It this critical thinking?Numeracy and

mathematical reasoning in the curriculum

It this critical thinking?—today’s 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

Math and Science RequirementsCollege 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 ?

KCC Gen Ed OutcomesAs 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?

a) Total = 3q + 1d + 2n + 4p

b) Total = 99

c) Total = 25q + 10d + 5n + 1p

d) Total = 94.

e) Total = q + d + n + p.

Mickey Mouse or Donald Duck

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?

a) Total = 3q + 1d + 2n + 4p

b) Total = 99

c) Total = 25q + 10d + 5n + 1p

d) Total = 94.

e) 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:a) I = RV

b) I = R/V

c) V = R/I

d) I = V/R

e) IV = R

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.

Situations1. Walking to work2. Driving to work3. Running to work

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

It this critical thinking?—today’s 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

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

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

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

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

What math should we teach?—standards of quality

Current Correctness Procedure Speed Neatness?

New Relevance Significance Assumptions Theory or principle Method Communication

It this critical thinking?—today’s 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

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

IntermediateAlgebra

CollegeAlgebra

Trig Calculus

Occu-pational

Non-scienceTransfer

Math builds on previous knowledge.

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