strengthening mathematics instruction cognitive complexity and instructional strategies

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Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies Dr. Vicki Vierra [email protected] Jim Short [email protected]

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Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies. Dr. Vicki Vierra [email protected] Jim Short [email protected]. California could add up to 15% Indicated by underlined text Adopted 2 options for grade 8 - PowerPoint PPT Presentation

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Page 1: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Strengthening Mathematics Instruction

Cognitive Complexity and Instructional Strategies

Dr. Vicki [email protected] [email protected]

Page 2: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

2

• California could add up

to 15%

• Indicated by underlined

text

• Adopted 2 options for

grade 8

• Added AP Probability

and Statistics and

Calculus

Page 3: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

The Common Core State Standards - Mathematics

3

The CCSS-M are divided into two groups:Mathematical Content StandardsDescribe what students should understand

and be able to do.Change from grade to grade.Standards for Mathematical PracticeDescribe ways in which students ought to

engage with mathematics.Carry across all grade levels.

Page 4: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Tulare County Office of Education

4

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Page 5: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Standards for Mathematical Practice

5

The 8 Standards for Mathematical Practice require students to think at a

high level and place an emphasis on

student demonstrations of learning.

How do we give students the opportunity

to engage in the Practices?

Page 6: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Math Task #16

Martha was re-carpeting her bedroom which was 15 feet long and 10 feet wide.

How many square feet of carpeting will she need to purchase?

Page 7: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Math Task #27

Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits.

1. If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

2. How long would each of the sides of the pen be if they had only 16 feet of fencing?

3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Page 8: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Compare and Contrast8

How are Martha’s Carpeting Task and

the Fencing Task the same and how are they different?

Page 9: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Math Task 1: Possible SolutionsMethod 1:

A = l x wA = 15 x 10

A = 150 square feet

Method 2:

Area = 150

Page 10: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Math Task 2: Possible Solutions

AREA

LENGTH

A) B)

C)

Page 11: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Similarities and Differences

Similarities Differences

11

• Both are “area” problems

• Both require prior knowledge of area

• The amount of thinking and reasoning required

• The number of ways the problem can be solved

• The way in which the area formula is used

• The need to generalize• The range of ways to enter

the problem• #1 a CST style problem,

#2 a SBAC style problem

Page 12: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Cognitive Levels of Tasks12

Higher-Level TasksProcedures with

ConnectionsDoing Mathematics

e.g. The Fencing Task, SBAC assessment items

Lower-Level TasksMemorizationProcedures without

Connectionse.g. Martha’s Carpeting Task, CST assessment items

Page 13: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Selected Response – Yes/No

13

Research based

More complex than traditional multiple choice

Worth multiple points

http://www.smarterbalanced.org/?s=item+specifications+math

Page 14: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Selected Response – Scoring Rubric

14

http://www.smarterbalanced.org/?s=item+specifications+math

Page 15: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

CST Equivalent:

Page 16: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Communicating Reasoning16

http://www.smarterbalanced.org/?s=item+specifications+math

Page 17: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Communicating Reasoning17

http://www.smarterbalanced.org/?s=item+specifications+math

Page 18: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

SBAC – Technology Enhanced

http://www.k12.wa.us/SMARTER/pubdocs/SBAC_Appendices.pdf

18

Page 19: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

http://www.k12.wa.us/SMARTER/pubdocs/SBAC_Appendices.pdf

19

SBAC – TECHNOLO

GY ENHANCED(CONTINUE

D)

Page 20: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Sample Performance Task – High School

www.smarterbalanced.org

20

• Addresses middle school and high school standards

• 2 sessions – no more than 120 minutes

• Calculator can be used

Page 21: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

www.smarterbalanced.org

21

Page 22: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

www.smarterbalanced.org

22

Page 23: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Cognitive Demands of CCSS-MCST items call for recall of procedures and

facts – low cognitive demand.SBAC items demand not only that recall,

but also the ability to apply and use that mathematical knowledge in meaningful ways – high cognitive demand

Page 24: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Mathematical Tasks24

It is the mathematical tasks selected and implemented by the

teacher that create the opportunity for students

to engage in these practices and learn mathematics.

SMI PD gives teachers tools to find tasks with high cognitive demands.

Page 25: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Outline of SMI PD Modules

Next Steps and Closure

Welcome

Page 26: Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

Value of SMI PDThe transition to the CCSS-M and the new

assessments needs to begin now.The obvious place to begin is with the

Standards for Math Practice.That shift calls for using math tasks with

high cognitive demand.SMI PD is focused on understanding,

finding, and creating such math tasks for high school courses.