EDUC 451A SECTION 120
INQUIRY PROJECT:
How can we improve students’ overall math skills in upper
elementary/middle school?
Sebastian Cabrera
Instructor: Yvonne Dawydiak
Date: March 23, 2015
Sebastian Cabrera
EDUC 451
Abstract
The following research explores the intersection of mathematics and technology in the
classroom. The purpose of the inquiry was to answer the question: “How can we improve
students’ overall math skills in upper elementary/middle school?” This is an important topic
because mathematics continues to be a subject that many students have difficulty with. The
effective use of technology to improve students’ overall mathematical skills in and outside the
classroom walls has led many educators to explore and adopt different approaches. Therefore,
this research begins by looking more closely at student use of the Internet for support with math.
In the next stage of the inquiry, the concept of Blended Learning is explored. The research then
hones in and focuses on the use of Flipped Learning - its benefits, and numerous creative ways to
incorporate it in the classroom. In conclusion, the flipped classroom is a strategy the researcher
will try in his own practice, with a prediction that it will make a substantially positive difference
in the way students learn mathematics and in their overall learning success.
Sebastian Cabrera
EDUC 451
Summary of Inquiry Project
The advancement of technology in the past couple of decades has impacted our everyday lives in
many ways. In education, the introduction of new technology such as smart boards, digital
media, graphing calculators, Internet, apps etc., has changed the dynamics of the classroom for
teachers and students alike. With increased access to technology, especially to the Internet,
online sites have become sources of knowledge for completing school assignments and projects.
The following research explores the intersection of mathematics and technology in the
classroom. Based on my observations during my teaching experience as a Math teacher in South
Korea, volunteering in an upper elementary classroom in Vancouver and through my Thursday
visits and short practicum, I saw first-hand the struggle and frustration some students
experienced during the process of learning Mathematics. My personal interest in and fondness of
Mathematics has motivated me to take the responsibility to find new and more effective ways to
improve my students’ overall math skills.
The purpose of my inquiry was to answer the question: How can we improve students’
overall math skills in upper elementary/middle school?” With a background in technology
application in the classroom as well, I was quickly led to the idea of connecting the two.
Mathematics continues to be a subject that many students have difficulty with, and many turn to
the Internet for help; a recent Google search reveals that 57,600,000 results for “help with
Mathematics” (Muir, 2014, p. 833) The effective use of technology to improve students’ overall
mathematical skills in and outside the classroom walls has led many educators to explore and
adopt different approaches. Could the average teacher, then, do more in and out of the classroom
to incorporate useful learning technologies, and creative strategies?
I began my inquiry by looking more closely at student use of the Internet for support with
math. As Muir (2014) points out, the current research is limited to the effectiveness of online
tutorial sites such as Khan Academy. However, she concludes that studies of students in grades
6-9 show that online tutorials and digital resources have the potential to be part of a student’s
learning experience, especially in Mathematics. According to research by Edwards and Rule
(2013), the level of achievement for online and face-to-face learning was equivalent, but students
found online learning more enjoyable. However, this sense of enjoyment decreased as time
progressed. I then realized teachers needed to strive for a combination of online and face-to-face
instruction so that enjoyment and motivation are optimal, hinting that the concept of Blended
Learning might meet the best of both worlds (Edwards and Rule, 2013)
In the next stage of my inquiry, I researched the concept of Blended Learning. In the big
picture, blended education refers to any time a student divides learning within the classroom and
online. Ash’s research (2012) asserts that blended learning is more effective than stand alone
face-to-face or online instruction. There are four models for blended learning –rotation, flex,
self-blended, and enriched virtual. The first model, rotation, was of most interest to me. In a
rotational model, “within a course or subject, students are rotated either on a fixed schedule, or at
the discretion of the teacher through different learning modalities, where at least one is online
Sebastian Cabrera
EDUC 451
learning” (Ash, 2012, p. S5). It is within this model that I found the concept of “Flipped
Learning”, an inspiring new learning strategy with much potential.
Next, realizing I had found exactly the new strategy I was looking for, I focused the rest
of my research on understanding the origins of flipped learning, its benefits, and numerous
creative ways to incorporate it in the classroom. The idea of flipping the classroom or “flipped
learning” is a relatively young proposition that utilizes technology to create learning outside the
classroom, thus creating more individualized time within the classroom. In essence, flipping the
classroom means switching time on task - rather than teachers delivering lessons in front their
classrooms, they convert their lessons/lectures to videos, podcast, or slide shows for students to
watch at home or elsewhere. By allowing students to learn outside the classroom walls, teachers
use their class time for more personalized learning, labs, and projects to engage and develop
deeper. (LaFEE, 2013)
Greg Green, a high school principal in Clinton Township, MI, piloted the first
documented success with flipped leaning. The school started with one class of underachieving
and undisciplined students. After one semester, the flipped classroom had better grades than its
traditional counterpart. The school then expanded the model to 140 incoming high school
freshmen and found: the failure rate dropped by 33% in English language arts, 31% in math,
22% in science, and 19% in social studies. As a result, standardized test grades went up,
attendance rates increased, and disciplinary problems declined 66%. Clinton’s success only
represents a single school, however, and more empirical data is needed to formally record the
efficacy of flipped learning on a broader scale (LaFEE, 2013)
Next, Bergman and Sams (2014) introduced ‘Flipped Classroom 101”, where students
watch a video tutorial of the concept to be learned, which can include the set up of mastery levels
for students to pass through, gamification, flipped peer instruction, and many more options. One
of the strongest reasons to use flipped learning is, according to Bergmann and Sams (2014), the
traditional classroom is normally only able to focus on only the first two levels of Bloom’s
Taxonomy - remembering and understanding, whereas the flipped concept allows class time to
be used for applying, analyzing, evaluating and creating. Finally, as the concept of flipping the
classroom has grown and developed over the past few years, there are now best practices
available such as Rath’s (2014) “Nine Flipped Classroom Best Practices”.
Some of the questions that arise from “flipped learning” are rooted in whether (1) this
approach is equitable in places where students or teachers do not have access or there is a lack of
technological resources. (2) Does it work in environments that go beyond classrooms with highly
achieving and motivated teachers and students? (3) Does it work better than current teaching and
learning models? (LaFEE, p.14) In talking with my supervisors and colleagues who have been
teaching for many years, I was cautioned to consider the following when using flipped learning:
Firstly, it is important to explain to the students the reasoning behind the concept so they
understand why they are asked to watch the tutorials at home, and furthermore, to make sure the
parents understand and are on board with the idea. Secondly the teacher must be sure the
Sebastian Cabrera
EDUC 451
resources are available for all students to be able to participate from outside the classroom, ie.
computer and Internet connection.
I concluded that the flipped classroom is a strategy I would definitely like to try in my
own practice and I predict that it will make a substantially positive difference in the way my
students learn mathematics and in their overall learning success. My next step was to design a
video tutorial myself to try with my students. If this is successful, I look forward to incorporating
the flipped learning through other approaches as well. I will also continue my own lifelong
learning to find the best learning strategies for my mathematics students, incorporating
technology in ways it is most useful.
Annotated Bibliography
Article 1: Google, Mathletics, and Kahn Academy: students’ self-initiated use of online
mathematical resources (Muir, 2014)
With the increased amount of student access to technology, especially to the Internet, online sites
have become sources of knowledge for school assignments and projects. Mathematics continues
to be a subject that many students have difficulty with as a recent Google search reveals that
57,600,000 results for “help with Mathematics”. The current research is limited to the
effectiveness of online tutorial sites such as Khan Academy (Muir, 2014). The study conducted
by Tracey Muir with students in grades 6-9 shows that online tutorials and digital resources have
the potential to be part of student’s learning experience, especially in Mathematics. While these
sites allow students to learn concepts at their own pace and to reinforce classroom lessons, they
do not omit the need for teacher-student interactions.
Article 2: Attitudes of Middle School Students: Learning Online Compared to Face to Face
(Edwards and Rule, 2013)
Online education has become a popular method of instruction. According to Edwards and Rule,
previous studies (unnamed) show that university and high school students perform similarly
with online and face-to-face methods of instruction respectively. Although there is a lack of
research for middle school students to determine their attitudes and academic performance to
online learning, Edwards and Rule suggest that middle school students (grade 6 in the US) in
their research preferred online methods of instruction for understanding mathematical concepts
(Edwards and Rule, 2013).
Sebastian Cabrera
EDUC 451
Students reported that one of the main factors that influenced their positive attitude toward online
learning was the independent self-pacing.√ One disadvantage to this self-pacing, however, was
that not all the students were disciplined enough to follow through with this approach and
therefore hindered their success (Edwards and Rule, 2013).
Their research concludes that the level of achievement for online and face-to-face learning was
equivalent. However, students demonstrated that online learning was more enjoyable, but this
sense of enjoyment decreased as time progressed. As a result, teachers need to strive for a
combination of online and face-to-face instruction so that enjoyment and motivation are optimal
(Edwards and Rule, p. 64).
Article 3: Blended Learning Choices –The Big Picture (Ash, 2012)
The interest in blending learning remains high in researchers radars because some studies claim
that blended learning is more effective than stand alone face-to-face or online instruction.
However, the need to determine which model of blending learning is more effective in terms best
practices as well as which model fits best to which types of learners.
Blended Learning Models:
1. Rotation: Within a course or subject, students are rotated either a fixed schedule or at the
discretion of the teacher through different learning modalities, where at least one is online
learning.
2. Flex: The content and instruction are delivered primarily via the Internet, students learn
through an individualized and fluid schedule between different modalities and the teacher is
onsite.
3. Self-Blended: Students has the choice to take one or more courses entirely online to
supplement their traditional courses. The teacher of record in the online teacher
4. Enriched Virtual: A whole school experience where each course students divide their time
between attending a physical classroom and learning remotely online. The content and
instruction is delivered online.
Article 4: Flipped Learning (LaFEE, 2013)
Sebastian Cabrera
EDUC 451
The idea of flipping the classroom or “flipped learning” is a fairly young proposition that utilizes
technology to create learning outside the classroom, thus creating more individualized time
within the classroom. In essence, flipping the classroom means switching time on task, rather
than teachers delivering lessons in front their classrooms, they convert their lessons/lectures to
videos, podcast, or slide shows for students to watch at home or elsewhere via the Internet or
other means such as DVDs and USB flash drives. By allowing students to learn outside the
classroom walls, teachers use their class time for more personalized learning, labs, and projects
to engage and develop deeper learning. (LaFEE, 2013)
Greg Green, a high school principal in Clinton Township MI, started implementing flipped
learning and has found success. The school first started with one government class made up of
students with history of underachievement and disciplinary behavior. After one semester, the
flipped classroom had better grades than the traditional counterpart. As a result, the school
expanded the model to 140 incoming high school freshmen (first year of high school) and found
the following: the failure rate dropped by 33% in English language arts, 31% in math, 22% in
science, and 19% in social studies. As a result, standardized test grades went up, attendance rates
increased, and disciplinary problems declined 66%. Clinton’s success is the data of a single
school, however, and more empirical data is needed to determine the efficacy of flipped learning
on a broader scale. (LaFEE, 2013)
Article 5: Flipped Learning (Bergmann and Sams, 2014)
The Flipped 101 classroom refers to having students watch a video at home and do the typical
homework in class. However, Flipped 101 should be seen as the entry point and not as the final
outcome. Other ways teachers incorporate to reach a deeper levels of students cognition and
engagement include:
1. Flipped Mastery: Students cannot move to the next level until there is evidence of mastery
within the content learned.
2. Flipped Mastery + Gamification: The basic idea is to look at what makes a game motivating
and see how you can apply it to the classroom. One tip for gamification is to play games. As you
play, try to figure out what aspects of the game are designed to motivate the player.
3. Flipped Peer Instruction: Student create their own videos to help classmates
Sebastian Cabrera
EDUC 451
4. Flipped Project Based Learning: Give students the time in class to engage in active learning
activities.
5. Flipped + Genius Hour: Students the idea from Google to take 20% of their time in the
classroom to explore or research questions they might have on the subject.
6. Explore-Flip-Apply (An inquiry Technique): Students explores guided questions in class,
teachers support their learning of the topic and students apply their knowledge in new ways.
Three elements that tie flipped classroom together:
1. Relationships: Helping students in the classroom with their homework shows that you care
about their learning and nurtures solid and meaningful interactions
2. Content: Since videos/tutorials are good for teaching lower level concepts (Bloom’s
Taxonomy), the time in the classroom creates the opportunity to go into deeper level of content.
3. Curiosity: The time in class is used for students to explore topics they’re interested in.
Article 6: Nine Video Tips for a Better Flipped Classroom (Raths, 2014)
Experienced educators offer nine flipped classroom best practices:
1. Devise a flipped strategy: Will you use your own videos? Use other’s materials or the
combination of both? What video creation software will you use and why? Most importantly,
how will you use the extra time in the classroom?
2. Start small: Do it in smaller chunks, one or two of their top lessons.
3. Get student buy-in: Decrease frustration levels at home, they have time in class to ask
questions. Depending on your students, explain Bloom’s taxonomy and how traditional
classroom focus on the first two levels, remembering and understanding. The l and class time can
be used now to applying, analyzing, evaluating and creating.
4. Teach students how to watch the videos: Take notes, write questions, check for understanding
by allowing students to answer questions in the videos or by filling out Google forms.
5. Teach parents too: Take the time to explain the concept to parents.
6. Encourage (Don’t punish): Avoid lecturing in class, if half of the students didn’t watch the
videos, give them time in class to watch them while the other students get help on higher-level
topics.
7. Don’t use videos as the only engagement tool: Mix it with blog posting if possible.
Sebastian Cabrera
EDUC 451
8. Make video short and interactive: The rule of thumb some teachers have adopted is one to
one-and-a-half minutes per grade level. (Grade 7: 7-10 mins)
9. Find fellow flippers: In order to maintain enthusiasm and get new ideas finding fellow flippers
allows for collaboration and sharing ideas.
Article 7: Refresh Your Flipped Classroom with Interactive Video (Bull and Kjellstrom,
2013)
Since the emergence of flipped classroom, the technology used to create material has improved
and moved from a linear progression of sitting and watching to a more interactive experience.
Here’s a list of a few technologies that promote interaction with the viewing students:
1. Popcorn Maker: Free video annotation editor allowing students to annotate during the video to
understand their comprehension.
2. Explain Everything: a combination of an electronic whiteboard with an inset window for an
instructor video/tutorial. Annotations while watching the video and sharing are also possible.
3. Knowmia: It’s a free Ipad app that once you publish a video you can add assignments that
track students’ responses in a database. Once the video is uploaded, Knowmia owns the
videos/tutorials and might distribute them to generate revenues.
4. Grokit Answers: Make it easy to create and link a private Q&A session to web video. It
doesn’t allow for tracking students responses but doesn’t own your videos unlike Knowmia. In
theory, the combination of Explain Everything and Grokit could replicate Knowmia features.
Sebastian Cabrera
EDUC 451
References
Ash, K. (2012). Blended Learning Choices. Education Week, 32(9), S4-S5. Retrieved from
http://www.edweek.org/ew/articles/2012/10/24/09el-overview.h32.html
Bergmann, J., & Sams, A. (2014). Flipped Learning. Learning & Leading With Technology,
41(7), 18-23. Retrieved from http://www.learningandleadingdigital.com/learning_leading/may_2014#pg20
Bull, G., Kjellstrom, W. (2013). Refresh Your Flipped Classroom with Interactive
Video. Learning & Leading With Technology, 40(7), 10-11. Retrieved from
http://www.learningandleading-digital.com/learning_leading/201305#pg12
Edwards, C. & Rule, A. (2013). Attitudes of Middle School Students: Learning Online
Compared to Face to Face. Journal of Computers in Mathematics and Science Teaching,
32(1), 49-66. Chesapeake, VA: AACE. Retrieved from
http://www.editlib.org.ezproxy.library.ubc.ca/p/40411/
LaFEE, S. (2013). Flipped Learning. Education Digest, 79(3), 13-18. Retrieved from
Muir, T. (2014). Google, Mathletics and Khan Academy: Students’ Self-initiated use of online
mathematical resources. Mathematics Education Research Journal, 26(4), 833-852.
doi:10.1007/s13394-014-0128-5 https://educ201.wordpress.com/2014/12/05/googlemathletics-and-khan-academy-students-self-initiated-use-of-online-mathematical-resources/
Raths, D. (2014). Nine Video Tips for a Better Flipped Classroom. Education Digest, 79(6), 1521.