1. Diane Leighty Nancy Taylor
Increasing Cognitive Demand in Algebra July 30-31, 2015 VAILL Conference
Diane Leighty
Nancy Taylor

2. Outline for Session 1 Introduction Levels of Cognitive Demand
Sorting Task in small groups
Re-organize groups to discuss placements
Return to original group to review placements
Share actual placements/additional discussion. Features of the tasks discussion
Define Categories
Modifying a basic problem to a HOT problem

3. Levels of Cognitive Demand
Memorization
Procedures without connections
Procedures with connections
Doing mathematics
How would you define these levels?
Each group should contribute as least one characteristic for each level to the poster paper

4. Sorting Activity
In groups, sort the problems into the categories to which they belong.
Switch groups to see what others have done
Return to your original group….any changes?

5. Record each letter in the appropriate column on the poster.

6. Discussion – Features of the tasks
Does a particular feature indicate that the task has a certain level of cognitive demand?
Is there a difference between “level of cognitive demand” and “difficulty”?
What effect does context (e.g. setting in which the task is used, students’ prior knowledge, etc) have on the level of cognitive demand required by a task?

7. Definitions of Levels Cognitive Demand Handout
Discussion – any changes you would make regarding placement of problems?

8. Handout of Problem Placement – University of Pittsburgh
Further Discussion

9. Break Time 5 minutes

10. Blooms Taxonomy NCTM Process Standards
Why Higher Levels?
Blooms Taxonomy
NCTM Process Standards
Teach to the big ideas

11. Rich Tasks Examples of rewrites of textbook problems
Pairs to work on rewrite of textbook problems
Share rewrites with entire group
Explore textbooks for problems to make “HOT”
Exit Questions

12. Textbook  Rich Tasks Examples:

13. Low Level Task

14. High Level Task

15. Word Problem ≠ Rich Task

16. Original Textbook Problem 1
Tickets to a concert cost $2.50 for students and $3.75 for adults. Suppose x represents the number of student tickets sold and y represents the number of adult tickets sold. Write an inequality that describes the condition that total receipts must exceed $1500.

17. REWRITE
Tickets to a concert cost $2.50 for students and $3.75 for adults. If the total receipts must exceed $1500 in order to make a profit, and there are only 480 seats in the auditorium, how many of each kind of ticket need to be sold? Try to find several combinations that will work. Can you generalize your solution?

18. Original Textbook Problem 2 –
Recently the cost c, in dollars of shipping a FedEx Priority Overnight package weighing 1 lb or more a distance of 1001 to 1400 miles was given by c = 3.1w , where w is the package’s weight, in pounds. Graph the equation and use the graph to estimate the cost of shipping a 6 ½ lb package.

19. Mailing Costs
Recently the cost of shipping a FedEx Priority Overnight package weighing 1 lb to Chicago was $32.17 while a package weighing 2 lbs shipped to Chicago cost $35.27, and a package weighing 5 lbs to Chicago cost $ How much will it cost to ship a 6 ½ lb package to Chicago?

20. Rich Tasks Are: Are accessible and extendable.
Allow individuals to make decisions.
Involve learners in testing, proving, explaining, reflecting and interpreting.
Promote discussion and communication.
Encourage originality and invention.
Encourage “what if?” and “what if not?” questions.
Are engaging and contain opportunity to surprise.

21. Original Textbook Problem 3 –
Use the data in the graph to complete the table.
Minutes
Depth (feet) 5 10 15 20
What’s your rewrite?

22. Developing your own….
Each pair of teachers will be given 2 problems to try to improve the level of cognitive demand.
Share your problems and your rewrites with the entire group.

23. Wrap-Up
Share the problem(s) you made improvements to and why you chose those problems.
Exit Question: What questions do you still have about what you have heard this morning? Is there something that needs more clarification?

24. Resources
Exeter Mathematics: