Synergies One STEM discipline bootstraps learning in another

Synergies One STEM discipline bootstraps learning in another STEM discipline • An important idea or practice is amplified as it is considered/experienced across multiple STEM disciplines •

Engineering Design Bootstraps Math Science A Output links B Fixed Pivots Floating Pivots Output Link Fixed Pivot Holder Input Link Front Back Levered machines are constructed from pegboard, links and brads. Brads take on one of two forms: floating pivots and fixed pivots. Floating pivots are formed by connecting two links and fixed pivots by connecting a link to the pegboard. Holders restricted a link’s sideways motion. Outputs are marked with stick figurines.

Supporting Synergy a b c

Weaving Among Experiences Embodiment Impossible Straight Path Mathematics Impossible Straight Path Walker’s Path Circle Rope “Holder” Radius “Walker” Center Point on Circle Reasoning about Physical System Impossible Straight Path Output’s Path Output Fixed Pivot Distance from the Fixed Pivot & Output When pushed up, the output rotates in a circle because one end of the link is held down by the fixed pivot. Figure 4. Disrupting “straight” through embodied circular walks with rope.

Microgenetic Analysis Before acting upon the drawing After acting upon the drawing A Sarah’s drawings of the embodied experience B Sarah’s attachment of the link at the end. C Sarah’s rotary gestures in predicting the movement of the little man 1. I drew me (points to top dot in her drawing) and then you (points to bottom dot in her drawing) and then (moves finger back to top dot) I was holding the rope and (moves finger back to the bottom dot) then when, no but that's wrong. 2, This one (points to center in lower panel) would be you. And me (points to dot on circle) holding the rope going around (moves her finger around the circle). 3. It [the link] can move around but, yeah like it can move around like rotating how we did. 4. It can only rotate in like this spot (points to the fixed pivot) and no other (somewhere else because this (points to the fixed pivot multiple times) is stuck to THAT (points to pivot again) place.

Classroom Interactions As we proceed with this work, we are finding that the design goals can be supported by the geometry of the system, which results in an increase in mechanistic reasoning, which perhaps also influences design (but if not, certainly trouble shooting) � But as students move across these experiences, an idea such as circle is also enhanced—circles are drawings, then they have properties, then these properties come to include motion generated by constraint, which leads to other surprises (the circumferences are longer than they are—and this matters for the motion produced by the toy). Etc. �

Modeling the Wild Backyard

Brady problematizes “bigness” Brady: What did you mean by the shade is bigger (pointing at Charles's writing on his evidence sheet). . . the shade is bigger Charles: The shade-the (touches drawing) pod of the shade is bigger Coby: [the pod? ] Mrs W: [the pod is? ] Charles: The plant… (holds hand vertically) the plant. Azhad: (reading Charles's writing) The shade is bigger than the sun + shade Brady: Are there any bumps. . . Are there bumps on the shade? Charles: (looks down at his drawing) No. Azhad: The shade… (stands up to look) Brady: Is this a bump right here? (points on screen to sun + shade drawing) Charles: Yes. Problematize means of knowing

Brady problematizes “bigness” Brady: What did you mean by the shade is bigger (pointing at Charles's writing on his evidence sheet). . . the shade is bigger Charles: The shade-the (touches drawing) pod of the shade is bigger Coby: [the pod? ] Mrs W: [the pod is? ] Charles: The plant… (holds hand vertically) the plant. Azhad: (reading Charles's writing) The shade is bigger than the sun + shade Brady: Are there any bumps. . . Are there bumps on the shade? Charles: (looks down at his drawing) No. Azhad: The shade… (stands up to look) Brady: Is this a bump right here? (points on screen to sun + shade drawing) Charles: Yes. Problematize means of knowing Definition of attribute: “bigness”

Brady problematizes “bigness” EM intervenes to ask whether Brady is agreeing or disagreeing; he says that he is disagreeing because the leaves are bigger. EM: And Charles, what were YOU thinking when YOU said the shade was bigger? Charles: Like the PLANT (holds hands up as if holding plant) in the shade. BW: Was bigger how? In [what way? ] Charles [Bigger in millimeters, ] in the height. BW: Taller. OH in the HEIGHT, OK. (about 30 seconds later) Malik: Umm. . . everybody who has the sun, their plant is SHORT but it's really. . . thicker (gestures out) than the ones who have the shade. Define attribute: “bigness” Differentiation of attribute

Brady problematizes “bigness” EM intervenes to ask whether Brady is agreeing or disagreeing; he says that he is disagreeing because the leaves are bigger. EM: And Charles, what were YOU thinking when YOU said the shade was bigger? Charles: Like the PLANT (holds hands up as if holding plant) in the shade. BW: Was bigger how? In [what way? ] Charles [Bigger in millimeters, ] in the height. BW: Taller. OH in the HEIGHT, OK. (about 30 seconds later) Malik: Umm. . . everybody who has the sun, their plant is SHORT but it's really. . . thicker (gestures out) than the ones who have the shade. Differentiation of attribute Recognize Contradictions

Relating measure, modeling, and opportunities for developing concepts Leaf size Bigness Bumps Contradictions Height Timing Resources in seeds