*I went to a workshop at Downey Unified a few weeks ago and Steve Leinwand was the speaker - it was a great day, full of thought-provoking problems and considerations to make in regards to math education. Here are my notes:*

Check out http://steveleinwand.com/ for so much more :)

__NOTES ON COACHING:__- Coaching Debriefs - Always start with something specific and positive
- What I really liked was…. What was really impressive is when…
- So tell me what your learning goals were for this lesson?
- What your plan for meeting these goals? (that is what activities, problems, tasks,questions)
- How well do you think your goals wereachieved?
- What would you do differently?
- Coaching-
- What do you want me to look for?
- What do you want me to listen for?
- What do you want me to do? (Model, Co-Teach, Cognitive)

__GROWTH AND CHANGE__- NCTM Article by Steve Leinwand - Four Teacher-Friendly Postulates for Thriving in a Sea of Change
- Change 10% ever year
- 6 minutes of every lesson
- 1 unit out of every 10
- Teachers need to observe other teachers at least once a week!!!
- Model lessons + videotape + debrief
- Coach and teacher both teach same day
- Post videos on secure website for teachers to share and collaborate
- Teachers bring an activity to PLC meeting & post it with a reflection and student work on secure website.
of us know it all. We__None__have different specialties. We__all__have something to bring to the table.__all__- THINGS WON'T CHANGE UNLESS... There is time for collaboration and coaching!

People won't do what they can'tenvisionPeople can't do what they don'tunderstandPeople can't do well what isn'tpracticedBut practice withoutfeedbackresults in little change, andWork withoutcollaborationis not sustaining

We must help people envision, understand, practice, receive feedback, and collaborate

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**

- Ideas for Collaboration:
- Time & Structure
- Structured & Focused Department Meetings
- Common Planning Time
- Subs for classroom visits (or coach/principal teach a period to free up teacher to visit colleagues)
- Debriefing sessions for any classroom visits
- Summer Workshops
- Strategies
- Classroom visits
- Demonstration lessons w/ debrief
- Co-teaching opportunities (join 2 classes together)
- Common readings assigned w/ discussion
- Technology demonstrations
- Video analysis of lessons
- Analysis of student work
- Development/Review of common finals or unit assessments
- "What's not working" sessions?

__COMMON CORE__- He admitted that the K-8 math CCSS standards are amazing, but the 9-12 are still an "abomination".
- Great online math resources - bookmark this site: https://sites.google.com/site/greatccssmathresources/

- We must have problems that
*allow*for multiple approaches. There is not one right way to solve it. Allow students to struggle and think through problems on their own first - you will be amazed with the methods they come up with. THEN, you can show them the "math" way that may be more efficient... but it's not the only right way! - Problems that allow for multiple approaches general have "nice" numbers to work with, so you can approach it in several different ways.
- Once they struggle through coming up with multiple approaches and sharing the different approaches (display student work and discuss the method), then pose a question that
*doesn't*have nice numbers as an extension, showing students the need for a more mathematical way of solving the problems. - *You are creating the
*need to know*! - Get students invested by making them
*guess*first. Estimation & Logical Thinking --> Justification for Estimates. "What are you thinking?" - This is one method of differentiation in the classroom - accommodating multiple ways of thinking

- In Singapore, the "Teach Less, Learn More" and "Talk Less, Listen More"
- Things we want our students to do:
*If given a set of data:*Organize it, identify trends,ask questions, develop and justify hypotheses, summarize data*If given a situation:*represent it, describe it, interpret it, make predictions, plan a course of action, decide what's fair, identify contradictions and rip-offs*If given a claim:*evaluate it*If given a set of constraints:*satisfy them, find an optimum solution*If given a model:*explain it, debug it, refine it, generalize it, evaluate it, apply it

*****VERY IMPORTANT*** - it's not the teacher's job to create all the modeling tasks (3-Act, Estimation 180, Would You Rather, 101 Questions, Open Middle, Robert's Problem-Based Tasks)... it's the teacher's job to bring them into the class! They are created! They are out there! Use them.**

- Every time, probe a little further... look for multiple approaches, multiple answers, multiple viewpoints. This gives students multiple access points to the content.

- Things we need to consider... Our students...
- Forget - so we need to more deliberately review
- See it differently - so we need to accommodate multiple representations
- Approach it differently - so we need to elicit, value, and celebrate alternative approaches
- Give ridiculous answers - so we need to focus on number sense and estimation
- Don't understand the vocabulary - so we need to build language rich classrooms
- Ask "Why do we need to know this?" - so we need to embed the math in context.

- Reading in math vs. Reading in English
- "Jane went to the store"
- Who went to the store? (literal comprehension)
- Where did Jane go? (literal comprehension
- Why do you think Jane went to the store? (inferential)
- Do you think it made sense for Jane to go to the store? (evaluative)
- In math, we stay at the "this is the right answer" - We don't ask "why" or "How do you know" or "Who has a different answer" or "Does it make sense".

__Steve's suggestion for Math Homework:__- 2 - Problems on new skill
- 4 - Ongoing review (one from yesterday, one from last week, one from the beginning of the year, one from last year)
- 2 - Problem Solving, Explain Answer, Reasoning, Conceptual
- Homework on Monday, Tuesday, Wednesday, Thursday. Friday is assessment or problem solving task day and there is no homework unless students want to preview material for the next week.

__Steve's suggestion for How Class Time is Spent:__- 5-6 minutes cumulative review
**not**problem solving- 5-6 questions that should be quick and automatic
- Example for Pre-Calculus: (sorry, no math type)
- 1. What is the value of tan(pi/4)
- 2. Sketch the graph if (x-3)^2+(y+2)^2=16
- 3. What are the equations of the asymptotes of f(x) = (x-3)/(x-2)
- 4. If log base 2 of x is -4, what is the value of x
- 5. About how much do I weigh in kg?
- Example for "Oh Crap I don't have Time to Plan"
- A term of the day
- A picture of the day
- An estimate of the day
- A skill of the day
- A graph of the day
- A word problem of the day
- 5 minutes - go over 2-4-2 homework with questioning in mind (no more than 5 minutes!)
- 20 minutes - chunk 1 teaching
- 20 minutes - chunk 2 teaching
- 5 minutes - closure & exit ticket

__What is math?__- Option 1: A set of rules to be learned and memorized to find answers to exercises that have limited real world value
- Option 2: A set of competencies and understanding driven by sense-making and used to get solutions to problems that have real world value

__Ideas for Activities in Class__- Put 2 numbers on the screen that mean something to you. He put 27 and 15. We had to reason and try to deduce what the numbers meant. Then, he put 27/50 and 15/196, and we had to continue to reason. Lastly, he put up 27/50 states and 15/196 countries and we were able to see what the numbers actually meant.
- Take a textbook word problem and put it on the screen one part at a time. After each part, discuss what is going on, what the question may be, etc. Although it may be a "silly" problem, some good conversation and critical thinking can come from this activity.
- "There are 310 million people in the US. There are 13,000 McDonalds in the US. There is a point somewhere in the lower 48 that is farther from a McDonalds than any other point. 1) What state? and 2) How far?. [Answer is South Dakota, 107 miles away]
- Follow up: McDonalds claims that 12% of all Americans eat at McDonalds each day. Make the case that this claim is valid or invalid.
- Open with an engaging video or image and ask students what they see (can use 3-act math tasks). At this point, you've got them hooked and wanting to jump in. Steve added prompts or questions to the pictures.
- "You Pour I Choose"
- just have a picture of the two glasses - "Tell your partner three things you see here"
- When they tell you something, ask "How do you know?" If they say "It's a cylinder", ask "What's a cylinder?"... get them thinking, get them talking mathematically.
- Play video - "Which glass has more soda?" - What is your guess, and share your guess w/ a neighbor, with justification
- Once they share their guesses, ask them "Convince me of your guess"
- Play video again - "Guess how much soda is in each glass right now?" (A can of coca-cola contains 12 ounces).
- Ask students - "What information is important here? How would you get it?"
- ... follow the rest of the 3 Acts, and there's even a sequel!
- Exit Ticket - have a Green/Yellow/Red poster on the wall by the door. Have students solve a problem or write a summary on a sticky note and place it on the wall on their way out depending on how they feel about it (Do they feel really confident? = Green)
- One tip to make sure this closure is happening is to have a student be the "five minute marker" for each class period. That student is in charge of telling the teacher when there are 5 minutes left in class.
- "Tell me what you see"
- Start by showing students numbers, a graph, an equation, etc and simply ask "Tell me 5 things you see"
- Have students solve a problem with multiple approaches (could be math, but could be with drawings, graphs, guess, and check, etc). THEN show them the "math" way. THEN have them apply their knowledge to a new situation
- example: You have $10, Big Macs cost $1.59. What questions can be asked??
- go through and discuss/solve,etc
- formative assessment at the end - Oops! They are on sale for $1.29 and you've got $20.
- Reconsider how we teach different math topics
- Adding/subtracting integers with rules "Keep the sign of the bigger one" vs. understanding why with real-world contexts and multiple representations

__Classroom Mantras:__
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