Does that make sense in the story? Cognitive journey: Get oriented to the mathematical situation Get oriented to “typical” implementations of problem solving Know what we’re up against and anticipate possible problems Articulate problems as clearly as we can Hear what happened in an actual classroom React to what happened in the classroom: Was it what we expected? Why or why not? Does what happened in the classroom justify our sense that “front-loading formative assessment” was what was needed? How do we tell the story to bring that focus out? How could the teacher have front-loaded sense-making? How did the teacher not front-load sense-making? In what ways is an investment of time needed? In what ways can small changes do the formative assessment work? Listen to what happened next: Again, how does this confirm or not confirm the idea of focusing on formative assessment? Can we characterize what was different this time? What ideas does this give you for in-the-moment focus on formative assessment during group work? Now think about presenting the problem to a whole class: Watch some Val videos Notice & wonder Reflect on what you see and the ways that Val is using formative assessment and adjusting

Introductions Name How are you feeling about the fact that it’s a Friday afternoon math workshop? What’s a hope or goal that you have for today?

Getting onto Wireless Connect to Asilomar Conference Password 1: conference Username: conf8690 Password 2: conf8690

About Me: Work at The Math Forum @ Drexel. Combined total of 60+ years of experience working with kids on persevering and revising their thinking, in writing, on non-routine tasks. Author of the book of that collected wisdom: Powerful Problem Solving

How I Lead a Problem-Solving Session Notice and wonder Check for and explore understanding of the context Independent/small-group work with targeted share-outs as check-ins Structured sharing-out with audience tasks

Trapezoid Teatime

What Did You See?

Trapezoid Teatime

What Did You See?

What Do You Wonder?

What Learning Goals Could You Probe For?

Thoughts? Concerns?

What Happened with Kids?

Keeping Kids Persevering Where could kids get unproductive? What kinds of work would be productive/unproductive for YOUR goal? What prompts or questions would encourage kids to change focus or persevere?

WWAD?

Break! Find your new table!

Frog Farming Farmer Mead would like to raise frogs. She wants to build a rectangular pen for them and has found 36 meters of fencing in her barn that she’d like to use. Design at least four different rectangular pens that she could build. Each pen must use all 36 meters of fence. Give the length and width for each of the pens. If each frog needs one square meter of area (1 m2), how many frogs will each of your four pens hold?

Context Halfway through a 5th grade textbook unit on area and perimeter Assessing their ability to apply what they’d learned Wondering about their conceptual understanding of area and perimeter No manipulatives available to us

WWYD? Talk in your groups about: Launching the task Preparing to support individual kids/groups who are stuck/unproductive Planning to have kids share their progress with the whole group

WWYD? Get Specific: Kinds of stuck? Questions to ask of those stuck kids? How will you help kids connect to the concepts? What strategies might you help kids to use? Will kids need help with procedures/facts? How will you help?

My Implementation Kids notice and wonder about scenario on projector: Think-Write-Share Reveal the question & pass out copies Teacher calls on a student to review what we are being asked to find Students work in their usual small groups to solve the problem

Frog Farming Farmer Mead would like to raise frogs. She wants to build a rectangular pen for them and has found 36 meters of fencing in her barn that she’d like to use. She knows each frog needs one square meter of area (1 m2).

They noticed & wondered We notice… We wonder… Farmer Mead would like to raise frogs Why does she want to raise frogs? She wants to build a pen What is a frog farmer? She has 36 meters of fencing How big is the pen? Each frog needs one square meter of area Why do frogs need one square meter of area? The frog is green How many frogs does she have? Farmer Mead is a girl The fencing is in her barn The pen is rectangular

What do we anticipate?

The ones who were stuck Student Situation: Some students couldn’t get started – they could identify one fact “She used 36 meters of fence.” Teacher Action: Tell students, “Right, that means the perimeter is 36 meters.”

The ones who were stuck Student Response: When 36 meters of fence was changed to “the perimeter is 36 meters” the students stayed stuck and didn’t use any strategies for finding side lengths give perimeter

The ones who took forever Student Situation: Some students used guess and check drawing different rectangles to find ones that used 36 meters of fencing. It was taking forever… Teacher Action: Remind students of a hint: “The first step is to divide it [the perimeter] in half. What is half of 36? Can you find two numbers that add to 18?”

The ones who took forever Student Response: When given the hint to “divide it in half” students start looking for four numbers that add to 18 because they look at their picture and remember rectangles have 4 sides.

Those who couldn’t do Part 2 Student Situation: Some students couldn’t start Part 2. They could identify one fact “Each frog needs 1 square meter of area.” Teacher Action: Say, “Great, what do square meters measure? Area? Yes! Now you need to find the area of each pen you came up with in Part 1.”

Those who couldn’t do Part 2 Student Response: When told to find area to solve Part 2, the students stop working and raise their hands to get more help: “I know how to find area but I don’t get what that has to do with how many frogs can fit in the pen.”

How would you coach the teacher?

What we tried next period Student Situation: only knew “she uses 36 meters of fence” Teacher Action: Confirm that matches the story, ask them to find a way she might have used the fence.

What we tried next period Student Response: draw rectangles and triangles and label them so they add up to 36 (sometimes takes some adjustment).

What we tried next period Student Situation: guessed and checked inefficiently Teacher Action: We got the group back together to list possibilities in an organized way – L W 10 8 9 9 8 10 7 11

What we tried next period Student Response: the whole class almost instantly started yelling out all the other possibilities as soon as they saw our organization

What we tried next period Student Situation: only knew “each frog needs 1 square meter of space” Teacher Action: Ask for guesses and reasons about how many frogs could fit in this pen.

What we tried next period Student Response: Make guesses that all show wrong thinking – 36 frogs fit in each pen, 9 frogs fit in each pen since each frog “takes up” 4 meters of perimeter.

What we tried next period Teacher Follow-Up: Invite students to use a drawing to show how many frogs will fit. Initial Response:

What we tried next period But then… “I did it this way but I wasn’t supposed to. It should be 45 frogs but I drew the boxes too small. All I had to do was multiply.” “I can just multiply these! 6 rows and 12 columns of frogs is 72 frogs!”

Reflections? Questions?

Current Reflections Something you saw that you’d like to implement or support a teacher to implement An insight into good questions or techniques for learning about students’ thinking while keeping them moving forward Other take-aways? Questions?

Stretch Break! At the end of 2 minutes Please form a spectrum Based on how much you are interested in baseball

All you need to know… A challenging problem An even more challenging context I’ll lead some of my favorite activities for understanding a context well enough to represent it algebraically

Find a WRONG ANSWER: How many innings had he played before the game started? How many runs had he given up before the game started? How many runs had he given up after his ERA changed? How many innings had he pitched after his ERA changed?

Final Reflections Something you saw that you’d like to implement or support a teacher to implement An insight into good questions or techniques for learning about students’ thinking while keeping them moving forward Other take-aways? Questions?