What a Difference

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What a Difference Five Minutes Can Make Pat
McKeague AMATYC 2007 Email
pat_at_mckeague.com Transparencies
www.mckeague.com
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Cuesta College 1974
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• Technology in 1970

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395

• Technology 1972 HP-35

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Study Skills Complaining
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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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Mathematics Around Us
  13-3-2-21-1-1-8-5 O Draconian devil! Oh, lame
saint!
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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
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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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Cuesta College 1974