < 0.001) and class
size squared (B = -0.01, p < .001) were significantly correlated with average final grades,
indicating that the parabola shape fit the relationship between class sizes and learning
outcomes. The effect size for class size linear term increased to was 0.084, and the effect
size for class size quadratic term was -0.0009. Both indicators of overall model fit were
higher for Model 2 (AIC = 99749.40, BIC = 99778.50) than for Model 3 (AIC =
99737.86, BIC = 99774.23), indicating that the latter fit the data better than the former.
This suggests that the non-linear relationship between class size and final grade was a
reverse-U shape, with peak academic performance occurring at class sizes of around 45
students (see Figure 3) when all academic subjects were considered collectively.
In Model 4, class size was not significantly related to average final grades (B =
0.69, p = .41), and neither were the class-size quadratic and cubic terms, suggesting that
this model did not fit the relationship between class size and learning outcomes. Model
4’s AIC (99739.60) was lower than that of Model 2 (99749.40), but its BIC (99783.24)
was higher than Model 2’s BIC (99778.50), confirming that Model 4 did not fit the
relationships in the data better than Model 3 did.
For Model 5, before performing FP, it was necessary to determine the best powers
for each parameter. This required fitting 44 models, as shown in Table 3. FP comparison
indicated that the second model, with power of two and two, was significantly different at
the 0.05 level both from the other FP models and from the linear model. Model 5
Class Size in Online High-School Courses
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therefore utilized the powers reported (i.e., two and two), and the results of HLM are also
presented in Table 4. The first class-size quadratic term had a coefficient of 0.02, and the
second, of -0.0003. When a power repeats in an FP analysis, it is multiplied by another
ln(x). The equation for class size is as follows:
grades = 60.505 + 0.082 * class size2 -0.019 class size2 * ln(class size) equation 1
The resulting curve of Model 5 is shown in Figure 4, and suggests that increasing
a typical class’ size had a positive effect on its students’ learning outcomes until such size
reached around 45 people, after which it had a negative effect. The overall shapes of
Figures 3 and 4 were very similar, each being a reverse-U with a peak around 45; but
after the peak point, Figure 4 had a sharper drop than Figure 3 did. Model 5 had a smaller
AIC and BIC than either Model 2 or Model 3, suggesting that it fit the data better than
they did.
Optimal Class Size for Each Subject
Because the FP-based model best described the relationship between class size
and learning outcomes for all six academic subject areas taken together, FP analysis with
multilevel modeling was next performed for each subject separately. To allow each
subject different powers for different class sizes, the powers for each of these FP analyses
were determined by the model with the lowest deviance. The results are presented in
Table 5 and Figure 5.
English. The model results for English classes revealed a trend in which final
grades increased as class size increased, but this relationship was not significant (B1 = -
387.456, p = 0.166; B2 = 0.000, p = 0.288). In other words, English class size did not
have an impact on students’ final grades.
Class Size in Online High-School Courses
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Foreign languages. In foreign languages, student achievement was highest in
classes with 15 students, and above that level, the relationship between class sizes and
final grades was consistently negative: i.e., a person’s final grade tended to decrease as
class size increased (B1 = -581.240, p = 0.525 and B2 = 556.506, p = 0.57). However, the
relationship between foreign-language class sizes and final grades was not significant, as
shown in Table 5.
Science. The relationship of science-class size to final grades was similar to that
across all subjects, but the position of its peak was different (B1 = 0.003, p = 0.05; B2 = -
0.001, p = 0.06). Specifically, students’ final grades increased as class size increased until
the latter reached 35; then, their final grades decreased as class size increased further.
This relationship was statistically significant.
Math. The relationship between class sizes in math and students’ performance
was also parabolic: final grades increased as class size increased up to a maximum of 38
students, but decreased if class size rose beyond that point (B1 = 0.004, p = .004; B2 = -
0.001, p = 0.006). This relationship was statistically significant.
Social science. The relationship between class size and students’ final grades in
social-science subjects was very similar to that in math classes (B1 = 522.413, p < 0.001;
B2 = -353.297, p < 0.001), albeit with the turning point falling around a size of 42
students, as opposed to 38 in math classes. This relationship was significant.
Other subjects. The relationship between class sizes and students’ final grades in
classes that did not fit into any of the above five categories (e.g., art) was very similar to
the previously described situations in social-science and math classes (B1 = 2090.210, p =
Class Size in Online High-School Courses
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0.011; B2 = 1323.329, p = 0.005), albeit with the turning point falling around 35 students.
This relationship was also significant.
Discussion
This study represents an important contribution to the body of research on class
size in K-12 learning, and extends it to an online K-12 learning context. Specifically,
findings from the present study address common false expectations about online-class
size in K-12 settings. In contrast to face-to-face settings, online learning is unconstrained
by physical space, and this sometimes results in extremely large K-12 classes (e.g., more
than 300 students in one section: see Miron & Gulosino, 2016). Meanwhile, as part of
efforts to provide niche courses that are not available in certain geographic areas or not
taught in physical schools at all, online K-12 learning sometimes features extremely
small classes, with just one or two students in some sections (see Watson et al., 2015;
also see Figure 1). The results of the present research suggest that extreme online-class
sizes, in either direction, are likely to have negative impacts on students’ learning
outcomes.
On the one hand, this implies that class-size reduction might be helpful, if the
original size is above a certain threshold, which aligns with findings from the majority of
peer-reviewed papers that support class-size reduction (Zyngier, 2014). However, the
present findings are considerably more robust than those of studies using observational
data in traditional K-12 settings, due to an unusual characteristic of our study context: the
fact that the online instructors were not responsible for the curriculum, making it
extremely unlikely that they taught classes differently because of differences in student
numbers. As Ehrenberg et al. (2001) noted, small class sizes can affect teaching in two
Class Size in Online High-School Courses
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ways. First, instruction may be improved; and second, certain teaching practices may
become more effective. In the current study, given that the curriculum was fixed, the
effects of class-size differences that were identified should have stemmed mainly from
such differences themselves.
On the other hand, in line with the findings of Rice (1999) and Dustmann, Rajah,
and van Soest (2003), the current study’s results suggest that reducing class size, when it
is already at or below a certain threshold, may actually have a negative impact on
students’ learning outcomes. One possible explanation is that smallness may impede
learner-instructor interactions, which prior research has shown to have a positive effect
on learning, after controlling for students’ individual differences in motivation and
learning strategies (Lin, Zheng, et al., 2017).
It is also worth noting that the optimal class sizes for self-paced courses reported
in this study (i.e., 38 in math, 42 in social science, and 35 in other non-language subjects)
are much higher than the average sizes of face-to-face high-school classes (i.e., 24.2: see
Coopersmith, 2009). This calls into question prior studies’ recommendations that online
classes always be smaller than face-to-face ones (e.g., Qiu, Hewitt, & Brett, 2012;
Sorensen, 2014). This discrepancy could relate to special characteristics of the present
study’s virtual-school research setting: for instance, the previously discussed lack of
responsibility for curriculum development on the part of its teachers, which could have
reduced their preparation time and thus enabled them to effectively teach larger classes
than might normally be possible.
This study raises several policy issues. Its more striking findings include the sharp
differences among academic subject areas in terms of the impact of class size on
Class Size in Online High-School Courses
20
students’ final grades. This confirms that decision-makers should avoid one-size-fits-all
approaches to setting class sizes, and instead remain sensitive to different subject areas’
divergent requirements, as Rice (1999) contended. However, the present findings should
not be used to generate prescriptive guidelines for optimal class sizes in different
subjects; nor are they in any way intended to suggest that class size be used simplistically
as a measure of school quality. Rather, they indicate that when an online class is of an
extreme size – whether large or small it may be detrimental to students’ learning, at
least relative to similar classes of a more normal size.
This study’s results also imply that policymakers should be more cognizant of the
balance that must be struck between maximizing educational access and having small
classes. Expanding access and providing curricular choices are among the primary
purposes of offering online courses to K-12 students (Barbour & Reeves, 2009; Berge &
Clark, 2005; Cavanaugh & Blomeyer, 2007). However, these purposes should not be
achieved at the expense of students’ learning outcomes. As illustrated by the current
study, being members of a small class may in certain circumstances actually be harmful
to students’ learning. When offering niche courses that are unavailable in students’ own
schools, online-learning providers should consider these potential disadvantages of small
classes, alongside better-known issues such as cost.
Conclusions
This study has provided empirical evidence of both general and subject-specific
class-size effects in self-paced online high-school courses. Its examination of the
relationship between class size and students’ learning outcomes in multiple subjects was
a major departure from the prior literature, which has focused primarily on math (e.g., Li
Class Size in Online High-School Courses
21
& Konstantopoulos, 2016). The relationships between class sizes and students’ final
grades can be depicted as a reverse-U shape for math, social science, and other subjects
(e.g., arts). In these areas, as class size increased, final grades increased until the peak in
this curve was reached; and once the class size rose to any level beyond the peak, it had a
negative impact on students’ final grades. In English, foreign languages, and science,
however, the impact of class size on learning outcomes was non-significant.
These unique findings contribute to the study of online learning in multiple ways.
To the best of the researchers’ knowledge, this is the first study that examines class sizes’
relation to academic outcomes in an online K-12 setting. Amid ever-increasing numbers
of K-12 students taking courses online, and the prevalence of very small and very large
classes in virtual schools, this study provides clarification of key issues for policymakers
and school administrators tasked with setting and modifying class sizes. In addition, its
results refine and extend findings derived from face-to-face settings. For the most part,
the results of HLM analysis in the current study indicated a significant, non-linear
association between self-paced online classes’ sizes and their students’ final grades. The
identification of the parabolic nature of this relationship may help to disentangle the
mixed results obtained from past research in face-to-face settings.
Several limitations of the current research need to be noted. First, it used
observational data, making it very difficult to isolate confounding or omitted variable
bias. The assignment of students and teachers to particular classes, for example, could
have been influenced by students’ characteristics – such as motivation and previously
identified abilities – as well as by interventions on the part of instructors, principals, and
parents. These omitted variables relating to student placement are difficult to measure,
Class Size in Online High-School Courses
22
and accordingly, causal inferences should be drawn from this study only with caution. In
future research, this limitation can be addressed in one of two ways: through a true
experimental design in which online students are randomly assigned to classes of
different sizes, or through modes of statistical analysis that can appropriately account for
omitted variables (Ehrenberg et al., 2001). Instrumental variables, used in combination
with regression discontinuity, have the potential to address the unobserved-variable issue
(see Konstantopoulos & Shen, 2016 for example), but a strong instrument that is
unrelated to unobserved variables had yet to be developed at the time of writing.
Second, the class-size effects we reported in this study with regard to self-paced
courses were relatively small, in keeping with the effect sizes reported in many meta-
analyses (see Hattie, 2005). Among many factors that have been shown to influence
students’ learning outcomes (e.g., feedback, instruction, and their own study skills), class
size has consistently been ranked at the lower end of the spectrum (Hattie, 2005, 2008).
The inherent limitations of this study’s data prevented examination of other factors that
might have explained some of the observed differences between classes. Although
reason-for-enrollment data was collected, a parsimonious model that fit this and the other
data well without violating statistical assumptions could not be identified within the time
available. And third, this study only examined online learning in a self-paced context,
meaning that its findings may not be generalizable to other online delivery modes such as
cohort-based online learning.
Future studies should aim to further disentangle the effects of class size by
considering additional factors. First, the difficulty levels of courses within a subject (e.g.,
Algebra versus Advanced Placement Calculus) should be included as model covariates,
Class Size in Online High-School Courses
23
to help determine whether the widely theorized positive effects of small class sizes are
present, but masked by the examination of hard and easy classes jointly. Second, course-
design factors that affect the amounts of time teachers spend preparing for classes and
providing feedback should be measured, as this could provide a clearer understanding of
the mechanism(s) through which class size affects students’ learning outcomes (e.g.,
Rice, 1999). Third, credit-recovery students may have lower levels of self-regulation
skills than other categories of students (Watson & Gemin, 2008), which in turn could
affect their learning outcomes. Therefore, including the percentage of credit-recovery
students in each class might shed further light on the small effect sizes reported in this
study. Lastly, in addition to final grades, we recommend that future research on the
effects of class size use other types of outcome variables, such as student satisfaction and
the amount of student-teacher interaction. Broader assessments of this kind will be
especially important when research in this area is extended to include other types of
online-course settings.
Class Size in Online High-School Courses
24
References
Akaike, H. (1998). Information theory and an extension of the maximum likelihood
principle. In Selected Papers of Hirotugu Akaike (pp. 199–213). Springer, New
York, NY.
Aragon, S. R. (2003). Creating social presence in online environments. New Directions
for Adult and Continuing Education, 2003(100), 57–68.
https://doi.org/10.1002/ace.119
Arbaugh, J. B., & Benbunan-Fich, R. (2005). Contextual factors that influence ALN
effectiveness. Learning Together Online: Research on Asynchronous Learning
Networks, 1, 123–144.
Arzt, J. (2011). Online Courses and Optimal Class Size: A Complex Formula. Online
Submission.
Babcock, P., & Betts, J. R. (2009). Reduced-class distinctions: Effort, ability, and the
education production function. J. Urban Econ., 65(3), 314–322.
Barbour, M. K. (2017). K-12 online learning and school choice : Growth and expansion
in the absence of evidence. In R. A. Fox & N. K. Buchanan (Eds.), The Wiley
handbook of school choice (pp. 421–440). Hoboken, NJ: Wiley Blackwell.
Barbour, M. K., & Reeves, T. C. (2009). The reality of virtual schools: A review of the
literature. Computers & Education, 52, 402–416.
https://doi.org/10.1016/j.compedu.2008.09.009
Bascia, N. (2010). Reducing class size: What do we know. Ontario Institute for Studies in
Education.
Class Size in Online High-School Courses
25
Berge, Z. L., & Clark, T. (2005). Virtual schools: Planning for success. New York:
Teachers College Press.
Blatchford, P., Bassett, P., & Brown, P. (2011). Examining the effect of class size on
classroom engagement and teacher–pupil interaction: Differences in relation to
pupil prior attainment and primary vs. secondary schools. Learning and
Instruction, 21(6), 715–730.
Blatchford, P., Russell, A., Bassett, P., Brown, P., & Martin, C. (2007). The effect of
class size on the teaching of pupils aged 7 – 11 years. School Effectiveness and
School Improvement, 18(2), 147–172.
https://doi.org/10.1080/09243450601058675
Brühwiler, C., & Blatchford, P. (2011). Effects of class size and adaptive teaching
competency on classroom processes and academic outcome. Learning and
Instruction, 21(1), 95–108.
Burruss, N. M., Billings, D. M., Brownrigg, V., Skiba, D. J., & Connors, H. R. (2009).
Class Size as Related to the Use of Technology, Educational Practices, and
Outcomes in Web-Based Nursing Courses. Journal of Professional Nursing,
25(1), 33–41. https://doi.org/10.1016/j.profnurs.2008.06.002
Cavanaugh, C. (2001). The effectiveness of interactive distance education technologies in
K-12 learning: A meta-analysis. International Journal of Educational
Telecommunications, 7(1), 73–88.
Cavanaugh, C., & Blomeyer, R. L. (2007). What works in K-12 online learning. Eugene,
OR: International Society for Technology in Education.
Class Size in Online High-School Courses
26
Cavanaugh, C., Gillan, K. J., Kromrey, J., Hess, M., & Blomeyer, R. (2004). The effects
of distance education on K-12 student outcomes: A meta-analysis. Learning Point
Associates/North Central Regional Educational Laboratory (NCREL).
Coopersmith, J. (2009). Characteristics of public, private, and Bureau of Indian
Education elementary and secondary school teachers in the United States: Results
from the 2007–08 Schools and Staffing Survey. Washington, D.C: National Center
for Education Statistics.
Education Next. (2007). Program on Education Policy and Governance (PEPG) 2007
Survey. Hong Kong. Retrieved from http://educationnext.org/files/EN-
PEPG_Complete_Polling_Results.pdf
Ehrenberg, R. G., Brewer, D. J., Gamoran, A., & Willms, J. D. (2001). Class size and
student achievement. Psychological Science in the Public Interest, 2(1), 1–30.
Elliot, A. J., Dweck, C. S., & Yeager, D. S. (2017). Handbook of competence and
motivation: Theory and application (2nd ed.). Guilford Publications.
Finn, J. D., Pannozzo, G. M., & Achilles, C. M. (2003). The “Why’s” of Class Size:
Student Behavior in Small Classes. Rev. Educ. Res., 73, 321–368.
Harfitt, G. J. (2013). Why ‘small’can be better: An exploration of the relationships
between class size and pedagogical practices. Research Papers in Education,
28(3), 330–345.
Hattie, J. (2005). The paradox of reducing class size and improving learning outcomes.
International Journal of Educational Research, 43(6), 387–425.
https://doi.org/10.1016/j.ijer.2006.07.002
Class Size in Online High-School Courses
27
Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to
achievement. Routledge.
Isenberg, E. P. (2010). The effect of class size on teacher attrition: Evidence from class
size reduction policies in New York State. US Census Bureu Center for Economic
Studies.
Kokkelenberg, E. C., Dillon, M., & Christy, S. M. (2008). The effects of class size on
student grades at a public university. Economics of Education Review, 27(2), 221–
233. https://doi.org/10.1016/j.econedurev.2006.09.011
Konstantopoulos, S., & Shen, T. (2016). Class size effects on mathematics achievement
in Cyprus: evidence from TIMSS. Educational Research and Evaluation, 22(1–
2), 86–109. https://doi.org/10.1080/13803611.2016.1193030
Konstantopoulos, S., & Sun, M. (2014). Are teacher effects larger in small classes?
School Effectiveness and School Improvement, 25(3), 312–328.
Li, W., & Konstantopoulos, S. (2016). Class Size Effects on Fourth-Grade Mathematics
Achievement: Evidence From TIMSS 2011. Journal of Research on Educational
Effectiveness, 0(0), 1–28. https://doi.org/10.1080/19345747.2015.1105893
Lin, C.-H., & Warschauer, M. (2015). Online foreign language education: What are the
proficiency outcomes? The Modern Language Journal, 99(2), 394–397.
https://doi.org/10.1111/modl.12234_1
Lin, C.-H., Zhang, Y., & Zheng, B. (2017). The roles of learning strategies and
motivation in online language learning: A structural equation modeling analysis.
Computers & Education, 113, 75–85.
https://doi.org/10.1016/j.compedu.2017.05.014
Class Size in Online High-School Courses
28
Lin, C.-H., Zheng, B., & Zhang, Y. (2017). Interactions and learning outcomes in online
language courses. British Journal of Educational Technology, 48, 730–748.
https://doi.org/10.1111/bjet.12457
McNeish, D. M., & Stapleton, L. M. (2016). The effect of small sample size on two-level
model estimates: A review and illustration. Educ. Psychol. Rev., 28(2), 295–314.
Miron, G., & Gulosino, C. (2016). Virtual schools report 2016: Directory and
performance review. Retrieved from Boulder, CO.
Mupinga, D. M., & Maughan, G. R. (2008). Web-based instruction and community
college faculty workload. College Teaching, 56(1), 17–21.
Oliver, K., Kellogg, S., & Patel, R. (2012). An investigation into reported differences
between online foreign language instruction and other subject areas in a virtual
school. CALICO Journal, 29(2), 269–296.
Orellana, A. (2006). Class size and interaction in online courses. Quarterly Review of
Distance Education, 7(3), 229–248.
Qiu, M., Hewitt, J., & Brett, C. (2012). Online class size, note reading, note writing and
collaborative discourse. International Journal of Computer-Supported
Collaborative Learning, 7(3), 423–442. https://doi.org/10.1007/s11412-012-9151-
2
Rice, J. K. (1999). The Impact of Class Size on Instructional Strategies and the Use of
Time in High School Mathematics and Science Courses. Educational Evaluation
and Policy Analysis, 21(2), 215–229.
https://doi.org/10.3102/01623737021002215
Class Size in Online High-School Courses
29
Royston, P., & Altman, D. G. (1997). Approximating statistical functions by using
fractional polynomial regression. Journal of the Royal Statistical Society: Series
D (The Statistician), 46(3), 411–422. https://doi.org/10.1111/1467-9884.00093
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2),
461–464.
Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling
change and event occurrence. Oxford university press.
Sorensen, C. (2014). Classrooms Without Walls: A Comparison of Instructor
Performance in online Courses Differing in Class Size. J. Online Learn. Teach.,
10(4), 569.
Taft, S. H., Perkowski, T., & Martin. (2011). A framework for evaluating class size in
online education. The Quarterly Review of Distance Education, 12(3), 181.
Tomei, L. (2006). The impact of online teaching on faculty load: Computing the ideal
class size for online courses. Journal of Technology and Teacher Education,
14(3), 531–541.
Watson, J., & Gemin, B. (2008). Promising practices in online learning: Using online
learning for at-risk students and credit recovery. Vienna, VA: International
Association for K-12 Online Learning.
Watson, J., Murin, A., Vashaw, L., Gemin, B., & Rapp, C. (2010). Keeping pace with K-
12 online and blended learning: An annual review of policy and practice.
Retrieved from http://www.kpk12.com/wp-
content/uploads/KeepingPaceK12_2010.pdf
Class Size in Online High-School Courses
30
Watson, J., Pape, L., Murin, A., Gemin, B., & Vashaw, L. (2015). Keeping pace with K-
12 digital learning: An annual review of policy and practice. Retrieved from
http://www.kpk12.com/wp-content/uploads/Evergreen_KeepingPace_2015.pdf
Zhang, Y., Liu, H., & Lin, C.-H. (2018). Research on class size in online K-12 learning.
In K. Kennedy & R. Ferdig (Eds.), Handbook of Research on K-12 Online and
Blended Learning (2nd ed., pp. 273–283). Pittsburgh, PA.
Zyngier, D. (2014). Class size and academic results, with a focus on children from
culturally, linguistically and economically disenfranchised communities. Evidence
Base, 1, 1–23.
Class Size in Online High-School Courses
31
Table'1. Reasons for Enrollment'
Enrollment reasons
Course unavailable
locally
Credit recovery
Learning preferences
Scheduling conflict
Other reasons
Total
Class Size in Online High-School Courses
32
Table 2. Hierarchical Linear Modeling for Class Size and Final Grades
Final grades
Model 4
Class size
0.69
(0.83)
Class size quadratic term
0.00
(0.07)
Class size cubic term
-0.00
(-0.51)
_cons
57.12***
(8.11)
Variance (between
class)
170.84***
(72.29)
Variance (within class)
617.4***
(452.47)
Observations
10,648
Intraclass correlation
AIC
99739.60
BIC
99783.24
Standard errors in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001
Class Size in Online High-School Courses
33
Table 3. Fractional Polynomial Comparisons for Class Size
Class Size in Online High-School Courses
34
Table 4. Fractional Polynomial Analysis for Class Size
Model 5
Class size term 1
0.082***
(0.015)
Class size term 2
-0.019***
(0.003)
_cons
60.505***
(1.809)
Random effect
Variance (between-
class)
170.725***
(12.14)
Variance (within-class)
617.737***
(8.77)
Standard errors in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001
Class Size in Online High-School Courses
35
Table 5. Fractional Polynomial Analysis of Class Size for Each Subject
Final grades
English
Foreign
language
Science
Math
Social
science
Others
Class size 1 power
-2
-2
3
3
-1
-2
class size 1
-387.456
-581.240
0.003
0.004**
522.413***
2090.210*
(-1.39)
(-0.64)
(1.93)
(2.86)
(3.65)
(2.53)
Class size 2 power
3
-2
3
3
-1
-2
class size 2
0.000
319.655
-0.001
-0.001**
-363.297***
-
1323.329**
(1.06)
(0.57)
(-1.86)
(-2.77)
(-4.15)
(-2.80)
Constant
54.748***
72.434***
67.385
59.076***
101.441***
79.470***
(13.64)
(30.14)
(28.30)
(23.83)
(18.06)
(50.16)
Variance between
classes
2.818***
2.545***
2.459***
2.716***
2.078***
2.268***
(25.88)
(35.64)
(23.63)
(32.42)
(20.57)
(30.16)
Variance within class
3.452***
3.205***
3.242***
3.269***
3.162***
3.196***
(129.40)
(213.36)
(160.15)
(173.03)
(205.90)
(248.91)
Observations
786
2,383
1,338
1,553
2,281
3,257
Standard errors in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001
Class Size in Online High-School Courses
36
Figure 1. Cumulative Percentage of Classes by Size
0
10
20
30
40
50
60
70
80
90
100
1357911 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Cumulative percentage
Class size
Class Size in Online High-School Courses
37
Figure 2. Linear Regression Fitting Line for the Effect of Class Size on Final Grades
Class Size in Online High-School Courses
38
Figure 3. Parabolic Regression Fitting Line for the Effect of Class Size on Final Grades
Class Size in Online High-School Courses
39
Figure 4. Fractional Polynomial Analysis of the Effect of Class Size on Final Grades
Class Size in Online High-School Courses
40
+
+
+
Figure 5. Fractional Polynomial Analysis of the Relationships between Class Sizes and
Final Grades, by Subject
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Empirical evidence on factors behind student success in secondary school online classes has been mixed and insufficient in its scope as well as data coverage. With a nationwide secondary school online class dataset with 26,345 students, this study attempts to identify factors of student success and first constructs a statistical model predicting the pass probability of online classes. The following student background variables are associated with a high pass rate: transfer students, graduation-year students, pass-experienced students, and students not re-registering for the course. With respect to learning activities, students who actively communicate with teachers/coordinators via messenger services or questions and answer sessions, or students who log in to the online class at the early stage of the semester are more likely to pass a course. Individual course characteristics are also found to be important for pass in courses requiring a summative exam, while courses for either subjects that have a good track record of students passing or courses for subjects that are taught by teachers with a good track record of students passing are correlated with a high pass rate. Logistic regression results suggest that the pass probability (odds ratio) is greatly increased when students have passing experience, actively interact with teachers/coordinators, or when the subject has a good student passing record.
Chapter
Research investigating why blended learning, despite many of its advantages, is usually difficult to scale up for classes of different size has been needed for a long time. Research data were obtained from 3 courses with different numbers of students: one course with 4 students, one course with 26 students, and one course with 94 students and the data were compared to identify factors that influence scaling up of blended education. All of the groups used Moodle as LMS. This study investigates differences in operational, instructional and technological factors between these three courses which adopted blended learning, in an effort to understand the challenges and obstacles inherent in the successful implementation of blended learning for classes of different size. Findings indicate that no significant differences exist in the effort required to set the course for each of the three groups, neither in managing the registration of students, however, significant differences existed in handling subsequent issues arising from selected delivery format options. Discussions about improving on-line and blended delivery methods are elaborated upon based on the research findings. We also discuss implications for deployment of blended learning for Universities.
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Student performance modelling is one of the challenging and popular research topics in educational data mining (EDM). Multiple factors influence the performance in non-linear ways; thus making this field more attractive to the researchers. The widespread availability of e ducational datasets further catalyse this interestingness, especially in online learning. Although several EDM surveys are available in the literature, we could find only a few specific surveys on student performance analysis and prediction. These specific surveys are limited in nature and primarily focus on studies that try to identify possible predictor or model student performance. However, the previous works do not address the temporal aspect of prediction. Moreover, we could not find any such specific survey which focuses only on classroom-based education. In this paper, we present a systematic review of EDM studies on student performance in classroom learning. It focuses on identifying the predictors, methods used for such identification, time and aim of prediction. It is significantly the first systematic survey of EDM studies that consider only classroom learning and focuses on the temporal aspect as well. This paper presents a review of 140 studies in this area. The meta-analysis indicates that the researchers achieve significant prediction efficiency during the tenure of the course. However, performance prediction before course commencement needs special attention.
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The number of K-12 students taking online courses has been increasing tremendously over the past few years. However, most research on online learning either compares its overall effectiveness to that of traditional learning, or examines perceptions or interactions using self-reported data; and very few studies have looked into the relationships between the elements of K-12 online courses and their students' learning outcomes. Based on student-, instructor-, and course-level data from 919 students enrolled in eight online high-school English language and literature courses, the results of hierarchical linear modeling and content analysis found that project-based assignments and high-level knowledge activities were beneficial to learning outcomes – though not necessarily among students who took these courses for credit-recovery purposes. The paper also discusses implications for both online course-design practices and future research on predictors of online-learning success.
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Class size is a crucial environmental factor for online administrators and educators to consider when designing K-12 online courses. Based on an examination of previous research on online class size in both K-12 and postsecondary settings, this chapter analyzes trends and research gaps in this area, and shows that there is no one-size-£ts-all solution to the ideal class size question. It suggests that it is vitally important to combine e¢ects of class size and other critical contextual factors (e.g., teaching, teacher experience, learning performance, interaction, subjects) in online learning to maximize students’ learning success. The study also provides practical and research recommendations for practitioners, policy-makers, and online instructors.
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The use of online learning at the K-12 level has seen exponential growth for much of the past two decades. Based on the limited research to date some students can experience success in the supplemental K-12 online learning environment, but other types of K-12 online learning are largely failing adequately to serve students. While proponents will argue that all types of K-12 online learning are forms of school choice, it is primarily cyber charter schools and course choice policies that are reflective of the policies and regulations proponents of online learning promote—as cyber charter schools and course choice policies are designed to open up markets to K-12 online learning providers. Yet, proponents continue to advocate for decreasing the amount of oversight for K-12 online providers. The combination of dramatic, unchecked growth and an almost complete inability to assure any measure of quality has resulted in abysmal student performance in many K-12 online learning environments.
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Interactions are the central emphasis in language learning. An increasing number of K-12 students take courses online, leading some critics to comment that reduced opportunities for interaction may affect learning outcomes. This study examined the relationship between online interactions and learning outcomes for 466 students who were taking high-school level online language courses in a Midwestern virtual school. Regression analysis was employed to examine how three broad types of interactions, learner-instructor, learner-learner and learner-content (Moore, 1989), affected students’ perceived progress and satisfaction. After controlling for demographic information, motivation and learning strategies, the results of multiple regression showed that learner-instructor and learner-content interactions had significantly positive effects on satisfaction, whereas learner-learner interaction did not affect satisfaction. Learner-content interaction was the only factor that affected perceived progress.
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As universities across the nation turn to online delivery formats for many of their courses, the question of optimal class sizes has become increasingly controversial. This article reviews the current multi-disciplinary research available to determine what, if any, guidance on online class size exists. The research to date offers no consensus regarding appropriate student-to-teacher ratios in online courses. The authors propose the use of three educational frameworks to guide class enrollment decisions that maintain educational quality: Bloom’s taxonomy, objectivist-constructivist teaching strategies, and the Community of Inquiry model. Further research is recommended to assess student learning outcomes across courses of varying size. (Note: see further research on this topic at: Taft, S.H., Kesten, K., & El-Banna, M.M. (2019, September). One size does not fit all: Toward an evidence-based framework for determining online course enrollment size in higher education. Online Learning Journal, 23(3), 188-233. doi: 10.24059/olj.v23i3.1534 URL: https://olj.onlinelearningconsortium.org/index.php/olj/article/view/1534)
Article
Students' active regulation of learning, through being motivated and a variety of cognitive and metacognitive strategies, is crucial to their online learning success. Despite the large numbers enrolled in online language courses, very little is known about students' motivation and strategy use in these learning environments, or how they may affect their online learning outcomes. This study helps fill this gap by examining students' motivation and learning-strategy use across a number of online language courses, and investigating the role of motivation and such strategies within the framework of self-regulated learning. Based on data about online language-learning strategies collected from 466 high-school-level online language students in a Midwestern virtual school, our findings indicated that online learning strategies operated at a moderate level in the process of foreign language-learning. Further analysis using structural equation modeling revealed that the use of online learning strategies predicted students’ online learning outcomes.
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With no physical walls, the online classroom has the potential to house a large number of students. A concern by some is what happens to the quality of instruction in courses with high enrollments. The purpose of this research was to examine online class size and its relationship to, and potential influence on, an instructor’s performance. Results were mixed indicating that class size had a positive relationship with some the variables meant to measure online instructor performance and a negative relationship with others. Online class size was seen as having the most concerning relationship and potential influence on an instructor’s ability to provide quality feedback to students and for his/her expertise to be used consistently and effectively.
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Class size reduction policies have been widely implemented around the world in recent years. However, findings about the effects of class size on student achievement have been mixed. This study examines class size effects on fourth-grade mathematics achievement in 14 European countries using data from TIMSS (Trends in International Mathematics and Science Study) 2011. We employ quasi-experimental methodology (i.e., instrumental variables and regression discontinuity) to facilitate causal inferences of class size effects. Although we find some evidence of class size effects in Romania and the Slovak Republic, overall there are no systematic patterns of class size effects across countries. The results indicate that in most European countries class size reduction may not improve mathematics achievement in fourth grade. 2016
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This important volume features contributions by top virtual school practitioners and experts in the field who talk about what virtual schools can do to plan for success. If you are interested in the details of launching virtual learning options for your school, district, region, or state, you likely have more questions that answers. Where do I begin? What kind of personnel will I need? What providers and resources are available to me? How do I hire and train teachers? What are the costs involved? This authoritative volume will answer these questions and many more.
Article
Class size reduction has been viewed as one school mechanism that can improve student achievement. Nonetheless, the literature has reported mixed findings about class size effects. We used 4th- and 8th-grade data from TIMSS 2003 and 2007 to examine the association between class size and mathematics achievement in public schools in Cyprus. We employ instrumental variables methods, and take advantage of a regression discontinuity design to examine causal effects of class size on mathematics achievement. The results indicate a non-significant relationship between class size and mathematics achievement in 8th grades. However, there is evidence of positive class size effects in 4th grade. The gender gap is significant and favoured males in 4th grade and females in 8th grade. SES indexes such as parental education and items in the home are positively and significantly related to mathematics achievement. Teacher and school variables are not significantly related with mathematics achievement.