Assessing a Conceptual Approach of
Rational Numbers
IPDM Conference 2016
Borough of Manhattan Community College
New York, NY
Presenters:
Jae Ki Lee, Ed.D
Susan Licwinko, Ed.D
Matthew Meangru, MA
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Need For the Study
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Borough of Manhattan Community College (BMCC) enrollment
record:
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More than 80% of freshmen are placed into remedial
mathematics classes
Of 80%, 35% are placed into Basic Mathematics classes
↗ The major reason: Fractions (BMCC 2011-2012 Report)
According to Researchers
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Freudenthal (1983): fractions are the fundamental source of
rational number concepts.
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Wu (2009): Students who are not fluent in understanding
fractions will not be able to understand the fundamental of
basic mathematics.
↗ Teaching method in community college are the same method
as elementary or secondary school method (Lee, 2011).
Teaching and Learning difficulty of
Fraction
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The failure to develop skills with fractions can make it difficult
for students to meet college requirements for general
education mathematics (Lee, 2011)
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The dilemma for both teachers and students is how to make all
the appropriate connections so that a mature and flexible
understanding of fractions and the wider domain of rational
numbers can be obtained (Clarke, Roche & Mitchell 2008)
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The fractions are traditionally taught as a set of procedures and
rules to be followed with very little emphasis on the reasoning
behind these algorithms (Bisenthal, 2006)
Do Students Think Fractions is an Important
Topic to learn?
1. “ I suppose fraction is a vital topic to learn. we use it in real life
events such as when one goes out to eat with friends and split the
bill equally amongst each other or helping out my dad, who works
in construction. When we go to the hardware store, he give me a
hard time when getting the [measurement] of materials. Because
he knows how bad I am in math.”
2. “ I think fractions are important to learn, just to know how to do
fractions. I don’t think we use fractions in real life. We mostly use
[fractions] in basic math.”
Common Core
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
Connecting the Standards for Mathematical Practice to the
Standards for Mathematical Content The Standards for
Mathematics
Researchers, Ball & Forzani (2009),Bisenthal (2006), Lee (2011),
and Wu (2009) suggest the “Group Discussion” Method
Group Discussion Methods
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Ball and Forzani (2009) and Bisenthal (2006) pursue “Group
Discussion” as students figure out all the procedures and
answers.
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According to them, teachers’ role are discussion leader
All the work must be done based on students’ discussion
Wu (2009) pursued a combination between “Group
Discussion” and teacher’s lecture.
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The instructor should confirm students’ work and fix any
misconceptions students may have
Purpose of the Study
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The previous study was successful: Most of the students
improved their grade
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No comparison study
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Previous study was conducted in MAT 12: not enough time.
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MAT 8 maybe more suitable courses for this study: We can
provide more time to study fractions
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Compare one control and research classes, and find the
significant difference between two groups
Group Discussion Method
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Most studies implemented at either elementary schools or
secondary schools
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Bisenthal (2006), Kim (2008), and Wu (2009) were all conducted
in elementary schools
Research Questions
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1. How does the Group Discussion method influence learning
for the students in remedial class setting at a community
college?
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2. Is there any significant difference between the control and
research group?
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3. What should be discussed and developed more of
implementing this method in remedial class setting?
Methodology
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The study showed a significant difference between pre- and
post-test from the previous MAT 12 group.
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However, there was no comparison group set up for the first
study.
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This study was the first comparison study of the research.
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Two instructors teach MAT 8: Basic Mathematics courses(MAT
8) at BMCC
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One instructor used a traditional teaching method, the other
used “Group Discussion” method
Methodology Continued
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Before the experiment:
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the investigators provides worksheets, pre- and post-tests.
The investigators and the research group instructor discuss about
Wu’s (2009) discussion method.
During the experiment
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The duration of the study was the total three weeks, and six different
class time periods.
Before starting the lesson, all students took the pre-test.
The instructor assigned groups, and all groups discuss about
worksheet problems.
The time is not enough to discuss all the problems.
Students are assigned worksheets as homework before starting the
discussion.
↗ In the class, students share their works and answers in groups; especially,
students shared how to solve problems
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Methodology Continued
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After the discussion, the instructor checks and clarifies
students’ group work.
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On the last day, students took the post-test.
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All the documents were reviewed by the investigators.
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The investigators interviewed the instructor, and discussed the
pros and cons of the study
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The statistician analyzed:
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the significant difference between pre- and post-tests
The relation between worksheets and post-test
Quantitative Results
Research Group Distribution
Control Group Distribution
Side-by-Side Comparison
Discussion
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Group Discussion method did not work well on MAT 8 setting
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t=0.041<0.05: Control group perform significantly better
compared to the research group.
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What could be the reasons
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The investigators and instructors discuss about this problems
Discussion with Research Group instructor
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What could be the reasons to receive this result?
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Students did not do homework
Lower attendance rate
Is it because of “Group discussion method”?
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Yes, it could be.
Students are really resistant to do group work because they are
very weak on fraction, so they did not talk each other
The professor had to teach the topic
Other potential factors
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It was not a good idea to begin the topic that is most terrified
for them.
Students need to be trained with easier topics, such as whole
numbers before beginning fractions
It would be better to use the same method for the entire
course: Not only for few chapters.
Interview with the Experimental Group Instructor
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Do you think “Online lecture video, and other resources”
would help them to understand the topic?
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Nope. Students are really passive, so we need to prepare how to
instruct them carefully
But, the online platform would be helpful.
What kind of method should be suitable for MAT 8 setting?
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It can be hybrid setting: Group discussion, Lecture, and Online
platform with online resources.
Students need support from the instructor
Interview with the Control Group Instructor
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Based on this result, “Group Discussion” method is not a right
method for MAT 8 setting. What do you think?
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Group Discussion method could be working. But, need to
prepare very carefully
The method must be run for the entire semester. Otherwise,
students would be confused.
Do you think online resources would work for MAT 8
students?
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If students use it during the class time in a Computer Lab
setting, it would work. However, if students watch it before
coming to the class, it would not work.
Conclusion
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The study showed significant disadvantage of using Group Discussion
method in MAT 8 classes
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The instructor could not utilize “Group Discussion” method because
students were very resistant, and did not participate in the study.
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Self learning method is pretty changeable for freshmen students
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Through this study, we found:
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It is not a good idea to select certain topics using different teaching
method.
Group Discussion method should be run for the entire semester
Hybrid setting between lectures and group discussion, would be more
suitable.
Works Cited
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Ball, D.L., Forzani, F. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497-511.
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Biesenthal, M. (2006). Students' Understanding of Fractions within a Reform-Based Instructional Program: An Action Research Analysis
(Masters dissertation). Retrieved from ProQuest. (AAT MR24051)
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BMCC 2011-2012 report. Borough of Manhattan Community College, Retieved October 2015 from
http://www.bmcc.cuny.edu/iresearch/factbook/2011- 2012/index.jsp
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Clarke, D. M., Roche, A., & Mitchell, A. (2008). 10 Practical Tips for Making Fractions Come Alive and Make Sense. Mathematics Teaching in
the Middle School, 13(1).
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Common Core States Standard (2015) Mathematics Standard, http://www.corestandards.org/Math/ Retrieved Octover, 2015
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Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Boston: D. Reidel.
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Kim, J. (2008) The Learner-Centered Mathematicas Instruction and Performance Assessment, Journal of Elementary Mathematics Education
in Korea No. 12-1. The Korea Society of Elementary Mathematics Education
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Kim, J. & Lee, J (2012) “What’s happening in the mathematics classroom? Discussion about RBI based on New national standard in Korea”,
East Asian Mathematical Journal Vol. 28 (2012) No. 2. pp 233-249.Written in Korean.
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Lee, J. (2011). An Asian Approach to Operations with Fractions: Can Achievement Be Enhanced by a Mechanistic and Heuristic? (Doctoral
Dissertation). Retrieved from ProQuest. ( UMI 3484371)
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Wu, H. (2009). What's sophisticated about elementary mathematics? American Educator 33(3), 4-14
Question?
Contact Information
Jae Ki Lee: jaelee@bmcc.cuny.edu
Susan Licwinko: slicwinko@bmcc.cuny.edu
Matthew Meangru: mrm2182@tc.columbia.edu
Thank you!!!