Thank you, Amy, for your post (and George for your agreement) - you got right to the heart of the matter!  To your first question, we have tried several ways to measure people's "math awareness" in these situations.  We found early on that just asking "did you do any math?" evoked people's images of "school" math - calculation and equations - and so they often didn't see any of that in the activities.  Later in the project, we moved to a list of prompts like "finding patterns" or "comparing angles."  This method was more successful in the sense that people did see that they had engaged in these activities, although we didn't study whether they then made the further connection to mathematics as they defined it.  It's really difficult to shift a person's concept of math,  shaped by many years of school, in a single experience.  One possibility for our future work: we have found that one of the most recognizable bits of mathematics is measuring, which is a natural part of many making activities.  We are considering a deeper dive into measurement as a way of making the math more visible.

As for the principles: my personal guiding principles is the first one:  make sure the math is consequential to the making.  That means that it must be integrated naturally into the making and help a participants achieve their making or design goals. That is why we have at times tinkered with the materials themselves, so that reaching a goal more naturally incorporates mathematical thinking.

What a fascinating find - that people struggle to see they are doing math because math to them is textbooks and trying to get the answer at the back of the book. It is long sums and solving for x. And of course there is a connection between what they are doing here and "school math." But the point is to help forge an awareness that mathematical thinking is broader, more beautiful, and more universally embedded in human activities.

It occurs to me that curating materials is something like what you are going to have to do with questions. You are now tailoring your questions to help bring out the associations - statements like "finding patterns" or "comparing angles" or possibly in the future, as you said, "making measurements,"  actually provide the language that allows participants to see. 

I love your use of the word consequential and it occurred to me you might enjoy viewing this video that also talks about the impact of consequential learning: https://stemforall2021.videohall.com/presentations/1910

Thanks, George - You were instrumental in getting us started on this route with your support of the Math Momentum in Science Museums project and the book that resulted from it.  As for the ESS pattern blocks - the older I get, the more I appreciate some of the wisdom and materials of the past (including TERC's Used Numbers materials that introduced elementary students to data).

Hi Kim!

How nice to hear from you!  It's hard to believe that wonderful workshop was 5 years ago!  It's still one of my favorite events ever.

So - visual cues - there are a few aspects to this.  First of all, we discovered in another project that designed and built a traveling exhibit called Design Zone that having recognizable math symbols  or terms (e.g. equations) signaled "math" to people, even if they didn't actually engage with them at a deep level.  So, that's in service of the goal of getting people to realize that they're engaging in an activity that involves mathematical reasoning. 

Second, we found in the weaving context that we could encourage people to explore geometric shapes in their weaving by having examples of such designs prominently displayed (this is mentioned briefly in the video).  In the same context, we found that having a sampler involving yarns of different thickness could prompt people to explore the relationship between yarn thickness and the length of a woven piece with, say, 10 rows.  These weaving examples were mostly there as inspiration - but could also be picked up by a facilitator and shared with a visitor in an appropriate situation.

I hope that helps - please ask more if not!

Yes, yes, yes!  May we borrow your daughter for our next video?  You (and she) clearly "get" the heart of our work.

You're right that our work has been focused on museums, especially given the explosion of maker and design spaces in those venues ( at least before the pandemic!).  One of our partners, the Children's Museum of Pittsburgh, actually has a growing partnership with a middle school co-located with the museum and we had hoped to work more closely with them in this project.  It can be challenging, though, to combine the free choice atmosphere of museums with the constraints of classrooms and standards.  This is definitely an area we're interested in; it's worth a full conversation of its own!

It sounds like we have a lot we might talk about!  Let's continue this conversation outside of the showcase.  If you found my profile, you probably also found my email, so if you email me, I'll also have your email and we can share more about the intersections of our work.

Thanks for your comment, Perrin.  I see you work with Sue Allen - please give her my regards!

The idea of sending out kits to community members came from our community liaisons at the New York Hall of Science, so we can't take credit for it and I'm not sure how much they're continuing that practice now that the pandemic has eased a bit.  We are, however, very interested in pursuing the whole idea of sewing and fiber arts as a way to connect with community funds of knowledge and as a context in which math is clearly relevant and consequential.  I would say that deciding to use mask-making as an opportunity for math is an example of looking at the world with "math eyes," which is part of the goal of this project.

Thank you for your comment, Natalie.  I was interested to notice several people from the Chicago Children's Museum viewed our video - and Kim was at the conference that launched this project!  I see from your video that we're interested in similar questions, especially around making and tinkering.  I assume you know about the narrative project that Dorothy Bennett led at NYSCI, where they also looked at what a narrative framing could add to design activities (including air-powered vehicles, which appears in our video).  I'm very curious what would happen if we pursued the "measurement" angle more deeply.

Also, if you don't know about the video-based professional development resources Scott and I (and a host of other folks) developed for museum staff - take a look at REVEAL.terc.edu - perhaps they would be useful to you!

Thanks for your comment, Tsivia.  We're hoping that the principles we've developed have broad applicability - and we continue to hone them, so stay tuned.  And thanks for your video as well - I enjoyed the Zoom scenes from home!

Questioning strategies, as I'm sure you know, are tricky.  We actually explored questioning strategies related to math in a previous project more explicitly - check out REVEAL.terc.edu for more information and some video-based PD materials that focus on facilitator-visitor interaction and inter-generational communication.

Your project sounds fascinating, Gerhard.  We would be happy to share any of our materials or experience that would be helpful to you.  Take a look at our website and feel free to get in touch if we can clarify or expand on anything that you find there.

You've hit the nail on the head, Martin!  This is one of the core dilemmas we deal with in this project.  One possible road ahead is to find those terms that are both clearly "math" and clearly "consequential" to making - measurement may be one of those.  Another approach (much harder) is to fundamentally change the way math is taught - and therefore perceived by many people.  But this is a very tough nut to crack.

I'd say the latter as a longer-term strategy is really essential. My 11-year old loves math when I make it consequential, which I find relatively easy to do, but the endless worksheets he encounters at school are not helping.  Here is a fun exercise I did with him when he covered angles in class: find a right angle outside in the yard in things not build by humans, and find non-right angles in the house. We then discussed why this is, and even talked about the psychology of architecture. Anyway, I wished school math were different...

There weren't any music/sound activities in this project - but in a previous museum exhibit development project called Design Zone  (https://omsi.edu/products/design-zone), we created several exhibit components that engaged visitors with music-making from an algebraic perspective, e.g. exploring the relationship between the length of a tube and the sound it makes and playing with multiple beat tracks to see how they line up.  It's a rich relationship!

Hi Barbara - yes, one of the facilitators pointed me to your video and I've been meaning to comment on it, as I definitely think our projects are related and we are thinking along similar lines.   I love the families in your videos narrating their sense of purpose.

Back in the 1980's when I was working on literacy with Chip Bruce, we used to talk about Functional Learning Environments - i.e. those that paid attention to students' authentic purposes.  We worked with a different community - Alaskan children of a variety of Native and non-Native backgrounds - whose communities were often very tight-knit.  We wrote a book called Electronic Quills about the purposes writing fulfilled for these communities.  I would love to talk more about our shared perspective on education.