Introducing Mathematicians in History into
the High School Classroom
By Gloria Rodriguez
Spring 2016
In Partial Fulfillment of
PED 4382 ̶ Senior Project
Department of Mathematics and Statistics
University of Houston-Downtown
Faculty Advisor:
Dr. Timothy Redl
Committee Member:
Dr. R. Judith Quander
Committee Member:
Dr. Jacqueline Sack
Department Chair:
Dr. Shishen Xie
Table of Contents
Abstract ......................................................................................................................................................... 2
Acknowledgements....................................................................................................................................... 3
Introduction .................................................................................................................................................. 4
Part One: Hispanics in Mathematics ............................................................................................................. 5
Argentina: Alberto Calderon, PhD ............................................................................................................ 5
Mexico: Isabel Hubard, PhD ...................................................................................................................... 8
Puerto Rico: Minerva Cordero, PhD ........................................................................................................ 10
California, USA: Richard Tapia, PhD ........................................................................................................ 11
Part Two: Introducing Mathematicians in History into the High School Classroom .................................. 13
Process .................................................................................................................................................... 13
Products .................................................................................................................................................. 15
Survey Results ......................................................................................................................................... 16
Challenges ............................................................................................................................................... 17
Observations ........................................................................................................................................... 18
Reflections .............................................................................................................................................. 19
Conclusion ................................................................................................................................................... 19
Appendix A .................................................................................................................................................. 21
Appendix B .................................................................................................................................................. 22
Appendix C .................................................................................................................................................. 23
References .................................................................................................................................................. 24
Abstract
The motivation for this project began in the summer of 2015 while taking the history of mathematics
course with Dr. Ryan Pepper. As a mathematics and educational major, I thoroughly enjoyed his course
because it helped me understand background information about my field of study and gave me the
knowledge I need in order to answer my students’ questions about how certain aspects of mathematics
were discovered. During the class we went over a myriad of mathematicians, the obstacles in their
paths, their contributions, and the applications of their findings. The majority of the mathematicians
were of European descent, which inspired me to wonder about my own heritage and whether there
were significant accomplishments made by Hispanic mathematicians - if so, what were they?
Another question Dr. Pepper inspired me to ask was “Why was this the first time I had been exposed to
the history of mathematics?” There have been many times throughout my education where we have
discussed and used theorems in the classroom, but never had we heard who or how these theorems
came about. Why? Why wasn’t I enlightened in middle or high school when, for example, we used the
Pythagorean Theorem, as to who Pythagoras was?
Acknowledgements
My deepest gratitude is extended to everyone who has helped me throughout my pursuit of higher
education.
Dr. Timothy Redl, thank you for your guidance and support throughout the course of this project. I could
not have done this project without you keeping me on track.
Dr. R. Judith Quander, thank you for your guidance throughout my time at UHD as my advisor,
committee member, and professor. Also, thank you for assisting me with obtaining the Noyce
Scholarship for Mathematics majors aspiring to become high school teachers.
Dr. Jackie Sack, thank you for encouraging me to pursue a secondary certification as well as an advisor,
committee member, and professor. Also, thank you for seeing enough potential in me to refer me to the
Noyce Scholarship.
Dr. Ryan Pepper, thank you for your passion and positivity during my time as your student in your
History of Mathematics course. It inspired me as a future teacher of mathematics and planted the seed
for this project.
To the Noyce Scholarship and its committee, including Dr. Nancy Leveille who has since retired, without
which I would not have been able to continue my pursuit of a Mathematics B.A. with a Secondary
Teacher’s Certification.
Thank you to my cooperating teacher, Mrs. Vanessa Beery, who guided me through my student teaching
semester. Thank you for being an excellent role model for myself and your students. For exemplifying
what an excellent high school teacher is. I am grateful to have had you as a cooperating teacher.
Tanisha Caballero, my best friend and confidant, you are the reason I returned to school in 2011 and the
reason I didn’t give up. You are my truest friend and I will never be able to thank you enough for all you
have done for me and my family.
Thank you to my children, my sons, Robert, Chris, and Alex, and my daughter, Lillian, thank you for all
the times you helped me prepare for my classes. Thank you for understanding when I couldn’t be there
for a special school event at times, knowing that I was there with you in spirit, and that it would all be
worth it in the end. Thank you for helping out whenever dad or I needed you to. Thank you for being the
best most respectful and loving kids we could have ever asked for.
To my husband, Jason, thank you for supporting me while I pursued my dream. Thank you for taking on
all the extra responsibilities and making it a priority to be there for our children, especially when I
couldn’t be there. Thank you for believing in me and for standing by my side through thick and thin.
Thank you for knowing that I was working towards a better future for us all, and not just for myself. I
love you and could not have done this without your support.
Introduction
I wanted to incorporate both mathematics and education into my project. In order to do this I split my
project into two parts. The first revolved around my Mathematics major, which involved researching
Hispanic mathematicians. The second revolved around my student teaching for the Secondary Teacher’s
Certification portion of my degree, which entailed introducing mathematicians in history to high school
classrooms.
For the first part of my project, I researched Hispanics in mathematics from different Latin American
countries. I did this because I wanted to explore mathematicians in not only my own heritage as a
Mexican- American, but also in other Hispanic cultures. I also looked into the statistics of the U.S.
population of Hispanics that go into the field of mathematics.
In my research of Hispanic mathematicians, I not only discuss their background and education, but also
whether or not they had to overcome any obstacles to achieve their goals. I also discuss why they chose
to become mathematicians? If so, what were they? What area of mathematics is their concentration?
What contribution have they made to mathematics? Where they are now or where did they end their
career?
For the second part of my project, I incorporated my research of mathematicians into my high school
classroom. In thinking about my History of Mathematics course it occurred to me that, before college, I
had never been educated about the background of the people responsible for the theorems we went
over in high school, or middle school for that matter. I asked myself why? So, I created a research
project that was made available to all students currently taking Geometry, which required them to
research a mathematician in history and provide their findings in a research paper and poster.
In this section, I document the process and issues which came about when introducing mathematicians
in history to my high school students. I discuss the resulting products and results of the surveys. Then I
document my observations and the reflections of the geometry teachers involved in the assignment, as
well as my overall reflections. I, then, discuss what my plan is for using this activity in my own
mathematics classroom. Finally, I answer how this part of my project affects my views as an educator?
Part One: Hispanics in Mathematics
The primary reason for this part of my project was because I was curious about my own heritage. I
wanted to know whether there were any Hispanic mathematicians. If so, who are or were they?
According to 2011 census records, about 116 million adults between the ages of 25 and 64 were
employed in the U.S. of which about 7.2 million were employed in STEM related fields. Of these 202,667
were employed in mathematical occupations, which included actuaries – 22,069, mathematicians –
2,450, operations research analysts – 133,100, statisticians – 42,358, and miscellaneous mathematical
science occupations – 2,690. The amount of Hispanics or Latinos employed in STEM fields was 6.1%. The
percentage of Hispanic/Latino mathematicians employed in 2011? Zero. So, where are the Hispanic
mathematicians?
Argentina: Alberto Calderon, PhD
Dr. Alberto Calderon was a world renowned mathematician. He was born
September 14, 1920 in Mendoza, Argentina. His mother was known as a “freespirited” woman and his father was a urologist. He was born into a family that
valued education. He had 2 siblings an older sister, Nenancha, and a younger
brother, Calixto, who also became a mathematician. Dr. Calderon was married twice the first to Mabel
Molinelli, who died in 1985, and the second to Dr. Alexandria Bellow, who is also a mathematician and
who was a mathematics professor at Northwestern University. Dr. Calderon had two children with his
first wife: Maria a PhD in French literature, and Pablo a mathematician.
As a young child, Dr. Calderon’s father stressed the importance of education in his children’s lives. He
encouraged his children to compute things on a whim and played classical music for them in order to
stimulate their brain. At the age of 12, after his mother died, Dr. Calderon’s father sent him boarding
school in Switzerland, where he spent two years studying at the Institut Montana Zugerberg.
Dr. Alberto Calderon received his thirst for mathematics in Switzerland. After getting into some trouble,
his professor, Dr. Save Bercovici, “punished” him by challenging him to create an isosceles triangle with
a ruler and compass given only the measurements of the height and the sum of length of the base and
one of its sides. Dr. Calderon solved this problem and his love for mathematics was born.
After returning to Argentina, Calderon completed his studies and eventually graduated from the
University of Buenos Aires with a civil engineering degree in 1947. In 1948, Calderon’s mentor at the
University of Buenos Aires, Dr. Alberto Gonzalez Dominguez, invited Dr. Antoni Zygmund, professor at
the University of Chicago and also a world renowned analytical mathematician, to speak at the
University of Buenos Aires. It was during this lecture that Calderon and Zygmund met. Dr. Zygmund tried
to convince him to pursue his doctorate at the University of Chicago. It wasn’t until 1949, after applying
for and being awarded the Rockefeller Scholarship, that Dr. Calderon finally left Argentina for Chicago to
obtain his PhD in mathematics, which he accomplished in 1950. For his dissertation, Dr. Calderon solved
three longstanding problems in ergodic theory – the study of the average behavior of dynamical systems
over a long period of time, and in harmonic analysis – the study of waves like sound waves interrelated
with the object where the wave originates. After Calderon completed his PhD, he went on to work at
Ohio State University, Institute for Advanced Study at Princeton, MIT, as well as at the University of
Chicago and at the University of Buenos Aires. Dr. Calderon had a total of 27 PhD students throughout
the different universities he was a part of. He recognized the importance of having Hispanics pursue
mathematics degrees and doctorates so much so that he even sponsored many students.
Even while Dr. Calderon was working as a professor at the aforementioned universities, he also
continued to work with Dr. Zygmund. Dr. Zygmund was focused on function operators in higher
dimensions from an analytical standpoint, whereas Dr. Calderon was concerned with the function
operators in relation to partial differential equations. Together they made an unstoppable partnership in
the field of mathematical analysis. Zygmund and Calderon made great strides in the theory of singular
integrals, established what came to be known as the “Chicago school of analysis” – where students
collaborated in Fourier analysis and partial differential equations, and they also made groundbreaking
discoveries in the field of real and complex analysis where the Calderon-Zygmund theory was
established.
Some of Dr. Calderon’s achievements, which he also wrote papers for, include his breakthroughs with
singular integral operators, the Cauchy problem for partial differential equations, the boundary value
problems for elliptic equations, the Cauchy integrals, interpolation, ergodic theory, and on an inverse
boundary value problem. He received many awards during his lifetime. He won the Latin American Prize
in Mathematics from the Instituto para la Promocion de las Ciencias, Letras y Realizaciones – Argentina
1969, the Bocher Memorial Prize from the American Mathematical Society – U.S. 1979, the Konex Prize
in Science and Technology – Argentina 1983, the Wolf Prize from the Wolf Foundation – Israel 1989, the
Steele Prize from the American Mathematical Society – U.S. 1989, and the National Medal of Science –
U.S. 1991. Dr. Calderon was given honorary degrees from the University of Buenos Aires – Doctorate –
Argentina 1969, from Technion – Doctor of Science – Israel 1989, from Ohio State University – Doctor of
Science – U.S. 1995, and from the Universidad Autonoma de Madrid – Doctorate – Spain 1997. The
Instituto Argentino de Matematica also honored Dr. Calderon by adding Alberto Calderon to their name.
Dr. Calderon was an immeasurable asset to the field of mathematics. He helped advance modern
theories in singular integral operators and partial differential equations. He discovered new methods
and techniques to problems that have had applications in other fields of mathematics apart from
analysis. He helped advance the career of not only Hispanic mathematicians, but of mathematicians
from a variety of backgrounds. Dr. Calderon continued to work for the University of Chicago even after
he retired in 1985 until he died in 1998.
Mexico: Isabel Hubard, PhD
Dr. Isabel Hubard was born in Mexico City, Mexico. She was one of three children
born to a mother who was an engineer and a father who was an accountant. Not
much is known about Dr. Hubard’s personal life except that her husband is also a
mathematician. As a child, mathematics came easily, but she never thought of
pursuing a career as a mathematician. She, instead, wanted to become a bullfighter. Luckily for the
mathematics world, Hubard had a teacher, Oscar Chavez, who inspired her to want to learn more about
mathematics. He introduced her to the world of mathematics Olympiads and helped her train for them.
After graduating from high school, Hubard attended la Universidad Nacional Autónoma de Mexico
(UNAM) and graduated with a mathematics degree. Hubard went on to attend York University in
Toronto, Canada, after graduating from UNAM, where she received her master’s and doctorate degrees
in mathematics with her dissertation covering the subject of chiral polytopes and abstract polytopes
without symmetry.
Dr. Hubard went back to UNAM to work as a professor and continue her research on abstract polytopes
without symmetry, chiral polytopes, combinatorics, geometric topology, and on convex and discrete
geometry. Her achievements in her research include assisting in proving theorems related to chiral
polytopes. Within the preceding decade, chiral polytopes were known for a rank 3 and 4 only, but Dr.
Hubard helped prove that chiral polytopes of rank 5 existed. She accomplished this in conjunction with
Daniel Pellicer and Eugenia O'Reilly Reguiero. The following theorem was the result of their
collaboration:
For all but finitely many positive integers n, both An and Sn are the automorphism groups of a
chiral 4-polytope with type {3, 3, m} for some m.
For every d > 3, there are infinitely many chiral d-polytopes with type {3, 3,…, 3, m} for some m.
Some of Dr. Hubard’s other accomplishments include being awarded the L’Oréal-UNESCO-AMC
Scholarship for Exact Sciences in 2012. She won two Mathematics Olympiads and is serving as the
delegate for Mexico City in the Mexican Mathematics Olympiad of the Mathematics Society.
Dr. Hubard loves what she does and showed her passion for mathematics in an audio message included
in a bulletin on the UNAM social media webpage where she states that “the world wants applications
and technology now, but mathematics isn’t created overnight it’s created over time. And what we
mathematicians do isn’t because of its applications, but because of the beauty of mathematics, because
we enjoy doing it, because we want to add our grain of sand to the construction of science, and to learn
more about the world.”
Dr. Hubard still currently works for UNAM as a researcher and a professor. She seems to take great pride
in her passion for the elegance of mathematics. She recognizes the importance of getting Hispanics
involved in mathematics and actively participates in inspiring the younger generation. Dr. Hubard
especially sees the absence of women in the field as troublesome because she noted that while she was
in school there were more females in the classes than there were males, but she found that most
women gave up their careers in order to start a family. She states that when, or if, they decide to start a
family they will have to share equal responsibility because she does not want to give up her career.
Puerto Rico: Minerva Cordero, PhD
Dr. Minerva Cordero was born to a mother and father who were both farmers in
Bayamon, PR. She was the fourth born of 6 children. Dr. Cordero’s mother was able
to attend school long enough to make it to the sixth grade, but her father only had a
second grade education. Knowing the struggles they faced, both of her parents encouraged her and her
siblings to embrace school. According to Dr. Cordero, her mother “always told us that the best gift she
could give us was an education, because that is the one thing that no one can ever take away from you.
She instilled a love for learning in all of us.” Dr. Cordero credits for her love of mathematics to her
seventh grade teacher, Ms. Figueroa, who took time to show her the fun side of mathematics by giving
her different puzzles and games to do. Later, when Dr. Cordero was in the 11th grade her teacher
showed her a different more sophisticated side of mathematics and she was hooked on the subject
forever.
Dr. Cordero attended the University of Puerto Rico and received a bachelor’s degree in mathematics.
She attended Berkley University in California, after being awarded the National Science Foundation
Graduate Scholarship for minorities, where she received her master’s degree in mathematics. Dr.
Cordero went on to graduate from the University of Iowa with her PhD in mathematics – choosing to
attend there because her sister, Olga, was also a student there. Her primary focus of research is in finite
geometries.
Having had the opportunity to communicate via email with Dr. Cordero, I asked her why she pursued a
career in mathematics to which she answered, “Because as a student I always enjoyed math and noticed
that not everyone did. I was totally intrigued and fascinated by math!! So I wanted to learn more math
and be able to help those who didn't understand it.” In response to why she chose finite geometry, she
said, “It has great applications to cryptography and many other areas of math and science.” According to
Dr. Cordero, she loves finite geometries “because it combines algebra and geometry with combinatorics,
all in the setting of discrete mathematics.”
Dr. Cordero has been acknowledged many times for the work in her field as well as for her efforts to
encourage minorities to pursue a career in mathematics. She was named Ford’s Legendary Woman of
2016. She was awarded a certificate of meritorious service from the Mathematical Association of
America. In 2005, the University of Texas at Arlington inducted Dr. Cordero into their Academy of
Distinguished Teachers. UT at Arlington awarded her the Chancellor’s Excellence in Teaching Award in
2009. She is a member of the Society for the Advancement of Chicanos and Native Americans in Science,
Mathematical Association of America, American Mathematical Society, National Council of Teachers of
Mathematics, Association for Research in Undergraduate Mathematics Education, and the Association
for Women in Mathematics.
Currently, Dr. Cordero works as a professor and Associate Dean of Academic Affairs at the University of
Texas at Arlington. She is married with two children and her husband, Dr. James Epperson, is also a
professor at UT at Arlington. In her email, she offered herself as a resource in my career, if needed,
which is something that I believe she does for many students because she seems to truly care about
their future.
California, USA: Richard Tapia, PhD
Dr. Richard Tapia was born 77 years ago in Los Angeles, California, along with
his twin brother, Bobby. Both of his parents were emigrated alone from
Mexico before they were even teenagers – his mother at the age of 11 and
his father at the age of 7. He had 2 sisters and a younger brother. Dr. Tapia describes his upbringing as
full of love and encouragement. Although his family was poor, he and his siblings never realized it.
Dr. Tapia’s family and especially his mother stressed the importance of an education because with it he
could achieve anything. Dr. Tapia graduated from UCLA in 1961 with a BA in Mathematics and then with
a master’s in mathematics in 1966. In 1967, he completed his dissertation at UCLA on “A Generalization
of Newton’s Method with an Application to the Euler-Lagrange Equation” and received his PhD in
mathematics.
He recalls the adversity he faced growing up as a Mexican-American. Just because he was born a US
citizen didn’t mean he wasn’t Mexican and because of this was treated unfairly by his neighbors and
peers. Even in Mexico he was not treated equally because he was American. So, he was seen as a person
who was not good enough to be an American in America or a Mexican in Mexico. There are a few
moments that have stayed with him the most.
In the tenth grade, his school was holding a contest sponsored by the American Mathematical Society,
which he won. Every year the winner of the contest would be given their certificate during an assembly
at the school, however, instead of having an assembly for him, they called him to the principal’s office
and just handed him the certificate. Dr. Tapia believes wholeheartedly that he was treated this way
because he was Mexican and they didn’t want to acknowledge the fact that he was equal to or better
than them.
Even after Dr. Tapia finished graduate school, he still faced racism. Dr. Tapia got a job at the University
of Wisconsin, so he and his wife, Jean, rented a house in Wisconsin prior to moving. However, one day
before they moved they received a letter stating they could not rent to them after all. This, according to
Dr. Tapia, happened because they found out they were Mexicans. So, he and his wife, with the help of
the University, found another house. Their new neighbors then proceeded to refer to Tapia’s daughter
as black because they didn’t know what to call Mexicans – they just knew these people weren’t white so
they called them black.
Rather than allow himself to be filled with hate and resentment, Dr. Tapia decided that he was going to
show people that he was worthy and just as good as them. He was going to show people that he
deserves respect. He has earned a tremendous amount of honors for his work in mathematics and his
efforts to get people from all cultures interested in STEM fields. He was the first Hispanic to be elected
into the National Academy of Engineering, he was appointed to the National Science Board by President
Bill Clinton, and he was named a University Professor at Rice – an honor that only 6 professors have
been given. In 2011, Dr. Tapia was awarded the National Medal of Science, which is the highest honor
given to a scientist or engineer, by President Obama for “his pioneering and fundamental contributions
in optimization theory and numerical analysis and for his dedication and sustained efforts in fostering
diversity and excellence in mathematics and science education.”
Currently, Dr. Tapia is still working at Rice University as University Professor and Maxfield-Oshman
Professor in Engineering, director for the Center for Excellence and Equity in Education, and director of
the Empowering Leadership Alliance. He continues to mentor and sponsor students in their studies and
helping all students advance their careers in STEM fields.
Part Two: Introducing Mathematicians in History into the High School
Classroom
Process
Inspired by my History of Mathematics course I wanted a project that could be done in a group of 3 – 4
students, during class, and where students would research a mathematician from a list I provided.
Students would be required to write an outline, a 1 ½ to 2 page paper, and create a poster of their
findings. The list I provided was filled mostly with mathematicians that helped advance the field of
geometry, since I was teaching in a Geometry classroom.
I presented the project to my cooperating teacher, Mrs. Beery, and because we were currently in the
right triangle unit, which students generally struggle with, she suggested we offer the assignment now
rather than later. However, rather than offer the assignment as group work, it would be done as either
an individual or with a partner and as an extra credit assignment rather than in class. It would be worth
20 points towards the student’s right triangle assessment grade and we would introduce it to the
geometry team at the next meeting.
After discussing the project with the team, we decided the maximum points a student could obtain on
an assessment was 110 and, because of this, any points over the max would be applied to the student’s
transformation assessment so students who scored 100 wouldn’t be penalized by not receiving the full
20 extra credit points. Also, rather than have students provide a 1 ½ to 2 page paper, students would
only be required to submit a rough draft of their outline as well as a final draft of their outline. The
requirements for the outline were that it would include background, education, accomplishments and
contributions, and an overview paragraph of the mathematician. We agreed that students were to be
given one week to research their mathematician and submit a poster as well as a complete a survey
about their experience. Students were provided a flyer that included the specific requirements and
would keep them on track. The flyer included a checklist with due dates, which I strongly encouraged
teachers to sign off on to assist students in accomplishing their task. Students were assigned the project
on February 5th and it was due on February 12th.
Products
The quality of the majority of the final products was great. The majority of students in all the classes
showed they had taken their time on their projects. They were creative with their decorations, they
provided samples of works with pictures and writing out formulas, and they showed proper applications
of their chosen mathematician’s contribution to mathematics. Students also provided background and
educational information as well as an overview paragraph. I graded a total of 72 posters for three of the
six teachers who participated in the extra credit assignment. Of these
37 students scored a 17 - 20.
Students who scored a 13 - 16 on their poster did so because they
didn’t decorate their posters or showed signs of rushing on their
assignment. Students that received this score also missed no more
than two of the required components. These products were similar to
the sample at right. Of the posters I graded, 12 students scored in this
range.
Students who received a 9 - 12 did so because they either missed or plagiarized 3 to 5 of the
requirements. Students who plagiarized were given credit for their original work and zero credit for any
requirements that were plagiarized. Of the posters I graded, 19 students scored in this range.
Students who scored below a 9 either did not include most
aspects of the requirements or they plagiarized most of the
work they supplied. These students, however, still
decorated their poster, provided pictures, and included
samples of their chosen mathematician’s work. Of the
posters I graded, only four students scored in this range. A
sample of a poster that scored in this range is to the right.
Survey Results
I received surveys from 152 students who participated in the project. Of those surveyed less than 20
students skipped questions and the most skipped question was on the back of the survey. This was
probably because these 16 students didn’t realize there was a back.
There seemed to be a correlation between how students answered the questions regarding the quality
of their work and their overall experience. When students were asked to rate the overall quality of their
poster, 55% of the students rated their poster as exceptional, .7% as disappointing, and 38% as in
between. I also had 3% of students skip this question, 2.6% who wrote in a 2.5, and .7% who wrote in a
4. When answering to rate the quality of their outline, 59% chose exceptional, 1.3% chose disappointing,
37% chose in between, 2% wrote in a 2.5, and .7% skipped the question. For their overall experience,
57% students chose exceptional, 1% chose disappointing, 40% chose in between, and 2% skipped the
question.
86% of students surveyed were able to get their first choice for mathematician. Of the 20 students who
did not receive their first choice, one wanted Katherine Johnson, two students wanted Plato, two
wanted Archimedes, seven wanted Isaac Newton, and eight wanted Pythagoras. However, even when
students didn’t receive their first choice, I found that they were still happy with their overall experience.
They also still found their findings surprising.
According to the short answer section of the survey, most students enjoyed the experience. They found
learning about the mathematicians very interesting. The most frequent answer was that they wished
there were more projects like this, but some of their reasons for this were because it would help their
grade. Another reason given frequently was that they wished doing projects like this was the norm
rather than worksheets or in place of assessments.
Challenges
As with most projects I have done, there were some challenges that arose while conducting my research
project. These challenges included not being able to offer the assignment as an in-class activity, cutting
out the written paper portion, the offering of the assignment a week late, surveys going missing, and the
non-participation of one of the teachers in the Geometry team.
The fact that I was a student teacher had a lot to do with the fact that I couldn’t offer this assignment
during class. The curriculum is set and teachers are only given so many days to cover the unit. Therefore,
it was completely understandable that I would not be able to fit in my assignment into their calendar.
However, I believe the alternative suggestion of offering it as an extra credit project was an excellent
alternative.
Another drawback was having to cutout the written paper portion of the assignment. The Geometry
team felt that students would not participate as much if they had to actually write a paper. The answers
I received to one of the questions on the survey seemed to support this. The survey asked what students
liked the least from this project to which most answered typing/writing or something along those lines.
So, I feel this was also the best decision; however, I would have liked to have read the papers I would
have received.
The last three issues are related in that I didn’t really have control over what other teachers did or didn’t
do. This was just part of being part of a team. It was me having to depend on others to do something for
me and hoping they would follow through. I don’t believe I could have done anything differently to have
prevented these issues from arising, but I learned that sometimes things do not work out as you’d like
and you just have to roll with it and do the best you can with what you’re given.
Observations
Participation in class seemed to closely relate to whether or not a student would participate in the
project. The students who actively participated in class were also the ones who were most interested in
participating. These students included mostly ones who were struggling to get a C or B. The A students
who participate in class felt there was no need to do the project because they were already at the top of
the class and it would serve as no benefit to them.
The quality of the work done for homework and in-class assignments also held true for the quality of the
posters students turned in. Students who usually turned their work in neatly and on time took their time
on their projects and turned in posters which received 17 points or higher. Students who normally
turned in things that were incomplete did the same with their projects.
In working with the Geometry team, I found that the same type of attributes which applied to the higher
and lower grades applied to their participation in the project. If the teacher did not come to the
Geometry team meetings regularly and/or did not offer to help with different aspects of planning for the
unit lessons, then they had issues with offering and following up on the project. The teachers who
participated in the discussions, changes, and followed up with their students were the ones that did the
same in the Geometry team meetings.
Reflections
Discussing the project with the teachers who participated gave me insight into different approaches to
the project. I spoke with the different teachers separately so that I could get their input individually. All
the teachers stated they liked the project, but they would have liked to have offered it later in the year. I
found this interesting because during the discussion about when to offer it they all agreed it should be
offered as soon as possible since students were in the right triangle unit and they could learn about the
origins of Geometry. However, when I spoke with them separately they were all in agreement that
giving it out later would have been the better choice.
One of the teachers also stated that they would offer the assignment as an in class assignment rather
than extra credit. She said that way more students would have to participate, they could then present
their poster to the class, and they could have a class discussion about the different mathematicians. This
was exceptionally interesting to me because that was my original intention for this project, but
unfortunately, it didn’t work out that way.
Another suggestion was that the directions needed to include information about plagiarism. This came
from four of the six teachers who participated. I completely agree with this. There was way too much
plagiarism going on for us not to address it the next time we offer this assignment. The consensus was
that we know the students know better than to plagiarize, but that we should still explain to them that it
is wrong, it should not to be done, and that if any student does plagiarize they will receive zero credit for
their project.
Conclusion
It was very important to me to find out whether or not Hispanic mathematicians existed, even though I
was sure they did. I knew that there had to be a lot of them, but I also knew that I would have to go
searching for them myself if I truly wanted to learn. I was very glad to have found these four people as
well as the others that came across my searches. All of them made it part of their mission to encourage,
not just Latinos, but all minorities to get interested in and pursue a career in Mathematics and/or a
another STEM related field. These mathematicians also never forgot their home states or countries.
They are still in touch with them and have worked with or for them after graduation.
As a future educator, I feel that learning the background of my craft is necessary for me to properly
educate my students. Students will not only expect me to be knowledgeable about how to compute and
solve problems, but also about how these things came about. One of the most frequent questions I
heard as a student teacher was, “Why does this even work?” or “How did someone even come up with
this?” This was what made my project even more special than I originally thought. Not only was I able to
learn more about mathematicians in history from my own culture, but my students were also able to
find out for themselves who the people behind much of their mathematics were. They were able to find
out how the contributions of these people were used then and how they are used now. Students were
also able to find out how formulas and discoveries were updated into their current states. Students
were genuinely surprised with their findings and were happy with the project. Because of this, I feel that
I will definitely use this project in my own classroom.
Appendix A
Appendix B
Appendix C
Mathematician
Thales of Miletus
Pythagoras
Plato
Euclid
Apollonius
Archimedes
Hero of Alexandria
Pappus of Alexandria
Brahmagupta
Hypatia of Alexandria
Omar Khayyam
Johannes Kepler
Rene Descartes
Blaise Pascal
Isaac Newton
Leonard Euler
Benjamin Banneker
Sophie Germain
Carl Friedrich Gauss
Simeon Denis Poisson
Jakob Steiner
Ada Lovelace
Charles Reason
Bernahrd Riemann
Max Noether
William Clifford
Kelly Miller
Emmy Noether
Marjorie Lee Brown
Katherine Johnson
David Blackwell
J. Ernest Wilkins
Vladimir Arnold
Phillip Griffiths
Karoly Bezdek
Born (some estimated)
624BC
570BC
427BC
300BC
262BC
287BC
10
290
598
415
1048
1571
1596
1623
1642
1707
1731
1776
1777
1781
1796
1815
1818
1826
1844
1845
1863
1882
1914
1918
1919
1923
1937
1937
1955
Name(s)
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