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