Wednesday, April 20, 2016

NCTM 2016 Days 2 & 3


Peg Cagle – promoting teaching as a profession
Michael Fenton – What we can learn about mathematical sequels from movie sequels
- best sequels take advantage of what we know about context and characters and hit the ground running
- balance between familiarity and innovation
- shed new light on original work
- know when to stop
- don’t wing it. You have to do the prep work
- do not abandon what works
Marilyn Strutchens – equitable classroom strategies --> positive math identities: math autobiographies, low threshold/high ceiling, math teaching practices, formative assessment, social justice activities, ask students what they want to study, students can contribute to the development of math, engage families in doing math
Andrew Stadel – allow time constraints to improve teaching: 20% of most effective functions should take up 80% of the time

Annie Fetter – students will be curious about (SWBCA) instead of students will able to (SWBAT). “People can’t understand solutions to problems they don’t have”
Max Ray-Reik – borrowed lessons are good because they come with a story, but it’s hard to build coherence with a hodge-podge of borrowed lesson. The ideal curriculum is not free and open-source, but open-story and crowd-engaged.
Tracy Johnston Zager – fluid and powerful collaboration comes from thinking partnerships (generative, supportive working side-by-side), cross pollination (credit for ideas becomes interesting), math disputes (representing own ideas, listening to others, publically changing your mind), and peer feedback (how do I make this better). We should only be working with other people when it’s beneficial to work with other people.
Lee StiffAll students deserve high quality education. We have created the achievement gap and we can change it.
Jennifer Wilson – The slow math movement.
Matt Larson – We should be engaging students not just in how to do math but in why and when.


Fumbling Toward Inquiry: Starting Strong in PBL

Geoff Krall
  • 5 design principles
    • notch some early wins where students are talking to one another about math and thinking of themselves as mathematicians (start short and successful)
    • provide an iterative framework and protocol (having a problem solving protocol(s) is more important than what the particular protocol is)
    • choose tasks that support targeted instruction and group-mate experience (example pull a kid from each table for a small group huddle and then send them back to be experts)
    • start slowly and strategically
    • don’t go it alone
  • Ira Glass: "Nobody tells this to people who are beginners, I wish someone told me. All of us who do creative work, we get into it because we have good taste. But there is this gap. For the first couple years you make stuff, it’s just not that good. It’s trying to be good, it has potential, but it’s not. But your taste, the thing that got you into the game, is still killer. And your taste is why your work disappoints you. A lot of people never get past this phase, they quit. Most people I know who do interesting, creative work went through years of this. We know our work doesn’t have this special thing that we want it to have. We all go through this. And if you are just starting out or you are still in this phase, you gotta know its normal and the most important thing you can do is do a lot of work. Put yourself on a deadline so that every week you will finish one story. It is only by going through a volume of work that you will close that gap, and your work will be as good as your ambitions. And I took longer to figure out how to do this than anyone I’ve ever met. It’s gonna take awhile. It’s normal to take awhile. You’ve just gotta fight your way through."
  • Select tasks that combine different content areas
  • Find a problem you are interested in and kids will probably be interested in it as well.
What I am wondering now: I used to primarily use tasks at the end of unit for students to solidify and apply their learning. Now I am often using tasks to introduce a topic and draw upon students’ prior knowledge and reasoning. I want to move towards integrating problem solving with mini-lessons and other instructions. What structures do I need to make this happen?

My Journey from Worksheets to Rich Tasks

Michael Fenton

What Math Teachers Do
- Answer questions
- Present “the notes”
- Assign Practice
Facilitate opportunities for students to engage meaningfully with math
Role of Math Teachers
- Answer-Provider
- Question-poser
- Thought-provoker
- Discussion-starter
- Math-instigator

  • Estimation 180:
    • Have them struggle with a specific estimation before giving the tools of too low/too high
    •  Too low/too high a confidence builder for students who think that wrong answers are “their game”
    • “If you say a million [as your too high] you get this conceptually but be brave”
  • Visual Patterns
    • fold paper into 4 parts, and reveal and have students draw 1 step at a time.
    • After each step ask students “How many in the next one?” (Acknowledge that this is unfair after step 1)
    • Make a table, sketch a graph, write an equation. Check with Desmos.
What I am wondering now: I am familiar and excited about all of the activities that Michael Fenton brings up as ways for students to engage meaningfully with math—3-act problems, estimation 180, visual patterns, would you rather, my favorite no, open middle, which one doesn’t belong. I have used them in isolation in my classroom. But I am really wondering how to fit them into the larger structure. How can really intentionally I use them to build the  math practices while working toward specific content goals.


Robert Kaplinsky – give power, gain influence
Gail Burrill – Listen to the voices in your head:
            - Think deeply about simple things (Ross)
            - Never say anything a kid can say (Reinhard)
- I know that my students understand when I see them in a place they have never been (Cuoco)
            - Let the students do the work (Wiliam)
Kaneka Turner – “When were you first invited to the math party and how did that feel?” Who will you invite to the math party?
Graham Fletcher – Really get to know your standards: be a wise consumer
- draw the standard or use tools to support your understanding
- be dumb… surround yourself with brilliance
- be vulnerable
Brian Bushart – explore, play, and find joy in doing math
Rochelle Guitérrez – These populations need access to math vs. We need this population’s contributions to mathematics

The Power of the Number Line: Understanding Fractions as Numbers

Ryan Casey
  • students often don’t distinguish between the tick-marks (addresses) and the intervals (distances) on a number line
  • in the common core, the fraction a/b is defined as “the quantity formed by a copies of size 1/b”
  • “mathematicians are convinced that if something is on a # line then it is a #”
  • prerequisite skills for putting fractions on a number line
  • principles of linear measurement
    • measurement is iterative
    • measurement involves partitioning
    • measurement involves processes that combine partitioning and iterating
What I am wondering now:  I really like the framework of using whole number understanding and leveraging that to extend into rational (or irrational) number understanding. I am wondering what would be good activities to do with both rational and irrational numbers in order to build my eighth graders’ understanding of irrationals.

The Life-Changing Magic of Tidying the Math Curriculum

Jason Zimba
Take-aways: How to tidy: teaching vs. turning in to a topic
  • Never ask about manipulatives on tests
  • Forget about calculators K-5
  • Formulas: throw most of them away
  • Headings: only for distinct topics
  • Methods: don’t teach too many (having too many around means less time on the challenging one that gets us over the next hurdle. Strategies go stale)
  • “Do mental calculation with multi-digit numbers, but save it for cases where a readily apparent mental strategy is both faster and more reliable than the standard algorithm”
  • Procedures: they are for procedural tasks
    • “A concept is worth 1000 procedures”
  • Terms that never appear in the common core
  • Store topics inside of one another
What I am wondering now: What am I teaching as a topic that isn’t really a topic? Exponent laws/Simplifying exponents. Solving systems using elimination (save that for high school). Anything else? And what are the most important methods that will get us over the next hurdle? Am I focusing on those? I think I need to spend some time tidying, but doing it with the text of the standards and the input of at least the other people in my department.

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