An example: building a simulator using learning seeds 62

to be more than the mere sum of plain CAI frames. An example of such a learning space is a simple simulator where each state of the simulated phenomenon forms a seed of its own; together they form a simulator that can clarify a complex concept.

For the purpose of our users, the simulator should be simplified some-how because of the learning disabilities caused by deficiencies in mental programming. Let us say that we are trying to teach the ecosystem in a restricted environment by having a world with two kinds of animals, rab-bits and foxes. When there are a lot of rabrab-bits, the foxes have plenty of food supply, so the number of foxes starts to grow. At some point the foxes consume more rabbits than the ecosystem can hold. Therefore, the amount of foxes is bound to diminish, since their food supply is not suffi-cient. This procedure forms a kind of a balance where the number of foxes and the number of rabbits are alternating unless a human interferes with the ecosystem by excessive hunting of the animals.

In the simulator, the user can hunt either one of the animals (decrease the amount of rabbits or foxes), and just let the time pass. Proceeding from one time stage to another can be a user-initiated function or self-evolving step in the learning space model. In a simulator, every state of the simulated world can be presented in a seed. The problem is that it requires a vast amount of seeds, even if the simulator is restricted, since the general formula for the amount of seeds needed in a simulator isx1∗x2∗...∗x_n, where n is the amount of dimensions (the variables in the simulated world), andx_i equals the amount of different states inidimension. However, if the author of the simulator wants the system to keep track of a learner’s characteristics in addition to states in the simulated world to enable individual adaptation based on the learner’s actions in the simulator, the amount of dimensions grows even larger.

Our example ecosystem (Fig. 5.6) has different states as follows:

5.1 Types of learning material suitable for learning spaces 63

End1

End2

2,2 4,2 6,2 8,2 10,2

10,1 8,1

6,1 4,1

2,1

Figure 5.6: A nearly-trivial ecosystem simulator with ten regular states and two ending states. The numbers in the seeds represent the amount of rabbits and foxes.

• The amount of rabbits can vary from 2 to 10 with the interval of 2 animals, giving a total of 5 states for rabbits.

• The amount of foxes can vary from 1 to 2 with the interval of 1 animal, giving a total of 2 states for foxes.

For the sake of clarity, only the time elapsing movements and “game-ending” movements are presented in Fig. 5.6, and not the links to other states when hunting the animals. The simulator stops in a situation where the ecosystem cannot sustain hunting an animal, i.e. when the amount of that particular animal is at its lowest point (rabbits two, foxes one). The transitions between the states presented with bold arrows are the transi-tions if the learner just lets the time pass. In such a case, the ecosystem is in an eternal loop. Only human interference with the ecosystem (i.e. hunting the animals) can end the game.

This simple simulator has 5∗2 states in the simulated world. Therefore, one has to build 10 seeds into a learning space to have such a simulator. The more realistic the simulator is, the more seeds must be prepared. When it comes to learning, the example above is not large enough to be feasible in learning the concept. One can imagine a simulator should have something like 20∗50 states so that a learner can have a good grasp of how the world is evolving. The amount of seeds would in that case be 1,000.

In practice, few thousand seeds in a learning space can still be manage-able, but there is a limit at some point. Therefore, the learning space model can only be used in restricted simulators, even though the seeds could be created with semi-automatic content generators. However, the restrictions

in simulators are not necessarily problematic. Common wisdom in early learning is that you should start with a simple phenomenon and remove it from any unnecessary noise.

5.2 Characteristics of learning material in the learning space model

Although the typical ways used in everyday educational software can be exploited with the learning space model, the total domain-independence of the schema allows variations in learning seeds and in collections of seeds, regardless of the learning content organization.

• Reflective material has links to the seeds which ask questions such as

“Do you understand?” or, “Do you know what this means?” which in turn have links to the next appropriate seeds.

• Alternatives in the style of the learning material. The learner can be forced to stay in a seed until the correct answer is found, by linking the wrong answers to the same seed, either straight or through a loop of seeds. Another extreme is that wrong or inadequate answers will be passed without any notification to the learner.

• Allowing fuzzy input, like “I don’t care”. Since every input is stored into the user’s profile, this type of fuzzy input can be used by a teacher or significant other in evaluating extra-curricular learner properties, such as motivation, after a learning session.

• Non-factual exercises where the line between correct and erroneous answers is vague. Exercises can contain problems with ethical or moral values, and the whole learning material can consist of an ad-venture in an imaginary world.

• Nested seeds can cover more profound learning objectives. Assume that a seed contains a simple problem to be solved. Thus, a complex problem can be represented as a sequence or even a tree of simple problem seeds linked together. This hierarchical structure of seeds yields a more profound evaluation of learning, compared to using only one seed. Another use of “sequential” objectives is the analysis of error types. As a simple example, consider multiplication and addition. If a learner answers 1∗1 with 2, it is possible that he or she confuses 1∗1 with 1 + 1. By presenting similar exercises the system provides a way to draw a conclusion that the learner does not

5.3 Learning material to support brain deficits 65 know how to multiply. From the learning theories’ point of view, one can also assess learning outcomes as the level of acquired automation.

During the learning process, the learner packages sequences of small seeds into a combined structure, and the level of mastery can be estimated as the size of these automated hierarchical structures. For example, most people do not partition a sum sequence 1 + 2 + 3 into smaller chunks but consider it as one chunk containing 6.

5.3 Learning material to support brain deficits

The underlying principle behind the learning space model has been serving people with disabilities and especially deficits in mental programming. In this section the use of the learning space model in supporting various brain deficits is presented. The model behind the human brain comes from the Russian neuropsychologist Luria.