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Productive Failure Manu Kapur Assistant Professor of Learning Sciences & Technology

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Manu Kapur

Assistant Professor of Learning Sciences & Technology

National Institute of Education, Singapore

ICET, Nov 22, 2007

- Set up the argument for productive failure
- Study 1 – online setting (in Indian schools)
- Study 2 – F2F setting (in a S’pore school)
- Draw common patterns across the two studies
- Draw implications using a complexity theory perspective

Argument for Productive Failure

The situative, socio-constructivist perspective: learners need to be participate/collaborate in authentic, ill-structured problem-solving activities for meaningful learning to take place

- Learners need to be scaffolded in their process of engaging in ill-structured tasks or else they may fail
- But does this mean there is little efficacy embedded in un-scaffolded, ill-structured problem-solving processes?

Argument for Productive Failure

1. A Logical fallacy

A implies B does not mean not-A implies not-B

2. Validity and reliability of measures

3. Several research programs point to the role of failure in learning and problem solving (VanLehn, 2003; McNamara, 2001; Schwartz & Martin, 2004, etc.)

4. The role of persistence vis-à-vis performance success

Demonstrating an Existence Proof for Productive Failure

To examine whether or not there is a hidden efficacy in un-scaffolded, ill-structured problem-solving processes

Context: Synchronous CSCL problem solving in Physics with N = 309, 11th grade science students across 7 high schools in India

WSP Individual

ISP Individual

Pre-Test

R

(Triads)

50 ISP Groups

WSP Individual

ISP Individual

Contrasting ISP with WSP

The Study in Brief

- Ill-structured groups showed:
- Struggle with defining & solving the problem (MANOVA)
- Complex and chaotic patterns of interaction (LSA)
- Low convergence in their discussions (computational)
- Poor group performance (ANCOVA),
- BUT, better individual performance on both well- and ill-structured problems (Hierarchical Linear Modeling)

- It seems that there is efficacy embedded in un-scaffolded, ill-structured problem-solving processes
- This efficacy can be extracted using a contrasting-case mechanism – a delay of structure
- This efficacy seemed to be embedded in the chaotic, divergent, all-over-the-place interactional dynamics in the ill-structured groups

- Question the default pedagogical rush to scaffold ill-structured problem solving
- The ontology of learning & problem solving
- Simple to complex – incremental, or
- Complex to simple - emergent

Exploring Productive Failure in a Singapore Classroom

- To test the productive failure hypothesis in a Singapore classroom, i.e., examine whether or not there is a hidden efficacy in un-scaffolded, ill-structured problem-solving and how it compares with traditional lecture & practice instruction
- Context:
- Clementi Town Sec School: A mainstream school
- N = 76; Two classes of Sec 1 express-stream math students taught by the same teacher
- Two curricula units, each lasting 7 lessons (about 2 weeks each);
- Estimation & Approximation; Rate & Speed

LECTURE-PRACTICE (LP) CYCLE

Pre-test

Pre-test

Lecture, practice

and feedback + HW

PF Group

Problem 1

Lecture, practice

and feedback + HW

PF Group

Problem 1 cont’d

Lecture, practice

and feedback + HW

PF Problem 1

Individual extensions

Lecture, practice

and feedback + HW

PF Group

Problem 2

Lecture, practice

and feedback + HW

PF Group

Problem 2 cont’d

Lecture, practice

and feedback + HW

PF Problem 2 Individual extensions

Lecture, practice

and feedback + HW

Consolidation Lecture

Post-test

Post-test

The Design in Brief

(N = 76 Sec1 math students from CTSS, Singapore)

Example of an Ill-Structured Problem

Gist of the Biking Problem (Speed Unit)

Two friends, Jasmine and Hady, had to get to an exhibition by a certain time. They could walk or ride a bike or both. The constraint was that they had to reach the exhibition at the same time despite having different walking and biking speeds. Furthermore, a little while into their journey, one of the bikes breaks down, requiring re-strategizing for the rest of the journey.

- Process Analysis:
- Problem Representations
- Group & Individual Solution Scores
- Self-report Confidence in their Solutions
- Self-report Lesson Engagement
- Rich interactional data remains to be analyzed
- Outcome Analysis:
- Pre-Post-test scores on rate and speed items: well-structured and ill-structured problem items

- Sample Well-structured Items
- The flight distance between Singapore and Japan is 5316 km. A plane takes 6 hours and 15 min to fly from Singapore to Japan. What is the average speed of the plane?
- David travels at an average speed of 4km/hr for 1 hour. He then cycles 6km at an average speed of 12 km/hr. Calculate his average speed for the entire journey in km/hr.

Ill-structured item

Hummingbirds are small birds that are known for their ability to hover in mid-air by rapidly flapping their wings. Each year they migrate approximately 8583 km from Canada to Chile.

The Giant Hummingbird is the largest member of the hummingbird family, weighing 18-20 gm. It measures 23cm long and it flaps its wings between 8-10 times per second. For every 18 hours of flying it requires 6 hours of rest.

The Broad Tailed Hummingbirdbeats its wings 18 times per second. It is approx 10-11 cm and weighs approx 3.4 gm. For every 12 hours of flying it requires 12 hours of rest. If both birds can travel 1 km for every 550 wing flaps.

If they leave Canada at approximately the same time, which hummingbird will get to Chile first?

Outcome Analysis: Overall Gains

Controlling for the effect of prior knowledge as measured by the pre-test

10%, p = .002, ES = .75

- We also wanted to know how the PF cycle prepares students to learn and apply new concepts on their own
- Extension Concept – Relative Speed
- Half the students in each condition (PF and LP) took a scaffolded item on relative speed, the other halves took an un-scaffolded version
- Then all students took an unscaffolded, conceptually difficult problem on relative speed.

- Item 1: You and your friend start running at the same time from the same position but in opposite directions on a 400m running track. You run at 5m/s whereas your friend runs at 3m/s.
- In 1 second, how many meters do you travel towards your friend?
- In 1 second, how many meters does your friend travel towards you?
- Therefore, in 1 second, how many meters do the two of you travel towards each other in total?
- How many seconds will it take for the two of you to first cross each other?
- Item 2: Two MRT trains on separate but parallel tracks are traveling towards each other. Train A is 100m long and is traveling at a speed of 100km/hr. Train B is 200m long and is traveling at a speed of 50km/hr. How many seconds will it take from the time that the two trains first meet to the time they have completely gone past each other?

- Productive Failure design seems tractable within local classroom context since the study was carried out within the timetable and curricula constraints
- It seems to suggest shorter-term inefficiencies and failure but longer-term gains on both standard, well-structured items and more higher-order, ill-structured problem-solving items
- The assessment experiment reveals that PF also prepares students to better use the structure provided for new concepts
- One of the reasons structuring from the outset may not work could be due to our assumption that learners are prepared to use the structure provided!

- Collaboration in small groups
- Engage students in complexity of solving complex, ill-structured problems
- Minimize a priori structure by not providing any external support or scaffolds
- Delay structure, be it in the form of a contrasting well-structured problem or a consolidation lecture
- Shorter-term inefficiency and failure but longer-term productivity

A Complexity Theory Perspective

- Structure imposes order on the learning & performance space
- Short term: efficient
- Long term: may lack flexibility and adaptability
- The laws of self-organization and complexity is: under certain conditions, as systems (biological, social, neural, etc.) comprising multiple interacting agents (genes, people, neurons, etc.) become increasingly complex over time, there comes a critical point where the system self-organizes and order emerges spontaneously from chaos.

A Complexity Theory Perspective

- So, order is important! But, how does it come about?
- Top-down vs. bottom-up order
- (efficiency) (flexible, adaptive)

Laws of Self-organization & Complexity (Kauffman, 1995)

ORDER

CHAOS

High Structure Processes

Low Structure Processes

Efficiency

Innovation

Self-Organization & Complexity

Do we engage learners more in efficient or innovative processes?

(OAC: Optimal Adaptability Corridor, Schwartz, Bransford, & Sears, 2005)

Innovation

OAC

Routine Experts

Novices

Efficiency

Traditional Approach

Balanced Approach

My Proposal

EFFICIENCY

INNOVATION

Implications for Adaptive Expertise

(Hatano & Inagaki, 1986)

A Working Hypothesis underpinning Productive Failure…

In the longer run, an innovation-dominant approach would be more optimal for the development of adaptive expertise than a balanced approach.

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