A Flipped Classroom Approach to Supporting At-Risk University Mathematics Students: Shifting the Focus to Pedagogy

Abstract

Many colleges and universities struggle to support underprepared first-year mathematics students [1]. A flipped classroom model is a promising approach to address at-risk, higher education mathematics students because it allows for increased interaction and support within the classroom after students have viewed instructional videos at home. However, previous research is somewhat limited with respect to examining in-class pedagogy in a flipped classroom. The purpose of the current study was to examine a specific set of in-class strategies that were used after students viewed content-specific and skill-based videos outside of the classroom. Specific in-class pedagogical strategies included making connections between mathematical ideas explicit [1], focusing on rich problem-solving tasks that support multiple solution strategies [2], encouraging peer-led collaborative learning [1-3]; and using diagnostic and formative assessments [4]. These strategies were tested with two mathematics classes of university students (n=62) in the Faculty of Business and Information Technology. Half the students enrolled in the course had previously failed or withdrawn from the course at least once; the other half were new students in the program. After employing technology to flip the classroom and combining this with supportive in-class pedagogy, 92% of the students (n=57) passed the course with an average grade of 76%. An end-of-course survey indicated that over 90% of students rated their overall experience with the course as very good or excellent, with a mean score of 4.5 on a five-point Likert scale. On average, students rated the following in-class strategies as being helpful to very helpful for supporting their understanding business math concepts: collaborative problem solving, support from in-class tutors (pre-service teacher candidates), and written feedback on assignments with Likert scores ranging from 4.1 to 4.5 on a five-point scale. Student comments on the open-ended survey questions were consistent with the quantitative ratings with the majority of comments referencing the in-class collaborative problem-solving approach and the support of the in-class tutors as helpful for their learning.

Full text

A FLIPPED CLASSROOM APPROACH TO SUPPORTING AT-RISK
UNIVERSITY MATHEMATICS STUDENTS: SHIFTING THE FOCUS TO
PEDAGOGY
A. Lesage, R. Kay, D. Tepylo
Ontario Tech University (CANADA)
Abstract
Many colleges and universities struggle to support underprepared first-year mathematics students [1].
A flipped classroom model is a promising approach to address at-risk, higher education mathematics
students because it allows for increased interaction and support within the classroom after students
have viewed instructional videos at home. However, previous research is somewhat limited with respect
to examining in-class pedagogy in a flipped classroom. The purpose of the current study was to examine
a specific set of in-class strategies that were used after students viewed content-specific and skill-based
videos outside of the classroom. Specific in-class pedagogical strategies included making connections
between mathematical ideas explicit [1], focusing on rich problem-solving tasks that support multiple
solution strategies [2], encouraging peer-led collaborative learning [1-3]; and using diagnostic and
formative assessments [4]. These strategies were tested with two mathematics classes of university
students (n=62) in the Faculty of Business and Information Technology. Half the students enrolled in
the course had previously failed or withdrawn from the course at least once; the other half were new
students in the program. After employing technology to flip the classroom and combining this with
supportive in-class pedagogy, 92% of the students (n=57) passed the course with an average grade of
76%. An end-of-course survey indicated that over 90% of students rated their overall experience with
the course as very good or excellent, with a mean score of 4.5 on a five-point Likert scale. On average,
students rated the following in-class strategies as being helpful to very helpful for supporting their
understanding business math concepts: collaborative problem solving, support from in-class tutors (pre-
service teacher candidates), and written feedback on assignments with Likert scores ranging from 4.1
to 4.5 on a five-point scale. Student comments on the open-ended survey questions were consistent
with the quantitative ratings with the majority of comments referencing the in-class collaborative
problem-solving approach and the support of the in-class tutors as helpful for their learning.
Keywords: flipped classroom, university, mathematics, at-risk.
1 INTRODUCTION
Many colleges and universities are grappling to support students in first year mathematics courses [1]
where failure rates are increasing and grades are decreasing [4]. Students not only struggle in pure
mathematics, but also with the mathematics needed for applied disciplines such as business [7]. While
there is substantial research exploring individual and institutional variables that predict a lack of success
in introductory mathematics courses, there is less research examining how changes in mathematics
pedagogy affect student learning and success [6].
One approach to deal with this problem is flipping the classroom where students watch instructional
online videos outside of class, then work with their peers and the instructor on problems and application
exercises in the classroom [8-9]. A flipped classroom approach can help students construct meaning
[10-11], uncover misconceptions [12-14], increase engagement and motivation [13, 15, 16], and improve
peer and student-teacher interactions [17, 18, 23]. However, research on the flipped classroom is limited
with respect to in-class instructional strategies and design of learning activities [20]. The purpose of the
current study was to examine a specific set of in-class strategies used after students viewed content-
specific and skill-based videos outside of the classroom.
2 METHODOLOGY
2.1 Participants
The research participants for this study included 62 undergraduate students enrolled in two sections of
a first-year business mathematics from January to April 2019. Both sections of the course included
Proceedings of ICERI2019 Conference
11th-13th November 2019, Seville, Spain
ISBN: 978-84-09-14755-7
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students who had failed or withdrew from the course in the previous term. Approximately half of the
students enrolled in the course had failed or withdrawn from the course at least once; while the other
half were new students in the business program.
2.2 Context
For many years, the first-year business math course at the Ontario Tech University has been a
bottleneck course within the Bachelor of Commerce program. Previous attempts to address this issue
focused on changing class size and conducting screening tests. Both strategies met with limited
success. This research documents efforts to change the pedagogy within the course to address the
problem of underprepared mathematics students.
Throughout the Winter 2019 term, two of the authors (mathematics teacher educators) worked
collaboratively to change the design, pedagogy and assessment practices of the Business Math I
course. The authors co-planned, implemented and assessed two sections of the course. The
mathematics and business concepts covered in the alternative Business Math I sections were
comparable to the other Business Math I sections taught previously or concurrently. However, the
alternative sections of the course incorporated features of effective mathematics instruction previously
highlighted in research, including:
• Making connections between mathematical ideas explicit [1];
• Focusing on rich problem-solving tasks that support multiple strategies while building efficient
procedures [2];
• Encouraging peer-led collaborative learning [1-3]; and
• Using diagnostic and formative assessments [5].
2.3 Teaching Strategies
A flipped classroom model was central to the organization of the revised Business Math I course. The
flipped classroom model for weekly classes was communicated to students through a detailed
description in the course outline, via the learning management system (LMS) email before the course
began and verbally during the first few weeks of classes.
The flipped classroom structure repeated weekly in the following sequence:
1 Introduce weekly course content through two short, direct instruction videos focussing on
vocabulary and business mathematics examples;
2 Students viewed videos prior to attending weekly lectures;
3 During weekly classes, students work collaboratively to solve business math context problems (of
varying degrees of complexity) on whiteboards mounted to the walls around the classroom;
4 During weekly tutorials students continued to work collaboratively to solve problems. These
problems were a continuation of concepts explored in the lecture or, occasionally, we introduced
them to new technology tools (e.g., Excel Solver).
It is important to note that during in-class collaborative problem-solving, the instructors did not model
the mathematical solution strategy we viewed as most efficient. Instead, we promoted productive
struggle to help students build their own efficient procedures. Students worked together to solve a
problem in a way that made sense to them. We encouraged students to collaborate with members of
their group or move about to speak with other students in the classroom. When most groups had arrived
at an appropriate solution, various groups shared their solution strategies with the class or with the
instructor, depending on time. Collaborative problem solving and classroom discourse, often lead to
multiple solutions for a problem - all of which were generalizable to other situations.
Eleven preservice teachers supported these collaborative problem-solving efforts, during lectures and
tutorials, in their second semester of a four-semester Bachelor of Education program. All of the
preservice teachers were preparing to teach secondary school mathematics. The third author taught the
Secondary School Mathematics Methodology course in the Bachelor of Education program to the
preservice teachers taking part in this study. Throughout the Math Methodology course (taught in the
same semester as the Business Math I course) we encouraged the preservice teachers to make
connections between mathematical ideas explicit; promote productive struggle while building efficient
procedures; and engage in purposeful classroom math discourse. The instructor also provided
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opportunities for preservice teachers to discuss how to support the Business Math I students’ sense-
making and how to provide formative feedback to the Business Math I students on their solution
strategies. The instructor and preservice teachers collaboratively created potential questions and
prompts that they could use with the Business Math I students to improve mathematical and business
understanding.
As the Business Math I course progressed, the business students’ understanding evolved from
numerical solutions to in-class problems to algebraic strategies / solutions. Throughout the semester,
we kept a focus of making sense of the problem and making connections to business math concepts
explored in the course. Our focus on sense-making was foundational to our pedagogical approach.
Sense-making differs from a traditional problem-solving approach as it does not focus on students
mirroring the instructor’s preferred solution strategy. Sense-making is student-focused and requires
students to take ownership in the problem-solving process. Students must make sense of the problem
and determine how to solve it in a way that makes sense to them.
2.4 Data Collection
To collect information about the flipped classroom approach, we administered a short survey after the
final exam by the assigned university proctor. The survey included eleven 5-point scale Likert questions
and two open-ended questions. The Likert questions were specific to teaching practices (n=6) and
students’ perspective / math efficacy (n=5). The two open response questions sought feedback on
aspects of the course students found most useful / applicable to their learning and requested
suggestions for improving the course for future students. Most students completed the survey (54/62)
with return rate of 87%. We measured learning performance using final course grades.
3 RESULTS
3.1 Student Perceptions
The mean scores of student responses to the 5-point scale Likert survey questions specific to
pedagogical approaches indicate that most of the students agreed that the teaching strategies used in
this course were helpful for their learning. Over 90% of the students agree that the overall course
experience helped them learn. Nine out of ten students agreed that the collaborative approach and
written formative feedback were the most helpful strategies. Three-quarters of the students agreed that
the written formative feedback was helpful for learning (Table 1).
Table 1. Survey Data on Flipped Classroom Approach for At-Risk University Math Students (n=54)
Mean(SD)
% Disagree1
% Agree2
Overall Course Experience
4.5 (0.7)
0%
91%
Collaborative Problem Solving was Helpful
4.6 (0.6)
0%
94%
Preservice Teachers were Helpful
4.4 (0.8)
6%
89%
Written Formative Assessment was Helpful
4.1 (1.0)
6%
74%
1 - Combination of Strongly Disagree and Disagree responses
2 - Combination of Strongly Agree and Agree responses
3.2 Student Comments
The open-ended survey responses support the Likert scale ratings of the instructional strategies. The
majority of student comments (16/26; 61.5%) specifically referenced collaborative problem solving
strategies as most helpful for learning. An additional five student comments referenced the course
tutorials that focused on collaborative problem solving supported by preservice teachers. As such, 81%
(21/26) of the open-ended survey responses highlighted the collaborative problem solving approach
used in lectures and tutorials as most helpful for learning. Sample student comments included:
“Collaborative working and feedback in person was easy, helped me finish and understand
assignments.”
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“The things that I've found most helpful while learning in this course is that the teachers got
us to work together in small groups and hear different thought processes. It helped us
answer our own questions and clearly see what mistakes were being made.”
“The best way of learning is with a team, and I find that most effective.”
“I love … the collaborative aspect to the learning with the white boards.”
“I loved the in-class learning where we do work and word problems. It really helped me
learn.”
“I found the teacher assistants helping us very important.”
“I found everything useful, but the video and tutorials were the best. The videos
summarized everything quickly and the tutorials helped understand further.”
“[I liked that there were] no boring lectures … [and] in class [we did] problems making us
move around, work and learn”
3.3 Learning Performance
Overall, students completing the alternative version of Business Mathematics I were successful. The
course average for students who passed the course was 76% (SD=10.3). Thirty-seven percent of the
students (n=23) attained a grade of A- to A+. Thirty percent (n=19) achieved a grade of B- to B+. Only
five students (8%) failed the course and four of these students elected to not write two or more of the
required course examinations.
An independent t-test, revealed the final grades for the alternative flipped classroom approach used in
this study (M=71.6, SD = 18.6) was significantly higher than the final grades for a traditional lecture
approach used in the same course a year earlier (M=63.1, SD = 19.2) (p <.05, t=2.49, df = 122).
According to Cohen (1988, 1992), the difference between these means (8.5%) was considered to be a
medium effect size (d=0.45).
4 CONCLUSIONS
Although the design of this teaching experiment did not allow us to identify the relative contributions
from each teaching innovation on student performance; in-class collaborative problem-solving and the
support of experienced tutors (pre-service teacher) were deemed important based on student feedback
and the authors’ collective classroom experiences.
The Business Math I students repeating the course commented that they preferred the flipped classroom
model to the traditional lecture model they experienced in the same course the previous term. These
students asserted that collaborative group problem-solving helped them better understand the business
mathematics concepts. However, encouraging struggling students to actively engage in collaborative
problem-solving involves more than having students work together in groups. As mathematics teacher
educators, we have expertise in teaching and learning mathematics and are comfortable negotiating
emergent learning. Given our focus on pedagogy, we planned each lesson. We selected, modified or
designed each task to scaffold learning and provide opportunities for students to make sense of the
mathematics through business applications. In addition, we worked with the preservice teachers to help
them develop their understanding of how to engage and support the Business Math I students.
During lectures and tutorials, the instructors and preservice teachers worked as an instructional team.
We did not tell students how to interpret or solve the in-class problems, instead we encouraged them to
learn to mathematize the problems and focus on sense-making. Collaborative problem-solving requires
the instructor to move from the podium at the front of the classroom and meander among the multiple
student groups. Having several preservice teachers in the lectures and tutorials meant that the Business
Math I students received Just-In-Time support. As such, they could struggle and negotiate the problem,
but before they became too frustrated, help was available from the preservice teachers or instructors.
The results described here indicate that the flipped classroom design used in this study is a viable option
for a first-year university business mathematics course. The flipped classroom model positively affected
the overall academic performance and student success rates in the course. Students positively received
the design and appears to have influenced their learning experiences and engagement with the course.
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