Transcript Presentation 1- Introduction to HOT Problems

Increasing Cognitive
Demand in Algebra
July 30-31, 2015
VAILL Conference
Diane Leighty
Nancy Taylor
Outline for Session 1
O Introduction
O Levels of Cognitive Demand
O Sorting Task in small groups
O Re-organize groups to discuss placements
O Return to original group to review placements
O Share actual placements/additional discussion.
Features of the tasks discussion
O Define Categories
O Modifying a basic problem to a HOT problem
Levels of Cognitive Demand
O Memorization
O Procedures without connections
O Procedures with connections
O Doing mathematics
How would you define these levels?
Each group should contribute as least one
characteristic for each level to the poster
paper
Sorting Activity
O In groups, sort the problems into the
categories to which they belong.
O Switch groups to see what others have done
O Return to your original group….any changes?
Record each letter in
the appropriate column
on the poster.
Discussion – Features of the
tasks
O Does a particular feature indicate that the
task has a certain level of cognitive
demand?
O Is there a difference between “level of
cognitive demand” and “difficulty”?
O 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?
Definitions of Levels
O Cognitive Demand Handout
O Discussion – any changes you would make
regarding placement of problems?
O Handout of Problem Placement – University
of Pittsburgh
O Further Discussion
Break Time
5 minutes
Why Higher
Levels?
Blooms Taxonomy
NCTM Process Standards
Rich Tasks
O Examples of rewrites of textbook problems
O Pairs to work on rewrite of textbook
problems
O Share rewrites with entire group
O Explore textbooks for problems to make
“HOT”
O Exit Questions
Textbook

Rich Tasks
Examples:
Low Level Task
High Level Task
Word Problem ≠ Rich Task
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.
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?
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 + 29.07, 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.
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
$44.57. How much will it cost to ship a 6 ½ lb
package to Chicago?
Rich Tasks Are:
O Are accessible and extendable.
O Allow individuals to make decisions.
O Involve learners in testing, proving, explaining,
O
O
O
O
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.
Original Textbook Problem 3 –
Use the data in the graph to complete the table.
Minutes
Depth (feet)
0
5
10
15
20
What’s your rewrite?
Developing your own….
O Each pair of teachers will be given 2
problems to try to improve the level of
cognitive demand.
O Share your problems and your rewrites with
the entire group.
Wrap-Up
O Share the problem(s) you made
improvements to and why you chose those
problems.
O Exit Question: What questions do you still
have about what you have heard this
morning? Is there something that needs
more clarification?
Resources
O https://sites.google.com/site/mathematicscap
stonecourseunits/
O Exeter Mathematics:
http://www.exeter.edu/academics/72_6539.as
px
O http://map.mathshell.org/materials/tasks.php