Minds On Math

Minds On Math by Wendy Ward Hoffer

This is an awesome book.  We are ordering a copy for all members of the math PLC.  These are the ideas we are focused on and connecting to our current work.  This book fleshed out the concepts nicely for us, providing shared understanding and language at last.

What is it?

1. Challenging tasks
2. Collaboration and discourse
1. model curiousity, how to talk about ideas, demonstrate and expect respect, teach empathy, "press pause"
2. Talk engages learners, promotes understanding, develops communication and collaboration skills, supports academic language development
3. Create, sustain, respect thinking and share the process all using talk.
3. Community and culture
1. Classroom Anchor Charts:  Norms -- Definition --- Examples
4. Conferring
1. Goal:  research -- coach -- reflect -- record
2. Class list:  Who's got it?  / "quotes" to use in lessons  / Who's off...reteach?
3. You are on the "pursuit of misconceptions"
4. Communicate:
1. You are capable
2. I will support you, but I will not take away the struggle.
3. I care about your as a thinker and a communicator.

PLanning:  How does your week build?  How do you plan to check for understanding across the week?

Workshop - goal:  connect the practices and content across the workshop:

1. Open - how is this time serving your purpose?
1. Welcome at the door
2. Problem that requires PK or service a purpose
1. Ex:  conceptual conversations (What was the key learning from yesterday?)
2. Accountability Structure - Think Pass, Weekly Tracker, Get on-Give one, Trios, Warm Call, Math notebook entry
3. Common Mistake or Error Analysis (based on earlier lesson)
2. Mini-lesson (on thinking)
1. Model thinking - don't show example
2. Model reasoning
3. Explicitly demonstrate thinking
4. focus on reasoning and understanding
5. invite students to share thinking
6. summarize key learning
7. Math practices
3. Work time
1. Parallel problems - Students do / Teacher models or summarizes / Students do more / Teacher interjects to summarize or model or clarify or push...
2. What are students doing and how are they doing it?
1. Content?
2. Product?
3. Process?
4. Grouping?
3. What is teacher doing?  
1. Promoting thinking via catch and release (push thinking)
2. Gathering data - expose thinking about mathematical accuracy, ability to justify, and conventions (work is legible, organized)
3. Trouble shooting
1. Inefficiency?  What tools could you use?
2. Stuck?  What questions could you ask?
3. Problems?  Invitational Groups
4. Model empathy - try, listen etc...
4. Accountability - give status, 5:1, reminders, 
4. Share and Reflect
1. student presents their thinking, reasoning, position
2. student explains why and how
3. response/reflection - peers respond with questions, feedback, compare/contrast with their ideas, share about other approaches
4. Revise thinking:  
1. synthesize (do you still agree?), 
2. observe growth (how has my understanding grown/changed?), 
3. extract learning (what was the lesson of this problem?) and 
4. reflect on self as a learner!
5. Goals:
1. Focus on thinking
2. Students understand the ideas of others and reconsider their own approaches
3. Teachers probe for deeper explanation, invite thinking, gather data
4. Role of errors:  explored to uncover and address the thinking that lead the problem astray.

HCT:  

• raise complexity and ambiguity, 
• synthesize math strands, 
• invite conceptual connections, 
• require explanation and justification, 
• require proposed solutions 
• creates interdependence
• Level / Demand
• 1 / Recall
• 2 / Skill and concepts (solve, organize, interpret)
• 3 / Strategic thinking
• 4 / Extend Thinking (design and conduct, sythesize, critique)

TAKE TIME (both: do it and let students discover them on their own time) TO UNCOVER ERRORS (remember, "you are in pursuit of misconceptions!"):

• via multiple solutions
• pinpoint decisions - critical decision points
• assess the impact of the error
• categorize mistakes
• identify signposts (what clues did you have along the way that your solution was right or wrong?)
• generalize - what do we need to remember?
• Role of errors:  explored to uncover and address the thinking that lead the problem astray.

You must control your thoughts:

1. Asset stance / Strength based protocols
2. Presume positive intent
3. Cultivate Compassion

Plan to check for understanding across the week:

• Monday
• ML: TT
• IWT:  small group
• SHARE: discuss
• Tuesday:
• ML:  review
• IWT:  stations / differentiated
• SHARE:  Summarize
• Wednesday:  L@SW
• ML:  Trouble shoot common errors
• IWT:  confer
• SHARE:  reflect
• Thursday:
• ML:  Graph / Bias
• IWT:  stations
• Share:  Share work
• Friday....

Teacher roles:  policing, directing, accounting, correcting, rescuing, socializing, praising