Mathematics InstructionIn the Age of Common Core State Standards

What Should Instruction Look Like?1. Mathematical Practices in Meaningful

Ways2. A Blend of Explicit – Interactive –

Implicit Instructional Strategies

CA Mathematics Framework (2013)•Adopted by the State Board of Education

in November 2013•Pre-publication edition available at http://

www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

•Publication edition should be available by this Summer

What Should Instruction Look Like?1. Mathematical Practices in Meaningful

Ways2. California Mathematics Framework (2013)

Adopted by the State Board of Education in November 2013

Pre-publication edition available at http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

Publication edition should be available by this Summer

What Should Instruction Look Like?1. Mathematical Practices in Meaningful

Ways2. California Mathematics Framework (2013)

Adopted by the State Board of Education in November 2013

Pre-publication edition available at http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

Publication edition should be available by this Summer

After School Job(4th/5th Grade)•Leonard needed to earn some money so he

offered to do some extra chores for his mother after school for two weeks. His mother was trying to decide how much to pay him when Leonard suggested the idea:

•“Either you pay me $1.00 every day for the two weeks, or you can pay me 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, and so on, doubling my pay every day.”

After School Job(4th/5th Grade)•Which option does Leonard want his

mother to choose? Write a letter to Leonard’s mother suggesting the option that she should take. Be sure to include drawings that explain that will explain your mathematical thinking.

Day Start with $1

Start with 1¢

1 $1 1¢2 $1 2¢3 $1 4¢4 $1 8¢5 $1 16¢6 $1 32¢7 $1 64¢8 $1 $1.289 $1 $2.5610 $1 $5.1211 $1 $10.2412 $1 $20.4813 $1 $40.9614 $1 $81.92

After School Job(4th/5th Grade)

Instructional Strategies Chapter•The purpose of this chapter is not to

prescribe the usage of any particular instructional strategy, but to enhance teachers’ repertoire.

Explicit Interactive ImplicitTeacher serves as the provider of knowledge

Instruction includes both explicit and implicit methods

Teacher facilitates students learning by creating situations where students discover new knowledge and construct own meaning

Much direct teacher assistance

Balance between direct and non-direct teacher assistance

Non-direct teacher assistance

Teacher regulation of learning

Shared regulation of learning

Student regulation of learning

Directed discovery

Guided discovery Self-discovery

Direct instruction Strategic instruction Self-regulated instruction

Task Analysis Balance between part-to-whole and whole-to-part

Unit approach

Behavioral Cognitive/metacognitive

Holistic

Instructional Models

General Instructional Models1. 5 E Model (interactive)

▫ Engage-Explore-Explain-Elaborate-Evaluate2. 3 Phase Model (explicit)

▫ I do – we d0 – you do3. Singapore Model (interactive)4. Concept Attainment Model (interactive)5. Cooperative Learning Model (implicit)

▫ Students work together to solve a problem and provide input

6. Cognitively Guided Instruction (implicit)7. Problem-Based Learning (interactive)

Additional Instructional Strategies•Discourse in the Mathematics Classroom•Student Engagement Strategies•Tools for Mathematics Instruction•Examples of Tasks Incorporating Math

Practices•Real World Problems

Evidence Centered Assessment

•ASSUMPTION: Assessment is the process of making an argument, based on evidence, that reasons about what students say, do or make in a particular task situation to a more general claim or inference about what they can know, do, or have accomplished

ELA Claims: 1. Reading2. Writing3. Speaking/

Listening4. Research

Math Claims: 1.Concepts and

Procedures 2.Problem Solving3.Communicating

Reasoning4.Modeling and

Data Analysis

WHEN WE GET SCORE REPORTSSBAC’s Achievement Levels

•Each level encompasses a range of student achievement.▫Thorough Understanding▫Adequate Understanding

▫Partial Understanding▫Minimal Understanding

Advanced?Proficient?

Basic?Below Basic & FBB?

Content Domains Grades K - 12

K-8 Areas To Understand DeeplyGrade Key Areas of Focus in Mathematics

K-2 Place value, addition and subtraction – concepts, skills, and problem solving

3-5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6 Ratios and proportional reasoning: early expressions and equations

7 Ratios and proportional reasoning: arithmetic of rational numbers

8 Linear algebra

NOT YOUR MOTHER’S ALGEBRA 1

(based on sample “Traditional” pathway in CA Framework draft)

These Standards are not intended to be new names for old ways of doing business.They are a call to take the next step.”

- CCSS (2010, p.5)

 Common

CoreGrade 8

  Pre-Algebra Some “1997 High School Geometry

“1997 Algebra 1A”

 Common

CoreAlgebra 1

  “1997 Algebra 1B” “1997 Algebra 2A “ Some AP Statistics Topics

 Common

CoreGeometry

  More “1997 High School Geometry

Transformational Geometry

Some AP Statistics Topics

 

 Common Core

Algebra 2

  “1997 Algebra 2B” 1997 Trigonometry Some Math Analysis Some AP Statistics Topics

Grade Level Chapter Outlines•Introduction to the Grade•Cluster Level Emphases•Connecting Math Practices and Content•Standards Based Learning at the Grade

▫Laid out by domain and interfaces with the shifts, emphases, and rigor

Setting Performance Standards• Setting standards for four Performance Levels at

each grade• September 2014, using Field Test data• Grade-level panels of 30 per content area

recommend cut scores▫At least two representatives from each

Governing State on each grade level panel• Concurrent “crowd sourced” recommendations

from the field• Recommendations presented to chiefs for

approval in late September 2014

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6th Grade Mathematics

3rd Grade Mathematics

4th Grade Mathematics

5th Grade Mathematics

7th Grade Mathematics

8th Grade Mathematics

11th Grade Mathematics