Using Feedback Control Engineering for Analyzing and Designing an Effective

Lecturing Model

M Abdulwahed1,2 and Z K Nagy2

1Engineering Centre for Excellence in Teaching and Learning, Loughborough University, United Kingdom

2Chemical Engineering Department, Loughborough University, United Kingdom

October 24, 2008

FIE 2008, Saratoga Springs, New York

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Overview

Towards Pedagogical Cybernetics. Why dynamical modelling of educational processes. Why considering feedback. Modelling the learning process. Considering the lecturing process:

Open loop lecturing model. Cascaded open loop model. Closed loop lecturing model. Cascaded closed loop model. Robustness of closed loop lecturing model.

Conclusions

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Towards Pedagogical Cybernetics

Why not viewing pedagogy as a SYSTEM? Why not viewing learning as a DYNAMICAL

PROCESS? Control systems methods have been successfully

applied to part of social sciences such as economy and finance.

Dynamical modelling and control systems are frequent engineering tools.

Why not to apply this knowledge to educational processes which we are involved with any way!

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Why Dynamical Modelling of Educational Processes

Most pedagogical models are conceptual or static Dynamical models are superior to conceptual and

static models Dynamical models allow investigating more

comprehensively the power of feedback Dynamical models are useful for:

Simulation Prediction of future behaviour Analysis Design and Control!

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Why Considering Feedback

Feedback is omnipresent in everyday life (biology, economy, etc.)

Control systems uses feedback as artificial tool for uncertainty management.

Feedback can make systems to behave well even by using imperfect components.

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Modelling The Learning Process

Modelling guidelines in control engineering: Approximation to a linear system whenever

possible. Consider the most important character for the

analyzed issue and ignore/simplify other features. Constructivist Learning is considered as a

process of knowledge construction (Kolb 1984).

Learning is a process of accumulating knowledge.

How do we model an accumulating process?

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Learning Process Model

Teacher

Student

Knowledge

Forgetting

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Learning Process Model

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Open Loop Lecturing Model

x is internal state representing the learning level (x0 – prerequisites).

u is control variable (set by the teacher). a is constant representing the average ability of students to

learn.

Lecturing

Open Loop Lecturing.

Teacher’s Input

Assumed learning

level

Prerequisites

dxau

dt

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L(1) L(2) L(3) L(n-1) L (n)

Block diagram of Open-loop lecturing model.

Student prior Knowledge

Module Outcome

1 1 12

2 23

0 0 0

0 00

0 0

00 0n n

n

x x aa

x xa u

x xa

1 1 12

2 23

0 0 0

0 00

0 0

00 0

at

n nn

x x aa

x xa e u

x xa

Cascaded Open Loop Model of Lecture Series

Forgetting Factor

Lack of Feedback, Reflection, and Practice will Lead to QuicklyForgetting The Taught Material in The Lecture. Hence, Close to

ZERO Learning Outcome of Open Loop Lecturing.

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Closed Loop Constructivist Lecturing Model

LecturingActual learning

-

+

LearningObjectives

Closed Loop Lecturing.

Feedback

dxa x r

dt

x is internal state representing the learning level. r is learning objectives. a’ is constant representing the average ability of students to learn. Feedback is achieved through formative assessment and reflection Teacher-in-the-loop versus constructivist lecturing approach Stable System!

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Lecture 1 Lecture 2 Lecture N

Block diagram of closed loop lecturing model.

Prerequisites

Lecture 2 Objectives

Lecture N Objectives

Final Module

Outcome

Lecture 1 Objectives

Closed Loop Model of Constructivist Series of Lectures

Break the complexity of the course into smaller cascaded loops.

Activate continuous formative assessment, reflection, and practical activities along each loop (e.g. each lecture)

Set clear learning objectives for each lecture.

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1 1 1 0

2 2 2

12 12 12

0 0 1 0 0

1 0 0 1 0

0 0 0 1 1

x x r xa

x x ra

x x ra

1 1

2 2

12 12

1 0 0

0 1 0

0 0 1

y x

y xY

y x

c cX A X B U

cY C X

Cascaded Closed Loop Model

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Robustness of Closed Loop Lecturing Model

( )dx

a x x rdt

( )c cX A X X B U

( )cY C X X

Lecture

Closed loop lecture with student’s uncertainty

Prior Needed

Knowledge

Lecture Objectives

Lecture Outcome

Feedback

Uncertainty

s

a

Students come with diverse learning abilities and learning styles. Hence, model uncertainties. Feedback can inherently accommodate model uncertainties.

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Lecture 1 Lecture 2 Lecture N

Block diagram of closed loop lecturing model

Prerequisites

Lecture 2 Objectives

Lecture N Objectives

Final Module

Outcome

Lecture 1 Objectives

Simulation of nominal vs. weak student performance

Robustness of Closed Loop Lecturing Model

Closed Loop Lecturing Model Leads to Close Learning

Outcome of Average and Weak Students in Case of Effective

Feedback, Reflection, and Practical Activities

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Hybrid Control Model of Project Based Learning Pedagogy

-

+

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Feedback via Technology Assisted Lecturing

Left the students attention more to the lecture.

Help overcoming the shyness or linguistic factors preventing students from engagement.

Quick identification of students’ level of understanding of the lecture.

Delivering automated formative assessment messages to the students in short time.

Using voting systems and SMS and email messaging to achieve the previous objectives.

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- A model of The Mobile Formative Assessment System m-FAS has been proposed and pilot study was done with messages delivered through SMS and emails.

- Students have appreciated the messages they got directly after the lecture, they wanted more details.

Identification (Questions)

Process(Student Learning)

Actuator(Teacher)

Automatic Feedback

DAQ(e-Voting)

Monitoring(Parents)

Classroom Voting with Mobile Learning, The m-FAS

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Conclusion

Mathematical Modelling of Two Models for Conducting Lecturing:

Open Loop Model (teacher centered approach).

Closed Loop Model (student centered).

In case of open loop model, the forgetting factor plays significant role in the low retention of information.

With closed loop models, the forgetting factor is eliminated.

Closed loop lecturing is stable, hence achieving the learning objectives.

Closed loop lecturing is robust, hence accommodating the learning uncertainties in the students’ model and bringing the weak students’ performance close to the that of the average students.

Its NOVEL to use control engineering for modelling educational processes.

From the engineering PEDAGOGY towards ENGINEERING the pedagogy!.