Math Instructional Framework:PDSA and Lesson Planning
Objectives: Develop an understanding of best practices in math instruction including:
– Proficiency Strands (National Research Council. (2001). Adding it up: Helping children learn mathematics. J Kilpatrick, J. Swafford, and B. Findell
– Mathematical Practices (from Common Core)– Process Standards (NCTM – National Council of Teachers of Mathematics)– 5 Practices for Orchestrating Productive Math Discussions (NCTM)
Present DRAFT Mathematics Instructional Framework – PDSA and Lesson Planning and demonstrate how the best practices (listed above) are woven throughout.
Outcomes: Team members will have deeper understanding of best practices in math instruction
Team members will learn about newly developed / draft PDSA and Lesson Planning Framework and provide input for next steps in PD for team and how to roll out to schools
Developed for Central Team PD – April, 2014
Process Standards
Proficiency Strands
Mathematical Practices
What Student Success Comprises
What Instruction Provides
How Students are Engaged
• Conceptual Understanding• Procedural Fluency• Strategic Competence• Adaptive Reasoning• Productive Disposition
• Problem Solving• Reasoning & Proof• Communication• Connections• Representation
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.
education.state.mn.us 3
Adding It Up: Helping Children Learn Mathematics
National Research Council – 2003
The National Academies PressWashington, DCwww.nap.edu
Mathematical Proficiency
Adding It Up :Helping Children Learn Mathematics
The National Academies Press (2003)
www.nap.edu
Mathematical Proficiency
education.state.mn.us
5
• conceptual understanding —comprehension of mathematical concepts, operations, and relations
• procedural fluency —skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• strategic competence —ability to formulate, represent, and solve mathematical problems
• adaptive reasoning —capacity for logical thought, reflection, explanation, and justification
• productive disposition —habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
Process StandardsThe Process Standards
highlight ways of acquiring and using content
knowledge.Without facility with these critical processes, a student’s mathematical knowledge is likely to be fragile and limited in its usefulness. Principles and Standards for School
Mathematics, NCTM (2000)
Process Standards
• Problem Solving• Reasoning & Proof• Communication• Connections• Representation
5 Practices for Orchestrating Productive Math Discussions
FIRST – need clear goal!• Anticipating• Monitoring• Selecting• Sequencing• Connecting
Instructional Math Framework Version 1.0
Essentials of a Mathematics Schoolwide Program:
The Six NCTM Principles
The Five Process Standards driving instruction in the
classroom
A Process-Standards based
Mathematics Program
Equity
Technology
Curriculum
LearningTeaching
‘How to’ tool:
Process Standards
Practice Profile ‘starters’
Implementation Drivers
Reflection Map
‘How
to’ tool:
Schoolwide or Systems Practices
Profile
‘How to’ tool:
Problem Solving
Reasoning & Proof
Communication
Connections
Representation
‘How to’ tool:
These tools:
* were developed by the regional Centers of Excellence math specialists.
* are a synthesis of evidence-based practices in math and what has been observed in focus and priority schools who are working to implement an effective mathematics program
* are meant to support a leadership implementation team in guiding the process of examining their current math program, using the frameworks of Implementation Science.
* contain a Practice Profile ‘starters.’ The ‘starters’ are meant to start the conversation with leadership teams and teachers about what best practices in math looks like at the classroom level. To fully develop this way of teaching can take 2-4 years of constant intention and professional learning. A leadership team may choose to focus improvement effort in only 1-2 of these standards during a year step out a more thorough and concrete Practice Profile to guide instructional development and the collection of walk-through data.
Program Research Sources:• NCTM research brief, “Effective Strategies for Teaching Students with Difficulties in Math” (2007)• NCTM: Principles and Standards for School Mathematics (2000)• NCTM: Essentials of a School Mathematics program • Common Core State Standards: Mathematical Practices (2010)• “Adding it Up : Helping Children Learn Mathematics,“ (2003)• “Shifts in Classroom Practice” in Leading in the in the era of Common Core State Standards: A toolkit for
mathematics coaches and leaders (Bay-Williams, McGath, Kebett, Wray) (in press) • Best Practice, (3rd Ed.). Zemelman, Daniels, & Hyde (2005).• “How Students learn Mathematics in the Classroom”• SISEP URL
Hint: The ‘red’ circles are documents from your
school advocate.
Assessment
Tools to Implement an Effective Mathematics Program
Curriculum
Brainstorming…. January, 2014Three Parts:
Getting Started, Working On It, Reflect and Connect
A possible lesson design framework to teach the MN Math standards
PlanUse the guiding questions detailed on back to plan a 3-part math lesson from scratch or modify a lesson from an existing resource.OR Get clear on the scope of the 3-part lesson your program has already developed for you and your studentsWhat a teacher
might do...
DoTeach the lesson to the plan, making adjustments as students’ needs arise.
StudyMonitor student progress throughout the lesson, deciding how to sequence the Reflect and Connect discussion.After the lesson, review ‘close problem’ or formative assessment results.
ActUse the results of monitoring student work and ‘close problems’ to inform tomorrow’s lesson plan.
Version 1
What a Teacher might do…
Getting Started (Plan)•Interacting with lesson objective through quick writes or other structures in math journals•With teacher guidance, recording models, pictures, and/or numerical representations to support the solving of a rich, relevant real-world problem.•Responding to writing and speaking prompts using the language of math as depicted on current and posted anchor chart
What you might see students
doing during...
Working on It (Do)•Utilizing concrete, pictorial, and abstract representations•Solving 1-2 rich, real world problems•Communicating thinking in intentionally selected groupings
Reflect and Connect (Study)•Sharing their solutions and thinking with the class in a 15-20 min whole-class discussion•Challenging, defending and exploring each other’s thinking•Exploring how the day’s lesson is connected to previous lessons•Reflecting on recent assessment results and setting goals for personal improvement
Close Problem (Act)Applying their insights from group work and discussion to independently solve a problem based on the daily learning target in their math journals.
What you might see Students doing …
How to bring it into the classroom..?
• Opportunity arose in school - decided to use lesson study approach
• Wanted to capitalize on their practice profile focus (formative assessment and academic vocabulary)
• Developed outline for a lesson study based on PDSA above and modified MSTP approach
• Needed to be able to use outline within a teachers existing classroom – meet them where they are at and provide opportunities to grow into incorporating best practices in PDSA
Version 2.0
• Will share using Focused Conversation approach
In t
he c
onfe
rence
room
…
Gather and review multiple sources of data to Explore the Useable Intervention to use to grow student understanding of math standards. Develop a Practice Profile, possibly from a Practice Profile ‘starter’, to articulate what practices you would see in the classroom. Decide how to collect data about the depth of implementation the teachers are making in classrooms and how the students are doing as a result of the changes; this is your Performance Assessment, derived in part from your Practice Profile. You’ll need to install a Data-Decision Making system to easily collect and review the data.
Craft an implementation action plan that maximizes the use of Drivers to implement the Intervention schoolwide.
As you chart next steps, use the Drivers to analyze where the most momentum can be
released to keep the Intervention propagating schoolwide.
What leaders might
do...
In learning networks, teachers periodically co-design a PDSA Lesson informed by the Practice Profile to learn from students in each other’s classrooms.
Teachers are freed up to visit each other’s classrooms while lesson is being taught to focus on how the practices in the Practice Profile help build student understanding of math standards.
Debrief the PDSA Lesson observed using the Debriefing Protocol
Apply ‘lessons learned’ to your next planning cycle.
What networks of
teachers might do...
From the conference room to the classroom: Fueling Math instruction with PDSAThis document was produced by the Regional Centers of Excellence, a partnership between regional Service Coops and MDE in March 2014. While it can be used in a myriad of ways to facilitate understanding of best practices in Math instruction, its first purpose was to help leaders and teachers see how to integrate the frameworks of Implementation Science to generate MN standards-based math instruction, to foster the kinds of math classrooms where teachers and kids love doing math because it is so much FUN!
BOLD TERMS = a defined process your advocate can share more about
Until you reach Full Implementation, your best sources of data about the effect of
your Intervention are classroom walk-through data based on your Practice
Profile. ACTions should be planned on how the adults are doing first, students
second, until your walk through data reveals that 50% of all staff are meeting the
‘gold standard’ defined by your Practice Profile.
For
the c
lass
room
…Use the guiding questions on the Daily PDSA Lesson Plan to design or modify a daily lesson.
Deliver the lesson to the plan, making adjustments as students’ needs arise.
Monitor student progress throughout the lesson, deciding how to sequence the
Reflect and Connect discussion. After the lesson, review ‘clōse problem’ or formative
assessment results.
Use the results of monitoring student work and ‘close problems’ to inform tomorrow’s
lesson plan. What individual
teachers might do...
Interact with lesson objective through quick writes or other structures. With teacher guidance, record models, pictures, and/or numerical representations to support the solving of a rich, relevant real-world problem. Respond to writing and speaking prompts using the language of math.
Share their solutions and thinking with the class in a 15-20 min whole-class discussion. Challenge, defend and
explore each other’s thinking. Explore how the objective is connected to previous lessons.
Apply insights from group work and discussion to independently solve a problem based on the
daily objective in a math journal and/or respond to further writing prompts or generate
follow up questions.
Possibly, reflect on recent assessments and set goals for personal improvement.
Use concrete, pictorial, and abstract representations to solve problems. Solve 1-3 rich, real world problems and communicate thinking in intentionally paired student groups.
the classroom
What you might see
students do...
