Common Core Math: 2 > 4

Super Week 2014

Norms

Silence your technology

Limit sidebar conversations

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

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.

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

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

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

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

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

Revisit assessment questions

At your table try to identify which Type of Knowledge corresponds to each of the four questions.

How does learning develop/grow?

How does learning develop/grow?

How does learning develop/grow?

Concepts Before Procedures

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

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.

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

Quick Write

Think about mental math. How do we use mental math in our everyday life?

Number Talks

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.

5 Key Components

1. Classroom Environment and Community

2. Classroom Discussions3. The Teacher’s Role4. Role of Mental Math5. Purposeful Computational Problems

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

2. Classroom Discussions

• Transfers the ownership of learning to the students

• Mistakes are an opportunity for learning

5 Key Components

3. The Teacher’s Role

• Facilitator• Questioner• Listener• Learner

5 Key Components

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

5. Purposeful Computation Problems

• Careful planning before number talks is necessary to design “just right” problems for the students.

5 Key Components

How Do I Prepare for Number Talks?

• Designated location allowing proximity

• Appropriate wait time• Accept, respect, and

consider all answers• Encourage student

communication

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

Having the opportunity to ponder other approaches strengthens our own

mathematical foundation and understanding.

Accountability with Students

• Finger Signals for Efficient Strategy• Keep records of Problems.• Small-Group Number Talks• Class Strategy Charts• Exit Ticket• Weekly Computation Assessment

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.

Instructional Supports

AssessmentsBenchmarksUnitsTimed Tests

Benchmarks

• Majority Selected Response

• Two Constructed Response (except for Benchmark 1)

Unit Assessments

Timed Tests

“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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