Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies Dr. Vicki Jim

2 California could add up to 15% Indicated by underlined text Adopted 2 options for grade 8 Added AP Probability and Statistics and Calculus

The Common Core State Standards - Mathematics 3 The CCSS-M are divided into two groups: Mathematical Content Standards Describe what students should understand and be able to do. Change from grade to grade. Standards for Mathematical Practice Describe ways in which students ought to engage with mathematics. Carry across all grade levels.

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

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?

Math Task #1 6 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 #2 7 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 Contrast 8 How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

Math Task 1: Possible Solutions Method 1: A = l x w A = 15 x 10 A = 150 square feet Method 2: Area = 150

Math Task 2: Possible Solutions AREAAREA LENGTH A) B) C)

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

Cognitive Levels of Tasks 12 Higher-Level Tasks Procedures with Connections Doing Mathematics e.g. The Fencing Task, SBAC assessment items Lower-Level Tasks Memorization Procedures without Connections e.g. Martha’s Carpeting Task, CST assessment items

Selected Response – Yes/No 13  Research based  More complex than traditional multiple choice  Worth multiple points

Selected Response – Scoring Rubric 14

CST Equivalent:

Communicating Reasoning 16

Communicating Reasoning 17

SBAC – Technology Enhanced ces.pdf 18

ces.pdf 19 SBAC – T ECHNOLOGY E NHANCED (C ONTINUED )

Sample Performance Task – High School 20 Addresses middle school and high school standards 2 sessions – no more than 120 minutes Calculator can be used

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Cognitive Demands of CCSS-M CST 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 Tasks 24 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.

Roles Background Looking at Student Work Setting the Stage Locating Cognitively Complex Problems Deconstructing Cognitively Complex Problems Algebra I & II Pre Calculus Geometry Integrating Topics and Concepts in Problems Outline of SMI PD Modules Next Steps and Closure Welcome

Value of SMI PD The 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.