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Mathematics Instruction. In the Age of Common Core State Standards. What Should Instruction Look Like?. Mathematical Practices in Meaningful Ways A Blend of Explicit – Interactive – Implicit Instructional Strategies. CA Mathematics Framework (2013). - PowerPoint PPT Presentation
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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
19
6th Grade Mathematics
3rd Grade Mathematics
4th Grade Mathematics
5th Grade Mathematics
7th Grade Mathematics
8th Grade Mathematics
11th Grade Mathematics