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Increasing Cognitive
Demand in Mathematics
Diane Leighty
December 7, 2015
Outline for Session
O Introduction
O Levels of Cognitive Demand
O Sorting Task
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/person should contribute as least
one characteristic for each level.
Sorting Activity
O In groups (individually), 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 worksheet.
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?
Sorting Solutions
O Handout of Problem Placement – University
of Pittsburgh
O Further Discussion
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
12 + 19 =
High Level Task
Find two numbers whose sum is 23 and
whose difference is 7. Is there more than one
possible answer? Why or why not?
Low Level Task
High Level Task
Word Problem ≠ Rich Task
Magic Vs
Place each of the numbers 1 to
of the V have the same total.
5 in the V shape below so that the two arms
How many different possibilities are there?
What do you notice about all the solutions you find?
Can you explain what you see?
Can you convince someone that you have all the solutions?
What
From
From
From
happens if we use the numbers from 2 to 6?
12 to 16?
37 to 41?
103 to 107?
What can you discover about a V that has arms of
length 4 using the numbers 1−7?
Number Detective
Follow the clues to find the mystery number
from the list below.
The number has two digits.
Both of the digits are even.
The digit in the tens place is greater that the
digit in the ones place.
The ones digit is not in the three times table.
The tens digit is not double the ones digit.
The sum of the two digits is a multiple of five.
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 NRICH enriching mathematics:
http://nrich.maths.org/students
O Middle School math activities:
http://map.mathshell.org/materials/tasks.php
O My Website: http://mthmtcs.net/