What a Difference

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What a Difference Five Minutes Can Make Pat
McKeague Cengage Workshop Nashville
2009 Email pat_at_mckeague.com Transparencies
www.mckeague.com
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Cuesta College 1974
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What quality is most important for success in
mathematics? Independence You want to become
an independent learner.
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• An Independent Learner
• Intends to succeed
• Is resilient with setbacks
• Knows their resources
• Instructors office hours
• Math lab
• Student Solutions Manual
• Group study
• Internet
• Doesnt mistake activity for achievement
• Has a positive attitude

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Number Sequences and Inductive Reasoning Sequence
of Odd Numbers 1, 3, 5, 7, . . . Sequence of
Squares 1, 4, 9, 16, . . .
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Odds 1, 3, 5, 7, . . .
Squares 1, 4, 9, 16, . . .
1 1 12 1 3 4 22
1 3 5 9 32 1 3 5 7
16 42 1 3 5 7 9 25 52
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Fibonacci Sequence 1, 1, 2, 3, 5, 8, . .
.
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Application The family tree of a male honey
bee.
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1
2
3
5
8
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Why do We Call it Algebra?
Postage stamp issued by the Soviet Union in 1983,
to mark the 1200th anniversary of the birth of
Al-Khwarizmi
Khwarizmi is now Khiva in Uzbekistan
Abu Ja'far Mohammed ibn Musa Al-Khwarizmi Father
of Ja'far, Mohammed, son of Moses, native of the
town of Al-Khwarizmi
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A Page from Al-Khwarizmis Book
The Compendious Book on Calculation by Completion
and Balancing Al-Kitab al-mukhta?ar fi hisab
al-gabr wal-muqabala (Arabic)
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Postage Stamp Issued by Tunisia in 1979
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Completing the Square
What is the square which combined with ten of its
roots will give a sum total of 39?
Solve
The manner of solving this type of equation is to
take one-half of the roots just mentioned. Now
the roots in the problem before us are 10.
Therefore take 5, which multiplied by itself
gives 25, an amount which you add to 39 giving
64. Having taken then the square root of this
which is 8, subtract from it half the roots, 5
leaving 3. The number 3 therefore represents one
root of this square
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The Muslim Empire 622-750
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The ink of the scholar is more holy than the
blood of the martyr
The Prophet Muhammad
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Amazon.com
First published in 1202 This translation 2003
MAA Online, March 2003 The Liber abaci of
Leonardo Pisano (today commonly called Fibonacci)
is one of the fundamental works of European
mathematics. No other book did more to establish
the basic framework of arithmetic and algebra as
they developed in the Western world.
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Community College Mathematics InstructorJob
Description

• Education Masters Degree in Mathematics or
  Mathematics Education
• Teaching 15 hours per week
• Office Hours 5 hours per week
• Committee Work 10 hours per week
• Class Preparation/Grading 20 hours per week

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Community College Mathematics InstructorGetting
There From Here
If you can pass three semesters of Calculus, you
can get a degree in mathematics.
Elementary Algebra Intermediate
Algebra Trigonometry College Algebra Calculus
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Community College Mathematics InstructorGetting
There From Here
What can you do now that will make you the kind
of student that can pass three semesters of
calculus?
Become an independent learner.
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Profile Community College Mathematics
Instructor THERESE JONES Studied music for two
years at a community college after high
school. Stopped going to school, got married,
had 7 children.
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Profile Community College Mathematics
Instructor THERESE JONES Went back to school at
age 37 and took elementary algebra. Chair,
Department of Science and Engineering, Amarillo
Junior College.
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Binomial Squares in Korean
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Binomial Squares in Korean
ab
a2
b2
ab
(a b)2 (a b)(a b)
a2 2ab b2
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Profile Community College Mathematics
Instructor Diane VanDeusen Began working in the
restaurant industry after high school.
(Continued in this profession for 25
years.) Enrolled part-time at Napa Valley
College at age 30 intending to become a nurse.
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Profile Community College Mathematics
Instructor Diane VanDeusen Took a beginning
algebra class. Currently Full-time
mathematics instructor at Napa Valley College.
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BINOMIAL EXPANSIONS (x y)0 1 (x
y)1 x y (x y)2
x2 2xy y2 (x y)3 x3
3x2y 3xy2 y3 (x y)4 x4 4x3y
6x2y2 4xy3 y4 (x y)5 x5 5x4y
10x3y2 10x2y3 5xy4 y5
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BINOMIAL EXPANSIONS (x y)0 1 (x
y)1 x1 y1 (x y)2
x2 2x1y1 y2 (x y)3
x3 3x2y1 3x1y2 y3 (x y)4
x4 4x3y1 6x2y2 4x1y3 y4 (x y)5 x5
5x4y1 10x3y2 10x2y3 5x1y4 y5
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BINOMIAL EXPANSIONS (x y)0 1 (x
y)1 1x 1y (x y)2
1x2 2xy 1y2 (x y)3
1x3 3x2y 3xy2 1y3 (x y)4
1x4 4x3y 6x2y2 4xy3 1y4 (x y)5 1x5
5x4y 10x3y2 10x2y3 5xy4 1y5
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• Pascal's Triangle
• 1
• 1 1
• 1 2 1
• 1 3 3 1
• 1 4 6 4 1
• 5 10 10 5 1
• 1 6 15 20 15 6 1

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Profile Community College Mathematics
Instructor KATHLEEN GIBSON Received high school
diploma through adult education at age 25. Age
30 single mom with three children. Enrolled in
college and took Review of Arithmetic/Introduction
to Algebra.
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Profile Community College Mathematics
Instructor KATHLEEN GIBSON BA degrees in
mathematics and philosophy, masters degree in
mathematics. Currently Full-time mathematics
instructor at Crafton Hills College.
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Profile Community College Mathematics
Instructor KATHLEEN GIBSON (Four of her
students who started in basic mathematics are
now math majors.)
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Pascal's Triangle 1 1 1 1 2 1 1 3
3 1 1 4 6 4 1 1 5
10 10 5 1 1 6 15 20
15 6 1
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The Connection Between Pascals Triangle and the
Fibonacci Sequence
1
1
2
1 1 1 1 2 1 1 3 3 1 1 4
6 4 1 1 5 10 10 5 1 1 6 15
20 15 6 1
3
5
8
13
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Al-Samawal Born about 1130 in Baghdad,
IraqDied about 1180 in Maragha, Iran
Describing how to construct the third row of
Pascals Triangle, on his way to finding
coefficients for the expansion of
If we transfer the 'one' in the second column
into a third column, then add 'one' from the
second column to 'two' below it, we obtain
'three' to be written under the 'one' in the
third column. If we then add 'two' from the
second column to 'one' below it we have 'three'
which is written under the 'three', then we write
'one' under this 'three' we thus obtain a third
column whose numbers are 'one', 'three', 'three',
and 'one'.
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Al-Samawal
Father Abul-Abbas Yahya al-Maghribi, Fez,
Morocco
Mother Anna Isaac Levi, Basra, Iraq
Al-Samawal converts to Islam in 1163
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Toledo, Spain School of Translation, 1150
Keith Devlin Latin was the language of the
European scholars, and thus the target language
for the translations. Since few European scholars
knew Arabic, however, the translation was often
done in two stages, with a Jewish scholar living
in Spain translating from the Arabic to some
common language and the visiting scholar then
translating from that language into Latin. In the
same way, many ancient Greek texts, from
Aristotle to Euclid, were also translated into
Latin, whereupon they began to make an impact in
the West
View of Toledo by El Greco
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Cuesta College 1974