© ascd 2013 | common core state standards bill and melinda gates/ascd grant: virtual learning...

© ASCD 2013 | Common Core State Standards

Bill and Melinda Gates/ASCD Grant: Virtual Learning Networks: Mathematics

Webinar 1: Demonstrating Mathematical

Understanding

Teacher Networks: Building Capacity for

Powerful Instruction

January 2014


Virtual Convening Agenda• WELCOME!• Introduction of ASCD Faculty Member

and attendees• Reminder of VLN Goals• Today’s Problem of Practice • Possible Next POP for Webinar 2?

ASCD/Gates Grant: Virtual Learning Networks



and attendees• Overview of the ASCD/Gates Grant• Eliciting Problems of Practice • Next steps



Nanci [email protected]



Poll 1:

Who are you?



Poll 2:

What do you do in education?



• Two Years• Five Webinars per year

• Content specific• Host by ASCD faculty member• Synchronous• Recorded and archived on EduCore



Goals:

1. Cultivate “Constructivist Community”

2. Help understand and facilitate the implementation of the CCSS-M

3. Develop a virtual team to support each other

4. Exchange resources



Phase One• 1 Virtual Convening• 4 Webinars

• Structured around “Problem of Practice”• Challenges identified by

participants in implementing CCSS in their classrooms

• Collaboration with trusted experts• Helpful feedback in a timely manner



ASCD Edge

• ASCD proprietary social networking platform

• Share comments and resources• Share video, audio, photos• Share upcoming events, updates,

alerts

PLEASE!!!

Join the conversation. Blog on the Edge. Respond to postings. Ask questions! Share ideas.



ascdedge.ascd.org


Something To Try First…

8 4 3 2

WHICH ONE DOES NOT BELONG AND WHY?

Short Answer Question 1: Please type your response in the question box!


Today’s Problem of Practice

How do we get students to engage with math like a mathematician through the Common Core?



Key Instructional Shifts: Mathematics

Focus: Focus on where standards focus - Deep not

wide!

Coherence: Think across grades and link to major topics - Progressions



Key Instructional Shifts: Mathematics, Cont.Rigor: Require fluency, application, deep

understanding – A balance of conceptual understanding and skill.

Math Practices

College and Career Readiness



Key Instructional Shifts: MathematicsToday’s POP looks more deeply at:

Rigor: Require fluency, application, deep

understanding – A balance of conceptual understanding and skill.

Math Practices




Rigor - Balance of Conceptual Understanding and Skills

Source: From “Balance of Conceptual Understanding and Skills,” by the Hunt Institute. www.hunt-institute.org




• Conceptual Understanding:

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• Procedural Skill and Fluency:5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

• Application:7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.


Green Flags and Red Flags

Adapted from Leading the Change to Common Core State Standards: Essential Tools for School and District Leaders by Sue Z. Beers and Judy F. Carr, © 2012 by ASCD. All rights reserved

Teacher-Controlled Actions





Equal intensity

Speed not an issue

Authentic, real-life practice and extended application

Little or no formative assessment

Timed tests as only mastery assessment

Tricks and mnemonic devices




Deep conceptual understanding and assessment

Feedback and next steps tied to standards

Justification

Strategies without fluency and conceptual understanding

Accepting steps without reasoning

Weak explanation




Fluency with number facts

Efficiency and accuracy

Judicious use of technology that does not impede fluency

Over use of tables and aids (including calculators)

No fluency expectations, or fluency achieved only outside of the classroom


Poll Question 3:What Green Flags are strongest in your class, school or district?


a. Speed not an issue

b. Authentic, real-life practice and extended application

c. Deep conceptual understanding and assessment

d. Fluency with number facts

e. Use of technology that does not impede fluency


Poll Question 4:What Green Flags need more attention in

your class, school or district?


a. Speed not an issue

b. Authentic, real-life practice and extended application

c. Deep conceptual understanding and assessment

d. Fluency with number facts

e. Use of technology that does not impede fluency


But, what about student- controlled actions?

Standards for Mathematical Practices




Mathematical Practices Standards1. Make sense of complex problems and persevere in

solving them. 2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning

of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning.



Mathematical Practices Standards1. Make sense of complex problems and persevere in

solving them.

Key IdeasBefore: Explain the problem; organize information; make a planDuring: Persevere!; monitor progress; check reasonableness; create new plansAfter: Check my answer and method; reflect on what worked

Student Actions• Display sense-making behaviors• Show patience and listen to others• Turn and talk for first steps and/or

generate solution plan• Analyze information in problems• Use and recall multiple strategies• Self-evaluate and redirect• Assess reasonableness of process and

answer

Nanci Smith, 2014



Mathematical Practices Standards2. Reason abstractly and quantitatively

Key IdeasContextualize and Decontextualize

Reasoning Habits include 1) creating an understandable representation of the problem solved, 2) considering the units involved, 3) attending to the meaning of quantities, and 4) using properties to help solve problems.

Student Actions• Represent abstract and contextual

situations symbolically• Interpret problems logically in context• Estimate for reasonableness• Make connections including real life

situations• Create and use multiple

representations• Visualize problems• Put symbolic problems into context

Nanci Smith, 2014



Mathematical Practices Standards3. Construct viable arguments and critique the reasoning of others.

Key IdeasConstruct arguments: justify and generalize; use examples and non-examples; use multiple representations including manipulatives and drawings

Critique reasoning: listen well; identify mistakes; ask questions to clarify thoughts and ideas

Student Actions• Questions others• Use examples and non-examples• Support beliefs and challenges with

mathematical evidence• Forms logical arguments with

conjectures and counterexamples• Use multiple representations for

evidence• Listen and respond to others well• Uses precise mathematical vocabulary

Nanci Smith, 2014



Mathematical Practices Standards4. Model with mathematics.

Key IdeasUnderstand and express how math models the real world

Represent Math through: concrete models symbols pictures oral real-world language situations

Student Actions• Connect math (numbers and symbols)

to real-life situations• Symbolize real-world problems with

math• Make sense of mathematics• Apply prior knowledge to solve

problems• Choose and apply representations,

manipulatives and other models to solve problems

• Use strategies to make problems simpler

• Use estimation and logic to check reasonableness of an answer

Nanci Smith, 2014



Mathematical Practices Standards5. Use appropriate tools strategically.

Key IdeasRecongnize that math tools are not all material tools but include mental strategies.Know HOW to use math tools. Know WHEN to use math tools. Know WHICH tool to use.Reason about the effectiveness of tools.

Student Actions• Choose appropriate tool(s) for a given

problem• Use technology to deepen

understanding• Identify and locate resources• Defend mathematically choice of tool

Nanci Smith, 2014



Mathematical Practices Standards6. Attend to precision

Key IdeasSpeak, read, write and listen mathematically.Calculate accurately and efficiently.Use correct notation, vocabulary and units of measure. Answer what a question asks.

Student Actions• Communicate (oral and written) with

precise vocabulary• Carefully formulate questions and

explanations (not retelling steps)• Decode and interpret meaning of

symbols• Pay attention to units, labeling, scale,

etc.• Calculate accurately and effectively• Express answers within context when

appropriate

Nanci Smith, 2014



Mathematical Practices Standards7. Look for and make use of structure

Key IdeasThe structure of numbers and operations make sense and I can use those structures to solve problems.Access the organization of numbers and space to solve problems.

Student Actions• Look for, identify, and interpret

patterns and structures• Make connections to skills and

strategies previously learned to solve new problems and tasks

• Breakdown complex problems into simpler and more manageable chunks

• Use multiple representations for quantities

• View complicated quantities as both a single object or a composition of objects

Nanci Smith, 2014



Mathematical Practices Standards8. Look for and express regularity in repeated reasoning.

Key IdeasLook for and use patterns.Use repeated reasoning to solve similar problems.Create “shortcuts” and strategies based on patterns.

Student Actions• Design and state “shortcuts”• Generate “rules” from repeated

reasoning or practice (e.g. integer operations)

• Evaluate the reasonableness of intermediate steps

• Make generalizations

Nanci Smith, 2014


Classroom Challenge: Interpreting Algebraic ExpressionsFound on EduCore™!



Interpreting Algebraic Expressionshttp://map.mathshell.org/materials/index.

php



Short Answer #2

Which Practices did the students exhibit and when?




and attendees• Reminder of VLN Goals• Today’s Problem of Practice • Next steps



Continue the learning:Archived webinar on Mathematical Understandings:

http://www.ascd.org/professional-development/webinars/nanci-smith-webinar.aspx






Short Answer #3

On what topics or Problems of Practice would you like next month’s Webinar to

focus?


Next Steps:

Post, Post, Post!!

Please use Edge to communicate! Let’s get a real dialogue going.



Our Webinars are scheduled for:

Thursday, December 12th

Friday, January 17th

Friday, February 21st

Friday, March 28th

Monday, May 5th

Be Sure to Join on Edge!!



Questions? Comments? Concerns? Quips? Quotes? Qualms? Or Conundrums?

Be Sure to Join on Edge!!

Invite Others.



Thank you!

Connect with me on:

ASCD Edge: Nanci Smith& VLN Mathematics Group

Email: [email protected]


© ascd 2013 | common core state standards bill and melinda gates/ascd grant: virtual learning...

Documents