Scottsboro City 6-8 Math September 3, 2015 JEANNE SIMPSON LESHELL SMITH AMSTI MATH SPECIALISTS.

Scottsboro City6-8 Math

September 3, 2015

JEANNE SIMPSON

LESHELL SMITH

AMSTI MATH SPECIALISTS

Welcome

Name School Classes you teach Share a classroom success and challenge from last year.

2

He who dares to teach must never cease

to learn.John Cotton Dana

Agenda

Aspire DataImplementing the Standards for Mathematical PracticeNumber TalksVertical Planning

acos2010.wikispaces.com

http://actaspire.avocet.pearson.com/actaspire/home

Reporting CategoriesAll questions are either measuring Grade Level Progress – mathematical topics new to the grade Foundation – topics learned in previous grades

Some questions are also categorized as Modeling – questions that assess understanding of mathematical models and

their creation, interpretation, evaluation, and improvement Justification and Explanation – giving reasons for why things work as they do,

where students create a mathematical argument to justify (constructed response)

Points by category

and grade.

Interpreting the Standards for Mathematical Practice

Session 1

edc.org Interpreting the SMP Course – Session 1 14

Introduction to the Course:Survey What We Know about the SMP

Consider how you would complete the following sentences:

• Something I know about the Common Core Standards for Mathematical Practice is…

• Something I want to learn about the Common Core Standards for Mathematical Practice is...

mathpractices.edc.org

http://mathpractices.edc.org/


Introduction to the Course:Preview the Course

Why are the Standards for Mathematical Practice, and the habits of thinking they describe, important?



Course Goals:

• Increase awareness of the Common Core Standards for Mathematical Practice (SMP)

• Develop understanding of the SMP connected to the Standards for Mathematical Content

• Cultivate capacity to identify the SMP in student thinking

• Develop ability to plan how to use instructional tasks in order to encourage student engagement in the SMP



Common Core State Standards for Mathematics

• Adopted by 43 states, District of Columbia, 4 territories, & Dept. of Defense Ed. Activity• National Governors Association Center for Best Practices, Council of Chief State School

Officers – www.corestandards.org • Grade level content standards for K-8 and High School:

– “Standards define what students should understand and be able to do.” “Clusters summarize groups of related standards.” “Domains are larger groups of related standards.”

• Standards for Mathematical Practice:– “…describe varieties of expertise that mathematics educators at all levels should seek to develop in

their students ”– “…describe ways in which developing student practitioners of the discipline of mathematics

increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.”

http://www.corestandards.org/



Common Core Standards for Mathematical Practice

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.(See handout with descriptions of each.)



Course Structure (see Course Overview handout):

• Ten two-hour sessions

– Sessions 1-2: Introduction

– Sessions 3-6: Focus on Algebra & Functions Contexts

– Sessions 7-9: Focus on Geometry Contexts

– Session 10: Conclusion & Consideration of Statistics Contexts

• All eight SMP highlighted over time – not every standard in every session nor a single standard per session.



Core Activities of Course:• Doing and Discussing Mathematics (All Sessions except Session 4)

– Exploring Mathematics Tasks as mathematical learners– Discussing use of Standards for Mathematical Practice (SMP)

• Examining “Student Dialogues” (All Sessions except Session 4)– Student Dialogues that offer examples of the SMP in student thinking– Discuss questions focused on SMP, mathematics, and classroom practice

• Planning Classroom Lessons (Sessions 3, 4, and 8)– Using tasks from Course (Session 3) or from your Curricula (Sessions 4 & 8)

• Analyzing Student Work From Your Students (Sessions 4, 5, and 9)– Using tasks from Course (Session 4) or from your Curricula (Sessions 5 & 9)



Planning lessons and collecting student work for analysis:

• After Session 3 use task from Sessions 1 or 3 with students

– Content for both tasks is in the domains of Operations & Algebraic Thinking and Expressions & Equations

– Session 1 task content: factors, multiples, relatively prime numbers

– Session 3 task content: numerical expressions

• After Session 4 use task from your own curriculum or of your choosing that highlights algebra, functions, number content

• After Session 8 use task from your own curriculum or of your choosing (could be from course) that highlights geometry content



Session 1 Goals:• Increase awareness of the Standards for Mathematical Practice (SMP).

• Develop understanding of the SMP and their connection to the Standards for Mathematical Content.

Session 1 Checkpoints: After engaging in this session, you should be able to…• State open questions or confusions about the SMP that should be addressed during the course.

• Explore and discuss mathematics and mathematical thinking with your colleagues in the group.

• Identify examples of one or more SMP in your own or a colleague’s approach to a mathematics task.

• Describe MP 1 (Make sense of problems and persevere in solving them) and MP 3 (Construct viable arguments and critique the reasoning of others)

• Identify examples of MP 3 in a Student Dialogue and provide justification for the examples.



Session 1 Agenda:Introduction to the Course Survey What We Know about the SMP Preview the Course

Mathematics Task Exploration Solve Mathematics Task Share Strategies SMP Exploration Discuss in Small Groups Share-Out and SummarizeStudent Dialogue Exploration Introduce Student Dialogues Read Student Dialogue Discuss Teacher Reflection Questions

Session 1 Mathematics Task and Student Dialogue:Integer Combinations—Postage Stamps


Mathematics Task Exploration:Solve Mathematics Task

• In other PD experiences working on mathematics tasks, what made those experiences productive?

• Individual work on task.– Track the twists and turns in your thinking.

• Small group work on task.


Mathematics Task Exploration:Share Strategies – Part I

Share and discuss:• How did you start out thinking about the task?• How did your thinking change, and what

prompted that change?• What conclusions, hypotheses, and questions

have you generated about possible and impossible postage amounts?


Mathematics Task Exploration:Share Strategies – Part II

Share and discuss:• Examples of thinking from your own or your colleagues’ work

on the task that illustrate the Standards for Mathematical Practice.


Standards for Mathematical Practice Exploration:Discuss in Small Groups

• Read the Standards for Mathematical Practice (SMP) handout.

• Re-read the descriptions of MP 1 and MP 3, highlighting key words and phrases.

• In small groups:– Discuss meaning of MP 1 and of MP 3.

– Create summary descriptions of MP 1 and of MP 3.• 2-3 sentences.• May include examples.• Write on large paper to share with rest of group.


Standards for Mathematical Practice Exploration:Share-Out & Summarize

Share and discuss summaries in whole group for:• MP 1: Make sense of problems and persevere in solving them.

• MP 3: Construct viable arguments and critique the reasoning of others.


Student Dialogue Exploration:Introduce Student Dialogues – Part I

• Dialogue between three fictitious middle grades or high school characters (either Sam, Dana, and Anita, or Chris, Lee, and Matei) working on a mathematics task

• The dialogues are intended to:– Clarify the meaning of particular SMP by showing what student

discourse could be

– Illustrate key ideas about the Standards for Mathematical Practice (SMP) in context using specific mathematical content

– Serve as an artifact to promote discussion among educators about the SMP, about mathematics, and about issues of teaching practice.


Student Dialogue Exploration:Introduce Student Dialogues – Part II

• Given the intention to illustrate the meaning and key ideas of the SMP:– Plausible student thinking, but the discourse may not always

sound realistic.

– The student characters are “caricatures,” intended to illustrate particular types of thinking and discussion.

– A teacher voice is intentionally not included.

– Discussion of whether or how a teacher might intervene, or of how to promote similar thinking with your own students, are productive avenues for discussion.


Student Dialogue Exploration:Read Student Dialogue

• Read the Student Dialogue out loud.

• Read the Student Dialogue individually – focus on mathematical thinking used by the students.


Student Dialogue Exploration:Discuss Teacher Reflection Questions

• Small groups: Discuss Questions #1-4 on the Teacher Reflection Questions handout.– Refer to the Standards for Mathematical Practice handout.– Be specific about what evidence you see in the dialogue.– Time permitting: Discuss any or all of Questions #5-6.

• Whole group: Discuss Question #2.

• Resource for later: Mathematical Overview


Homework Review

• Homework before Session 2:– Read the Introduction to the Standards for Mathematical

Practice handout.– (Optional) Review the Mathematical Overview handout

(information about today’s math task and student dialogue).


Number Talks

NUMBER TALKS

Helping children build mental math and computation strategies!

Number SongsHow well do you listen?

KEY COMPONENTS

Classroom environment and community

Classroom discussionsThe teacher’s roleThe role of mental mathPurposeful computation problems

PREPARING FOR NUMBER TALKS

Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.

Provide appropriate wait time for the majority of the students to access the problem.

Accept, respect, and consider all answers.Encourage student communication

throughout the number talk.

52 x 18

45 x 30

DISCUSSIONContact Info: [email protected]

[email protected]

mailto:[email protected]


edc.org

Planning Time

• Choose a standard that you will be teaching soon.• Work with the teachers in your grade level to plan a task for

this standard using the planning questions.• Be prepared to share.


Next Meeting – Friday, November 13

• Today I learned….

• A question I still have is….

edc.org

Contact Information

[email protected]@uah.edu

[email protected]



Scottsboro City 6-8 Math September 3, 2015 JEANNE SIMPSON LESHELL SMITH AMSTI MATH SPECIALISTS.

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