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
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?
Tasks Proposed to Children
• Children were presented with 8 pegboard machines.- Presented from simplest to most complex- 3 general types:
One inputOne output
One inputTwo outputs
One inputIntermediary Link(s)One or Two Outputs
• Children were asked questions about each machine:
Notice
Predict Motion ??
Explain Prediction
Describe and Explain Motion
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
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)
• Development of coding scheme to characterize student reasoning as they explained the motion of levered machines:
Method - Analysis
• 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%.
Preliminary Coding Scheme
Video Noticings (Jordan & Henderson, 1995)
Iterative refinement of the Preliminary Coding Scheme
Finalized Coding Scheme
Coding Scheme
Structure
Cause-Effect Association
Noticing
Talking about the appearance and components of the machine.
“It looks like a cross.”
Describes how machine’s parts are organized.
“I see the brads are farther apart.”
Connects a simple motion (effect) with another simple motion or structural element (cause).
“This [input] moving is going to make this part also move.”
“[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.”
Mechanistic Reasoning
Transmission of MotionBrad Covariance
Linked Direction
Elements of Mechanistic Reasoning
Constraint of Holder
Constraint of Fixed Pivot
Lever Arms
Rotation When the input is pushed up, the output travels down.
The holder (guide) constrains the horizontal movement of the input. Without the holder,
the input would travel in an arc.
The fixed pivot constrains the movement of the output, causing the left side to go down.When the right side moves up, the left side also moves down, in a coordinated motion.
The coordinated motion of the lever arms follows a rotary path, turning
around the fixed pivot.
Categorizing Student Talk and Gesture at Thematic Level
Categorizing Student Talk and Gesture into Sub-categories
0
20
40
60
80
100
LinkedDirection
Rotation Lever Arms Constraintfixed pivot
Constraintholder
BradCovariance
Transmissionof Motion
Pe
rce
nta
ge
of
Stu
de
nt
Pe
rfo
rma
nc
es
Elements ofMechanistic Reasoning
Cause-EffectAssociation
Mechanistic Reasoning was often Fragmented and Varied by Child
Linked Direction
Rotation Lever Arms
Constraint – Fixed Pivot
Constraint - Holder
Greg
Anne
Don
Beth
Brian
Chuck
Katie
Sam
Kim
10 or more
5-93-41-2
Number ofCodedInstances
Association of Mechanistic Reasoning with Correct Prediction
41% of Performances Included a Correct Prediction
0
5
10
15
20
Predicted Correctly Predicted Incorrectly
Nu
mb
er o
f S
tud
ent
Per
form
ance
s
No Elements
Single Element
Multiple Elements
Example of Orchestrating Elements of Mechanistic Reasoning
Fixed Pivot
Floating Pivot
Coordinating Multiple Elements of Mechanistic Reasoning
Constraint Via Fixed Pivot
these [fixed pivots] will stay
And this one over here
they’ll kind of twist
and then so …this link right here, the bottom one.
Rotation
Overlapping & Embedding Elements of Reasoning
Physically tracing the flow of motion
Use of linking words to connect ideas
Overlapping & Embedding Elements of Reasoning
and then so
Use of linking words to connect ideas
Coordinating Multiple Elements of Mechanistic Reasoning
Overlapping & Embedding Elements of Reasoning
Physically tracing the flow of motion
Use of linking words to connect ideas
Visualization of invisible paths traveled by links
Dynamic Reasoning
Gesture to indicate motion of links
• 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.
Summary
• N = 11, grade 3 and 6
• Embodied experience of rotation and constraint
• Mathematization of experience
Microgenetic Study of Learning
Are embodiment and mathematization viable resources for supporting the
development of mechanistic reasoning?
• 1:1 teaching, 7.2 hrs over 8 days (median)• Students solved design challenges drawn from
the MechAnimations curriculum
Embodiment Mathematics
Reasoning about Physical Systems
Supporting Learning
Design of Study
Embodied Rotation:Disrupting “Straight”
Impossible Straight Path
Impossible Straight Path
r1
r2
Impossible Straight Path
Impossible Straight Path
Fixed Pivot
Embodied Experience
Mathematics Physical System
A person holds one end of a rope. Another person holds the other end.
A point (center) is drawn with a line (radius) (r1) extending out from it. Another point is drawn at the other end.
A link is attached to a pegboard at the end with a fixed pivot. The other end is marked as the output (with a figurine).
One person tries to walk straight while the other rotates in place. His straight path is quickly disrupted by the constraining force of the rope held by the other person.
One end of the radius cannot be swept in a straight path without moving both ends of the line.
The output cannot be moved in a straight line without removing the fixed pivot.
The person walking is forced by the rope onto a path going around the person rotating in place. The walker is always the same distance from the center person.
A circle is created by sweeping the radius (constant length) around the center point.
The output rotates around the fixed pivot. At any point in the rotation, the output always remains the same distance from the fixed pivot.
The rope is now exchanged for a shorter rope and the person walking again attempts to walk straight.
The new, shorter, radius (r2) is created. Again, the radius cannot be swept in a straight path without moving both ends of the line.
The output (figurine) is now moved in closer to the fixed pivot. Again, the output cannot be moved in a straight line without removing the fixed pivot.
The walker is again forced onto a path going around the person rotating in place. This time, the path is shorter and the walker goes around faster.
A new smaller circle (with smaller circumference) is created when the shorter radius is swept around the center point.
The output again rotates around the fixed pivot. This time, the path looks smaller.
A person holds one end of a rope. Another person holds the other end.
A point (center) is drawn with a line (radius) (r1) extending out from it. Another point is drawn at the other end.
A link is attached to a pegboard at the end with a fixed pivot. The other end is marked as the output (with a figurine).
r1
Case Study Example: Sarah
S: it [the link] can move around but, yeah like it can move around like rotating how we did.
Making connections to the embodied experience:
Attaching a Link
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.
Noticing new relations:
Predicting Motion
Correctly predicted motion of little man :
T: If I were going to push it, what do you think [the little man] would do?
S: …like this [the link] would be right here…cause when you like hit it, this will spin.
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.
After moving, Sarah explained how she knew the path would curve:
Examples of MechAnimations
Acknowledgements
• Metropolitan Nashville Public Schools:– Belinda Wade (grade 3) – Deborah Lucas (grade 5)
• Vanderbilt– Lyle Jackson – video
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 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