It this critical thinking?

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It this critical thinking?. Numeracy and mathematical reasoning in the curriculum. It this critical thinking? —today’s outline. How I became interested in this (mixed up general education requirements) Some practical problems requiring “numeracy” (focus on probability)

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### It this critical thinking?

Numeracy and mathematical reasoning in the curriculum

It this critical thinking? —today’s outline
• How I became interested in this (mixed up general education requirements)
• Some practical problems requiring “numeracy” (focus on probability)
• What math content should we teach?
• Recommendations
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.
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.
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.
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.
Objective 5: Interpret and use formulas to solve problems.

In electronics, Ohm’s law sates that V = IR, where V is voltage, I is current, and R is resistance.

Another form of Ohm’s law is:

• I = RV
• I = R/V
• V = R/I
• I = V/R
• IV = R
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

It this critical thinking? —today’s outline
• How I became interested in this (mixed up general education requirements)
• Some practical problems requiring “numeracy” (focus on probability)
• What math content should we teach?
• Recommendations
The math goal:

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

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?
Do you have cancer?
• The test is 98% accurate:
• If you have cancer, test is positive 98% of time
• If you don’t , test is negative 98% of time
• About 0.5% of people have this cancer
• Your test result is positive
Type I and Type II errors (statistics)
• Type I: confirming a false hypothesis
• Type II: rejecting a true hypothesis
It this critical thinking? —today’s outline
• How I became interested in this (mixed up general education requirements)
• Some practical problems requiring “numeracy” (focus on probability)
• What math content should we teach?
• Recommendations
Current

What is multiplication?

Fraction/ratio/percent

Area/perimeter/volume

New

Estimating

Probability

Data

Story problems

Inductive reasoning

Guessing properties and rules

What math should we teach? —elementary
Current

Algebraic variables

Cartesian coordinates

Trigonometry

Logarithms and exponents

New

Big numbers

Scientific notation

Significant figures

Combinatorics

Symmetry

Graph theory

Game theory

What math should we teach? —secondary
Current

Correctness

Procedure

Speed

Neatness?

New

Relevance

Significance

Assumptions

Theory or principle

Method

Communication

What math should we teach? —standards of quality
It this critical thinking? —today’s outline
• How I became interested in this (mixed up general education requirements)
• Some practical problems requiring “numeracy” (focus on probability)
• What math content should we teach?
• Recommendations
Recommendations
• Practice, practice, practice!
• All learning is developmental
• There are many right ways
• We’re never done
• Reform curriculum (standards based)
• Include some discovery
• Create safety
Math builds on previous knowledge.

IntermediateAlgebra

CollegeAlgebra

Trig

Calculus

Occu-pational

Non-scienceTransfer

Recommendations
• Practice, practice, practice!
• All learning is developmental
• There are many right ways
• We’re never done
• Reform curriculum (standards based)
• Include some discovery
• Create safety
Michael Masterson

mastersonm@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