Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

transcript

Strengthening Mathematics Instruction

Cognitive Complexity and Instructional Strategies

Dr. Vicki Vierravvierra@vcoe.orgJim Shortjshort@vcoe.org

• California could add up

to 15%

• Indicated by underlined

• Adopted 2 options for

grade 8

• Added AP Probability

and Statistics and

Calculus

The Common Core State Standards - Mathematics

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.

Tulare County Office of Education

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

Standards for Mathematical Practice

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?

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?

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.

Compare and Contrast8

How are Martha’s Carpeting Task and

the Fencing Task the same and how are they different?

Math Task 1: Possible SolutionsMethod 1:

A = l x wA = 15 x 10

A = 150 square feet

Method 2:

Area = 150

Math Task 2: Possible Solutions

LENGTH

Similarities and Differences

Similarities Differences

• 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

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

Selected Response – Yes/No

Research based

More complex than traditional multiple choice

Worth multiple points

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

Selected Response – Scoring Rubric

CST Equivalent:

Communicating Reasoning16

Communicating Reasoning17

SBAC – Technology Enhanced

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

SBAC – TECHNOLO

GY ENHANCED(CONTINUE

Sample Performance Task – High School

www.smarterbalanced.org

• Addresses middle school and high school standards

• 2 sessions – no more than 120 minutes

• Calculator can be used

www.smarterbalanced.org

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

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.

Outline of SMI PD Modules

Next Steps and Closure

Welcome

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.

Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies

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