Molly Bolger, Marta Kobiela, Paul Weinberg, and Richard Lehrer Vanderbilt University

1. Analysis of Children’s Mechanistic Reasoning about Linkages and Levers in the Context of Engineering Design Molly Bolger, Marta Kobiela, Paul Weinberg, and Richard Lehrer Vanderbilt University

2. Research Questions What are the typical ways children reason about links and levers? What do they tend to notice? How do they explain the motion of the machines?

3. Notice One input Intermediary Link(s) One or Two Outputs One input One output One input Two outputs Explain Prediction Describe and Explain Motion Predict Motion Tasks Proposed to Children • Children were presented with 8 pegboard machines. • - Presented from simplest to most complex • - 3 general types: • Children were asked questions about each machine: ??

4. Task Order Use of paired contrasting machines drew students attention to relevant features of the machines. Building machines requires a different set of competencies than noticing and explaining. May help students understand the functional relevance of structural elements. Ongoing work: Study of one-on-one instruction Study of classroom instruction If you do this one like that [the output] goes up but then if you do up on this one [the output] goes down but I think it’s because of this one right here is not on that side

5. Study Setting • Schools: • Two neighboring urban schools - elementary school (Grades K-4) and middle school (Grades 5-8) • Southeastern region of the United States • 60-80% student population qualify for free or reduced lunch from year-to-year. • Participants (N=9, 5 male) • Ethnically diverse (6 African-American, 1 Middle Eastern, 2 Indian and 1 Samoan) • Five from Grade 2 (ages 7 and 8); Four from Grade 5 (ages 10 and 11)

6. Video Noticings (Jordan & Henderson, 1995) Preliminary Coding Scheme Finalized Coding Scheme Iterative refinement of the Preliminary Coding Scheme Method - Analysis • Development of coding scheme to characterize student reasoning as they explained the motion of levered machines: • Application of coding scheme: • Each student performance was coded independently by • two raters. • Of instances agreed to be codable (n=586), mean inter- • rater agreement at the thematic level was 89%.

7. Coding Scheme Structure Noticing Cause-Effect Association Mechanistic Reasoning Connects a simple motion (effect) with another simple motion or structural element (cause). Describes how machine’s parts are organized. Talking about the appearance and components of the machine. Transmission of Motion Brad Covariance “[I]f you have the brads on the same side, [the outputs will] go the same way and if you have them on a different side, they’ll go the opposite way.” “It looks like a cross.” “This [input] moving is going to make this part also move.” “I see the brads are farther apart.”

8. Linked Direction Constraint of Holder Constraint of Fixed Pivot Lever Arms Rotation Elements of Mechanistic Reasoning The fixed pivot constrains the movement of the output, causing the left side to go down. The holder (guide) constrains the horizontal movement of the input. Without the holder, the input would travel in an arc. The coordinated motion of the lever arms follows a rotary path, turning around the fixed pivot. When the right side moves up, the left side also moves down, in a coordinated motion. When the input is pushed up, the output travels down.

9. Categorizing Student Talk and Gesture at Thematic Level

10. Elements of Mechanistic Reasoning Cause-Effect Association Categorizing Student Talk and Gesture into Sub-categories

11. Mechanistic Reasoning was often Fragmented and Varied by Child Number of Coded Instances 1-2 3-4 5-9 10 or more

12. Association of Mechanistic Reasoning with Correct Prediction 41% of Performances Included a Correct Prediction

13. Fixed Pivot Floating Pivot Example of Orchestrating Elements of Mechanistic Reasoning

14. Use of linking words to connect ideas Use of linking words to connect ideas Overlapping & Embedding Elements of Reasoning Physically tracing the flow of motion Overlapping & Embedding Elements of Reasoning they’ll kind of twist and then so …this link right here, the bottom one. And this one over here these [fixed pivots] will stay and then so Coordinating Multiple Elements of Mechanistic Reasoning Constraint Via Fixed Pivot Rotation

15. Use of linking words to connect ideas Overlapping & Embedding Elements of Reasoning Coordinating Multiple Elements of Mechanistic Reasoning Physically tracing the flow of motion

16. Gesture to indicate motion of links Visualization of invisible paths traveled by links Dynamic Reasoning

17. Summary • Despite apparent transparency of workings; mechanisms behind these simple levered machines were largely invisible to children. • Children’s ability to predict machine motion was associated with use of multiple elements of mechanistic reasoning. • Children who consistently predicted motion of these objects were more able to visualize the motion of the various parts and coordinate multiple elements of mechanistic reasoning. • Few children “saw” rotation and constraint of fixed pivot.

18. Are embodiment and mathematization viable resources for supporting the development of mechanistic reasoning? Microgenetic Study of Learning • N = 11, grade 3 and 6 • Embodied experience of rotation and constraint • Mathematization of experience

19. Embodiment Mathematics Reasoning about Physical Systems Design of Study • 1:1 teaching, 7.2 hrs over 8 days (median) • Students solved design challenges drawn from the MechAnimations curriculum Supporting Learning

20. Impossible Straight Path Impossible Straight Path Impossible Straight Path Impossible Straight Path r2 Fixed Pivot r1 Embodied Rotation: Disrupting “Straight”

21. r1

22. Predicting Motion Attaching a Link Making connections to the embodied experience: Correctly predicted motion of little man : After moving, Sarah explained how she knew the path would curve: S: it [the link] can move around but, yeah like it can move around like rotating how we did. S: It's not going up, it's just on one brad and when you hit it, it will go, that way cause it [fixed pivot] can't always go straight. Yeah cause it can't move up. It's in its place. Noticing new relations: S: …like this [the link] would be right here…cause when you like hit it, this will spin. T: If I were going to push it, what do you think [the little man] would do? S: …it can only rotate in like this spot and no other spot…you can only start here and not start somewhere else because this [fixed pivot] is stuck to THAT place. Case Study Example: Sarah

23. Examples of MechAnimations

24. Metropolitan Nashville Public Schools: Belinda Wade (grade 3) Deborah Lucas (grade 5) Vanderbilt Lyle Jackson – video Acknowledgements

25. If you do this one like that [the output] goes up but then if you do up on this one [the output] goes down but I think it’s because of this one right here is not on that side Learning About Mechanisms? • Use of paired contrasting machines drew students attention to relevant features of the machines. • Building machines requires a different set of competencies than noticing and explaining. • May help students understand the functional relevance of structural elements. • Ongoing work: • Study of one-on-one instruction • Study of classroom instruction