Common Core Math: 2 > 4 Super Week 2014. Norms Silence your technology Limit sidebar conversations.
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Transcript of Common Core Math: 2 > 4 Super Week 2014. Norms Silence your technology Limit sidebar conversations.
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Common Core Math: 2 > 4
Super Week 2014
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Norms
Silence your technology
Limit sidebar conversations
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Objectives
• Understand the different types of knowledge• Understand the definition of fluency• Create a common understanding of a number
talk • Familiarize ourselves with the new scope and
sequence, pacing guide, and assessments
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Four Assessment Questions
Directions: Solve each of the following problems. Under each problem write a brief description of 1) the type of knowledge used; 2) the length of time and amount of challenge faced; 3) how you solved it. Think of how each question varied in each of these areas.
Keep these four problems in mind during our discussion about the four Types of Knowledge. We will revisit them at the end and identify how they relate.
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Major Shifts in Mathematics1. Focus
Students have sufficient time to think about, practice, and integrate new ideas
2. CoherenceAcross grade levels and link to major topics within
grade levels
3. RigorIn major topics, pursue with equal intensity:
a. deep conceptual understandingb. procedural skill and fluencyc. application and modeling
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Skills (Procedure)
Description
• Procedures• Usually Doing
Something• Verbs
Characteristics of Assessment Questions
• Routine• Little or No
Context• Focus on
Procedure and/or Answer
• One Short Answer
• Length Varies
How this Knowledge is Learned &
Retained
• Modeling• Repeated
Practice of the Same Steps
• Repeated Exposure
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Facts
Description
• Descriptions• Vocabulary• Formula
Recollection
Characteristics of Assessment Questions
• Routine• No Context• Focus on Recall• One Short
Answer• Closed• Length Varies
How this Knowledge is Learned &
Retained
• Repeated Exposure
• Memorization Techniques (songs)
• Drill
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Concepts
Description
• Ideas• Understanding
Things• Nouns
Characteristics of Assessment Questions
• Non-Routine• In Context• Focus on
Explanation• Extended Answer• Open Middled or
Open Ended• Medium Minutes
How this Knowledge is Learned &
Retained
• Exploration Inquiry/Discovery Experimentation
• Hands-On/Manipulatives
• Sufficient Time for In-Depth Study
• Experienced in New Contexts
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Relational Knowledge
Description
• Application of Multiple Types of Knowledge
• Synthesis• Analysis or
Evaluation
Characteristics of Assessment Questions
• Non-Routine• In Context• Focus on
Applying Knowledge
• Extended Answer• Open Middled or
Open Ended• Longer Minutes
How this Knowledge is Learned &
Retained
• Exposure to Open-Ended Questions
• Class/Group Discussions
• Collaboration• Authentic
Experiences
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Revisit assessment questions
At your table try to identify which Type of Knowledge corresponds to each of the four questions.
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How does learning develop/grow?
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How does learning develop/grow?
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How does learning develop/grow?
Concepts Before Procedures
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Defining Fluency
• Number off 1 -2 at your table• Read the corresponding text
1. Simple, Fast, and Accurate? I Think Not!2. CCSS California Framework
• Engage in a table discussion around the major points of the readings
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One Liner Defining “Fluency”
As a group, come to consensus on what fluency is and define it using a “one liner” on a piece of 8.5 x 11 paper.
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Our classrooms are filled with students and adults who think of
mathematics as rules and procedures to memorize without understanding
the numerical relationships that provide the foundation for these
rules.
Number Talks, page 4
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Quick Write
Think about mental math. How do we use mental math in our everyday life?
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Number Talks
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What is a number talk?• A number talk is a quick (5-15 minutes) classroom
routine used to develop computational fluency that promotes students to:– Clarify thinking.– Investigate and apply mathematical relationships.– Build a repertoire of efficient computational strategies.– Make decisions about choosing efficient strategies for
specific problems.– Consider and test other strategies to see if they are
mathematically logical.– Build connections between key conceptual ideas.
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5 Key Components
1. Classroom Environment and Community
2. Classroom Discussions3. The Teacher’s Role4. Role of Mental Math5. Purposeful Computational Problems
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1. Classroom Environment and Community • Students should feel
comfortable– Offering responses for
discussions– Questioning themselves and
their peers– Investigating new strategies
• Accept all ideas and answers
5 Key Components
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2. Classroom Discussions
• Transfers the ownership of learning to the students
• Mistakes are an opportunity for learning
5 Key Components
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3. The Teacher’s Role
• Facilitator• Questioner• Listener• Learner
5 Key Components
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4. The Role of Mental Math
• Encourages students to build on number relationships
• Encourages students to utilize the value of the entire number
199 + 199 =
5 Key Components
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5. Purposeful Computation Problems
• Careful planning before number talks is necessary to design “just right” problems for the students.
5 Key Components
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How Do I Prepare for Number Talks?
• Designated location allowing proximity
• Appropriate wait time• Accept, respect, and
consider all answers• Encourage student
communication
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Recording Student Thinking
• Anticipate how students will respond• Think through possible strategies
beforehand• Consider which mathematical ideas you
want to highlight• Make sure your notation is mathematically
correct30 + 30 = 60 – 3 = 57 should not be written
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Having the opportunity to ponder other approaches strengthens our own
mathematical foundation and understanding.
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Accountability with Students
• Finger Signals for Efficient Strategy• Keep records of Problems.• Small-Group Number Talks• Class Strategy Charts• Exit Ticket• Weekly Computation Assessment
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Starting with Small Steps
1. Start with smaller problems to elicit thinking from multiple perspectives.
2. Be prepared to offer a strategy from a previous student.
3. It is all right to put a student’s strategy on the back burner.
4. Limit your number talks to 5-15 minutes.5. Be patient with yourself and your students as
you incorporate number talks into your regular math time.
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Instructional Supports
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AssessmentsBenchmarksUnitsTimed Tests
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Benchmarks
• Majority Selected Response
• Two Constructed Response (except for Benchmark 1)
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Unit Assessments
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Timed Tests
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“To achieve mathematical understanding, instruction and learning must balance mathematical procedures and conceptual understanding…Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks.”
- Introduction to the Common Core p. 6
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