It this critical thinking?

1
It this critical thinking?

• Numeracy and mathematical reasoning in the
  curriculum

2
It this critical thinking? todays outline

1. How I became interested in this (mixed up general
   education requirements)
2. Some practical problems requiring numeracy
   (focus on probability)
3. What math content should we teach?
4. Recommendations

3
Math and Science Requirements
College Gen Ed
NMC math or science plus math competency
KCC critical thinking
LCC math and science
OCC math or science
GRCC math or science
DC none
HFCC ?
JCC math and science
KVCC math or science
Macomb ?
4
KCC Gen Ed Outcomes

• As a result of completing an associate degree
  from Kellogg Community College, students will be
  able to
• Demonstrate written, verbal, nonverbal, computer,
  and listening communication skills.
• Demonstrate critical thinking skills in
  gathering, analyzing, interpreting facts, and
  problem solving using scientific inquiry.
• Demonstrate knowledge of the creative process and
  the ability to appraise the significance of
  visual, literary, or performing arts.
• Demonstrate knowledge of the implications of
  living in a culturally-diverse society and
  contemporary global community.
• Demonstrate knowledge of the implications of
  physical, mental, and community health
  principles.

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Objective 5 Interpret and use formulas to solve
problems.

• A boy wishes to calculate the total value of
  coins in his pocket. He has 3 quarters, 1 dime, 2
  nickels, and 4 pennies. Which formula is most
  useful in this type of situation?
• Total 3q 1d 2n 4p
• Total 99
• Total 25q 10d 5n 1p
• Total 94.
• Total q d n p.

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Mickey Mouse or Donald Duck
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Critical thinking is

• Reasonable, reflective thinking that is focused
  on what to do or believe.
• Learning how to argue.
• Improving ones thinking by skillfully taking
  charge of the structures inherent in thinking and
  imposing intellectual standards upon them.

8
Objective 5 Interpret and use formulas to solve
problems.

• A boy wishes to calculate the total value of
  coins in his pocket. He has 3 quarters, 1 dime, 2
  nickels, and 4 pennies. Which formula is most
  useful in this type of situation?
• Total 3q 1d 2n 4p
• Total 99
• Total 25q 10d 5n 1p
• Total 94.
• Total q d n p.

9
Objective 5 Interpret and use formulas to solve
problems.

• In electronics, Ohms law sates that V IR,
  where V is voltage, I is current, and R is
  resistance.
• Another form of Ohms law is
• I RV
• I R/V
• V R/I
• I V/R
• IV R

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Objective 6 Represent data graphically and be
able to interpret data represented graphically.

• Three graphs are shown in the figure below. They
  refer to distance traveled versus time for a
  person who either walks, runs, or drives to work,
  along the same route. Each graph (A, B, C)
  represents one of the three situations (1, 2, 3)
  described beside the graph. Look at the three
  graphs A, B, and C and match to the described
  situation 1, 2, and 3 using the pull down menus.

Situations 1. Walking to work2. Driving to
work3. Running to work
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It this critical thinking? todays outline

1. How I became interested in this (mixed up general
   education requirements)
2. Some practical problems requiring numeracy
   (focus on probability)
3. What math content should we teach?
4. Recommendations

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The math goal

• Solve a problem and communicate the solution so
  that the receiver is convinced that your solution
  works.

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It is unlikely for unlikely events not to occur.

• What is the probability that two of us share a
  birthday?
• How many people are necessary to be certain of a
  shared birthday?
• How many people are necessary to be 50 certain?

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Do you have cancer?

• The test is 98 accurate
• If you have cancer, test is positive 98 of time
• If you dont , test is negative 98 of time
• About 0.5 of people have this cancer
• Your test result is positive

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Type I and Type II errors (statistics)

• Type I confirming a false hypothesis
• Type II rejecting a true hypothesis

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It this critical thinking? todays outline

1. How I became interested in this (mixed up general
   education requirements)
2. Some practical problems requiring numeracy
   (focus on probability)
3. What math content should we teach?
4. Recommendations

17
What math should we teach? elementary

• Current
• What is multiplication?
• Fraction/ratio/percent
• Area/perimeter/volume

• New
• Estimating
• Probability
• Data
• Story problems
• Inductive reasoning
• Guessing properties and rules

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What math should we teach? secondary

• Current
• Algebraic variables
• Cartesian coordinates
• Trigonometry
• Logarithms and exponents

• New
• Big numbers
• Scientific notation
• Significant figures
• Combinatorics
• Symmetry
• Graph theory
• Game theory

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What math should we teach? standards of quality

• Current
• Correctness
• Procedure
• Speed
• Neatness?

• New
• Relevance
• Significance
• Assumptions
• Theory or principle
• Method
• Communication

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It this critical thinking? todays outline

1. How I became interested in this (mixed up general
   education requirements)
2. Some practical problems requiring numeracy
   (focus on probability)
3. What math content should we teach?
4. Recommendations

21
Recommendations

• Practice, practice, practice!
• All learning is developmental
• There are many right ways
• Were never done
• Reform curriculum (standards based)
• Include some discovery
• Create safety

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Math builds on previous knowledge.
IntermediateAlgebra
CollegeAlgebra
Trig
Calculus
Occu-pational
Non-scienceTransfer
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Recommendations

• Practice, practice, practice!
• All learning is developmental
• There are many right ways
• Were never done
• Reform curriculum (standards based)
• Include some discovery
• Create safety

24

• Michael Masterson
• mastersonm_at_kellogg.edu
• Innumeracy, by John Allen PaulosHill and Wang,
  1988
• Critical Thinking Theory, Research, Practice,
  and Possibilities, by Joanne G. KurfissASHE-ERIC
  Higher Ed Reports, 1988