INCORPORATING HISTORY INTO A MATH CLASSROOM 1
Effectiveness of Incorporating the History of Mathematics into the Sixth Grade Math classroom
over a Three Six-Week Grading Period.
Kelsey Sellers
Emory and Henry College
INCORPORATING HISTORY INTO A MATH CLASSROOM 2
Introduction/Rationale
Math is known to be a high anxiety subject. What if we could lessen that anxiety by
incorporating other subjects into this content area? My experience has been that all teachers
know that if you can relate the material you are teaching to the student’s real life experience they
will retain the information and have a deeper understanding for why they are learning the
material. Educators are always researching strategies and techniques on how to engage their
students. Many teachers have found success in integrating two content areas to reinforce
previous knowledge or to set up for new material. Most teachers like to combine History and
Language Arts or Science and Math. Although these areas work well together, we find that
students are still struggling with math. Many students say that math just isn’t their subject;
however, math can be everyone’s subject if you just find a way to make it interesting. Math and
history have an intertwining relationship of which many people are unaware. Incorporating the
history of mathematics into a sixth grade math classroom can have an effect on how students
learn math concepts. The students will learn the origins of mathematical tools, equations,
notations, and groundbreaking mathematicians. Through this integration, the students will
develop a sense of purpose. The point of this integration is to show students that math doesn’t
have to a stressful subject. Hopefully, integration of the two subjects will help students forget
that they are learning math. If you allow your students to explore and ask questions about the
origins of the material, you are broadening their outlook on the world around them.
INCORPORATING HISTORY INTO A MATH CLASSROOM 3
Literature Review
Mathematics has a reputation as a “dull drill” subject, and relevant studies report a steady
decline in students’ attitudes toward the subject through high school (Liu, 2003). Many authors
suggest that incorporating the history of mathematics in the classroom leads to a heightened
awareness and appreciation of mathematics, aids in looking at problems from a different
perspective, and helps students understand why mathematics is important (Bellomo and
Wertheimer, 2010). Many studies have been done to show the correlations between
incorporating history and student’s achievement. Some showed some difference in test scores
and others had no significant effect on improving students’ attitude towards mathematics (Liu,
2003).
Characteristics of a Sixth Grader
In order to understand how to conduct this research is to understand what is happening
developmentally with a sixth grader, which is approximately 11 to 12 years old. First we must
establish that every child’s development is unique (Glendale, 2010). We must cover the
physical, social, emotional, and intellectual development of the 11 and 12 year old. The
following lists provided by Glendale (2010) include the basic characteristics of an 11and 12 year
old:
The Eleven-Year-Old
Physical Development

Vast appetite for food, physical activity, and talking

Growth spurt of early adolescence for some girls, may feel awkward and clumsy

Girls ahead of guys in physical maturity
INCORPORATING HISTORY INTO A MATH CLASSROOM 4

Wide differences among individuals in rate of development

Curious about opposite sex
Social and Emotional Development

Less overt affection and attention shown to parents

Impulsive, unaware

Focus on self

Experience extremes of emotions
Intellectual Development

Mostly interested in the present

Increased ability to de-center and see world from various perspectives

Development of ideals and selection of role models

Many experiment with dangerous risk-taking behaviors
The Twelve-Year-Old
Physical Development

Growth spurts

Physical activities and sports valued

Eating patterns change, over concern for dieting

Feel awkward and may worry about body
Social and Emotional Development

Struggle with sense of identity
INCORPORATING HISTORY INTO A MATH CLASSROOM 5

Moodiness

Friendships with both sexes are important

Complain about parents interfering with independence

Peer vocabulary important
Intellectual Development

Hormonal and physical demands of puberty may cause slowing of rate of cognitive
development during early adolescence

Increased ability to think abstract in intellectual pursuits

Lack of understanding of cause and effect

Idealistic; may offer “ideal” solutions to complex problems (Glendale, 2010)
Standards
When teaching in a sixth grade math classroom you will have standards that need to be
achieved by your students. In order to create lessons to incorporate history, you have to
know what you are teaching. The following are some standards that are covered in a sixth
grade math classroom in Virginia: Relationships among Fractions, Decimals, and Percents;
Problem Solving with Area, Perimeter, Volume, and Surface Area; Practical Applications of
Statistics; and Variable Equations and Properties (Virginia’s Standards of Learning, 2009).
Previous Research
The merits of incorporating history into mathematics education have received
considerable attention and have been discussed for decades (Liu, 2003). Researchers have
many reasons for the using the history of mathematics in school curricula: history can help
INCORPORATING HISTORY INTO A MATH CLASSROOM 6
increase motivation and helps develop a positive attitude toward learning; past obstacles in
the development of mathematics can help explain what today’s students find difficult;
historical problems can help develop students’ mathematical thinking; history reveals that
humanistic facets of mathematical knowledge; and history gives teachers a guide for teaching
(Liu, 2003) and (Bellomo and Wertheimer, 2010).
One specific research study by Bellomo and Wertheimer was done in a secondary
classroom where the history of mathematics was conducted into the curricula of an Algebra
classroom over twenty-seven weeks. They incorporated history by introducing students to a
given objective. Many lessons involved students reading a prepared summary; or at times,
students were asked to research on their own (Bellomo and Wertheimer, 2010). Also, to
introduce or close a lesson, handouts on mathematicians throughout history were provided.
On occasion, historical problems and methods were studied, worked on, and compared to
current methods (Bellomo and Wertheimer, 2010). One could argue that there is insufficient
time to include historical objectives. However, to ensure no time is taken from the
mathematics curriculum; history should not be an extra activity- it should be incorporated
into lessons (Liu, 2003). Another problem is classroom resources are not conducive to
teaching history of mathematics, so it’s up to the teacher to supplement the material with
their own background research and preparation (Bellomo and Wertheimer, 2010). Lastly, the
amount of time it takes in planning historical lessons that link to classroom objectives can be
significant. The internet quickly provides numerous lessons, readings, and teaching
strategies. The effort is worth the reward, and research urges teachers to take it upon
themselves to investigate historical topics (Gulikers and Blom, 2001). Research by Bellomo
and Wertheimer compared the average of the student test scores for each class. The pretest
INCORPORATING HISTORY INTO A MATH CLASSROOM 7
was administered each class began with an average pre-test score of 85%. Also there was a
comparison of the averages of semester one grades, where the control group was at a slightly
higher average (81%) then the history class (79%). Finally, when comparing the average
grades at the end of the study, the history class has an average that is 10 percentage points
higher than the control group (Bellomo and Wertheimer, 2010). In conclusion of classes,
there is a significant amount of difference to prove that incorporation of history of
mathematics improves student performance. According to Bellomo and Wertheimer, they
study enhanced teaching practices and they grew as professionals.
However, some other researchers stress that you should understand how you are
going to use history in your classroom when you are incorporating. The main argument is
using history as a tool. This argument means that history can be a motivating factor for
students in their learning and study of mathematics (Jankvist, 2009). Jankvist also says that a
historical approach may give mathematics a more human face and perhaps make it less
frightening. Lastly, often pieces of the mathematical development over which past
mathematicians have stumbled will also be troublesome for today’s students of mathematics
(Jankvist, 2009).
My Action Research
Based upon this review incorporating history in a math classroom can bring positive
effects to learning math concepts. It also strengthens the relationship between history and
mathematics and shows that my research will be able to have comparable results with previous
research. Overall, the previous research will be a foundation to my research and I’ll be able to
add to the scholarly literature pertaining to incorporating history into a mathematics classroom.
INCORPORATING HISTORY INTO A MATH CLASSROOM 8
Research Design
The topic of my action research is the effectiveness of incorporating the history of
mathematics into a sixth grade math classroom over a three six weeks grading period. My
literature review justified the reasons and positive outcomes of this study. To conduct this study I
will have two groups of six grade students. There will be 20 students in each group. One group
will receive the instruction of the History of Mathematics in supplement to their Math
instruction. The other group will be the control group and will just receive the regular math
instruction without the treatment. These groups will be chosen from general education students
with average grade distribution and will be picked at random. The students will be divided up
boys and girls and every third boy and girl will be split evenly between the treatment group and
the control group.
The research will take place over a three six weeks grading period. This amount of time
will allow the results to be conclusive. Both groups will be given assessments on the same
material, and each quiz and test will be recorded throughout the three six weeks to show how the
incorporating of history into mathematics effects the students class averages. The quizzes and
tests will be recorded in Table 1. The results recorded in Table 1 will then be converted into a bar
graph to visually display the data that was collected.
Instruction for both groups will begin with a practice problem or going over the previous
night’s homework. Both classes will then move into to their regular math instruction for the day.
The treatment group for the last fifteen minutes of class receives supplement instruction by
incorporating information about the history of mathematics. The students will either be required
to research a topic in the history of mathematics or they will be given a handout on
INCORPORATING HISTORY INTO A MATH CLASSROOM 9
mathematicians. Sample 1 illustrates an example of what a lesson or activity would look like
when given to the treatment group. The control group for the last 15 minutes will be working on
other subjects other than math so they will not get any extra practice or support that would
influence the results. The classes will be held on a modified block scheduling. The control group
will have class 9:30 to 10:30 and the treatment group will receive their instruction at 10:30 to
11:30.
The treatment group and control group at the end of the three six weeks grading period
will be given a survey and be used as supplemental information for the study. See Sample, which
is an example of the survey/questionnaire. The survey will be used to produce feedback on if the
instruction meets the student’s needs.
INCORPORATING HISTORY INTO A MATH CLASSROOM 10
Sample 1
Lesson 3: Internet Search
What will students be learning?
STANDARD(S)
Students develop number sense, understand and use appropriate math vocabulary, understand
and use numbers and number relationships in problem-solving situations, and communicate
the reasoning used in solving these problems. (M1)
Students read to locate, select, evaluate, and make use of relevant information from a variety of
media, reference, and technological sources. (RW5)
BENCHMARK(S)
Students construct and interpret number meanings through real-world experiences and the use
of hands-on materials and relate these meanings to mathematical symbols and numbers.
Students understand the structure, organization, and use of various media, reference, and technological
sources as they select information for their reading, writing, and speaking purposes.
Students paraphrase, summarize, organize, evaluate, and synthesize information.
OBJECTIVE(S)
Students will increase their understanding of the Mayan numerical system and Mayan architecture
by using the Internet as a resource.
SPECIFICS
Mathematics: The Mayan number system can be located on the Internet at many different
addresses.
Architecture: The Maya built entire cities containing many different types of structures, including
temples, pyramids, castles, housing units, markets, and plazas. In fact, the Maya even built
courts to play a hand ball game. The Mayan cities were ceremonial cities rather than commerce
cities. This can be witnessed in the types of buildings constructed. Students should be able to
find many sites on the Internet that contain colorful pictures of these architectural structures.
What will be done to help students learn this?
INSTRUCTIONAL STRATEGIES
Student-directed activity
Reading comprehension
PRELIMINARY LESSON PREPARATION
Obtain signed Internet permission slips before allowing students to use the Internet. Review
process of how to retrieve information on the Internet with students.
ACTIVITY
Search for “Maya” by using a search engine. Record any URLs that refer to Mayan numbers
and/or architecture. Summarize your findings on Worksheet 6.
Lesson 3 (cont.)
RESOURCES/MATERIALS
Internet permission forms
Internet access
Summary sheet (WS 6)
URLs:
http://www.okcommerce.com/terra/cultures/mayan/mayan1.html
History of Mayan Culture
http://www.kn.pacbell.com/wired/fil/pages/huntmayancivi.html
Digging for the Ancient Maya
http://www.astro.uva.nl/michielb/maya/links.html
http://www.civilization.ca/membrs/civiliz/maya/mmc01eng.html
ASSESSMENT
Summary sheet (Worksheet 6) demonstrates thorough research.
Goals 2000 Partnership for Educating Colorado Students 20
INCORPORATING HISTORY INTO A MATH CLASSROOM 11
Internet Search: Worksheet 6
Directions: Please list ten URLs you have found that relate to Mayan mathematics or Mayan architecture.
1. _______________________________________________________________________
2. _______________________________________________________________________
3. _______________________________________________________________________
4. _______________________________________________________________________
5. _______________________________________________________________________
6. _______________________________________________________________________
7. _______________________________________________________________________
8. _______________________________________________________________________
9. _______________________________________________________________________
10. _______________________________________________________________________
Directions: Summarize, in your own words, information gathered about Mayan mathematics
or Mayan architecture from Internet sites.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Sample 2
Survey/Questionnaire:
-Students will be asked to rate each question on a scale from 1 to 5 if they agree or disagree
with the statement. (1- strongly agree, 2- agree, 3- neutral, 4- disagree, 5-strongly disagree)
1.
2.
3.
4.
Checking assignments in class improved my overall understanding of concepts.
Relating objectives to English improved my overall understanding of concepts.
Relating objectives to Science improved my overall understanding of concepts.
Relating objectives to Social Studies/History improve my overall understanding of
concepts.
5. Participating in discussions with peers improved my overall understanding of
concepts.
6. Reading about mathematics improved my overall understanding of concepts.
-Students will write down their likes and dislikes to each question.
7. What have you liked about your past mathematics classes?
8. What have you liked in your current mathematics class?
9. What have you not liked about your past mathematics classes?
10. What have you not about your current mathematics class?
(Bellomo and Wertheimer, 2010)
INCORPORATING HISTORY INTO A MATH CLASSROOM 12
Table 1
Grades
1st Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz4
Test 2
Quiz 4
Quiz 5
Test 3
Average Quiz
Scores:
Average Test
Scores:
2nd Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz 4
Test 2
Quiz 5
Quiz 6
Test 3
Average Quiz
Scores:
Average Test
Scores:
rd
3 Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz 4
Test 2
Quiz 5
Quiz 6
Test 3
Average Quiz
Scores:
Average Test
Scores:
Control Group
Treatment Group
INCORPORATING HISTORY INTO A MATH CLASSROOM 13
Justifying the Construct of the Study:
I’ve decided to study this question: Effectiveness of Incorporating the History of
Mathematics into a Sixth Grade Math classroom over a Three Six Week Grading Period. I have
completed my literature review and design to conduct my action research. I will be using Table 2
to record and analyze the quantitative results.
The table will be used to collect the control group and treatment group grades throughout
the three six weeks grading periods. The results of the grades will be averaged to see the
difference between the two groups. The results will be converted into a bar graph to show the
comparison between each six weeks with the control group and treatment group compared. See
the example of the bar graph in Figure 1.
As indicated in the literature review of the study conducted by Bellomo and Wertheimer.
In order to establish a quantitative result, “the students average test scores from the treatment
group and control group must be recorded” (Bellomo and Wertheimer, 22). Also, it is important
to record the qualitative result as well. “At the end of the research the students will be provided a
questionnaire for teachers to receive feedback about how the material and instruction meets their
needs” (Bellomo and Wertheimer, 22). The results of questions one through six of the
survey/questionnaire will be put into a horizontal bar graph. See Figure 2, the
survey/questionnaire, and see the Figure 3, an example of the horizontal bar graph that will be
used. The survey/questionnaire will provide the qualitative result to the quantitative result
collected by the study and will justify the conducting of this study.
INCORPORATING HISTORY INTO A MATH CLASSROOM 14
Grades
1 Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz4
Test 2
Quiz 4
Quiz 5
Test 3
Average Quiz
Scores:
st
Average Test
Scores:
2nd Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz 4
Test 2
Quiz 5
Quiz 6
Test 3
Average Quiz
Scores:
Average Test
Scores:
rd
3 Six Weeks
Quiz 1
Quiz 2
Test 1
Quiz 3
Quiz 4
Test 2
Quiz 5
Quiz 6
Test 3
Average Quiz
Scores:
Average Test
Scores:
Table 2
Control Group
Treatment Group
INCORPORATING HISTORY INTO A MATH CLASSROOM 15
Figure 1
(Bellomo and Wertheimer, 2010)
Figure 2
Survey/Questionnaire:
-Students will be asked to rate each question on a scale from 1 to 5 if they agree or disagree
with the statement. (1- strongly agree, 2- agree, 3- neutral, 4- disagree, 5-strongly disagree)
1.
2.
3.
4.
Checking assignments in class improved my overall understanding of concepts.
Relating objectives to English improved my overall understanding of concepts.
Relating objectives to Science improved my overall understanding of concepts.
Relating objectives to Social Studies/History improve my overall understanding of
concepts.
5. Participating in discussions with peers improved my overall understanding of
concepts.
6. Reading about mathematics improved my overall understanding of concepts.
-Students will write down their likes and dislikes to each question.
7. What have you liked about your past mathematics classes?
8. What have you liked in your current mathematics class?
9. What have you not liked about your past mathematics classes?
10. What have you not about your current mathematics class?
(Bellomo and Wertheimer, 2010)
INCORPORATING HISTORY INTO A MATH CLASSROOM 16
Figure 3
Comparison of Results of the Students Responses of Questionnaire
(Bellomo and Wertheimer, 2010)
INCORPORATING HISTORY INTO A MATH CLASSROOM 17
Graphic for Data Analysis and Findings:
A multiple bar graph will be used to display the data that is collected from table 2 that
was shown in the justification of my study. Graph 1 shows what the multiple bar graph will look
like.
Average Quiz and Test Scores of the Control and Treatment Group
100
90
80
70
60
Avg. Quiz (CG)
50
Avg. Test (CG)
40
Avg. Quiz (TG)
30
Avg. Test (TG)
20
10
0
1st 6 Weeks
2nd 6 Weeks
3rd 6 Weeks
Graph 1
The Second graphic that will be used is a horizontal bar graph. The horizontal bar graph will be
used to display the data analysis of the first six questions of the survey/questionnaire, which was shown in
Sample 2 of the research design. Graph 2 shows an example of the horizontal bar graph.
INCORPORATING HISTORY INTO A MATH CLASSROOM 18
Comparison of Results of the Students Responses of Questionnaire
Graph 2
(Bellomo and Wertheimer, 2010)
INCORPORATING HISTORY INTO A MATH CLASSROOM 19
Research Site:
School Division:
The school division has seven Elementary Schools, four Middle Schools, six High Schools,
and two technical schools, which a grand total of nineteen schools in the School division. The
configuration of the schools in the division is broken down as follows: K-5 Elementary School,
6-8 Middle School, 9-12 High School, and 9-12 Careers and Technical School.
School Site:
Middle School located in Southwest Virginia. The school has 325 students. The student
populates is 99% White/Caucasian and less than 1% is another ethnicity. Gender breakdown is
50/50 roughly between boys and girls. The school has 46% free/ reduced lunch, so the school is
considered low-income socioeconomic status (LSES). The school has 30 full time teachers, 2 full
time administrators, one guidance counselor, and one full time nurse. The school is configured
into 6th, 7th, and 8th grade with block scheduling.
General Education Classroom in the 6th Grade:
All classes have about 14-20 students. There are 5 licensed 6th grade teachers who each teach
two subjects. Most students will have three different teachers throughout the day. The classes are
50/50 in gender ratio. The class ethnicity is mostly white with two students being African
Americans.
Research Classroom:
Teacher is English speaking and newly licensed with a Master’s Degree in Education for
Professional Studies. The teacher has a background in teaching history and mathematics. The
INCORPORATING HISTORY INTO A MATH CLASSROOM 20
teacher has two 6th grade Math classrooms. Each class has 20 students per group. Classroom will
be 50/50 boys and girls and the groups are chosen randomly based on grade distribution. All
students will be facing the teacher, see Figure 1 to see how the classroom will be set up. The
control group will have their math instruction at 9:30 to 10:30 a.m. and the treatment group will
have their instruction at 10:30 to 11:30a.m.
Figure 1
Smart Board
Student’s Desks
Door
Teacher’s Desk

Window
Window
White Board
INCORPORATING HISTORY INTO A MATH CLASSROOM 21
Findings and Implications based on Data Analysis:
Based on the data that was shown in Graph 1, in the graphic for data analysis, the
students in the treatment group received the best average quiz and test scores at the end of the
three six-week grading period. The implication of this data shows that incorporating the History
of Mathematics into a Math classroom has a positive effect on the students who received the
treatment versus the control group.
Based on the data that was collected for the survey/questionnaire in Graph 2, shown in
the graphic for data analysis, 100% of the students of both groups strongly agree that reading and
researching about the history of mathematics would help understand the concepts of math. This
result has the implication that students strongly need to read about the history of mathematics to
better understand concepts of math. This reinforces that incorporating the history of mathematics
into a math classroom has a positive effect on students.
Limitations of the study design:
There are limitations of this study due to the research design. One is that treatment group
is too small with only 20 students. Second, the sampling pool of the mostly white population
lacks diversity. Third, the study is not conducted long enough to truly get an accurate assessment
of the treatment group and control group. Fourth, there are uncontrollable factors which could
serve to disrupt the study. For example, assemblies, clubs, and other extracurricular activities
that sometimes result in disruptions to the regular class schedule. Finally, the study is limited to
one geographic area.
INCORPORATING HISTORY INTO A MATH CLASSROOM 22
Suggestions for Future Research:
Future research should include all students in a selected math class rather than just those
in the C average grade range. . Future research should also be expanded to include a more
ethnically diverse student population. Another suggestion would be to conduct a study over the
course of an entire year in order to gather more longitudinal data. A camera could be installed to
record each class to make sure students who miss class are getting the same treatment and
consistency. Future research should examine more resources for students with learning
differences.
INCORPORATING HISTORY INTO A MATH CLASSROOM 23
References
Bellomo, Carryn & Wertheimer, Cassidy. (2010). A Discussion and Experiment on
Incorporating History into the Mathematics Classroom. Journal of College
Teaching and Learning, 7(4), 19-24.
Glendale-River. (2010). Developmental Characteristics of Sixth Graders.
Gulikers, Iris & Blom, Klaske. (2001). A Historical Angle, A Survey of Recent Literature
on the Use and Value of History in Geometrical Education [Electronic Version].
Educational Studies in Mathematics, 47(2), 223-258.
Jankvist, Uffe Thomas. (2009). A categorization of the ‘whys” and “hows” of using
history in mathematics education. Springer Science, 71, 235-261.
Liu, Po-Hung. (2003). Do Teachers Need to Incorporate the History of Mathematics in
Their Learning? Mathematics Teacher, 96(6), 416-420.
Virginia Standards of Learning. (2009). Six Grade Mathematics. Mathematics Standards
of Learning for Virginia Public Schools.