It this critical thinking?

1. It this critical thinking? Numeracy and mathematical reasoning in the curriculum

2. 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

3. Math and Science Requirements

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.

5. 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.

6. Mickey Mouse or Donald Duck

7. 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, 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

10. 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

11. 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

12. The math goal: Solve a problem and communicate the solution so that the receiver is convinced that your solution works.

13. 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?

14. 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

15. Type I and Type II errors (statistics) • Type I: confirming a false hypothesis • Type II: rejecting a true hypothesis

16. 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

17. 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

18. 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

19. Current Correctness Procedure Speed Neatness? New Relevance Significance Assumptions Theory or principle Method Communication What math should we teach? —standards of quality

20. 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

21. 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

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

23. 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

24. 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