
Inverting a Developmental Mathematics classroom—A Model that uses
Technology and Best Practices to ensure Developmental Student Success
Abstract
The inverted classroom model was motivated by the limited research regarding this delivery
and its effects on developmental mathematics students in a community college. The model
consists of a set of pre-module videos with lectures and examples; a daily check-in with
faculty to ensure that students are watching videos and taking notes correctly; and daily ingroup and in-class exercises that can be used to enhance the materials that were delivered
online. Finally, the model delivers an online exam review and an exam check in period with
students that struggle with exams or doing poorly in class. Assessment results from various
student surveys and class comparison statistics are shown. The class format, results and
assessments are included and the results are positive.
Introduction
The number of students that take developmental mathematics across community colleges in the
country is increasing (Hodges & Kennedy 2004). These students often fall one or up to three
levels down from college-level courses. Reports that only a handful of those who placed into the
lowest levels of developmental mathematics ever pass college algebra (Boylan, 2011 ) Many
models and tools are being developed by schools across the country to help these developmental
students step up to where they need to be and succeed. The completion agenda is becoming a
national trend and colleges need to develop systems, pathways and courses to help these students
succeed. Math success is an institutional responsibility (Boylan, 2011)
One of the models introduced in the recent years deals with having the students work in an
inverted set-up where they listen to lectures at home and perform higher order skills in the
classroom. This inverted model asserts that based on Bloom’s taxonomy students can perform
the lower-cognitive skills on their own, and come to class to assimilate and perform the higher
cognitive skills in the classroom with their teacher. This model ensures that the teacher presence
is there “to design, facilitate, and direct the cognitive and social presence for the purpose of
realizing personally meaningful and educationally worthwhile learning outcomes (Garrison,
Anderson & Archer, 2000).
The model predicts that if a student can successfully listen and master a skill with the teacher and
a group, the student will be more likely to succeed. This has been proven in many studies in
engineering schools (Papadopoulos, Santiago-Roman & Portela.(2010) as well Statistics (Dollar
& Seif) and Economics (Lage et al.) courses, but very little research exists in developmental
education with students in community colleges. Research has shown that developmental
students test into developmental courses by placing lower in the cognitive skills tests (Gerlaugh,
Thompson, Boylan, & Davis, 2007). This would fit this model well, by allowing students to
perform lower cognitive skills like listening and taking notes to be done on their own. Sedlacek
(2004) argues that the weaker a student's cognitive skills, the more important other affective
factors in student success. These affective factors include, attitude toward learning, motivation,
autonomy, willingness to seek and accept help, desire to affiliate with peers or instructors, and
willingness to expend effort on academic tasks (Sedlacek, 2004). The bulk of the model tries to
tackle each affective behavior directly.
Motivation and attitude are closely linked ( Hannula 2006). Overcoming fear of failure and
believing in the possibility of achievement are key to student success( Hammerman & Goldberg,
2003). In this model by giving positive value to a relatively low cognitive task, the student loses
the fear of failure because watching a video and taking notes is significantly easier than
homework problems. The student begins to tackle the motivation, fear and attitude toward
learning factors. The importance of the role of the teacher in identifying and supporting
struggling math students is undeniable (Middleton &Spanius, 1999). In this model the dailycheck in allows the teacher to identify and support a struggling student early into the course and
it tackles the affective factor of autonomy, willingness to seek help and consequently to expend
effort on academic tasks. The model goes one step further in allowing developmental students to
interact in groups daily thus creating a social presence where the student can communicate
purposefully in a trusting environment, and develop inter-personal relationships by way of
projecting their individual personalities (Garrison , 2000)
Although there is a large body of research on developmental students and their affective
behaviors. Little is known about how an inverted model can affect developmental students in
community college mathematics courses. In this study, the model looks at the practice of
inverting the classroom and the direct effect on the affective behaviors that are often associated
with student failure in these courses. The study provides missing information that can inform
practice and research with a community college perspective.
The Inverted Classroom Model
The “inverted” classroom model is a relatively new phenomenon in Developmental Ed, which
began primarily as a portion of the NCAT Emporium Model of instruction. In the “Inverted
Classroom” events that take place inside the classroom now take place outside the classroom and
vice versa (Lage et al.) Inverted instruction usually requires that the content lecture take place
outside of the classroom usually through videos or power point slides that can be viewed online.
The in-class work then becomes the activities that enhance and incorporate the learning of the
material.
The inverted class model designed for this project required the use of videos through
Coursecompass. The videos were presented as daily homework assignment. The students were
required to watch the videos prior to attending class and to provide evidence of their
participation they submitted daily video notes for evaluation. The teacher would then have a
daily “check-in” with each student to verify that the videos had been watched. The notes had to
be carefully prepared based on a rubric before the students could receive credit for their
homework. During class and while the teacher was checking-in with each student, the other
students worked on in-class problems and/or projects that were directly related to the previous
evening video lecture. Students were expected to work in groups as the teacher graded the daily
homework. After the teacher checked in with each student, the class was then free to ask
questions about the group problems or projects. The teacher worked primarily with the students
that were falling behind or had problems with the assignment. At the end of the period students
would post solutions of the group assignments on the board for open class discussion. If the
material was a “threshold” concept, or one that required additional practice, the same videos
were assigned as homework for the next evening. Students were expected to re-write notes and
emphasize their video notes on the material that they had discovered to be challenging during the
team exercises. The second day the students would bring their video notes for another daily
check in. In the meantime the class was working on standard “homework” problems that were
done during class with their respective groups.
Since the study was performed in a developmental math classroom, many of the components of
the model were designed to work on the affective factors of developmental students. Sedlacek
(2004) argues that the weaker a student's cognitive skills, the more important other affective
factors in student success.
By making video watching the daily homework, the student had less of a cognitive load to
perform on their own and had a more positive attitude toward learning because the fear to fail at
watching a video is relatively low. The cognitive skills to watch and write notes from videos are
low and the risk of not performing the task correctly is decreased. By providing the students
with instruction and support on how to positively watch and record video messages; students feel
more confident that the homework will be relatively easy to perform. The affective behavior of
positive attitude toward learning can begin to change by having positive daily outcomes.
Since the daily video homework was required, the model allowed for points to be used to
measure the success of the activity. This was created to directly work on the motivation of the
student to perform the task. If the video watching portion is not validated, the student might not
value it and will not perform it. Since watching the video is imperative to understanding the
material, the design must allow for validity by grading the activity of note-taking. This affects
the motivation factor of developmental students. This measure also allows for student to not
hide under autonomy, since the teacher will have daily individual check-in with students. The
teacher will know immediately if the student is having problems with the assignment or with any
other factors that may contribute to the success in the class. Furthermore, if the teacher performs
daily check-in the student is no longer required to seek and ask for help. Both the teacher and
the student will know when the student is struggling and they can work to overcome the affective
barriers.
Finally, the affective factor of students to affiliate with peers and instructors is directly imbedded
into the model. Students will deal daily and directly with the instructor and their peers. The
instructor daily check-in will allow the student to interact with the teacher, and the a daily group
and team projects as well as team homework allows the student to work in groups with
classmates creating relationship and connections that might not have been otherwise available.
Activities and Outcomes
In addition to the inverted classroom model, the students in this study were required to watch
video reviews of in-class Exam preparation reviews, as well as periodic check in with teachers if
their overall class grade started to decrease. Students that received a grade of C- or lower in any
exam were expected to meet with the teacher to debrief on the exam and to go over test and time
management skills.
During the observation of the study students in these courses were given surveys regarding their
experience in the inverted classroom. Students generally indicated that they liked the inverted
method over the traditional format (82%) and that they felt their learning was at average or above
average most of the time (84%). A great majority of the class felt that the classroom time was
either review or learning time (91%) while 95% of them felt that they were highly or above
average engage in the course during the course time. The majority of the class (77%) completed
the “math homework” in class and were able to watch the videos daily before class (75%). The
videos were also described as additional resources by 25% of the students. They felt that when
they were unable to perform a task at home or during exam review they would review the videos
to help them increase understanding.
The strongest evidence of the effectiveness of the inverted classroom model over the alternative
“traditional” format was the overall class-grade distribution. In the traditional classroom the drop
rate for students in the developmental courses over the past three years was 39%. The drop rate
using the inverted method fell to 18 %.( n=80). In other words the class was able to keep over 80
% of the students in the class as opposed to the national average of about 66%. The grade
distribution of the remainder students also saw a slight improvement in the A and B grades of
about 23% and 24% for both the inverted and traditional courses. The major increase of passing
students occurred in the grade of C. The traditional classroom had an average of 27% C grades
at the end of the course, this was definitely improved in the inverted classroom were 41% of the
class passed with a C. Overall the traditional lecture classroom had 78% of the students that
remained in the class passing with a C or better. The inverted method had a 93% of the students
passing with a C or better. The overall numbers show that the students stayed in the class and
more of them were successful in the completion of the course.
Clearly, further data must be taken over longer periods of times to determine if the numbers
sustain at the same rates and that the students continue improve through the developmental
courses. Also more data pertaining to the success rate of the passing students in subsequent
courses is required to determine if the passing students were able to perform beyond the course
studied on this research.
Conclusions
The initial assessment of the inverted model for developmental mathematics courses is generally
positive and justifies further studies and development for further use outside of a few classrooms.
The inverted classroom model will be evaluated by other faculty members using the same
methods to see if the model is transferable with the same results in other parts of the mathematics
sequence. The inverted model presented on this paper will be used for the platform to deliver a
unified methodology to further the study of this process.
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