I want to use this space to make a pitch for a conference session.
See, there is this thing called Twitter Math Camp. It is professional development by teachers, for teachers—nearly all of us connected through Twitter. It takes place this summer near Tulsa, OK.
I am presenting with Malke Rosenfeld. Our official description is copied below.
Malke and I have developed a really productive collaboration this year. You can browse both of our blogs to see the kinds of questions and learning this collaboration has developed for each of us.
Here is my pitch for our session…
We are planning a session that will force our groups (including ourselves) to wonder about the origins of mathematical knowledge. We will question our assumptions about terms such as concrete, handson and kinesthetic.
We will participate in mathematical activity both familiar and strange—all in the service of better understanding the relationship between the physical world and our mathematical minds.
We will dance.
We will make math.
We will laugh and possibly cry.
Below is an example of Malke’s work. When I participated in a workshop last summer, my head was spinning with math questions as a result. It’s great stuff and we will use it as a launching point for inquiry into our own classroom teaching.
So if you’re coming to Tulsa, please consider joining us for our three 2hour morning sessions.
Of course you’ll miss out on other great people doing other great sessions. But you won’t regret it. I promise.
And if you choose a different session (perhaps because you’re leading one of them!), I have a hunch there will be after hours percussive dancing in public spaces. Come join in!
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Our session description
This workshop is for anyone who uses, or is considering using, physical objects in math instruction at any grade level. This threepart session asks participants to actively engage with the following questions:

What role(s) do manipulatives play in learning mathematics?

What role does the body play in learning mathematics?

What does it mean to use manipulatives in a meaningful way? and

“How can we tell whether we are doing so?”
In the first session, we will pose these questions and brainstorm some initial answers as a way to frame the work ahead. Participants will then experience a ‘disruption of scale’ moving away from the more familiar activity of small handbased tasks and toward the use of the whole body in math learning. At the base of this inquiry are the core lessons of the Math in Your Feet program.
In the second and third sessions, participants will engage with more familiar tasks using traditional math manipulatives. Each task will be chosen to highlight useful similarities and contrasts with the Math in Your Feet work, and to raise important questions about the assumptions we hold when we do “hands on” work in math classes.
The products of these sessions will be a more mindful approach to selecting manipulatives, a new appreciation for the body’s role in math learning, clearer shared language regarding “handson” inquiry for use in our professional relationships and activities, and public displays to engage other TMC attendees in the conversation.
This sounds awesome. Can I join this group?
Dear Mr. Daniels,
I am a math teacher in a very small homeschooling community who has been appreciating your math site for about a year now. Thank you so much for all you do.
I have two questions that I asked my fourth grade group recently that became accessible for them, only after I introduced manipulatives. (Seven 10 year olds) They were unable to come up with a sketch or numbers on paper that could grease the skids of their thinking toward a solution, but as soon as manipulatives were introduced all seven were able to solve them. I thought perhaps these might be of interest to you as you puzzle the role of manipulatives in learning.
Question 1 – A treasure chest contains rubies and sapphires – 10 precious stones total. Whichever seven stones you take out of the chest, you always get at least one ruby. Whichever five stones you take out of the chest, you always get at least one sapphire. How many stones of each kind are there in the chest? They puzzled for a few minutes with mostly confused looks and a blank page in front of them, but when I offered flat craft marbles as jewels to explore the story, they were able to use the marbles to understand what was happening. It was fascinating watching how they moved the marbles to make sense of what the story even meant, back and forth with combinations to bring meaning to ‘take 5 and always get at least one sapphire’.
Question 2 – Spencer was browsing the exotic pet store. Three iguana and four hairy spiders cost $50. An iguana and a spider together cost $15. How much does each animal cost? After some quiet time with little progress, I provided unifix cubes of two colors for them to model the situation. They quickly paired off iguanas and spiders, revealing the cost of 1 spider and solving the problem. We spent some time after talking about ‘what could they have sketched to see this story without colored cubes’ as they have not yet developed that skill as a way to start their solution.
Even though we talk about sketching mathematical ideas often, they did not seem to know what to sketch for these two problems. The manipulatives helped my kiddos bridge the gap from just mentally imagining relationships, toward my goal of having them sketch relationships in a more complex story. I am not even sure what they would have sketched in question 1 that would have given them the same flexibility and instant comprehension that the marbles did.
Hope this helps,
Jeanie