## The dynamics of the learning system

**Ninad Jagdish**

Tanvi doesn’t quite like physics! She’s in the 9^{th} standard in a prominent school in your neighbourhood. She feels that there are just too many equations and problems to remember! It’s just too difficult! Kashyap, a 10^{th} class student in the same school, has a dislike for literature, and in particular, for Shakespeare’s plays. He doesn’t understand why we need to study a play written in an archaic language and often loses interest in the plot and characters. They seem too far removed from his life. Pratima and Dheeraj don’t really have a problem scoring well in the exams. They know the facts and understand the concepts in abstraction, yet fail to ground them in reality. Pratima knows about the atom and electrons, but doesn’t realize that electrons are everywhere and in everything; actual physical contact between two objects can never really happen because each surface has a layer of electrons which would repel each other. Dheeraj knows about gravity and gets all the calculations right, but doesn’t realize that the gravitational force acts between all bodies – even between himself and the person in front of him.

The stories above, though not of actual students, are certainly not untrue. Look around and you’ll be sure to find them in your own school if not in your own class! These stories are not about problems with a particular student’s ability to learn or of the teacher’s ability to teach. Rather they are likely to be symptoms of deeper issues in the current educational system. Let’s take a look at what some of these issues may be.

First, students are always taught how to solve each problem before they are actually given a chance at it themselves. This is in contrast with the real world where people often do not know, beforehand, how to solve the problems that they face. This cultivates a unilateral pattern of thinking in the students’ minds. Going forward they may fumble when faced with problems they do not know how to solve.

Next, the method of teaching is often very authoritarian. The teacher teaches and the students receive the subject. The students do not have the chance to explore the subject or play an active role in the teaching-learning process. This makes it easy for them to disassociate themselves from what is being taught.

And finally, the education system today tends to promote last-minute studying and rote learning. This results in a lack of true understanding of the concepts and facts that are being learnt. Students can pass their exams with flying colours without really understanding the subject matter. Those students like Tanvi, who cannot cope with the vast amount of information and formulae to memorize, end up disliking the subject.

For over two decades now, a method of study called **System Dynamics** (SD) has been used in schools across the United States of America, Germany and in certain Scandinavian countries, to help overcome such issues in their educational systems. The results thus far have been promising with the teaching-learning experience becoming more effective and fun for both the teachers and the students. Using System Dynamics in schools creates an engaging, interactive and grounded environment for learning.

**So what exactly is System Dynamics?**

To describe it in one sentence, it is a general method for defining, studying and solving problems. It uses computers to model problems and capture the interconnectedness of multiple causes and effects, the influence of time, delays, and feedbacks. It is a method that emerged close to 60 years ago from work done by Prof J.W. Foresstor at the Massachusetts Institute of Technology (MIT). After being used successfully in business consulting and public policy, it is now finding its use in making schooling better.

Before going further and discussing examples of how exactly SD has been used in schools it is important to get a sense of what a system dynamics model looks like. At a basic level, system dynamics models consist of **stocks (levels)** and **flows (rates)**.

A simple stock-flow diagram used in system dynamics

A stock is like the level of water in a bucket, the water coming into the bucket from the tap per unit time is a rate or flow. As long as the bucket doesn’t overflow (let’s imagine a very, very large bucket), the SD model for this bucket filling up with water from the tap can be shown as:

Simple stock-flow diagram of water flowing into a bucket

The amount of water in the bucket is simply the sum of all the amounts flowing from the tap in each time period. For example if 10 units of water flow from the tap per second, after 20 seconds, there will be 200 units of water in the bucket.

Now imagine that the bucket has a hole in it. The water will also flow out and this can be shown as:

Simple Stock-flow diagram of water flowing into a bucket with a hole

Again the amount of water is the sum of the net amount flowing into it in each time period (i.e the sum of water flowing in – the water leaking out). The outflow will depend on the size of the hole, the location of the hole and the amount of water already present in the bucket. The influence of these factors is included in the model by adding them as ‘attributes’ as shown here. The arrow linking the water amount to the outflow is what can be called a ‘feedback’. The outflow affects the level of water which in turn affects the rate of outflow.

Stock-flow diagram of water flowing into a bucket with a hole – with more details

**How can SD help in schooling?**

Let’s start by taking a look at how system dynamics can make physics easier to learn! Horst P. Schecker, at the Institute of Physics Education, Germany, writes about the attitude of students toward physics. *“Students look upon physics knowledge as a bulk of specific formulae for specific problems, rather than as a limited set of widely applicable concepts and principles. They may learn textbook physics for the next exam but they hardly apply physical concepts to everyday phenomena outside the physics lab”,* he states. Scheker goes on to provide an example of how system dynamics can be used to remedy these problems, and the same is described here.

Consider the simple concept of forces causing motion. This must be taught in the 8th standard if not earlier. Force on a body of a certain mass causes an acceleration (a change in its momentum), which leads to a change in its velocity, and effectively, in its position. The equations for this are shown in the accompanying box.

F = ∆p/∆t [force is the rate of change of momentum (p: momentum; t: time; ∆: a change or difference in the corresponding value )]

p = m x v [momentum is the product of mass and velocity (m: mass; v: velocity]

v = ∆s/∆t [velocity is the change in position over time (s: position)]

The stock-flow model for the application of a force on a body is shown. Take a minute to see if the diagram is all right. **The force is like a flow which increases or decreases the momentum (a stock)**. Depending on the mass, the velocity varies with changes in momentum and consequently influences the position (a stock). When simulated on the computer, the model will give exactly the same results as the equations of kinematics, i.e. velocity = acceleration x time (v= a x t).

Simple enough, right? But why use a stock-flow model and a computer for something that has been and can be done with a pencil and paper? To answer that, consider a phenomenon not often taught in schools because it is deemed too difficult, that of a Newtonian frictional force. Such a force basically increases in proportion to the square of the velocity i.e.

F = k. V^{2} (Where k is some constant)

The final kinematic equation for velocity in this case is

No wonder this isn’t taught at the school level! It seems much more difficult than the earlier v = a x t equation! The two equations seem so different in their level of complexity that one may feel that they must be quite disconnected!

Yet take a look at the stock-flow model for the second scenario and compare it to the earlier one.

The difference between this and the earlier model is minimal! The only addition is the link relating the force to the velocity at each instant. The computer simulation takes care of the math and students have the opportunity to observe the behaviour of and understand a more complex, and more realistic scenario!

If complex physics can be simplified by adopting such models and using them, even the simpler physics that is currently taught in schools will be made easier for students to understand and relate to what they are learning. The model reduces the need for students to learn things in abstraction and allows them to play around with the situation presented.

The stock-flow models can help Tanvi to learn the concepts behind the equations instead of spending time and energy trying to memorize a tonne of equations. They can also help Dheeraj and Pratima ground what they have learnt in reality.

But what about Kashyap and Shakespeare’s plays? Can system dynamics help there as well?

Pamela Lee Hopkins, an English teacher at Desert View High School in Tucson, Arizona, used a system dynamics model of the Shakespearean play, *Hamlet* to make reading it more fun. The beauty of Shakespeare’s plays is not only in the use of language but also in the complex psychology of the characters and in the engaging, emotional events that he created.

Pamela writes, *“It was my intent to have the students use a systems thinking approach in understanding Hamlet so that they could examine human nature and the interaction between events in one’s life and one’s personality. Therefore, I did not teach them how to use the computer to create a model….”*

The students went through the acts of the play in groups and came up with their list of events and impacts on the characters and hence the plot. The students decided on values to capture these aspects in the model and then simulated it to discuss the results.

*“The amazing thing was that the discussion was completely student-dominated. For the first time in the semester, I was not the focal point of the class…. Instead of my having to force them to keep their attention on the task, they directed and were in control of the learning…. They were talking directly to each other about the plot events and about the human responses being simulated. They talked to each other about how they would have reacted and how the normal person would react. They discussed how previous events and specific personality characteristics would affect the response to each piece of news”,* says Pamela.

The result was an increase in the level of performance of the students in the class. **Students who were labelled as failures began doing well because they could associate with what they learnt. They now had a framework to which they could tie all the information they had gathered.**

Pamela further notes, *“Many people assume that only the “best” students can adapt to the style of education here suggested. But who are the best students? Results so far indicate no correlation between students who do well in this program and how they had been previously labelled as fast or slow learners. Some of the so-called slow learners find traditional education lacks relevance. They are not challenged. In a different setting they come into their own and become leaders. Some of the students previously identified as best are strong in repeating facts in quizzes but lack an ability to synthesize and to see the meaning of their facts. Past academic record seems not to predict how students respond to this new program.”*

So in this way, system dynamics can provide a framework for students to ground abstract concepts, make learning easier and avoid rote learning. If used smartly, system dynamics has a huge potential to support learner-centred learning, and also empower students by giving them a way of thinking that will help them succeed in the 21^{st} century. Let’s look at these claims one by one!

Learner centred learning is about giving the student a chance to participate in creating an understanding and is somewhat linked to the much quoted Chinese proverb which states, ‘I do, I understand’. In the conventional schooling system, the student merely receives what is taught and it is his or her responsibility to assimilate it. With system dynamics, the teacher has a greater opportunity to act as a facilitator of learner-centred learning. Students can work in groups to come up with inputs and suggestions for building the models with the teacher providing only as much support as needed. The point is to give over some control to the students. Even if they are building an inadequate model, showing them the right way may not be best teaching tool. Once the model is run and doesn’t show an expected behaviour the students will themselves realize the inadequacy. **System dynamics can thus give students the chance to easily try out and test what they think is right, or fail and correct course – a very powerful and lasting process of learning.**

System dynamics can also teach students a way of thinking and approaching problems that can help them succeed in today’s highly complex and interdependent world. Human organizations today are larger in scale and impact potential than ever before in history. Conventional thinking is linear as displayed in the following figure. System dynamics, with its emphasis on feedback, trains people to think of interconnectivities between problems, causes, actions and effects – a more relevant way of looking at things.

It also helps understand general patterns of macro behaviour at a very early age. For example, J.W. Forrestor points out how the dynamics of a swinging pendulum and that of a production-inventory business cycle, something people normally learn about in business school, are actually quite similar. Students who are taught using system dynamics will be more easily able to identify such similarities across scales and draw upon their educational experiences to solve them.

System dynamics thus has great potential to revolutionize and simplify the learning process in schools. Apart from physics and literature, it has been used to teach a variety of subjects including mathematics, social studies, history, economics, and biology. Yet, one should note that system dynamics, at the end of the day, is a ‘tool’ and it is how the tool is used that makes all the difference. Further, it is not the only tool that needs to be used in our journey towards improved schooling. Schools are the places where the most change can be effected. It is where future leaders, businessmen, politicians, artists, poets, thinkers and doers take their first steps. It is in those formative years of schooling that tools like system dynamics can bring about a shift in peoples’ thinking, a shift towards making it more holistic and comprehensive. The current article only scratches the surface of what system dynamics is and how it can be used in schools, but hopefully it has given you a taste of just what might be in store! Many more resources are available online for those interested, yet the proof of what has been said here will only truly emerge once you experience the magic of the modelling process yourself! After that, the sky is the limit!

### Using SD in schools

**Frank Draper, 8 ^{th} grade biology teacher, Tucson, AZ:** “…our classrooms have undergone an amazing transformation. Not only are we covering more material than just the required curriculum, but we are covering it faster (we will be through with the year’s curriculum this week and will have to add more material to our curriculum for the remaining 5 weeks) and the students are learning more useful material than ever before. ‘Facts’ are now anchored to meaning through the dynamic relationships they have with each other. In our classroom, students shift from being passive receptacles to being active learners. They are not taught about science per se, but learn how to acquire and use knowledge (scientific and otherwise). Our jobs have shifted from dispensers of information to producers of environments that allow students to learn as much as possible.”

**Timothy Joy, high school English teacher, Milwaukie, Oregon:** “…I taught writing and literature for 13 years and always suspected I was party to some intellectual crime. Why is it that so many students thought the world of language began and ended at the door of the classroom? Then I discovered system dynamics. …System dynamics has a logic-based grammar, a universal language that students can readily learn and manipulate to create meanings. What have I found? Creating “meaning” results in bolder QUESTIONS, whole new views which do not house traditional understandings. …In some ways, it’s been terrifying. I have to give over some portion of the direction and instruction of the material to [the students’] own instincts and inquiry. It’s slower at the start, but the curve steepens as we discuss and build models.”

### Tips for teachers

**What you will need:**

a) At least one computer and a display system

b) Some training and exposure to system dynamics

c) A supportive school administration

**How to go about it:**

- Try not to teach system dynamics as a separate subject but use it to make what is currently being taught more interesting and meaningful
- The point is to spark a fire in the students and not to explain things; Monotony makes students question the significance or relevance of what is being taught. Go straight to the model and show them the magic
- Spend time exploring the models yourself, before trying them out in class
- Try and shift to a learner-centric mode of teaching. Such an environment is where system dynamics can be most effective in helping students learn better.

### Key Resources

**Vensim** is a system dynamics modelling and simulation software. The personal learning edition is a fully functional version with sample models that is free for educational and personal use. It can be downloaded online at http://www.vensim.com/

**The Creative Learning Exchange** is a non-profit that works towards the development of *systems citizens*. Their website (http://www.clexchange.org/) has a lot of material for learning and experimenting with system dynamics, including material that is targeted toward using system dynamics in schools.

The author holds a Master’s degree in Technology and Development from IIT Bombay and has worked in the field of sustainability consulting. He can be reached at ninad.jag@gmail.com.

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