by Sherry Parrish

Helping Children Build Mental Math and Computation Strategies

Session 1

Tuesday, February 11, 2013

from 4:00-7:00

Facilitated by: Sunsie Suarez

Goals/Agenda

Welcome

Overview

Sample Number Talks

Videos

Routine

Teacher’s role

Student expectations

Common Core Standards: Standards for Mathematical Practice

Next Steps

Wrap Up/Session 2

Evaluations

Why Number Talks?

The practice of number talks is one of the most powerful vehicles I know for helping students learn to reason with numbers and make mathematically

convincing arguments, for building a solid foundation for algebraic reasoning, and for teaching mathematics as a sensemaking process. If all teachers make this shift in their practice, it would represent a profound advancement in mathematics education.

- Ruth Parker

Common Core Standards: Standards for Mathematical Practice

Mathematically proficient students:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Book Overview

Important Tables xxi-xxxii

Chapter 1: What is a Classroom Number Talk? (P.3)

Chapter 2: How Do I Prepare for Number Talks? (P. 17)

Chapter 5: Addition and Subtraction Strategies in the 3-5 Classroom (P. 157)

Chapter 6: Designing Addition and Subtraction Number Talks in the 3-5 Classroom (p. 182)

Chapter 7: Multiplication and Division Strategies in the 3-5 Classroom (p. 230)

Chapter 8: Designing Multiplication and Division Number Talks in the 3-5 Classroom (p. 262)

What does it look like at my grade-level? (p. 316)

Actual Number Talk problems are provided within

Purposeful.

Focused on number relationships and number theory.

Solved mentally.

Reasoning skills developed.

What are Number Talks?

“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".

Chapter 1- What is a Classroom Number Talk?

Read pages 3 – 10 (top of page).

Highlight parts that stand out to you.

Select three ideas and record these on a post-it.

Be prepared for a standup-hand up-pair up activity.

“

Accuracy

denotes the ability to produce an accurate answer;

efficiency

refers to the ability to choose an appropriate, expedient strategy for a specific computation problem;

and

flexibility

means the ability to use number relationships with ease in computation.”

Calculate the following mentally.

Be prepared to share strategies aloud.

**70 - 34**

Classroom Clip: 3.4

As you watch the third-grade number talk for 70-34, consider:

How are students using number relationships to solve the problem?

How would you describe the classroom community and environment?

Which strategies demonstrate accuracy, efficiency, and flexibility?

How are the students’ strategies similar or different from your strategy?

Discussion Questions:

What structures are present in the classroom community that allow:

Mary to be comfortable thinking about her errors with the class,

Incorrect answers to be posted, or

Students to change their answers when presented with other students’ reasoning?

Read the strategies listed on page 350.

Classroom environment and community

Classroom discussions

The teacher’s role

The role of mental math

Purposeful computation problems

Read page 10-15 and highlight the sections of the key components

Key Components of Number Talks

Classroom Environment and Community

Safe, risk-free environment.

Student comfort.

Classroom acceptance on all levels.

Community of learners.

Classroom Environment and Community

Teacher writes problem on board and give students time to solve the problem mentally.

Once students find an answer, they are encouraged to continue finding efficient strategies while others are thinking.

Students indicate when they are ready with a solution by quietly raising a thumb against their chest.

They indicate they have other approaches by raising another finger for each solution.

Classroom Discussions

The quiet form of acknowledgement allows for more student think time at the same time as challenging students that already have an answer.

All answers- correct and incorrect- are recorded.

Students share strategies and justifications with peers.

The Teacher’s Role

Teacher’s role shifts in process

Guide students to ponder and discuss examples that build upon teacher’s purposes.

“How did you get your answer?”

“By changing my question from

“What answer did you get”

to

“How did you solve this problem?”

I was able to understand how they were making sense of mathematics.”

Benefits of Sharing and Discussing Computation Strategies

Students have the opportunity to:

Clarify their own thinking.

Consider and test other strategies to see if they are mathematically logical.

Investigate and apply mathematical relationships.

Build a repertoire of efficient strategies.

Make decisions about choosing efficient strategies for specific problems.

Wrong Answers

Students are asked to defend or justify their answers to prove their thinking

Students have a sense of shared authority in determining whether an answer is accurate

Teacher is not ultimate authority

Wrong answers are used as opportunities to unearth misconceptions

Students investigate their thinking and learn from mistakes

Mistakes play an important role in learning and provide opportunities to question and

analyze thinking, bring misconceptions to forefront, and solidify understanding

The Role of Mental Math

Mental computation.

Build on number relationships.

Develop strategies.

Place value understanding.

(examples pages 13-14)

Purposeful Computation Problems

Craft problems that guide students to focus on mathematical relationships

Teacher’s goal and purpose should determine the numbers and operations that are chosen

Examples- Pages 14 - 15

Number Talks are a Purposeful Vehicle

Make sense of mathematics

Develop efficient computation strategies

Communicating mathematically

Reasoning and proving solutions

Overview

Daily, 5-15 minutes

Mental math problems posed

Students are given think time and indicate a solution and multiple strategies

Students share solutions and explain their thinking

Encourages students to communicate about math

The teacher acts as a facilitator and his/her primary function is to question students in order to guide the discussion

As you watch the Number Talk, consider:

What procedures are in place that allow students to share their thinking?

What opportunities exist for the teacher to informally assess student understanding?

How is student communication encouraged and valued?

How would you describe the teacher’s role during the number talk?

**Classroom Clip 5.3:**

16 x 35

16 x 35

Read pages 16 - 21

What are the Four Procedures and Expectations Essential to Number Talks?

What practical considerations does the author make for these procedures and expectations?

Four Procedures and Expectations Essential to Number Talks

Select a designated location. (pages 17-18)

Provide appropriate wait time. (page 18)

All answers are accepted, respected, and considered. (page 19)

Encourage student communication throughout the number talk. (page 19-21)

Routine

Daily, 5-15 minutes

Consistent location

Students in close proximity, seated on the floor or in chairs

Easy visibility for teacher and students

Teacher records student thinking on the whiteboard and/or chart paper

Problem or string of problems are posed

Students are given think time

Teacher facilitates a conversation around

the problem(s) posed that day

Classroom Clip: 3.1

Discuss:

How does the teacher’s recording of each strategy provide access for all students?

Which strategies are easiest for you to understand?

Which strategies are more challenging to follow?

What mathematical concepts are being addressed during the number talk.

How did the teacher bring these ideas to the forefront for the class?

Six Ways to Develop Accountability with Students

Ask students to use finger signals to indicate the most efficient strategy.

Keep records of problems posed and the corresponding student strategies.

Hold small-group number talks throughout each week.

Create and post class strategy charts.

Require students to solve an exit problem using the discussed strategies.

Give a weekly computation assessment.

5 Small Steps Toward Teaching for Understanding

Start with smaller problems to elicit thinking from multiple perspectives

Be prepared to offer a strategy from a previous student

It is okay to put a student strategy on the back burner

As a rule, limit to 5-15 minutes

Be patient with yourself and students as you

incorporate Number Talks into your regular math time

Teacher Responsibilities

Plan problems with a purpose/goal in mind

Pose the problem(s) for the day

Record student responses to reflect how they were explained (not the teacher’s interpretation)

Practice notation to represent student thinking accurately

Provide the structure and procedures to facilitate the Number Talks

Post sample prompts to helps students structure their explanations or questions in front of the class

Be aware of the equal sign and use it

properly

**Teacher’s role**

Planning - be purposeful in the selection of problems

Facilitating

Questioning

Recording answers/student thinking

Accepting – accept and record answers/explanations without confirming or denying

Planning - be purposeful in the selection of problems

Facilitating

Questioning

Recording answers/student thinking

Accepting – accept and record answers/explanations without confirming or denying

**Student participation**

All students work to find an answer

Signal that they have an answer and if they have multiple strategies

Share and explain their thinking

Defend their thinking

Inquire about the thinking of others

All students work to find an answer

Signal that they have an answer and if they have multiple strategies

Share and explain their thinking

Defend their thinking

Inquire about the thinking of others

**Strategies**

Discuss with your partner at least four different strategies to solve 28 + 29.

How will you teach alternate strategies to students?

Discuss with your partner at least four different strategies to solve 28 + 29.

How will you teach alternate strategies to students?

**Next Steps**

Try a few Number Talks with your students

Reflect on the experience and bring back notes to share with the group

Session 2: Tuesday, February 25th from 4:00-7:00

Try a few Number Talks with your students

Reflect on the experience and bring back notes to share with the group

Session 2: Tuesday, February 25th from 4:00-7:00