Thank you to all of you who have posted introductions. This looks like a great group for the online conversation. (If you havenâ€™t posted yet, feel free to at any time: http://www.informalscience.org/prompt-1-introductions.)

We would like to continue the discussion with a fundamental question:

**Do you believe mathematics is integral to making and tinkering experiences? If so, give examples. If not, why not?**

Weâ€™ll focus on this question until Tuesday, 4/5, when we post the next thread.

Looking forward hearing from you!

Sincerely,

Scott Pattison, Andee Rubin, and the *Math in the Making* team Â

I think math is involved in some, but not all of making.Â It depends on the definition of "making", which I know we're going to discuss!Â In the olden days, making was done in two places at school:Â Home economics for girls, and shop for boys.Â There was some math involved in the projects we did in these classes, but we usually followed recipes or patterns, which were prescribed.Â It seems like the more prescribed a project is, the fewer mathematical opportunities there are.Â On the other hand, if a project is more open ended, like "make a Halloween costume for your dog", there's a lot of math involved!Â I've got to measure my dog, figure out how I'll translate these measurements to some kind of pattern or template, keeping in mind the 3-dimensions of my dog as I work on a flat piece of fabric.Â I've got to figure out how to fit the costume over a dog that has 4 paws and a tail.Â Â I admit I don't do much making, and haven't made Halloween costumes for dogs.Â But recently, my corgi had a hot spot, and I had to make her a diaper-like device to cover the spot firmly so she couldn't lick it.Â It was hard to do, and I used a lot of visualization.Â I finally bought a dog diaper, and cut out part of it, so she could pee (figuring out what part to cut out was challenging.)Â But it was too small, so I used the one I bought to make something bigger.Â In that case, I was scaling up and using proportional reasoning.

Â

I believe thereâ€™s math hiding in many making experiences â€“ Janâ€™s example is a great one, as it highlights some of the â€śbitsâ€ť of math that can occur during an extended â€śmakingâ€ť project, often unnoticed.Â In addition to the mathematical domains Jan called out, Iâ€™ve been thinking recently of a kind of â€śmeta-mathematicalâ€ť perspective that is critical in many of my physical interactions with the world: understanding how the need for precision changes, according to context.Â While itâ€™s important to know how to use measuring instruments precisely (see Sherry Hsiâ€™s comment under prompt #1, for example), Iâ€™m interested in the fact that sometimes measuring precisely is less necessary â€“ or even counterproductive.Â I almost never worry about measuring to the half-inch when I hang a picture; Iâ€™m more concerned that it

lookslike itâ€™s hung in the right place (e.g. centered) than that it really is.Â But if Iâ€™m making 6 parts of an origami box that are going to fit together snugly, they had better be identical in terms of size â€“ and I had better fold them all very carefully so that I donâ€™t end up with uneven sides (which, I must admit, is usually what happens to me when I do complicated origami).Can you think of other meta-mathematical perspectives that come up in making and tinkering?

I always marvel at what people can make when they are allowed to follow their interest, develop a passion, and simply get used to the idea of making more. I personally am drawn to folk toys that are made often with found objects, and are put together in a rather low-tech fashion with immense creativity and imagination. I also am fascinated by everyday utilitarian objects made by very ordinary people at their homes. Take for example the newspaper bags that come in different sizes to hold anything from a single egg to one-kilo rice that you still find in not-so-posh stores in India.

Â

Making things, especially the habit of tinkering â€“ bricolage â€“ is naturally multimodal and multidisciplinary. It augments our ideas on epistemological pluralism. Mathematics, in some instances more visible, is deeply embedded as problem posing; but it has very little resemblance to the test items that tries to standardize our minds.

Â

Hereâ€™s a TED talk by Arvind Gupta (https://www.ted.com/talks/arvind_gupta_turning_trash_into_toys_for_learn...)

Where Have I personally used math in making?Â Â

When I am creating Bead BraceletsÂ I find myself measuring (with and without quantities).Â Also, while wrapping presents I am visualizing sizes for amount of and orientation of patterned papersâ€¦.

Wrapping presents reminds me of a video (Between the Folds) where Iâ€™ve SEEN math in making.Â Â It portrays artists and scientists who create original and unusual origami art often using mathematicsâ€¦

http://www.imdb.com/title/tt1253565/

Check it out. You can get it on Amazon...

Where else have I seen potential for math in making?Â

I was a K-2 teacher in the beginning of my career and now that I look back, we often provided experiences (a station at choice time, or a group activity) that resemble â€śmaking/tinkering experiencesâ€ť.Â Â For example, the â€ścollage tableâ€ť or the â€śtake apart stationâ€ťâ€¦.Iâ€™m not sure how explicit the math was, but it was part of kidsâ€™ experiencesâ€¦

When teachers walked over WHILE children were working, or later, when kids chose to present what theyâ€™d made to the class, teachers naturally brought up questions that were scientific or mathematical, for example, about how things fit together (related to Andeeâ€™s question about precision). Â Once, when an adult volunteer came in one day, he simply sat quietly at the collage station, cutting out paper spirals.Â Then he hung them from his glasses.Â The kids thought this was a riot and began to try to understand how to cut spirals, and were fascinated by the bounciness of paper, etcâ€¦. This lead teachers to think about this and we brought in related materials (metal springs)â€¦

For me, this raises questions about how facilitation and design in Making/Tinkering environments (both in and out of school) relate to explicitness of mathematicsâ€¦.Â

Hi Tracey,

I love your question about the role of facilitation and design in bringing out the math in making. At Chicago Children's Museum, we are into a two month focus on math and early learning. Some of our drop-in programming for our general visitors has been created speicially for this venture, such as "Fraction Action Pizzaria" where children can take orders, match ingredients, andÂ interact with a 8 foot Â oversized pizza pie (we like to go big :). However, some of our programming that we are bringing out are tried and true activities that we are making explict the math concepts that are being explored. "Hammer Time" is typically presented as a fine motor activity for our 5 and under crowd, however, we are now calling out spacial awareness and pattern making in this activity. Same activity, different facilitation. Here's more on our math programming: http://www.chicagochildrensmuseum.org/index.php/experience/mathemania

In answering this question, I am struggling with the goals of the activity. Certainly I believe there is opportunity to use and explore mathÂ in almost any making context involving quantities of material. Whether those opportunities are recognized and seizedÂ (by the maker, the instructor, parents) is less certain. And this uncertainty might be perfectly acceptable in some contexts (perhaps museums exhibits, summer camps, afterschool programs) and less so in others (perhaps math classrooms, homework assignments). I'm interesting in designing for math classrooms, where math learning is a primary goal, so I'm wondering about ways (activity design, facilitation, etc.)Â to highlight math as part of making for that kind of environment, though I don't believe all making should have math as a primary focus.

Artists for Humanity (AFH) is an after-school jobs program. On the wall in or near each studio, a graphic wall-cling makes some math connections explicit for the participants in each studio. The idea was to help connect some of what our participants do in studio to concepts they might learn in school, hoping maybe to underscore relevance of math learning.Â

Here's the list:

The many moments you use math in the GRAPHICS studio:Â· When you do tiling and youâ€™re rearranging and measuring things, youâ€™re using rotations, scale, and translations which make up

TESSELLATIONS in GEOMETRY!Â· When youâ€™re determining where assets should lie on the grid in order to take all of the elements a client wants to make a balanced product, youâ€™re using coordinates on a Cartesian plane in

ALGEBRA!Â· When youâ€™re setting up graphics on x/y lines and adding the â€śzâ€ť space, youâ€™re using the Cartesian plane in

GEOMETRY!Â· When youâ€™re using quadrants and giving a line a slope to make the motion more interesting in Motion Graphics/Animation, youâ€™re using

ALGEBRA!Â· When you have to scale items proportionally and do cross multiplication of ratios to determine how big to make a photo, youâ€™re doing

GEOMETRY OF SCALE and ALGEBRA!Â· When youâ€™re doing Large Format Printing such as wallpaper and other big prints, and you have to figure out square footage for area and pricing, youâ€™re using

to determine how much of the graphic can fit on the paper size!GEOMETRY of scale and ALGEBRAÂ· When you calculate circumference for wrapping text around a circular graphic, youâ€™re doing

GEOMETRY and ALGEBRA!Â

The many moments you use math in the PAINTING studio:Â· When you translate a drawing from sketchbook to canvas youâ€™re using ratios and scale and coordinates and translation, which are all a part of

ALGEBRA and GEOMETRY!Â· When you recognize the shapes inherent in the pieces, youâ€™re looking at Geometric shapes (Euclidian and Non-Euclidian) in

GEOMETRY!Â· When youâ€™re mixing colors to get the exact shade youâ€™re looking for, youâ€™re solving for unknowns in

ALGEBRA!Â· When you calculate one part to the whole with respect to size in order to represent an object without any distortions, youâ€™re using

GEOMETRY and PROPORTIONS and SCALE and even solving equations!Â· When you measure the size of a canvas for storage or marketing, youâ€™re solving the number of x space that can fit in the y space with

ALGEBRAAnd the storage space is the sum of the integrals of everything that will fit inside it.!Â· When you sketch from a photograph for an urban landscape and youâ€™re trying to make the painting 3-dimensional, youâ€™re using nonparallel lines and triangles and

THE PERSPECTIVE THEOREM!Â· When you measure to find the middle of the canvas for reference points, youâ€™re doing division in

ARITHMETIC!Â· When you represent visual distance, you use nonparallel lines and use perspective distortion in

GEOMETRY!Â· When you use lines, angles, and shapes to represent a 3-dimensional object on the canvas (which is a 2-dimensional surface), youâ€™re using acute, obtuse, and right angles AND perpendicular and parallel lines in

GEOMETRY!Â· When you work as a group to make a mural, youâ€™re drawing to scale and working with coordinates in order to make something so large-scale.

Â

The many moments you use math in the PHOTOGRAPHY studio:Â· When youâ€™re Cataloguing and your mentorÂ tells you not to shoot from different angles because it will cause parallelograms, youâ€™re doing

PHYSICS and GEOMETRY!Â· When youâ€™re measuring Light & Exposure to determine your shutter speed and aperture, youâ€™re calculating velocity with

PHYSICS and ALGEBRA!Â· When youâ€™re measuring proportions, Image Resolution, and DPI (pixels per inch) in order to change the resolution of a print, youâ€™re using

PROPORTIONS and ALGEBRA!Â· When you have to determine how many pixels a final product has to be in order to make the size the client wants for a Kaleidoscope and you have to break up the image into smaller pieces to put together on the wall, youâ€™re using

GEOMETRY AND ALGEBRA to determine how many (x) pixels will fit into the (y) space AND youâ€™re using TESSELLATIONS! (Btw, tessellations are an overlapping pattern of lines and shapes)Â· When youâ€™re hanging artwork and you have to measure the wall, youâ€™re using right angles and straight angles in

GEOMETRY!Â

The many moments you use math in the 3-D/SCULPTURE studio:Â· When youâ€™re in the Woodshop and measuring wooden template for patterns, youâ€™re using angles and parallel and bisecting lines in

GEOMETRY!Â· When youâ€™re thinking about capacity and space for a mold, youâ€™re solving equations with

ALGEBRA and using SPATIAL GEOMETRY!Â· When youâ€™re making models, youâ€™re using

SCALE and RATIO (which are fractions)!Â· When youâ€™re selling pieces and you have to know the prices and what your commission will be, youâ€™re doing

ECONOMICS and FINANCEÂ· When youâ€™re creating a pixel table top, youâ€™re using a grid and thus youâ€™re

graphing with coordinates in ALGEBRA and GEOMETRY!Â· When you use a level to make sure the resin pour is even, youâ€™re working with

inclines in GEOMETRY and PHYSICS!Â· When you measure resin and hardener pours, youâ€™re measuring volume and using

GEOMETRY!Â· When youâ€™re making magazine folds and have to count out how many are needed for each table top size, youâ€™re using

ALGEBRA to determine the (x) number of folds that will fit in y (the table top)!Â· When you look at angles to make sure the pixels are perfectly lined up, youâ€™re thinking about

GEOMETRY and using parallel lines!Â· When youâ€™re folding origami pieces for tops, youâ€™re doing

GEOMETRY!Â· All of your magazine designs use

fractal designs, concepts of rotation, scale, translation - i.e. the Penrose tiles and tessellationsÂ

The many moments you use math in the SCREENPRINTING studio:Â· When youâ€™re heating chemicals and determining parts-to-parts

ratios, youâ€™re doingALGEBRA!Â· When you measure the placement of films on the screens for proper alignment, youâ€™re doing

ALGEBRA including measuring ratios and angles, and using Cartesian planes!Â· When you mix ink and you fill in how many grams of certain colors are needed in order to get the desired color, youâ€™re doing

PHYSICS and ratios!Â· When you discuss the volume of the color and how it would change the ink recipes, youâ€™re doing

GEOMETRY!Â· When youâ€™re counting in dozens when packing shirts, youâ€™re using

multiplicationand doingALGEBRA!Â· When youâ€™re pricing orders, youâ€™re doing addition, subtraction, multiplication, and some division in

ARITHMETIC!Â· When youâ€™re working with the exposure of light, youâ€™re using

PHYSICS and ALGEBRA and CHEMISTRY!Â

The many moments you use math in the VIDEO studio:Â· When you have to calculate a ratio to determine the resolution of a screen, youâ€™re using

ALGEBRA!Â· When you use 3D space in after effects, youâ€™re doing

SPATIAL GEOMETRY!Â· When you measure decibels to make sure the sound is correct, youâ€™re calculating the amplitude of sound waves with

PHYSICS!Â· When you measure time for substituting clips and editing, youâ€™re solving problems using

andALGEBRAPHYSICS!Â· When youâ€™re shooting and you hold the camera at varying angles to make more dynamic shots, youâ€™re doing

and you are varying the lines of sight of planes of motion that youâ€™re shooting inGEOMETRY,!Â

The many moments you use math in the WEB studio:Â· When youâ€™re designing shapes, youâ€™re piecing together geometric shapes in

, and when you have to follow a standard size based on the number of pixels available on the screen, youâ€™re usingGEOMETRYRATIOS and ALGEBRA!Â· When youâ€™re researching the average computer resolution and most popular browsers to inform building templates, youâ€™re using

STATISTICS!Â· When you break down a page into sections and margins, youâ€™re using

ALGEBRA AND SPATIAL GEOMETRY!Â· When you adjust the size of the space between text lines (the leading), youâ€™re using proportions and scale in

ARITHMETIC and GEOMETRY!Â· When youâ€™re Image Mapping with coordinates by making part of the image a link but leaving the rest of the image and screen alone, youâ€™re doing

ALGEBRA I & II, specifically using TOPOGRAPHY and CARTESIAN PLANES!Â· When you change the image size by using motion and you use 3-Dimensional coordinates to shift images around on an x and y axis, youâ€™re

GEOMETRY for the image rotation, scale and translation, ALGEBRA to calculate the motion, and some CALCULUS using intervals for the change in dimensions!Â· When youâ€™re using â€śIfâ€¦ thenâ€¦â€ť statements (conditional and variable) in programming, youâ€™re doing

ALGEBRA and THEORETICAL MATH and PROOFS!Â· When you write a formula for how to switch images based on time, for example, making a slideshow, youâ€™re solving equations with

ALGEBRA!Â· When youâ€™re resizing, youâ€™re using scale in

ARITHMETIC and GEOMETRY!Â

Great list, Christine. Thanks for sharing. Do you have a sense of how program participants are responding to this information? Are you trying to make explicit links to certain types of math or do you hope to communicate a more general sense that "math is everywhere"?

Scott

Hi Scott,

I think the original impetus for making these wall signs (which are mostly just outside the door of the studios) was to try to encourage our teens to connect what they do in our art studios to concepts they might be learning in school. Not surprisingly, our programs attract a relatively high number of unconventional learners. But they might not realize everything they actually know and use. For example, a young woman who professed to 'hate math' was the one who solved a problem of decorating a wall with a single photographÂ (without it being boring) by slicing a triangle out of a photo of a tree and flipping, rotating and duplicating the slice into a beautiful design that few casual observers recognized as a repeated piece of a tree. It was kind of like, we've got news for you, dear artist, you just did a whole lot of math. We really want our teens to know they can do school thinking too because it is so vital in the current economy that they graduate high school, and we try to help them access and persist through college.

I do think the studio mentors Â differ in the extent to which they point out the STEM learning in our art studios and if the participant surveys are valid, thenÂ probably only about half our participants claim cognizance ofÂ math involved in their studio work.

Â

I think this must be a fairly common experience for many people across the spectrum, from those who hate to those that love math. The image of math as getting out the calculator 'to do the math' is pervasive. The more creative ways in which math can be used are often not recognized as such.

In situations like this one (ie the girl that hated math but really creatively and spontaneously engaged in the geometry of rotation and translation), I think it is important to highlight 1) that math was used, and 2) how it was used. Such situations also provide an opportunity for opening oneself towards math. A follow up activity might be posed that would capitalize on the existing interest and creativity that is now present. A push to further explore the math of translation, rotation, and possibly new ideas like dilation. How might she tile the wall with a different shape (another one she found to beÂ aesthetically pleasing)? With a combination of shapes? With different sizes, rotations, etc? Questions that will encourage her to delve deeper in to the math, BUT in service of a desired aesthetic effect or the tandem exploration of an aesthetic ideal.

Indeed, Bohdan, that event was just the start. She also taught her method to others in the photo studio and a whole series of what they calledÂ Kaleidoscope tiling began. Since then, our studios have been very much working on the "opening" our teens to their abilities and contributions in all kinds of authentic STEM/STEAM activities. Our program is really a jobs program, the Youth Arts Enterprise and our studio mentors pro-actively pursue commissions from STEM clients in our Boston neighborhood ("Innovation District") and beyond. I am not directly involved in the teaching/mentoring so I can't speak to how it happens, but a team from Education Development Center is studying that. I could post a list of recent projects that caused our artists to learn STEM concepts, because good design requires solid understanding of your client ;-) And since 83% of our teens are from low to very low income families and 91% are teens of color, we feel AFH (Artists for Humanity)Â isÂ positioned to help diversify the STEM pipeline. This also touches on eglash's point about Making, STEM ed, and Social Justice, which if I'm dragging the correct link out of email would be here:

http://informalscience.org/comment/79#comment-79

Thoughts from our Tinkering Studio Lead, Whitney Tidwell on how we see math incorporated into some of our activities:

We use kaleidoscopes to talk about symmetry and multiplication!Â Sometimes we can use wind tubes to talk about balance and equality, but that oneâ€™s a little bit more abstract.Â Also, I have a lesson plan from when I taught sixth grade math and science that uses circuit blocks to explore multiplication and the number line that Iâ€™ve been trying to tinkerify for a while.Â Actually, I think if we just sat down a looked at it, we could probably find math in most tinkering activities, I think it just takes time to explore those concepts with our guests (plus, you kind of have to do it on the sly, since many people flee in terror when they hear the word â€śmathâ€ť)

In my mind, there is no way to describe or manipulate the world around us without using math. I believe that math is the language of science. Making is science, even the creative aspects of it. In making you manipulate science to meet your needs.

Math comes into play every time you make something. You measure, count, recognize patterns and shapes, and follow a logical procedure. And although you may not be using standardized units, you are still doing all these calculations in your head.

If my need was to annoy my cubicle neighbor, I might consider making a pompom launcher out of a cup, balloon and some tape. When choosing my materials, I would consider the size of the pompoms compared to the cup and balloon (ratio). If a taught balloon launches pompoms further than a loose balloon, how tight can I make the balloon before it crushes the cup (measurement)? Do I have enough tape to wrap the circumference of the cup three times (geometry)? These are just a few math-related considerations for this making project. And that is just to build the launcherâ€¦ wait until I start launching! (I wonder how many times I can hit my neighbor with a pompom before she gets annoyed?)

A problem that we face as museum educators is that if we market our programs to parents or teacher as specifically math programs that hit math standards, they donâ€™t book them or attend the program. It seems that the public perception of math is that it is boring or dry. How can we start to change this perception? Iâ€™d like to be able market our math-related programs for what they are, and not incorporate math as a hidden agenda.

Thanks so much for bringing this issue up, Stephanie.Â It feels like so much of what we haveÂ talked about so far on this forum revolves around the tension among our goals as educators, the audience we are trying to reach, and our approach to the expliciteness of the math. It's been interesting to hear different takes depending on whether folks are coming from a making/tinkering perspective or a math education perspective.

This will definitely be an important topic during the in-person workshop.

Scott

I think that finding any math at all in making is an important first step, because it offers an existence proof,Â but I don't think it goes far enough. Some of the math "hidden" in making will feel trivial or at least irrelevant to the makers engaged in the activity. I'd like to see us find the important, relevant andÂ

helpfulÂ math in making. (As Scott asked, is there math that's integral to the making?) I like Jan's example of the costume for a dog, because I can imagine thatÂ mathematical thinkingÂ skills and knowledge might actually help people engage in that maker project. Perhaps one way to determine the importance of theÂ math in aÂ making activity is to assess how the making shifts when theÂ maker isawareof the math. Â In Jan's example, would creating a costume for your dogÂ be easier or go further if you consciouslyÂ broughtÂ to bear the mathematical knowledge you have about scaling, curvature and the like?ÂI agree withÂ many of the above posts thatÂ there are frequently opportunities for practical applications of math in most making activities. I've found it's useful to unpack the different mindsets people are engaged in while making and thinking about math. I've found that for many types of makers, especially artists, making isÂ anÂ intuitive process.Â Each subsequent creative decision is informed by the previous action in an exploratory fashion. Makers often rely onÂ mathematical concepts while engaged in intuitive and exploratory making,Â butÂ I think their mindset can be at odds with theÂ analytical mindset associated withÂ formal math. One artist I interviewed in my research framedÂ this tension by describing how she always struggled with math in school, but recognized how in her artwork, she was capable of creating spatially complex compositions that clearly relied on principles of geometry and symmetry.Â

In my own experience, the opportunity to think analytically about the mathematical principles involved in a project has proved to be very powerful, yet at times it feels that form of thinking is in conflict with the way I think when I'm creating withÂ my hands. I'm curious how we can provide opportunities for both intuitive explorationÂ and analytical reflection in making activities- andÂ how we can scaffold the transition between these mindsets.Â

This is a fascinating distinction, Jennifer,Â with some interesting implications for how we might design experiences that integrate math and making. I'm curious if some folks on the forum from the math education community might also have thoughts about how engaging in math can be more intuitive, artistic, and exploratory as well.

Scott

I too am fascinated by the topic of intuitive/qualitative understanding of math (andÂ science) in making (and other informalÂ experiences...). IN FACT, intuitive/qualitativeÂ understanding was an explicit goal in the design as well as the evaluation elements of the MathCore project. (Some of thisÂ project'sÂ teamÂ will be at the workshop and they and others are part of this forum.) Â Anyone else want to weigh in here????

On a related note, I've been wondering what role Embodied Understanding plays in the world ofÂ Makers and Tinkerers? Â Does anyone have any examples? Â

I've also been thinking about:

How might movement (full body motion, gesture, gaze,etc.)Â contribute to learners' experiences? Â

How might we as educators see and understand better what's going on with Makers who don't necessarilyÂ articulate in words why they are making certain choices in their designs? Â

Tracey:

While I haven't yet seen Math-In-the-Making project's definition of making, we use a broad definition of making to include performance and visual arts, too. In our case, learning to unicycle ( an afterschool and extended school-year program - http://woodsideonewheelers.org )Â is full-body learning of the math and physics of classical mechanics literally by the seats of our pants and the soles of our feet. If you don't intuititively learn to control balanced and unbalanced forces, you can't ride more than a couple of feet. We face a similar challenge that others have articulated in this forum: How do we help learners to see the math (and science) in the activities they do intuititvely?

One approach that we use is to conduct research into unicycle mechanics in order to make our program more inclusive. We incorporate insights into the coaching and mentoring activities. Movement and intuition definitely support learning and sharing, e. g.: STEM Art? - http://buildinprogress.media.mit.edu/projects/3335/steps?step=18751

Steve

Several thoughts come to mind around this interesting topic of making... when my husband and I were at the Museum of Math in NYC when it first opened, we were fascinated by all the rich experiences that illustrate math... and at the same time, walked away disappointed because of the many missed opportunities for the math of those fun experiences to be realized. For example, the concentric tracks where tricycles run on them, have two different sized wheels proportional to the distance they are from the center of the track. That's what allows them to travel smoothly. Lots of math, yet mostly adults and kids were just fascinated to ride the trikes... on a wall, there were pieces you could move around that tesselated, but all that was happening was the moving. So, lots of fun engagement, and you could easily walk out with a "that was fun!" Being explicit about the math, or at the least asking questions that promote thinking would have been a plus (and perhaps that's now part of the Museum).

In a summer tinkering school/camp for middle and high school kids, they build a catamaran and to do that, draw plans, do lots of angle measurements, and have to figure out, for example how Â to put a 25â€˛ boat on a truck with a 12â€˛ bed and not need a forklift to get it off. Lots of math to get there, so there is definitely math in the making.

I'm curious to continue to hear from you all and think about how to pul the math out of (or into) the making, yet keep the making fun, since that's the big motivator for so many students.

Â

That there is math in making is I think indisputable (there is also language, creativity, skill building, art, artisanship, etc.).

The question I think is what kinds of teaching strategies can help to make math practicesÂ (and even vocab and ideas and skills) transparent to students

.... in ways that don't turn them off or seem gratuitous or adult-centric

.... in ways that can build their repertoires of practice, their identity, and their capacity to seek out future opportunities to use and expand math practices in other settings (ie, in ways that empower them)

Â

Our research would argue that making math transparent, available, and positioned as a useful for realizing students' valued goals/outcomes is critical for equity.Â To my mind this is an issue of professional learning for educators: How can they do this well, this is particularly fraught in the informal setting (lack of time/consistency of participation, orthodoxy around "student-centered," lack of pedagogical language, etc.)

Well put, Bronwyn. Thank you!

Scott

Hi all,Â

A thousand apologies for only posting now, when topic #3 is already up! I've really enjoyed reading through all of the posts on this thread, and many comments resonate with my own personal making experiences as well as making experiences that I've observed as a researcher. I hope it's not out of place for me to bring some formal ed ideas into the conversation here - but what this conversation really made me think of was some of the STEM Integration work that we've been doing with middle school math and science teachers recently. As part of a two week summer institute on our campus, we begin by immersing the teachers as learners in an intense engineeringÂ design project that authentically embeds and integrates math and science - much in the same way that making experiences like those described above can do. After this experience, we "pull back the curtain" and reflect on the pedagogical choices that went into the experience, as well as how the disciplines were integrated throughout. During this discussion, we purposefully have teachers reflectÂ on where they engaged with their own content area during the experience, as well as the other (i.e. if they're a science teacher, we ask them to identify the math). The teachers seemed really empowered by reflecting on both content areas, not just their own, and identifying all the ways they'd touched on and succeeded with the "other" content area.Â

That's a really rambling story, but what it got me thinking about was this: we, as researchers and educators, can definitely identify examples of math in making. But the big payoff might be when the maker acknowledges those connections, just as Bronwyn mentioned above.Â How can we help makersÂ "pull back the curtain" on the math they engage in? How can we help them use this type of reflection to potentially reposition themselves relative to math and/or redefine their identity related to math? How and when do we call out the math in the making when we see it, and when is it better/essential to just let the maker make for a bit?Â

Thanks everyone!

Â MyÂ virtual jump roping skills and timing are off.Â Chiming in late again.Â Apologies. In response to the prompt, is math integral to making and tinkering? I believe mathematical reasoning and math thinking practices are embedded in many maker activities, but they might not surface without the help of some goodÂ externalÂ representations (overlays,Â labeling,Â models, symbols, etc.)Â andÂ a skilledÂ facilitator to makeÂ Â these math aspects more noticeable and apparent to the young maker.Â

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Over the winter holiday, there was a craft fair at my son's school. I had theÂ fortune to make theseÂ Temari-likeÂ ornaments. Using two pieces of square cardboard, pins, and embroidering thread, I was able to wrap colorful thread into a pattern. In some cases, I had to skip every other pin (odd, even), and in some cases, I had to skip every third pin (1-skip-3, 4-skip-6). There was a pattern of threading and counting the pins to get the right pattern like counting up or skip counting (like knitting). In the case of 3DÂ TemariÂ balls (foam ball or ball of yarn wrapped in more yarn and string), the same thread Â (line) is fashioned over a 3D surface (non-Euclidean geometry.) The prep involved in placing the pins at regular intervals can be done by just eyeballing where the pins go (estimation) or doing a calculation of dividing the circumference into segments.Â

Here is a link to a story about one grandma's collection ofÂ Temari ball.Â Â Can you see other opportunities for math?

My second example is from the Paper Mechatronics project where we have been hosting robot petting zoos. Using cardboard, two servo motors, and Scratch, a simple cardboard robotic pet can be made to wiggle its ears. I can see the computational thinking (variables, recursion, loops), but finding the math is a bit harder. A maker could experiment Â and play with numbers in the code and moving the motors, translating a symbolic number into a physical position. If the robot had ambulatory motorized legs through some mechanical gear attachments, Â there could be some figuring of numbers into linear motion across the floor reminiscent of a Logo turtle.Â

I am enjoying this discussion and look forward to meeting you all soon.

[Technology tip of the day: I was having trouble uploading images from my computer to this forum. Imgur to the rescue! Upload there, then link to them from here.]

I clicked too soon! Here are two images from the Robot Petting Zoo example.Â

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Two projects we've explored in the Boston Arts Academy STEAM Lab involves

computational thinkingandtensegrity.CT looks at a problem in a way that a computer can be used to help solve it. StudentsÂ can design complexÂ algorithms,Â spotÂ patternsÂ and useÂ abstraction, for example creating programs to draw geometric patterns seen in flowers and creatingÂ simulations. Fabrication involves scaling, proportion and measuring to create a physical object from a computer-based simulation or model.

TensegrityÂ (tension + integrity) is modeled mathematically as a configuration of points or vertices. Cables keeps vertices close together; struts keep them apart. Students can use wooden sticks or dowels, rubber bands, or latex tubing to create their own structures.

In both cases mathematics is integral.

I'd agree with many other posts that there's tons of math going on in any making experience, and it's just a matter of how deep you want to go to find it, and how explicit you want to make it for the learner. The facilitation plays a big role in how much math is uncovered, and ideally the facilitator guides the learner to feel like they're the one leading the mathematical discovery.

The maker/learner is always developing an intuitive sense of mathematics, but at any point they can step out of that process and just like they can stop to take a picture and reflect through language on what's going on, they can take a mathematical picture and see what mathematics is at play, whether its #'s being calculated, shapes being arranged, or connections b/t variables being made.

Good Q re: what's the right amount of math to highlight during the making process. Not enough and so many great mathematical connections (& opps for the learner to realize they love math!) are missed, but too many might take the learner out of their creative flow of the making process. I'm looking forward to tinkering with this together at the workshop to find a good balance.

Speaking of loving math, my favorite t-shirt a friend gave me: Deep down inside, we all love math.

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Yes!!! I think in NYSCI's Design Lab exhibit, Peggy Monahan and I have experimented with creating design opportunitiesÂ that engage visitors in deep mathematical reasoning while trying to make their designs work. Â The perfect example to me is a costume design activityÂ we had in our backstage area, which really involves geometric and spatial thinking (alongside grappling withÂ volume andÂ surface area)Â when trying toÂ assemble 2D shapes into 3D designs that will fit your own or yourÂ friend's body. Â The best example of math in the making is when our own staff were attempting to make a superhero "brief" and how hard they worked to firstÂ visualize what component shapes they needed to create and then puzzling through how they would fasten them together to cover the sides, as well as theÂ front and back of the body. Â This is what people who sew think about constantly as they read and createÂ their own clothingÂ patterns. Â I think as others have said, facilitation is key to perhaps make this math more explicit to visitors, but I want that facilitation to go beyondÂ Â "wow, see you are doing math" to here are some math tools that might help you see what you need to create or improve your design. Â I also think the timing of that facilitation is important-it is important for visitors to have the chance to bump up against when their designs and initial visualizations don't work. Â These are the teachable moments we would like to train our explainer team to hone in on and build on. Â