Increasing Cognitive Demand in Mathematics Diane Leighty December 7, 2015

Outline for Session Introduction Levels of Cognitive Demand Sorting Task Share actual placements/additional discussion. Features of the tasks discussion Define Categories Modifying a basic problem to a HOT problem

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

Sorting Activity In groups (individually), 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?

Record each letter in the appropriate column on the worksheet.

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?

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

Sorting Solutions Handout of Problem Placement – University of Pittsburgh Further Discussion

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

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

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 5 in the V shape below so that the two arms of the V have the same total.

How many different possibilities are there 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 happens if we use the numbers from 2 to 6? From 12 to 16? From 37 to 41? From 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…. 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.

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?

Resources NRICH enriching mathematics: http://nrich.maths.org/students   http://nrich.maths.org/students Middle School math activities: http://map.mathshell.org/materials/tasks.php My Website: http://mthmtcs.net/