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Common Core State Standards

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Title: Common Core State Standards


1
Common Core State Standards
  • Instruction, K-5Mathematics

Anthony QuanConsultant II, STEM Belinda
ListerMath Consultant Division of Curriculum and
Instructional Services
commoncore.lacoe.edu
2
Agenda
  • Effective Instruction
  • Rigor/Relevance Framework
  • Mathematics
  • Standards for Mathematical Practice
  • Research-Informed Instructional Practices
  • Model Task

3
Fraction Models
  • Area Model
  • Sharing Model
  • Linear Model
  • Rates Model
  • Set Model

4
Effective Instruction
  • A long line of students has established that the
    single most important school influence on student
    learning is the quality of the teacher.
  • as presented by Linda Darling-Hammond (2007)
  • How would you describe a classroom where
    effective instruction and learning is taking
    place?

5
California Standards for the Teaching Profession
  • Engaging and supporting all students
  • Connect to students prior knowledge
  • Use a variety of instructional strategies
  • Promote autonomy, interaction, and choice
  • Engage students in critical thinking/problem
    solving
  • Engage students in reflecting on their learning
  • Understanding and organizing content
  • Organize curriculum to support understanding
  • Interrelate ideas and information

6
California Standards for the Teaching Profession
  • Planning instruction
  • Establish clear goals for student learning
  • Design short- and long-term plans
  • Modify plans according to student needs
  • Assessing student learning
  • Collect and use multiple sources of information
  • Use results to guide instruction
  • Involve students in assessing their own learning

7
Learning Pyramid
ActiveLearning
adapted from Ntl Institute for Applied Behavioral
Science (n.d.)
8
Rigor/Relevance Framework
9
Rigor/Relevance Framework
International Center for Leadership in Education
(n.d.)
10
Quadrant A Acquisition
Students gather and store bits of
knowledge/information and are expected to
remember or understand this acquired knowledge.
A Acquisition
Application 3
International Center for Leadership in Education
(n.d.)
Comprehension 2
Awareness 1
11
Quadrant A
  • Verbs
  • name
  • label
  • define
  • select
  • identify
  • list
  • memorize
  • recite
  • locate
  • record
  • Products
  • definition
  • worksheet
  • list
  • quiz
  • test
  • workbook
  • true-false
  • reproduction
  • recitation

12
Quadrant B Application
Students use acquired knowledge to solve
problems, design solutions, and complete work.
B Application
Application 3
International Center for Leadership in Education
(n.d.)
Comprehension 2
Awareness 1
13
Quadrant B
  • Verbs
  • apply
  • sequence
  • demonstrate
  • interview
  • construct
  • solve
  • calculate
  • dramatize
  • interpret
  • illustrate
  • Products
  • scrapbook
  • summary
  • interpretation
  • collection
  • annotation
  • explanation
  • solution
  • demonstration
  • outline

14
Quadrant C Assimilation
Students extend and refine their knowledge so
that they can use it automatically and routinely
to analyze and solve problems and create
solutions.
Evaluation 6
C Assimilation
International Center for Leadership in Education
(n.d.)
Synthesis 5
Analysis 4
Application 3
15
Quadrant C
  • Verbs
  • sequence
  • annotate
  • examine
  • report
  • criticize
  • paraphrase
  • calculate
  • expand
  • summarize
  • classify
  • diagram
  • Products
  • essay
  • abstract
  • blueprint
  • inventory
  • report
  • plan
  • chart
  • questionnaire
  • classification
  • diagram
  • discussion
  • collection
  • annotation

16
Quadrant D Adaptation
Students think in complex ways and apply
acquired knowledge and skills, even when
confronted with perplexing unknowns,to find
creative solutions and take action that
furtherdevelops their skills and knowledge.
Evaluation 6
D Adaptation
International Center for Leadership in Education
(n.d.)
Synthesis 5
Analysis 4
Application 3
17
Quadrant D
  • Verbs
  • evaluate
  • validate
  • justify
  • rate
  • referee
  • infer
  • rank
  • dramatize
  • argue
  • conclude
  • Products
  • evaluation
  • newspaper
  • estimation
  • trial
  • editorial
  • radio program
  • Play
  • collage
  • machine
  • adaptation
  • poem
  • debate
  • invention

18
Rigor/Relevance FrameworkTeacher/Student Roles
International Center for Leadership in Education
(n.d.)
19
Instructional Model Three-Part Lesson Format
  • Before
  • During
  • Beyond

20
Before Phase
  • Introduce problem or task
  • Be certain the problem is understood
  • Activate useful prior knowledge
  • Establish clear expectations

20
21
Candy Store Problem
  • The local candy store purchased candy in cartons
    holding 12 boxes per carton. The price paid for
    one carton was 42.50. Each box contained 8 candy
    bars that the store planned to sell individually.
    What was the candy stores cost for each candy
    bar?

21
22
During Phase
  • Students work with partners or in teams
  • Teacher
  • - listens as students work
  • - provide appropriate suggestions
  • - observes and accesses

22
23
After Phase--Processing
  • Encourage student dialogue
  • Accept without evaluation
  • Request explanations to accompany answers
  • Call on students for their ideas

23
24
Graphic OrganizerInstruction

Instruction


25
CCSS for MathematicsInstructional Implications
26
Dan Meyer
http//www.youtube.com/watch?vBlvKWEvKSi8
27
CCSS for Mathematics
  • Provide focus and coherence
  • Organized around mathematical principles
  • Stress conceptual understanding of key ideas as
    well as skills
  • Prepare students for college and career
  • What are the implications for instruction?

28
Influence on Student Learning
  • teachers themselves need to understand the
    standards. Teachers must have deep and
    appropriate content knowledge to reach that
    understanding they must be adaptable, with
    enough mastery to teach students with a range of
    abilities and they must have the ability to
    inspire at least some of their students to the
    highest levels of mathematical achiev

teachers themselves need to understand the
standards. Teachers must have deep and
appropriate content knowledge to reach that
understanding they must be adaptable, with
enough mastery to teach students with a range of
abilities and they must have the ability to
inspire at least some of their students to the
highest levels of mathematical achievement. Ewing
(n.d.) The Common Core Math Standards
29
Standards for Mathematical PracticeSeek to
Develop in Students
  • Strands of Math Proficiency
  • Adaptive Reasoning
  • Strategic Competence
  • Conceptual Understanding
  • Procedural Fluency
  • Productive Disposition
  • NCTM Process Standards
  • Problem Solving
  • Reasoning and Proof
  • Communication
  • Representation
  • Connections

30
Standards for Mathematical Practice
2. Reason abstractly and quantitatively. 3.
Construct viable arguments and critique the
reasoning of others.
1. Make sense of problem and persevere in
solving them. 6. Attend to precision.
4. Model with mathematics. 5. Use appropriate
tools strategically.
7. Look for and make use of structure. 8. Look
for and express regularity in repeated reasoning
adapted from McCallum (2011) Standards for
Mathematical Practice
31
Create a Frayer Model Poster
Essential Characteristics Teaching Methods
Examples of What Students Will Be Doing Non-examples of What Students Will Be Doing
Standards for Mathematical Practice
  • Work with a table group on one of the Standards
    for Mathematical Practice.
  • Create a Frayer Model Poster connecting student
    actions and teacher actions.

32
Frayer Model Poster Carousel
  • Display your poster.
  • Examine the poster to the right of your groups
    poster.
  • Look for evidence of the processes and
    proficiencies.
  • Rotate to the right and continue until you have
    finished examining all posters.
  • Be ready to share out any questions or ahas.

33
Research-Informed Best Practices
  • Access prior knowledge and address students
    misconceptions
  • Provide routines and structures that help
    struggling learners organize critical content
  • Engage students with challenging tasks that
    involve active meaning making
  • Use formative assessment and provide timely,
    specific feedback
  • Provide on-going cumulative distributed practice
  • Promote learners beliefs about their own
    intelligence (growth mindset vs. fixed mindset)
  • adapted from Briars (2011) Intensified Algebra
  • Access prior knowledge and address students
    misconceptions
  • Provide routines and structures that help
    struggling learners organize critical content
  • Engage students with challenging tasks that
    involve active meaning making
  • Use formative assessment and provide timely,
    specific feedback
  • Provide on-go

34
Cognitively-Guided Instruction Process
Start the study of a new concept with a rich
problem or hypothesis
Use your understanding of student thinking to
guide further instruction
Invite your students to engage in the problem
Communicate multiple representations of solutions.
Question, justify, and critique thinking
Gendron (2011) So, Whats New in the Common Core
State Standards?
35
Debrief the CGI Process
Table Pattern Task
Asked questions to unpack the problem
Use results to plan next steps
Asked questions to check for understanding during
and after the task
Asked questions about strategies and relationships
Gendron (2011) So, Whats New in the Common Core
State Standards?
36
Students Beliefs About Their Intelligence
  • Fixed Mindset
  • Avoid learning situations if they might make
    mistakes
  • Try to hide, rather than fix, mistakes or
    deficiencies
  • Growth Mindset
  • Work to correct mistakes and deficiencies
  • View effort as positive increase effort when
    challenged

Briars (2011) Implementing the More Challenging
Aspects of Common Core State Standards
37
Students Can Develop Growth Mindsets
  • Explicit instruction about the brain, its
    function, and that intellectual development is
    the result of effort and learning has increased
    students achievement in middle school
    mathematics.
  • Teacher praise influences mindsets
  • Fixed Praise refers to intelligence
  • Growth Praise refers to effort, engagement,
    perseverance

Briars (2011) Implementing the More Challenging
Aspects of Common Core StateStandards
38
Expectancy Can I Do This?
  • Attribute successes to high effort or effective
    strategy
  • Attribute failures to low effort or ineffective
    strategy
  • Avoid saying, Youre smart
  • Discuss the different views of intelligence
  • Be explicit about what sorts of effort lead to
    success
  • Design instruction to support successful
    learning experiences

Dweck (2006)Presentation on Intelligence Theory
39
Value Is This Important?
  • How many of us have used the its on the
    test to emphasize the importance of a skill or
    assignment?

40
Value Is This Important?
  • Connect classroom activities to personal
    short-term goals.
  • Connect classroom activities to personal
    long-term goals.
  • Place classroom activities in personally
    meaningful contexts.

41
Growth Mindset and Productive Disposition
  • Just as students must develop a productive
    disposition towards mathematics such that they
    believe that mathematics makes sense and that
    they can figure it out, so too must teachers
    develop a similar productive disposition.
  • National Research Council (2005)
  • Adding It Up

42
What about Technology?
43
  • Proficiency with technology allows students to
    succeed in college and careers. The Common Core
    Standards include basic technology skills to help
    them succeed but in the bigger picture, they
    call for students to use technology to help them
    learn in all areas.

44
  • Whether it be using tools to solve math
    problems, to access information, or to promote
    literacy and communication skills, technology is
    part of the learning solution. It needs to be
    viewed that way rather than a separate
    competency.

45
Closing
46
Best Practices for the Common Core
  • Engage students with challenging tasks that
    involve active meaning making
  • Quadrant B, C, and D learning opportunities
  • Cognitively-Guided Instruction with a focus on
    the Standards for Mathematical Practice
  • Questioning to facilitate thinking and learning
  • Promote learners beliefs about their own
    intelligence (growth mindset vs. fixed mindset)
  • Design instruction to support student success
  • Explicitly reinforce high effort and students
    use of effective strategies
  • Repackage content using real-world
    connections,puzzles, and games
  • Model a productive disposition

47
Your Task
  • Upon your return to your school site, try to
    incorporate some of the lessons, activities or
    learnings into your practice.
  • Bring back work samples of things you have tried.
  • Bring your textbook or other instructional
    materials.

48
Reflection
  • Think about what you learned today.
  • Decide on one thing you will do differently to
    start transitioning to the Common Core State
    Standards.
  • Share your ideas with a partner.

49
For Further Investigation
  • Californias Common Core State Standardshttp//ww
    w.cde.ca.gov/ci/cc
  • Common Core State Standards Initiativehttp//www.
    corestandards.org
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