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Chapter I
Introduction
High school students are at an exciting time in their lives. They have reached an
avenue where they will make some of the largest intellectual, behavioral, and physical
changes. Students will often lean on their peers, often in a team mentality, for support
during these uncomfortable transitions. Research has shown that harnessing a Team
Based or Cooperative Learning mentality will improve student output
(Kortering, Debettencourt, & Braziel, 2005). Taking that information a step further; this
thesis will attempt to answer to what degree will a Team Based Mathematical program
produce an improved quality education in the areas of student mathematical
communication, concept retention, improvement of test scores, and overall enjoyment.
Currently in most schools mathematics is seen as a mundane, boring, and
individual oriented subject. Some students seem to spend their days in most mathematics
class asking themselves two main questions: 1) when does this class end? And 2) when
will I ever use this? To make matters worse, students fall into the systematic process of
learning a formula, process, or concept; utilize it for a small amount of time; complete
some sort of formal assessment; only to forget the pervious material when a new unit is
begun. It is time that students have an avenue that increases their enjoyment in the class
and their application of the material. The Team Based Learning program will be a means
for students to collaborate with their peers in a positive and productive manner. During
this process students will communicate using math vernacular comfortably and
confidently. These benefits will require some work on the educator’s part, but will not
force the educator to revolution their teaching style. Ultimately, this study aims to help
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produce a curriculum that will integrate the strengths of Team Based Learning,
combining it with the strengths of the instructor, and to form a hybrid strategy that works
for all parties involved.
The Purpose of the Study
The purpose of this action research project will to create and implement a program
using Team Based Learning in a Mathematics classroom. The following research
questions will be addressed:
I. To what degree will Team Based Mathematics improve student’s ability in
mathematical communication?
In the researcher’s experience, vocabulary is one of the best indicators of both
intelligence and concept mastery. Currently students are having difficulty understanding
a question, and therefore will have an exponentially more difficult time solving a
problem. It is important to push current high school students beyond the basic math
vocabulary of add, minus, multiply, divide. A deeper mathematical vocabulary is vital for
a high school student’s development and confidence in the subject matter.
II. To what degree will Team Based Mathematics improve a student’s ability to
retain previously covered material?
The Team Based Mathematics Learning model makes learning an experience, and as an
experience, it will help those students retain information. Mathematics is a science where
each step builds upon the previous, and if the prior skills have been diminished in any
way, it puts a student’s ability to master the new material at a serious disadvantage. It is
unacceptable for a student to simply memorize, regurgitate, and forget.
III. To what degree will Team Based mathematics improve a student’s test score in
during individual formal assessment?
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The current education system is showing that frequent and standard testing of all students
is the most efficient way to map a student’s development. The aim of this Action
Research Project is not to debate, confirm, or debunk the validity of that statement. It is
however, the goal of this project to see how the effects of Team Based Mathematics
translate quantitatively to individual and collective assessment. In this manner, a
successful program that can improve a student’s standardized test score will prove to be
invaluable.
IV. To what degree will Team Based Mathematics improve a students overall
enjoyment in a mathematics class?
Team Based Learning is a process that students have undeniably asked for more of in
their current education. As educators, it is important to incorporate the students’ need for
the social as well as the academic. If students favor a particular type of activity, they
often work harder at it, and will look forward to doing it again the future.
Program Overview
The Team Based Mathematics Program will be conducted in two distinct groups
of high school students. One group will be the Experimental Group, and will be
experiencing the Team Based Learning program. The other group will be the Control
Group, and they will receive a more traditional educational program. These two groups
however will be in the same subject, Algebra 1-2, and will not be classes who are
considered Advanced Placement/ Honors. Both groups will be receiving the same
preassessments, assignments, formal assessments, and surveys. The same educator using
the same type of delivery system will teach both groups. This will help produce two sets
of data which will be used to deduce the degree to which Team Based Mathematics
answers the research questions stated above, and minimize any potential biases.
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This program will be conducted using a series of important steps. These steps are
carefully placed in order to promote team chemistry, concept retention, and overall
effectiveness.

Team Building and Team Chemistry Development - Its focus will be creating an
atmosphere suitable for Team Based Learning to take place. This step will consist
of a series of increasingly difficult and intrusive team building activities requiring
more and more student involvement and interaction.

Team Alignment - Students will be required to fill out a variety of pretests
including mathematical preassessments, personality tests, and learning styles
tests. Students will be placed into balanced groups based upon those results.
After those initial steps have been completed it is time to start teaching the
material

Concept Delivery - An educator will deliver the material to a student in a manner
as they see fit. This is where the bulk of the new information will be given to the
students.

Team Reliance / Peer to Peer Interaction - The team will then check to make sure
each student in the team understands the new material, and makes sure the each
student’s notes are complete and accurate. The group will then begin to
collectively complete a group assignment.

Individual Practice / Independent Practice – After showing a solid basis at a
group level, students will then have individual assignments to solidify their
individual skill level in the new covered material.

Individual Assessment - At the conclusion of each unit, the students will engage a
phase where each student will be assessed individually. There will be no group
work in this assessment in order to see if the student has comprehended the
material, and not simply rely on their group.

Group Assessment - In this phase, student will be assessed collectively using a
different assessment types that go beyond the obvious, create creative
mathematical paths, and arrived at a possible solution. This could include real life
examples of the concept, or portfolio activities.

Survey - Students will take surveys to evaluate the effectiveness of the method
and their enjoyment of the process.
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After all the steps have been completed, the quantitative and qualitative information will
be analyzed in Chapter Four. The results and conclusions will be available in Chapter
Five.
Vocabulary
Frequently used terms in this study are:

Team Based Learning – a strategy in which students work together over a six to
eight weeks in order to help improve the skill level of all students involved.

Cooperative Learning – a strategy in which students work together to complete a
single task, and then the group will be disbanded

Team Building Activity or Team Builder – an activity whose goal is to enhance a
students trust in each other and improve cooperation among students

Individual Assessment – a formal assessment whose goal is to test the retention,
and application of a concept. It is to completed by a student without the help of
their peers.

Free Loader – an individual in a group setting who do a minimal amount of the
work, while others (Workhorse) do the majority of the work. The satisfaction and
rewards of shared goal is spread evenly to both the Free Loaders and Workhorses.

Workhorse – an individual in a group setting who does the majority of the work,
while others (Free Loaders) do a small amount of work. The satisfaction and
rewards of shared goal is spread evenly to both the Free Loaders and Workhorses.
This program is aimed at addressing the issues some of the issues identified with
mathematics classes. With the current economic strain, it is extremely beneficial to
incorporate strategies that have a track record of success, and will not break the bank.
With a successful Team Based Mathematics Program, educators will have a new avenue
to create a more effective classroom. While standing on the shoulders of the predicators
of Team Based learning, this Team Based Mathematics Program will incorporate all the
previous successes, suggestions, as well as interjecting some new characteristics.
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Chapter II
Mathematics: A Need for Reform
It is math education in the United States, which has
received blow after blow from recently released studies on
top of the continuing ferment about a host of issues -- too
much or too little arithmetic, calculators or no calculators,
problem solving versus calculation, and the perennial
problem of unqualified math teachers. One's eyes get bleary
watching the game. (Lewis, 2005, p. 420)
Mathematics at the high school level has been the same from quite some time.
The application and use of the Pythagorean Theorem, or Slope Intercept form has
remained the same. However, the children that receive that instruction as changed
substantially through the ages. (Knowles, 1999, p. 24) Teachers are not focusing on a
diversified learner, and the strategies used educate the generations before are also
becoming antiques. Not to say that all the strategies of the current math educator are
archaic, but educators must then ask themselves, “Is this strategy really effective, or
something that is just ‘norm’?” (Marshall 356) To remain competitive in a many
different fields, mathematics scores need to climb.
The most recent TIMSS study conducted in 2007 shows that the United States is
making a small improvements, however we are still well behind where we need to be. In
the past two years, the United States has risen six points on average. However, the
United States is behind China by over 100 points in some areas. If the United States is to
remain competitive in many different fields of involving science, mathematics, and other
academic trades; it cannot be trailing the leader by 100 points, and only increasing by six
points. In another study by the National Academy of Sciences, the US finished 24th out
of 29 leading industrialized countries on the 2003 Programme for International
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Assessment study, which tested 15-year-olds' math abilities. The study then released this
quote, “The answer to the question posed above is as troubling as our kids' inability to
solve it--even accounting for population size, the US trails emerging global forces China
and India in technology and engineering. IT and engineering skills so dependent on math
and science skills, our future as the last remaining superpower is in question. (Kuttan &
Peters, 2006) These studies and others show us that the numbers of our current system
don’t add up, and that there needs to be a change in the delivery of the math education.
A ten year longitudinal study done in Denver, Colorado showed that the least
favorite subject of 6th and 8th grades was math, and math meagerly improved to 2nd
least favorite in the 10th and 12th grades."(Helwig, 2004) For years the train of thought
was that students feared math because they were just simply bad at it. However, a
growing body of research shows a much more complicated relationship between math
ability and anxiety. It is true that people who fear math have a tendency to avoid mathrelated classes, which will then decreases their math skill even further. (Ruffins, 2007)
If students fear math, then they will be less likely to engage in careers involving
mathematics. On February 26th 2005 Bill Gates gave a speech to the National Education
Summit on High Schools summarizing the state of education “When I compare our high
schools to what I see when I'm traveling abroad, I am terrified for our workforce of
tomorrow. In math and science, our fourth graders are among the top students in the
world. By eighth grade they are in the middle of the pack. By twelfth grade, US students
are scoring near the bottom of all industrialized nations.” (Higgins, 2009) There is
indeed a need to reform how teachers teach Mathematics.
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Often times the very basis of mathematics vocabulary can set a student back. At
an early age students understand the concepts of add, subtract, multiply and divide.
However, when they get to high school it is no longer that simple. Terms like "divisors,"
"integers," "quotients," "multipliers," "differences," "products," "multiplicands,"
"inequalities," and "sum," to name a few. (Cornell, 1999) Those same words are used in
textbooks, and in lectures in great numbers. A student who cannot always distinguish
between denominator and numerator cannot always grasp the concept of equivalent
fractions. An inferior grasp on math vocabulary can also lead students to have more
problems throughout their mathematical carriers. (Hale, 2007) If students can
communicate to each other correctly and confidently in mathematic, their success grows
exponentially. (Lee & Herner-Patnode, 2007) There needs to be an avenue were students
can converse with their peers using this mathematics vocabulary daily. If not, students
won’t have a chance to get a question correct because they don’t understand the
information of the question or what it is asking.
Tradition lecture based classrooms are no longer the best way to get the
information from the educator to the student. For most students, mathematics is an
endless sequence of memorizing and forgetting facts and procedures that make little
sense to them. Numerous scientific studies have shown that the traditional methods of
teaching mathematics are not only ineffective, but also seriously stunt the growth of
students' mathematical reasoning and problem solving skills. Yet the traditional lecture
based style continues which not only hurts the students, but also the nation. (Marshall,
2003, p. 193)
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Students need the opportunity to combine their knowledge of mathematical
concepts with their use of language and practical experience. When a student runs into a
concept they have trouble with, they need to be guided to the correct resolution by
someone whose knowledge they trust. (Hale, 2007) Traditional lecture based instruction
does not allow the student to have the exchange. The information is on a one way train
starting from the educator, and ending in the trash can when the bored student fails to
understand what they are really trying to do mathematically.
Education in the United States has received blow after blow from all sides.
Calculators, or no calculators; too much or not enough arithmetic, right process versus
the right answers; and the list of mathematics education issues goes on. (Lewis, 2005, p.
420) It Unlike in mathematics, a string of these negative terms will not multiply to make
a positive term. (Marshall, 2006, p. 356) It’s time for change in math education.
A Call for Cooperation
By encouraging children and adolescents to learn and work
together, cooperative learning attempts to create a shift
from the paradigm of knowledge transfer from an active
teacher to passive pupils, to one of social constructivism,
where knowledge is actively created by students through
social interaction on academic tasks (Mitchell, Rosemary,
Bramwell, Solnosky, & Lilly 2004).
To most secondary students, and to most adults, math is a subject that is usually
seen as a boring, individualized, and complicated systematic process. Some students
remember their math class using only time one used team or group work would be in a
frantic last minute crunch before an exam. Math can be that way however one is missing
out on the beauty of mathematics. Math problems are ideally intended for open
discussion because they can frequently be solved by many different approaches
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(Robertson, Davidson, & Dees 1999). Group oriented instruction can often not only help
deepen an understanding of a concept, it can also develop a passion for the creativity that
lies within mathematics.
Learning in all areas and subjects tends to be a social experience. “Students learn
by talking, listening, explaining, and thinking with others (Robertson, Davidson, and
Dees 1999).” Of the countless modalities and different learning styles, there is only one
that involves interpersonal reflection; learning is at its very basic core is cooperative and
intrapersonal exchange (Stonewater, 2005). Math should no longer be a subject where
students rely on passive or apathetic involvement, and students who do not buy into their
education will not get the maximum benefit of it. Students working as a team will pull
from their individual strengths to help enhance the potential of their teammates. The
continued success of the group will then encourage the students to strive further then
before (Slavin, Shlomo, & Sharan 1999). With a new found confidence of the group and
the individual the learning process will perpetuate itself.
Students will continue to use team-based work for the rest of their lives. One
university used team-based academics for all of their freshman class, and were pleased to
see the increase in the retention of their student population (Callback, Campbell, &
Borland 2000). Team-Based work will also be the number one desired trait of the
workforce for Fortune 500 companies of the 21st century (Demoulin 1999). The process
will also help produce the key aspects of teamwork including, Problem Solving,
Interpersonal Skills, Oral Communication, and Listening (Demoulin, 1999). Team Based
Mathematics will not only make students better at mathematics in general; it will also
help produce a better communicator, co-worker, leader, and problem solver.
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Team Based Education; not simply Cooperative Learning
Many see team based education and cooperative learning synonyms for the same
strategy; and even used interchangeably in broad generalities. Educators often call a
cooperative learning environment a “team” in order to promote a higher dedication to the
work. In both systems, a group consists of peers ranging from three to five who gather to
complete a task or a range of systematic tasks. There is a need for a basic level of trust
and a positive group dynamic. If at anytime, there is a negative component, either
emotional or personal, the entire body fails to work to its full potential. These two
systems though seemly synonymous, yet each one has deeper complexity, and specific
function.
Cooperative learning is when a group of individuals work collaboratively for a
specific short-term goal. The goal is often times very specific, and once the goal has been
achieved the group disbands. This body is usually small and exists only for a finite period
of time. The system is best suited for small projects. It requires limited buy-in from the
participating students, and is less impacted by external forces. However students will
often split up the workload to lessen the burden, and completing the task becomes the
overall object not learning or mastery of the material. Cooperative learning could also
produce a division of labor where students a small part of the group are doing all the
work, and the other students who are just along for the free ride (Eastman, & Swift,
2002). Cooperative learning and short-term learning groups provide an environment for
many of the objections produced by critics of Team Based Learning.
Team Based Learning
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Team Based Learning asks the students to push themselves beyond the temporal
group work of Cooperative Learning. Team Based Learning is a group of students that
work collectively over a long period of time to address a series of collective and
individual goals. (Michaelsen, Knight, & Fink, 2002, p. 1-26) Students put more effort
into building the fundamentals of the group-dynamic; however they also receive more out
of the total process. Students in these cohorts are in place for a long period of time,
which requires and creates a trust system as well as a support system for the group as a
whole and the students individually. They have to overcome challenges, examinations,
and assignments as a group. Regardless of the complexity or simplicity of their current
goal, they must complete it, and complete it in such a manner that only improves trust
and team chemistry. Initially students must participate in team builders; or activities
whose purpose is to unify a group; at the beginning of the course to increase productivity
of the group. As it is commonly stated in many walks of life, a team is only as strong as
its weakest member, therefore the students must work diligently to make sure that each
member is succeeding (Su, 2007). If a challenge or goal is not met, which is another
opportunity for personal group for the students and the group; the group comes up with
more conducive working practices for the next situation (Pretzer, Rogers, & Bush, 2007).
The group also must create networks to work more efficiently outside of the traditional
classroom, and must utilize other avenues of communication including, but not limited to,
study sessions; group e-mails; phone; and internet chat like AIM, MSN, e-mail, Twitter.
The group also has rotating responsibilities, split up the work evenly so that there can be
no dominate leader nor a chronic freeloader (Williams, 1996). Team Based Learning will
produce a more productive, and enjoyable experience.
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Successes of Team Based Learning
Team Based Learning is not a new tactic; it has a long history with an equally
long track record of success. Team Based Learning isn’t simply group work. Its much
more like a sports team, a group of students with a series of short term goals leading to a
common long term goal. They are constantly working together, and communicating
together. Teamwork is a natural instinct for educators in schools already. Most students
have participated in some group work in at least one of their classes if not more
(Callback, Campbell, & Borland 2000). In small groups students that were allowed to
work together and communicate, those students produce higher cognitive stimulation
rather then when they listen to a lecture (Change & Mao 1999). While increasing the
communication between students and the educator, small groups increase the test scores
of unannounced examinations by five percent (Potthast 1999). Data supports the general
effectiveness of small groups, and that success can be enhanced further with a small
amount of healthy competition (Sherman, & Thomas, 1986). Students who worked
collaboratively have performed significantly better on exams involving application of a
concepts when compared to those who worked individually (Chang, & Mao, 1999).
Research has shown that Team Based Learning leads to higher achievement; more
productive learning environments; positive relationships with their peers; and a greater
sense of achievement then other individualistic learning experiences (Potthast, 1999).
Group work has placed an important role solidifying material into the long-term memory
system of the brain (Demoulin, 1999). With the current increasing standards focusing on
test scores by national and local entities; Team Based Learning is an ideal strategy to
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satisfy teachers and administrators alike, and most importantly helping the students
succeed.
Beyond the clearly stated gains in academia, Team Based Learning has other
significant results. When using this process, one university professor noticed that his
attendance continually climbed to a stunning 99% when he used this strategy (Fink,
Knight, Michaelsen, 2002). This strategy also effects students’ general outlook towards a
subject. When the student couples their group with success their attitude towards the
subject becomes more optimistic (Thornton, 1997). The Team Based Learning process
also produces students who are more equipped to look a situation, make hypothesizes,
and use the data to create creative answers to logical problems, and it’s also clearly
evident that Team Based Learning goes beyond its traditional academic focus (Davidson,
Dees, & Robertson, 1998).
There is statistical evidence found over multiple studies that suggest that when
students work together in groups, they produce “higher cognitive levels of Bloom’s
taxonomy.” (Chang & Mao 1999) It has been found to be effective in all subjects ranging
from reading to science including mathematics. This is also not simply a local
phenomenon, and it has been proven to also have statistical success in such diverse
educational systems including Taiwan (Chang & Mao 1999). The success of this strategy
is also not specifically oriented to any one type of student; it is statistically beneficial for
Special Ed students as well as the mainstreamed students (Tateyama-Sniezek, 1990).
Personally, I liked the new format for this class. It made me
take ownership for my own education and I felt much more
engaged in learning. I feel those that oppose this teaching
style are uncomfortable with change itself. Some people
tend to resist change because it forces them to step out of
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their comfort level and think outside the box. (TateyamaSniezek, 1990).
Many people go into the profession because of a deep love for the subject matter,
and they also want to make a difference in the lives of young people. To increase the
impact education has on students, educators need to listen and involve student voice in
education discussions (Marshall, 1993). When student’s were consulted, 76% stated that
they would like to have more assistance, included in that was more assistance / peer
involvement. In the same survey, there was a majority of the research participants
concluded that they wanted to work more often in groups (Kortering, Debettencourt &
Braziel, 2005). In another survey, students responded in a large margin of 80% stating
they would like more group-work (Stonewater, 2005). Most students realize that the
purpose of school is to learn, and they will form the most enjoyable, yet optimal, avenue
to complete that objective (Wiest, Wong, Cervantes, Craik, & Kreil, 2001).
Students enjoyed the learning aspect, as well as the opportunity to help out their
peers. One student reflected on Team-Based Learning saying, "I could not have learned
as much without the help of my group. I also learned from helping them. This two-way
flow of information that ingrains the material better than just reading or listening to
lectures.” (Tateyama-Sniezek, 1990) These results provide initial evidence of what
students think can improve their success, and as the patrons of the education system; it is
crucial to keep the customer’s opinion in mind when making decisions (Kortering,
Debettencourt & Braziel, 2005).
Students are not the only advocates of this program; young and seasoned
educators alike have found success using Team Based Learning, although most of them
will agree that the whole processes of implementing the groups, making team oriented
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activities, and the team building can quite time consuming (Oitzinger, & Kallgren, 2004).
Some educators with over twenty years of high school experience feel that his is a
worthwhile enterprise (Mitchell, Rosemary, Bramwell, Solnosky, & Lilly, 2004). At the
end of one educator’s carrier, they took the time to talk about their success with the teambased approach. The educator remarked that they would never entertain the thought of
returning to an individual based approach. They also remarked,
Because Team Based Learning has become a standard in
my courses, I was given a special faculty award for
outstanding innovation in the classroom. And, incidentally,
my student evaluations have significantly improved, even
beyond the level I was used to under the old lecture
approach. Although I am close to the standard retirement
age, I am really having fun again and I am actually looking
forward to meeting my classes. Team Based Learning has
rejuvenated me to such a degree that I could teach forever.
(Michaelsen, Knight, Fink, 2002).
Many educators have used this type of strategy and faced steadfast skepticism from their
peers. Although after successful trial after successful trial, practitioners cannot always
convince others to use Team Based Mathematics. However, those using the strategy have
become well respected for their pedagogy, and received awards for their innovation in the
classroom (Fink, Knight, Michaelsen, 2002).
Educators are often times looking for a strategy what will both empower their
students, and invigorate themselves. Those educators who have already tried Team Based
education can attest to its effectiveness in their teaching practices. Some educators also
look to play to the programs strengths to eliminate traditional examinations and
implement more practical assessments (Fatt, 2000). To be realistic, team based teaching
is not the magic pill that will fix every classroom. It is however, a tactic that will provide
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a deeper passion for material, produce a more effective outcome, and will produce a more
enjoyable experience for the patrons – the students.
Common Criticism of Team Based Learning
There is evidence that Team Based Learning that has some to be skeptical of the
strategy. In some cases Team Based Learning will only produce a favorable outcome if it
is associated with a desired extrinsic reward (Tateyama-Sniezek, 1990). As mentioned
before, there is also the opportunity for a division of the workload for efficiency
purposes, and not for the quality of work purposes. There is also still the opportunity for
there to be freeloaders, and workhorses within the group make-up. The research suggests
that if a cohort is made up of the clashing personalities or bad team chemistry it can delay
the learning process, and unfortunately even damage a student’s drive to comprehend the
subject (Michaelsen, Knight, Fink, 2002). However, any time a learning environment
can be damage an educator must be cautious in executing that strategy. All these
criticisms bring to light the importance of making teams intelligently, that are effective,
and that are balanced. In addition there is a need for intense teacher proximity to ensure
positive working conditions.
A student’s socio-economic status, drug and alcohol use, dysfunctional families,
unnecessarily lengthy tasks, cultural forces, and other external forces could be the result
of unfavorable results for prior Team Based Learning experiences (Wiest, Wong,
Cervantes, Craik, & Kreil, 2001). These are common factories underlying all strategies
and theories in modern education, and are realities that all educators will face regardless
of their teaching location.
Team Based Learning is not the magic pill that will cure all the ills of education.
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This is a strategy with a positive track record, yet it has its drawbacks like most education
techniques. However, Team Based Learning is a worthwhile strategy and has the
opportunity to make a classroom more enjoyable, memorable, and effective. Students are
social beings; this strategy harnesses that nature to create a very productive and helpful
avenue for intellectual development (Cooper, & Robinson 1998). Even with some of the
criticisms, Team Based Learning can be an effective strategy using the following
methodology.
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Chapter 3
The Purpose of the Study
The purpose of this action research project will be to create and implement a program
using Team Based Learning in a Mathematics classroom. The following research
question will be addressed:
V. To what degree will Team Based Mathematics improve student’s ability in
mathematical communication?
In the researcher’s experience, vocabulary is one of the best indicators of both
intelligence and concept mastery. Currently students are having difficulty understanding
a question, and therefore will have an exponentially more difficult time solving a
problem. It is important to push current high school students beyond the basic math
vocabulary of add, minus, multiply, divide. A deeper mathematical vocabulary is vital for
a high school student’s development and confidence in the subject matter.
VI. To what degree will Team Based Mathematics improve a student’s ability to
retain previously covered material?
The Team Based Mathematics Learning model makes learning an experience, and as an
experience, it will help those students retain information. Mathematics is a science where
each step builds upon the previous, and if the prior skills have been diminished in any
way, it puts a student’s ability to master the new material at a serious disadvantage. It is
unacceptable for a student to simply memorize, regurgitate, and forget.
VII.
To what degree will Team Based mathematics improve a student’s test
score in during individual formal assessment?
The current education system is showing that frequent and standard testing of all students
is the most efficient way to map a student’s development. The aim of this Action
Research Project is not to debate, confirm, or debunk the validity of that statement. It is
Naughton 19
however, the goal of this project to see how the effects of Team Based Mathematics
translate quantitatively to individual and collective assessment. In this manner, a
successful program that can improve a student’s standardized test score will prove to be
invaluable.
VIII.
To what degree will Team Based Mathematics improve a students overall
enjoyment in a mathematics class?
Team Based Learning is a process that students have undeniably asked for more of in
their current education. As educators, it is important to incorporate the students’ need for
the social as well as the academic. If students favor a particular type of activity, they
often work harder at it, and will look forward to doing it again the future.
Program Overview
The Team Based Mathematics Program will be conducted in two distinct groups
of high school students. One group will be the Experimental Group, and will be
experiencing the Team Based Learning program. The other group will be the Control
Group, and they will receive a more traditional educational program. These two groups
however will be in Algebra 1-2, and will not be classes who are considered Advanced
Placement/ Honors. Both groups will be receiving the same preassessments, assignments,
and formal assessments. The same educator using the same type of delivery system will
teach both groups. This will help produce two sets of data which will be used to deduce
the degree to which Team Based Mathematics answers the research questions stated
above.
Limitations
This study will only be for one semester at one school. Seven research
participants started the study, but due to outside circumstances, were removed after the
Naughton 20
first test. This was usually due to withdrawal from the class. Beyond these limitations,
all other data was introduced into the study, and no data set was otherwise excluded from
the calculations. This left one group of thirty research participants for the control group
and another group of twenty-nine research participants for the experimental group.
Fifty-nine research participants seemed like an acceptable number to yield definitive
results.
Because of scheduling issues, the control group will also be participating in the
Team Building activities. Initially the study called for five full days of team building
activities. After receiving some pressure from veteran teachers at the high school, the
studies last two days of team building were cut from the study from both the control
ground and the experimental group. The staff felt that with a full five days of team
building, I [the educator] would not be able to complete the necessary topics the research
participants [students] would need to complete Algebra 1. Since the first purpose of the
researcher was to be an educator of Algebra 1, the last two days were cut in order to start
actual instruction. It was also evident that three days of team building would be
sufficient, although not ideal. The team decorum could also be gained through the longterm interaction in their groups during the guided practice activities. Also because of
scheduling issues, a pre-test was not administered.
The experimental group was the first class that received the material. This means
that the control group would receive the same material, but could have an augmented
delivery system based on the success or lack their of the first round of instruction with the
experimental group. The facilitator goal is to produce an un biased action research
project, while simultaneously create an effective instruction for all parties involved.
Naughton 21
Facilitator
The facilitator of both the instruction and data is a second year educator. He feels
that teamwork is essential not only to education, but to life. Through this action research
project, the researcher hopes to create an effective curriculum that allows other educators
to use Team Based Learning in their own classrooms. It is created in a manner that will
allow educators to use their own method of instruction, and also the benefits of the Team
Based Learning. It is in the facilitator’s hopes that this program will go father then just
the study of mathematics.
Research Participants
The research participants will be from a highly populated (2300+) high school in
Nevada. They will be randomly selected by the administrators/counselors of the high
school. There will be no grouping based on terms of age, sex, ethnicity, or religion. They
will vary from socio-economic status, sex, intelligence, ethnicity, and skill level. The
research participants will be grouped by the school, which is based out of scheduling for
all the students requiring Algebra 1-2. The participants will be divided into two groups a
control group, which will be all in one class period, and an experimental group which
will be in another class period. Each group will consist of about thirty students. The
groups will be constructed by the research using the data collected during the first week.
In each of those groups, it is the goal of the research to include ten to fifteen from each
for the study, although more research participants will not be discarded. The parents and
the students will be informed of the study, and will be given the option to have their child
excused from the study at any time. The participants were informed that they were
participating in a study where the facilitator was comparing two classes. The research
Naughton 22
participants and their parents will be assured that this study would not negatively affect
their academic grade in the class, and that the participant’s identity would stay
completely confidential. The parents will not be informed about the Team Based
Learning unless their parent/guardian requested more information.
Data Collection and Data Analysis
The quantitative data will be used to address the first three research questions. It
will be collected through three unit tests (known as “Celebrations of Knowledge”). The
two groups’ data will be compared to see if there are any statistically significant
differences in test scores. The data will be analyzed by various different means
including, but not limited to, mean, median, mode, range, two variable t tests, and
graphically. This information will be given in chapter four.
The qualitative assessment for the last research question will be done by a
researcher-developed survey at the conclusion of the study (See Appendix). The will
coded through a series of values from one to five, five being the most helpful and one
being counterproductive. This survey will ask questions specifically oriented towards
each research question, as well as the study as a whole. This data will be used to record
the voices of the research participants. Those voices will remain confidential and be
assigned a random number and letter. The survey can be found in its entirety in the
appendix. This information will be available in chapter four.
Team Building and Team Chemistry Development
The control and experimental groups will participate in a week long series of
preassessments, and team building activities. Its focus will be creating an atmosphere
suitable for Team Based Learning to take place, and will last for one week. There are
Naughton 23
particular activities for each day, and for homework that evening. The activities start out
with very low risks for students physically, socially, and emotionally. As the week
continues, they become increasingly more difficult requiring a deeper amount of trust,
participant collaboration, intellectual and physical activity. Day 1 activity “If I were…”
is an example of an easy activity, and Day 5 activity “Jump Rope Run” is an example of
a more difficult activity. The result will provide the researcher with data about class
dynamics, and help in group formation. During the activities, the researcher will be
making diligent and thorough observations that will help him construct the groups after
Day Five. Theses activities are not particular to any Team Based Learning program, but
are a collection organized by the researcher. Additional information for all activities
including printable worksheets is available in the appendix.
Day One
During the first day, the students will be given out the syllabus of the class, and
the letter of consent about the study. The research participants will then go into a name
game named “If I Were…” (Canfield & Siccone 1995, 145-147). In this activity,
research participants will use the If I Were… Worksheet to interview their classmates with
a low amount of disclosure.
For homework, the research participants will complete “The Danger of Dracula.”
(Johnson & Johnson 2006, 22-24) This activity will be done individually. The purpose of
the activity is to categorize the best ways to kill “Dracula.” The reason for this activity is
for them to have some background knowledge before the next day’s sharing activity. If
the research participants have some background knowledge, it is the researcher’s opinion,
that they will then perform better in the group in Day two.
Naughton 24
Day Two
The second day’s activity will to put the research participants into groups of three
to four, and have them share their analysis on how best to kill Dracula. Then as a group
they will complete the same activity as a group. The purpose of this activity is to see how
the individuals interact with each other. It is important to look at the differences between
the leaders, and those who are withdrawing from the group activity.
After this activity, the research participants will engage in a similar activity,
“Navy.” The research participants will get into groups of three to five, and it must be
different from prior groups. In this activity, research participants will be ship wrecked on
an island, and they can only bring thirteen items which they have to select from a very
specific list. The group mindset is survival and rescue. Unlike “The Danger of Dracula”
the research participants will not have any background knowledge. They will have to
complete this activity as a group. After each group has finalized their lists, the will be
asked to compare and contrast their list with the list produced by the United States Coast
Guard.
The homework for Day 2 will be a learning styles test known as a Learning Styles
Test. Research participants will answer a questionnaire about their learning practices.
This will produce a basic idea of the research participant’s dominate and passive learning
styles. This will beneficial for the research and the research participants to know, and will
help in group formation.
Day Three
In Day Three, the research participants will grade a learning styles test from the
night before and have a class discussion on the results. Following the discussion, the
Naughton 25
research participants will once again get into group of three to four. Research participants
will participate in “Coop Square Building. (Canfield & Siccone 1995, 435-438).” In this
activity, research participants will receive a couple of envelope filled with polygons of
different sizes and shapes. The research participants will have construct four congruent
squares using all the polygons only once. The purpose of this activity is to see how the
individuals interact with each other. It is important to look at the differences between the
leaders, and those who are withdrawing from the group activity.
The homework for Day Three the students will take home a math pretest. This
will measure the current level of each research participants’ skill level. This is important
to help shape the groups. This will allow the researcher to make groups as equal as
possible in their math skill level.
Day Four
In Day Four, the initial activity for the research participants will be to grade the
pretests from the night before. The researcher will then record the information only for
the purposes of group formation and no academic grade will be given based on accuracy.
The research participants will get into groups of four for the team builder “Blind
Square.” In this activity, research participants will be blind-folded and asked to make a
regular square, rectangle, and triangle. The research participants will have to rely on
auditory commands, and other types of communication to complete the task. It is
important to look at the differences between the leaders, and those who are withdrawing
from the group activity.
The second activity of the day will be the “Pantyhose Stuff.” In this activity, the
research participants will again be in different groups of three to five. The objective is to
Naughton 26
place as many objects into pantyhose without breaking the stocking or creating a “run.”
The groups will have two minutes to brainstorm, and then two minutes to complete the
activity. The group will only have one pair of pantyhose so it the brainstorming step will
be crucial. This focus of this activity is the brainstorming aspect since they [research
participants] only have one opportunity to win the activity. The researcher will be looking
for creativity, leadership, and teamwork, and applying that observational data to group
forming.
The third activity of the day will be the “Egg Drop.” In this activity, the research
participants will be placed into groups of three to four. The researcher will be placing the
research participants into these groups based on preliminary data. The researcher
participant groups will be given twenty popsicle sticks, a balloon, ten plastic straws, six
cotton balls, seven sheets of notebook paper, three feet of string, and three feet of duct
tape. From those supplies the research groups will have to construct an apparatus / shell /
contraption that will help a non-hard boiled egg withstand a ten foot drop. The groups
will have fifteen minutes to brainstorm and construct. Afterwards, each group will drop
their egg from ten feet to see if their contraction was successful.
For Day Four’s homework assignment, the research participants will take a
conflict analysis test (Johnson & Johnson 2006, 374-379). The research student will
answer questions to see how they react when confronted with difficult and unpleasant
situations.
Day Five
Day Five will start with grading the prior night’s Conflict Test. The researcher
will take those into account when he makes the groups at the conclusion of Day Five.
Naughton 27
There will be a brief discussion on expectations, and successful procedures when
conflicts arise in a group atmosphere. The first activity of the day will be the “Jump Rope
Run.” In this activity, all the research participants get from one side of a jump rope to the
other. While it is swinging, only one research participant can run under the rope at a time,
and the others must follow without skipping one rotation of a rope. If the rope does skip,
the whole group must start over again.
Second activity on Day Five will be the “Human Knot.” The research participants
will be placed into groups of three to five. The research participants will get into a circle,
and grab another person’s hand (Note: a researcher participant must be holding two
different people’s hand). The objective is to untangle themselves without letting go of the
other research participant’s hand.
The final activity of Day five will be “Tarp Flip.” The research participants will
be placed on a tarp, and they must get everyone onto the other side of the tarp without
stepping off the tarp. These final activities are aimed to produce a group trust, and to
finalize the group dynamic for the researcher. After this activity, the researcher will take
all the data and observations, and place the research participants into groups of three to
five (preferable four). The experimental group will be placed into those groups for the
duration of the three-unit study. Those groups will be arranged into seating clusters, and
will reside in that area for the rest of the study. The control group will not be placed into
groups, and will be seated in traditional rows and columns.
Concept Delivery
The delivery of the mathematical vocabulary, topics, and methods will be the
same for the experimental group and the control group. There will be a number of
Naughton 28
different strategies depending on the topic of the day. This is where the researcher (and
other educators) can use their own personal strengths, and strategies to educate the
research participants. There will be no data, or observations from this section; its
purpose is specifically teaching mathematical concepts to the research participants.
Team Reliance / Peer to Peer Interaction
This step will be specific to the experimental group, and the control group will not
use this step. After the completion of the days lecture, or part of the lecture, the team will
check to make sure each student understands the new material, and makes sure that the
each research participants’ notes are complete and accurate. The researcher will distribute
Team Reliance worksheets where each research participants of the team must work
together to complete. The research will check for accuracy and that all students
participated by using colored pencils. The purpose is to 1) check for understand of the
research participants, and 2) teams are working collectively. Once this step is completed,
the research participants will then complete their Independent Practice or Homework
(known to the research participants as “Homefun”). There will only be observations taken
in this section, and no qualitative or quantitative data will be taken.
Group Assessment
This step will be specific to the experiment group, and the control group will not
use this step. In this phase, research participants will be assessed collectively using a
different assessment types. This could also include real life examples of the concept, or
portfolio activities. They will be required to work together to complete the formal
assessment. The goal of this section for the research participants to see a version of an
assessment in test type situation, and hope to finalize any problems before the individual
Naughton 29
assessment is administered. The data collection will be used to help determine the
effectiveness of the group’s team chemistry and work habits of the experimental groups.
That data will be analyzed and available in chapter four and five.
Individual Assessment
This step will be used in both the experimental group and the control group. At
the conclusion of each unit, the research participants will be assessed individually. There
will be no group work in this assessment in order to see if the research participant is
comprehending the material, and not simply relying on their group to succeed. The first
was through the assessment (Test) scores of the Experimental scores as they compared
the Control Group. After three sections of covered material, the research participants
would take a test do measure their competency in the covered material. The research
participant needed to get the entire problem correct to receive one point. If a research
participant missed one part, however minute, resulted in not receiving a point for that
question. In each test there are nine possible points. The data was collected and analyzed
individually and comparatively to the other group.
It is also providing the main source
of quantitative data that will be used to compare the degree of effectiveness between the
experimental group and control group.
Survey
This step will be used in both the experimental group and the control group,
however each group will have different surveys. Research participants will take surveys
to evaluate the effectiveness of the method and their enjoyment in the process. The
survey will be structured so that the research participants can rate the effectiveness of
Team Based Learning as it pertains to each individual research question. The survey will
Naughton 30
also give them a voice to share their thoughts on the study as a whole. This is will be
main source of qualitative data for the study. The surveys are organized in the following
order, 5 – Very Helpful, 4 – Moderately Helpful, 3 – Of little Help, 2 – No Help, and 1 –
Distracted me from learning, and was counter productive. Both surveys can be seen in
the Appendix.
Methodology in Closing
It is crucial for the research, and those who are recreating this action research
project, to use effective classroom management. As noted in chapter two, Team Based
Learning can be very effective, or it can be very distracting to the learning process. The
researchers best tool in this experiment will be proximity to the research participants and
keeping the groups on task. In Team Based Learning especially, the research participants
can become good friends, and want to participate in other distractive activities. This is not
a study of classroom management. The main focus of Team Based Learning is to the
capture the social nature of the research participants, and harness that energy to enhance
the learning process.
Naughton 31
Chapter 4 - Data Analysis
1. To what degree will Team Based Mathematics improve student’s ability in
mathematical communication?
To answer this research question, the researcher used questions five and six of the
survey given at the end of the study. These questions were answered by the twenty-nine
research participants of the experimental group. Question five read, “To what degree did
the team based approach help you [the student] use the vocabulary more frequently.”
Question six read, “To what degree did the team based approach help you [the student]
use the vocabulary more confidently?” In survey question five, 14 of 29 (48.276%)
responded with a rating of 3, 12 of 29 (41.379%) responded with a rating of 4, and 3 of
29 (10.345%) responded with a rating of 5. No research participant gave a rating of 2, or
1 (See Figure 4.1). A research participant felt that the communication from their peers
was helpful because, “[Team Based Learning] allowed me to hear it from another point
of view.” Another research participant recalled that the best part of the Team Based
Learning Groups was that he learned a lot, but his least favorite was that there was often
times too much talking from their group and others around him. Question five had the
following data in data table 4.1.
Table 4.1
Survey
Question
5
Number
29
Mean
3.6552
Mode
3
Median
4
In survey question six, 1 of 29 (3.448%) responded with a rating of 2, 11 of 29
(37.931%) responded with a rating of 3, 11 of 29 (37.931%) responded with a rating of 4,
and 6 of 29 (20.690%) responded with a rating of 5. No research participant gave a
Naughton 32
rating of 1 (See Figure 4.1). One research participant felt that the communication from
their peers was helpful because, “[Team Based Learning] allowed me to hear it from
another point of view.” This Question five had the following data in data table 4.2.
Table 4.2
Survey
Question
6
Number
29
Mean
3.7586
Mode
3 and 4
Median
4
2. To what degree will Team Based Mathematics improve a student’s ability to
retain previously covered material?
To answer this research question, the researcher used question four of the survey
given at the end of the study. This question was answered by twenty-nine research
participants of the experimental group. Question four read, “To what degree did the team
based approach help you [the student] retain the previously covered material?” In survey
question four, 3 of 29 (10.345%) responded with a rating of 3, 12 of 29 (41.379%)
responded with a rating of 4, and 15 of 29 (51.724%) responded with a rating of 5. No
research participant gave a rating of 2, or 1 (See Figure 3). One research participant
stated that, “what I liked the best about Team Based Learning was if I didn’t understand
something, I [research participant] could ask my team mates for help.” Another research
participant stated that, “if you don’t understand something, another student can help you.
So can the teacher, but from another student it’s more understandable.”
Question five
had the following data in data table 4.3.
Table 4.3
Survey
Question
7
Number
29
Mean
4.3793
Naughton 33
Mode
5
Median
4
3. To what degree will Team Based Mathematics improve a student’s ability to
retain previously covered material?
To answer this research question two different means will be analyzed. The first
is the series of three tests given to the Experimental Group (n = 29) and Control Group (n
= 30). The two groups will be compared throughout the process. On Test 1, the
Experimental Group had a mean of 4.9310, and the Control Group averaged 4.8333 out
of nine points possible. While the Experimental Group had a higher average, the
difference was not statistically significant (p > 0.05). Here is the following data for test 1
(Table 4.4). See figure 4.4, and 4.5 for graphical representations including box and
whisker plot, and bar graph.
Table 4.4
n
Experimental 29
Control
30
mean
4.9310
4.8333
Standard
Deviation
2.0445
2.1023
Degrees
of
Freedom
56.9999
T value
-0.202798
P value
0.5799
On Test 2, the Experimental Group had a mean of 4.8621, and the Control Group
averaged 5.4667 out of nine points possible. While the Control Group had a higher
average, the difference was not statistically significant (p > 0.05). Here is the following
data for test 1 (Table 4.5). See figure 4.5, and 4.6 for graphical representations including
box and whisker plot, and bar graph.
Table 4.5
n
mean
Standard
Deviation
Naughton 34
Degrees
of
Freedom
T value
P value
Experimental 29
Control
30
4.8621
5.4667
1.3289
2.0126
50.4330
-1.3659
0.9110
On Test 3, the Experimental Group had a mean of 3.2414, and the Control Group
averaged 3.1667 out of nine points possible. While the Experimental Group had a higher
average, the difference was not statistically significant (p > 0.05). Here is the following
data for test 1 (Table 4.6). See figure 4.7, and 4.8 for graphical representations including
box and whisker plot, and bar graph.
Table 4.6
n
Experimental 29
Control
30
mean
3.2414
3.1667
Standard
Deviation
1.6617
1.8953
Degrees
of
Freedom
56.4735
T value
P value
0.1612
0.4363
The other means was through question seven of the survey given at the end of the
study. This question was answered by twenty-nine research participants of the
experimental group. Question seven read, To what degree did the group assessments of
the team based approach help you [the student] understand the concept? In survey
question seven, 5 of 29 (17.241%) responded with a rating of 3, 9 of 29 (31.034%)
responded with a rating of 4, and 15 of 29 (51.729%) responded with a rating of 5. No
research participant gave a rating of 2, or 1 (See Figure 4.9). Question seven had the
following data in data table 4.7.
Table 4.7
Survey
Question
7
Number
29
Mean
4.6897
Naughton 35
Mode
5
Median
5
4. To what degree will Team Based Mathematics improve a students overall
enjoyment in a mathematics class?
To answer this research question, the researcher used questions eight and nine of
the survey given at the end of the study. This question was answered by twenty-nine
research participants of the experimental group. Question eight read, “To what degree
did you find the team based approach to mathematics helpful in the overall learning
Mathematics?” In survey question four, 1 of 29 (3.448%) responded with a rating of 3, 8
of 29 (27.586%) responded with a rating of 4, and 20 of 29 (68.966%) responded with a
rating of 5. No research participant gave a rating of 2, or 1 (See Figure 4.10). One
research participant said that math was fun until the Team Based Learning groups
stopped. Another research participant said, “Team based [learning groups] helps you
interact with classmates, and it’s fun to learn that way.” And another research participant
echoed stating, “Team Based [Learning], I think its more fun and if class is fun kids are
ganna want to come and learn.” Question eight had the following data in data table 4.8.
Table 4.8
Survey
Question
8
Number
29
Mean
4.6552
Mode
5
Median
5
Question nine read, “To what degree did you find the team base approach to mathematics
enjoyable?” In survey question four, 1 of 29 (3.448%) responded with a rating of 1, 2 of
29 (6.897%) responded with a rating of 3, 9 of 29 (31.034%) responded with a rating of
4, and 17 of 29 (58.621%) responded with a rating of 5. No research participant gave a
rating of 2 (See Figure 4.10). One research participant said, “The Team based approach
because having your friends help you with that you is a lot better then someone you
Naughton 36
barely know [the educator].” One research participant said that math was fun until the
Team Based Learning groups stopped. Another stated, “No, I like things how they are
[meaning the more traditional lecture style approach].” Another introverted research
participant stated that they did not enjoy it at all. Some students did not appreciate doing
it every day. One research participant showed one of the flaws in the Team Based
Learning when they answered the same question. “No, because I like working in groups
with other people it helps me out a lot, but when I am with my friends I get distracted
from the work and start talking.” Question nine had the following data in data table 4.9.
Table 4.9
Survey
Question
8
Number
29
Mean
4.4148
Naughton 37
Mode
5
Median
5
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Figures
Figure 4.1
15
10
Frequency
Question 5
Question 6
5
0
1
2
3
4
5
Rated Answer
Figure 4.1 Shows the answers to survey questions 5 and 6. This information is used to
answer Research Question 1. See Chapter 4.
Figure 4.2
15
10
Frequency
5
Question 4
0
1
2
3
4
5
Rated Answer
Figure 4.2 Shows the answers to survey questions 4. This information is used to answer
Research Question 2. See Chapter 4.
Naughton 48
Figure 4.3
8
6
Frequency 4
Experimental
2
Control
0
0
2
4
6
8
Test 1 Scores
Figure 4.3 shows the Test 1 scores. This information is used to answer Research
Question 3. See Chapter 4.
Test 1
Comparative Summery
0 1 2 3 4 5 6 7 8 9
Experimental
Control
Figure 4.4 shows the box plot of Test 1 scores. This information is used to answer
Research Question 3. See Chapter 4.
Naughton 49
Figure 4.5
10
8
6
Frequency
4
2
0
Experimental
Control
0
2
4
6
8
Test 2 Scores
Figure 4.5 shows the Test 2 scores. This information is used to answer Research
Question 3. See Chapter 4.
Test 2
Comparative Summery
0 1 2 3 4 5 6 7 8 9
Experimental
Control
Figure 4.6 shows the box plot of Test 2 scores. This information is used to answer
Research Question 3. See Chapter 4.
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Figure 4.7
10
8
6
Frequency
4
2
0
Experimental
Control
0
2
4
6
8
Test 3 Scores
Figure 4.7 shows the Test 3 scores. This information is used to answer Research
Question 3. See Chapter 4.
Test 3
Comparative Summery
0 1 2 3 4 5 6 7 8 9
Experimental
Control
Figure 4.8 shows the box plot of Test 3 scores. This information is used to answer
Research Question 3. See Chapter 4.
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Figure 4.9
15
10
Frequency
5
Question 7
0
1
2
3
4
5
Rated Answer
Figure 4.9 shows the answers to survey question 7. This information is used to answer
Figure 4.2
15
10
Frequency
5
Question 4
0
1
2
3
4
5
Rated Answer
Research Question 3. See Chapter 4.
Figure 4.10
20
15
Frequency
10
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Question 8
Figure 4.10 shows the answers to survey questions 8 and 9. This information is used to
answer Research Question 4. See Chapter 4.
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