Math and Making Open Conference Notes
4. Math Ed in the Making
Facilitators: Jasmine Ma and Molly Kelton
Making practices writ large…
What would it look like to let that genuinely speak back to mathematics education?
What constructs would we want to keep from that literature?
What possibilities for mathematics education would exist if we can “unclench” the constraints for 45 minutes…?
what might look like learning?
what can mathematics look like?
Pretend that we don’t have standards. constraints.
X – role of art, the aesthetic in making projects. Art teacher started getting excited about tools that have math in them. All about perspective. Authentic way into the mathematics. What is the role of aesthetics? Role of making practices? Things that involve other skills/dispositions make math deeper?
Proportions in the face – difficult, but with this tool, they can begin to get at these ideas with the photo mash ups. Perspective and painting – image size, forced proportionality – gradations of color, where do colors disappear, what mathematics? Designing something.
Making can happen in the digital context – not just in the physical way.
Infinity and limit – kids can see these better in the art.
Y – worked with Shelly Goldman. Understand the family as a context for mathematical context. Understand how richly complex problem solving in family contexts – math was included, and also was heavily influenced by values. Real math is not school math, but the math that happens in the application and the family context. This is an experience we can draw on.
Mathematics as a leading activity – only occurs in schools and for mathematics, in almost every other context, math comes after the context. Jasmine
Z – sharing experience with refugee children working with strawbees – child built something you can expand and collapse. Witnessed joy and wonder, structures being made. How do you explain this to others – what counts as learning in this context. So tangible and joyful for students… but it’s just straws!! Can’t say, though, in math ed terms, what learning has happened.
Molly – micro politics of writing things down. Example of the child taking on the Hulk identity… asserting that as “yes, this should count for us, as general mathematical reasoning”. Similar to moment of trying to make sense of the Hulk… multiplicity of experiences that count as math; child de-positions that activity as math. Struggling with politics and ethics of doing this.
W – Using mathematical definition imposed on work.
In a way, that elevates it, but in a way it also codes it. Struggling with that as a researcher.
T – are you elevating it, but to who?
S - So there’s a whole range of what happens – we wanted to fix something… sometimes people really know what they’re doing as math, and it’s explicit. Sometimes it’s implicit – they didn’t say it, but we as researchers say, we saw that. Then there’s the whole people are doing things that they don’t recognize as math. Who does this matter to? As a researcher there’s a good thing to know this, then we don’t run the risk of thinking that people are “dumb” and “failures”.
Jasmine – there is a mathematics that we don’t have a category for it. Art crate project, owl with wings out. Translational geometry – rotation, etc. – but it’s not that.
Another example from not the first world. Vernacular engineering – to go deep sea fishing – very simple tools. Piece of rope that is a tool. The cannot read or write. Nobody has ever asked to them to talk about what they are doing. You know there is a lot of mathematics? How do you capture that knowledge? It will die away with globalization. Complex knowledge of “the other” – but I struggle with this. Am I so self absorbed that I want to put my own work on a pedestal? How do we capture that knowledge for the sake of them, and not us?
Analogy of language and grammar – you don’t have to know grammar to do it. What matters is your audience, how do you make this comprehensible to others.
Can’t we just leave this alone? Educational
U - making of what’s happening outside of schools changing what’s happening inside. That’s the Trojan horse of what maker movement can do.
Aren’t people making the same argument with Standards.
Instances that we’re talking about – vignettes, stories. People’s histories are really valued. If we value those ways of making.
X – that’s where the potential for making is. The string in the pocket. What are people going in measurements. Early Childhood – teachers are turned in. How do we help them learn to see? That string/rope will serve you for life. Always astounded by ways kids come up with making things more precise. How can we document those and elevate them? How do we make people see this?
V – we are in a place of privilege – in math, 3,4,5 example. We hold that knowledge, and we see that. It’s our job to help people, kids, communities, have access to what we have. PCK. People we know. We have this responsibility.
We do, but we have to be careful about the route of this. Complexity is around the questions – why? How?
We can’t just assume that we’re helping people – what can we learn from them?
Affordances of maker movement is because the outside world values that. “Engineers do that, that must be good.” People have been doing this for years, centuries. We can use making to convince people who make decisions that this is a good idea. Why do this? First, Voice. Parents see power in seeing something as mathematical, we don’t need to put a mathematical lens, but if you want to, here are some tools. Translation – we have to think about how academic math. Why do we want to?
Have you ever met a math major who didn’t find a job? Do something to elevate people’s opportunities. This is one of the big goodies.
Are we getting circular? We want to mathematize to help people be introduced to culture of power… but are we still honoring their lives?
We want to respect what people are doing, but we are providing them with opportunities. It’s a major gatekeeping thing…
Real mathematics has real power…
Hulk reenactment… awesome!
What concepts was that child using to do that that would enable him to do something else. Take something you’ve learned in one situation and use it in another question?
How do we get access to the real power of mathematics?
Point same question – in making context? What would be real math in making context, what is it? In making?
Language – math. Using it in so many ways – school math. Mathematical ideas… Hulk – change in size, have a lens towards the ideas, even if they are not labeling it as math. All of these examples have ideas in them… when I start to see the ideas, that’s what the crux of this is.
T – what I got excited about in math – access though relationships. Some of the ways I thought about this thing, are related to things over. In making, lots of ideas that are relational. Heel in a sock, bananas growing, why would that happening?
Power of these mathematical ideas. Ability to transcend individual domains, from one to another. This idea of rethinking, education that happens in makerspace, moving to a different kind of thing, with a skilled facilitator point you back.
Big question: how do you make those ideas accessible?
Before that, how do you decide what you make visible?
Unanticipated stuff happens – might be noise, but in making, kids can chase it. But if learning goal is different from that? What is learning objective, trajectory, PCK?
M – what you want is educators to recognize moments when to go deeper. Preschool educators – identifying what kids are doing. False polarities in the meeting… maybe we should start off in organizing making in a structural way – but we want to make it equitable and inclusive.
N – we seem concerned about the constraints that we’re putting on making, but we do want some constraints. Is that engineering?
O – Vignette with peas, histogram. Then teeth. What would make it more making? Why is that not engineering…
How many constraints can you put on something with it still being