PED3124
Donna, Fariborz, Jennifer, Justin, Kofi
February 11, 2013
History of Mathematics
 Mathematical origins are rarely discussed in class
 Numeral systems: a writing system for expressing
numbers
Decimal numeral system
 base ten system
 likely motivated by the use of ten fingers
 first seen in pictorial form in hieroglyphics in ancient
Egypt
Egyptian numerals,
c. 3000 BCE [1]
[1]
Vigesimal numeral system
 base twenty
 uses all twenty fingers and toes
Maya numerals [2]
Sexagesimal numeral system
 base-60
 Babylonian system of mathematics (c. 3100 BCE) used
a sexagesimal system
 From this we get 60 seconds in a minute, 60 minutes
in an hour, and 360 degrees in a circle (60 × 6 = 360)
Babylonian numerals were written in cuneiform
Hindu–Arabic numerals
The first Hindu–Arabic numerals in the Western world,
from the Codex Vigilanus [3]
Hindu–Arabic numerals
 Originated in India
 Later adopted in Syria and Persia (c. 9th century CE)
 Were used by Persians and Arabs for the next few
hundred years, until...
Hindu–Arabic numerals
 Leonardo Pisano (aka Fibonacci) introduced the
Arabic numeral system to Europe in 1202 in his book
Liber Abaci
 Convinced people at the time that they
were superior to the inferior
Roman numerals
 Now used throughout the world
Hindu–Arabic numerals
“It is India that gave us the ingenious method of expressing
all numbers by means of ten symbols, each symbol
receiving a value of position as well as an absolute value; a
profound and important idea which appears so simple to us
now that we ignore its true merit. But its very simplicity
and the great ease which it has lent to all computations put
our arithmetic in the first rank of useful inventions; and we
shall appreciate the grandeur of this achievement the more
when we remember that it escaped the genius of
Archimedes and Apollonius, two of the greatest men
produced by antiquity.”
- Pierre-Simon Laplace [French mathematician, 1749-1827]
“Presumably no one would argue that the conservative
view on the sum of 14 and 27 differs from the liberal
view, or that the mathematical function that is its own
derivative is the exponential in the northern
hemisphere but some other function in the southern.
And regular periodic function can be represented to
arbitrary accuracy by a Fourier series in Muslim as well
as in Hindu mathematics. Non-commutative algebras
(where A times B does not equal B times A) are as selfconsistent and meaningful for speakers of IndoEuropean languages as for speakers of Finno-Ugric.
Mathematics might be prized or ignored, but it is
equally true everywhere – independent of ethnicity,
culture, language, religion, ideology.”
- Carl Sagan, The Demon-Haunted World
GENDER & MATH
• Thoughts?
Studies show…
• Females are equal to males in math skills. Differences
have proven to not have any biological basis
• Gap is becoming almost non-significant in standardized
tests
• Countries with the highest gender equality tend to
have the lowest gender performance gaps; boys as well
as girls do better (socioeconomic connection)
• “Boys still outnumber girls by more than about 3-1 at
extremely high levels of math ability and scientific
reasoning”
SOCIOCULTURAL FACTORS
• The “stereotype threat” theory
• Popular culture:
• http://www.youtube.com/watch?v=NO0cvqT1
tAE
• Male dominance of math role models
• Culture of competition in males
SOCIOECONOMIC STATUS &
MATH: the construction of the learner
• “The class in the high socioeconomic school
constructed content that was perceived as
required for entry into higher education while the
low socioeconomic school constructed
mathematics needed for everyday life
transactions” – Atweh Study
• The academic achievement gap for children from
different income level families has been growing
for the past 50 years, alongside the income gap
• Public school funding:
• “Because private funding initiatives reflect
the wealth of communities, some schools
do better than others in a system where
inadequate public funding is replaced by
private donations and commercial
activities”
• Parent involvement, neighborhood and
teacher quality are all possible contributing
factors
The role of teachers
• Math Teachers Demonstrate a Bias towards
white male students, study finds
• Female elementary school teachers transfer
their fear of math to girls
• What can teachers do to avoid these biases and promote an
equal environment?
QUESTIONS FROM ALL OVER
Answer the Following Questions in
Whatever Order You Wish
 In the first quarter of the
NBA finals, Lebron James
sunk a field goal, 2 lay-ups
and a dunk. How many
points did he scored?
• In the 3rd inning of the
2009 Cricket Grand Slam,
Pakistan scored two
boundaries and a run.
How many points did
they score that inning?
• In the Rugby World cup
final, Daniel Carter
scored a try and made
two try-conversions. How
many points did he
score?
• In round 1 of the Barclay’s
Premiere League, Cazorla,
Walcott, and Podolski each
scored 3 goals. How many
points did Arsenal score in
that game?
Constructivism
• We create meaning based on
our constructs
– Our perception of the world
• Constructs are based on our
previous experiences, beliefs,
etc.
• New information is either
assimilated into or
accommodated by our
constructs
– Information given to us that fits
into an existing construct is more
easily learned
 If we show relevance between the curriculum and a
students’ life, it becomes easier to learn
 i.e. S.T.S.C. in Science
 If we take the time to formulate questions around the
various experiences of our students, it can make the
math principles easier to learn and questions easier to
answer
 This means taking the time to learn about or students
 Interests, cultures etc.
Food for Thought...
 Don’t let the fact that you can’t reach them ALL keep
you from trying to reach SOME!
Assume you are a lawyer in the following situation:
A company has 25 employees, 6 of whom are minorities.
Five employees are randomly selected to receive a bonus
of $10 000.
The selection is made, and the selected group of 5
contains no minorities.
The minority group suspects discrimination. They come to
you with the thought of taking legal action against the
company.
Would you, as a lawyer, take this case? Does the group
have reason to suspect discrimination in the selection
process? Is there reason to think that the group of 5
was not randomly selected?
Questions?
Comments?
References & Resources
[1] http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Egyptian_numerals.html
[2] https://commons.wikimedia.org/wiki/File:Maya.png
[3] https://upload.wikimedia.org/wikipedia/commons/3/3b/Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg
https://www.scientificamerican.com/article.cfm?id=experts-time-division-days-hours-minutes
The Construction of Gender, Social Class and Mathematics in the Classroom
Bill Atweh and Tom Cooper
Educational Studies in Mathematics , Vol. 28, No. 3, Mathematics and Gender (Apr., 1995), pp. 293-310
Nicole M. Else-Quest, Janet Shibley Hyde, Marcia C. Linn. Cross-national patterns of gender differences in mathematics: A meta-analysis.. Psychological
Bulletin, 2010; 136 (1): 103 DOI: 10.1037/a0018053
Jonathan M. Kane and Janet E. Mertz. “Debunking Myths about Gender and Mathematics Performance.” Notices of the American Mathematical Society, Dec.
12, 2011 DOI: 10.1090/noti790.
Shaker, E. (2006). Beyond the bakesale: Exposing schoolhouse commercialism. Our
Schools Our Selves. 73-94.
University of Missouri-Columbia. "'Women worse at math than men' explanation scientifically incorrect, experts say." ScienceDaily,
18 Jan. 2012. Web. 10 Feb. 2013.
Melting Pot Math
http://www.fi.edu/school/math3/index.html
Multicultural Education and Math
http://www.edchange.org/multicultural/sites/math.html
Multicultural Math Lessons
http://www.deltacollege.edu/dept/basicmath/Multicultural_Math.htm
Lessons from the Mayas
http://www.nea.org/tools/lessons/47756.htm
Multicultural Math Games
http://www.ehow.com/list_5982504_multicultural-math-games.html