Saturday, May 9, 2009

Learning, Models and Other Tricks

Have you ever thought why models are so often used in teaching and learning? They formed part of what used to be called teaching aids, more recently termed learning resources.

In the high school that I attended, we had a resource room. Senior students were given access to this room for study purposes and when helping a teacher prepare lessons. The day I was permitted into the resource room I could not stop thinking about the amazing things I saw stored there. It was only years later when I became a teacher that I realised why my teachers had guarded the room and its content so vigilantly and with such reverence.

Effecting learning

I recently ran my blog through Wordle. The result at the head of this post shows what has obviously been the most important thing on my mind when I wrote recent posts. It also made me think that despite my familiarity with the word, learning and how it is brought about is not always looked upon as common ground when discussed in depth with others in the field. Tony Karrer’s recent post has hosted a debate on ways of learning and associated ideas, a follow up to his post on Learning Goals.

Learning by association

The renowned scientist, Dr Jacob Bronowski, who was also an intellectual, expert code-cracker, mathematician and author, gave celebrated lectures on BBC TV in the 1960s. During one of his lectures, he demonstrated how a feat of memory through association could be performed, and he displayed this both by his own memory acumen and with the help of a trained member of his audience.

The 'trick' involves some preparation. A list of (say) 20 commonly known items, personal to the memoriser, is committed thoroughly to memory so that not only the list order can be recalled but also the position in that list of any of its component items.

Once this is accomplished, the memoriser is then shown a series of up to 20 new items in sequence, such as cards drawn randomly from a full pack of playing cards. For each new item shown, the memoriser simply ticks it in the mind by association with each of the previously memorised personal items in sequence.

When complete, the memoriser is asked to name an item by its number in the list and knows what the item is. As splendidly amazing as this act appears when first seen, it is based on learning by association. While it is true that this method has limited application to some learning, it shows how rapid and facile the mind and memory can be in the simple act of learning content.

Models and their place in learning

Learning by association is not a new idea.
It is the working part of how learning is assisted when a model is used. It is called upon when a map is used in learning geography or an elaborate digital model is used in learning the function of interior parts of a plant cell. Models work by drawing on previous experiences and learnt ideas, and relating to these when learning something new.

Model of DNAOften the simplest models are the best, even when they may relate to a complicated theory, concept or phenomenon. Though elaborate models may look fascinating, they rarely convey useful learning to the beginner. Learners need to be already familiar with parts of the model itself. As intricate and captivating as the Watson, Crick and Wilkins model of DNA may be, it conveys nothing about its chemistry to those who have never learnt elementary Chemistry.

Learning and memory

It is well known that before any skill can be acquired learning a second language, knowledge of vocabulary is fundamental. It is also becoming recognised by educators that the language of a subject, and knowledge of vocabulary in particular, is required for the learner to be able to think in terms of the subject and also to converse about it with others.

Without the vocabulary of a hitherto unknown subject it is impossible for a beginner to acquire any useful subject skill. Motor skills have similar fundamental elements when it comes to the first time learner picking up the ropes of a new skill.

There is no evidence to suggest that the memory required while learning and remembering a vocabulary (content learnt by association) is fundamentally different from that needed to learn and remember the higher skills. When concepts or skills to be learnt become more complicated as the learner progresses, a stage is invariably reached where the learner has to work at them to make the leaps. Once made, these too can be learnt and remembered. Higher thinking skills are required to be learnt to continue to progress. This is often forgotten by the expert who is addressing learning in the subject, the so-called cognitive apprenticeship theory.

Learning is recursively elaborate

A concept, idea or formula learnt in one discipline can find a use in another that’s seemingly unrelated. A child who recognises the relationship between similar patterns of learning in two distinct disciplines makes a cognitive leap. Intelligence is intimately linked with the ability to connect patterns in this way.

The animated equations depicted here are of elementary algebra. They show how the same basic tactic can apply to two distinct areas of learning in Science. A child who masters the simple algebra relevant to this also learns the skill to work within an unbelievably large number of its applications. The scope for it is huge, and it finds use in many common everyday tasks, from a simple calculation in an expenses return to estimating how long a car journey is likely to take.

This recursive application of algebra is by no means a unique feature in learning, for there are many millions of patterns that cross seemingly unrelated disciplines. The ability to understand and recognise these patterns is one that is familiar to the compilers of intelligence tests. It was believed that such tests, according to various scales, could be used to classify and measure cognitive ability. Though there may well be some merit in the idea of pattern recognition being linked to cognitive ability, the means created to measure this fell short of something useful, never mind fairness.

Cutting corners

The recursive nature of learning often compels us to take short cuts that sometimes lead to a misunderstanding that a concept has been learnt. It may even suggest that it doesn’t need to be learnt; the word content springs to mind. I’ll use an example from elementary Chemistry to demonstrate this.

Finding the chemical formula for a simple compound, such as aluminium oxide, can be done a number of ways, all of which have the potential to yield the same answer:
  1. use Google - provided the student can apply the search routine and recognises a reputable site when one is brought up, the correct formula might be found,

  2. recall the chemical symbols for the elements oxygen and aluminium, and that oxygen has a valency of 2 and aluminium has a valency of 3, then apply the recalled rule for writing correct chemical formulae,

  3. referring to the periodic table of the elements (or just simply knowing it) the student uses the atomic number of oxygen to write the electron configuration of its atom - having used a similar process to write the electron configuration of aluminium, the student may determine the common valencies of both elements and then apply method 2.
Understanding how the formula is found is part and parcel of understanding so-called ‘valency theory’ in Chemistry. Learners who can Google the formula for any simple chemical compound don’t really need to know much chemistry. While method 2 barely touches on some of the principles involved in valency theory, knowledge of how to use method 3 takes the learner closer towards how to apply that theory and to understanding why chemical compounds form between elements in the first place.

Most students who go on to study Chemistry in senior school will learn both methods 2 and 3. They may become so proficient at writing chemical formula using method 2 that they can write several correct formula in the time it takes another student to type in the Google search criteria in following method 1, let alone what’s needed to choose a suitable trustworthy site to browse.

All of the above methods for finding a formula can be learnt and each method has its merit depending on the need. But to say that all a learner needs to know is how to use an Internet search engine to find the formula of a simple chemical compound is not actually learning any Chemistry. Yet this is often used as an argument for not teaching content. There comes a time when the learner just has to face learning some content, and this applies to many distinct disciplines.

Models can be conflicting

One of the many curious phenomena studied in secondary school Science is that of the behaviour of light. This well studied topic requires a series of models to explain how light can behave in different circumstances. A feature of two celebrated models for light, that of the particle or photon and that of the wave, is that neither model explains all the observable properties of light.

While both these models can be used to explain and predict the behaviour of other phenomena not directly related to light, it takes an enlightened learner to understand that they are just models. This peculiarly useful awareness is a higher learning skill. It allows the learner who is very familiar with models used within a discipline to understand their limitations and permits recognition of when a particular model is applicable and when it is not. Recognising that a model and the phenomenon it mirrors are not the same things is extremely important in Science.

The lesser analogy

Unlike the model, an analogy is not trying to depict in any way how the thing or concept exists. It is a direct mapping between unrelated elements of one idea and another. There is no need for there to be any true resemblance between the thing or concept and its parallel used in analogy.

Unfortunately, analogies are often used erroneously as models. For the learner, the analogy is far more involved, the behaviour of one thing being considered while thinking of the associated behaviour of another.

It calls for the most use of imagination, being a parallelism that’s left mainly up to the ingenuity of the thinker. As they are necessarily specific, analogies are severely limited in their broader application.

Facile in association

The mind seems to be facile in the way it can link seemingly unrelated things and learn by association. Perhaps this is why the model enjoys its time honoured place in learning at all levels, for it is so successful.

Models enable a direct mapping of what is seen onto what is being learnt. Good models permit this to be assimilated easily by the learner so that they can apply what’s learnt. Through pattern recognition learners can find further application of what they have learnt.

The enlightened learner, who also understands the difference between the model and the idea, concept or phenomenon that it is mirroring, can flip between models used to reflect these. Introducing the learner to this important difference between the model and what it reflects is the province of good teaching.

Ngā mihi nui – Best wishes


V Yonkers said...

Wow, is this post rich! I'm going to just address three things that jump out at me however.
1) Kathrine Nelson has a great study on how infants and toddlers "learn" language. The words that we use are more than vocabulary (which is the problem I have with giving a bunch of words to memorize and then say someone "knows" the language). For example, in an anthrolinguistics field study, we worked with a native speaker of Eki Guissi (a minor language spoken in Kenya that is beginning to die out) to come up with "rules" for the language. We developed a working vocabulary of about 25-40 words. We would then put those words together to form sentences based on our hypothesis of the grammar. One of my classmates said "the son goes to the forest with his mother". The "expert" started to laugh because, as she explained to us, "going to the forest" meant going to the bathroom. We had the words, but not the meaning that putting certain words together gives.

2) My son is very good at learning processes and facts that he has been shown just once. This is why he is such a successful student. The problem, as he gets into higher concepts, is that he can go through the process without ever understanding what he is doing! This is really affecting him this year as he gets into trigonometry without really understanding the basics of algebraic formulas. I agree with you that we are not developing a strong enough foundation on which to build more complex learning. It is not the CONTENT that we should be focusing on, but the UNDERSTANDING of what that content means that is being lost (and that teachers and assessment tools should be focusing on).

3) I think models are more than just helping with memory. I think they are the bridge to content and understanding. In fact, I find it much easier to create a model when I am having trouble understanding a complex idea. That is why I think it is important for students to create their own models (not just in their head) as a learning tool.

Many of my students hate that aspect of my class because they say it is too difficult (they would rather just take a test). However, I can look at a model, simulation, or project and tell right away what a student understands and where they might be off. Students know also! That is when they come for help when they can't conceptualize or make something concrete.

This is a new insight for me. I never realized how important STUDENT modeling was and want to try it out in my classes next semester!

Clark said...

Ken, great post. I love models, and just blogged about them too. I think that models are a powerful tool for solving problems, with the caveats you espouse about internalizing them.

I'd like to quibble a wee bit about the weakness of analogy: it's considered by many to be fundamental cognition, and in my own PhD thesis I found that it was amenable to intervention. It's part of that pattern-matching that is what leads to innovation and learning. Yes, we tend to focus too much on the concrete, but can facilitate the abstraction.

But I'm totally with you on the power of models to be a tool for comprehension.

Blogger In Middle-earth said...

Tēnā kōrua!

Kia ora Virginia.

Thanks for your input here. Of course, in 1) you speak of how language is learnt. Learning vocabulary when learning a second language is learnt in different circumstances than how we learnt our (first) language as a child. When I referred to learning a language, I meant learning a second language. I am not so sure that these are the same things we are referring to.

2) Learning process is useful nevertheless. In mathematics is was usual for us to learn things from first principles, such as how to differentiate in differential calculus. But it becomes a hampering method if it is used every time differentiation is required. Eventually the student needs only to recognise where differentiation can be done and is appropriate. In those instances the rule (process) is applied, and it is appropriate.

3) You are right about models being more than just helping with memory. The important thing to remember is, however, that the model is not the real thing. It is only a model and may not actually behave, in all circumstances, like the idea/concept/phenomenon it's depicting.

Kia ora Clark.

Yes I'm familiar with the cynefin concept by Dave Snowden.

While I concede that analogy 'appears' to be fundamental to cognition, I still find it hard to believe that it has an elementary place there.

I have always regarded the theory of analogy as being fearfully academic. To me, 'analogy' has always been contrived, a sophisticated mental tool.

Some analogies are better than others, of course.

I'm aware that there is a school of thought that believes that analogy is the core of cognition, that the sequential processes of thinking are impelled by the continuous creation of analogies throughout the various levels of thinking - highly abstract. While it may be a way of thinking, I'm uncertain about its use in beginner learning. I'd need more convincing to use it as a learning tool.

V Yonkers said...

Many of us second language teachers feel that, yes, there is some difference in learning a first and second language. However, the traditional way of teaching second language was not effective because, like learning a first language, vocabulary needs context for it to be understood.

In other words, the meaning of a word with both first and second language learners is dependent on the context in which that word is learned. In first language learners and learners as a second language (those that are learning the language within the second language environment) the meaning of the word and the boundaries of that meaning are learned through experience. A child might call anything round "a ball". However, soon they discover that there are nuances in the language. "A ball" is not an orange or a circle.

Second language learners (learning in context) also have the first language to draw from. So they know that "Fruit" can describe an orange as can the name "orange" as long as they have been exposed to oranges in their own country. However, if that concept is not in their working vocabulary in their first language, then like a child just learning the language, they will learn the meaning of the words in context. I understand what a "resume" is in French from the context of use when I studied in Switzerland. I sometimes misuse it in English as we don't have an equivalent for how it is used in English. I understand the parameters of the word which would be difficult for me to articulate to someone who has not learned it in context. I learned this word much as an infant would learn this word.

The last group of language learners, learners of a language as a foreign language, only have their own understanding of a concept in their own language to work off of. Here, I would agree that they would need to have a working vocabulary based on their understanding of meaning of that word in their own context. In other words, they learn the words that they can translate directly, with the same meaning word for word.

However, learning language this way means a person is limited to only the ideas that have the same cultural meaning in both languages. This limits the language interaction between a native and non-native speaker to culturally shared values. This is why the traditional language teaching methods don't work in preparing language learners to COMMUNICATE in a foreign language.

When I taught English as a second language, we began with language learning strategies (how to learn a language) and non-verbal communication skills. We then taught commonly used phrases and had students generate their own list of vocabulary based on listening. Pronunciation was very important and these are the skills we worked on more than vocabulary building. In fact, my students were vary comfortable communicating with very few words and grammar, but good communication and pronunciation skills.

One group we were sending to the states for training was combined with groups from 6 other countries that had been trained using a more traditional method. While our group "tested" lower, they ended up translating for their fellow students and learning much more English while in the states (many returning quite fluent after 6 months training in the US). Did they have a wide variety of vocabulary and perfect grammar? No. Did they have the ability to make meaning from a situation even if they did not understand specific vocabulary? Yes.

Blogger In Middle-earth said...

Tēnā koe Virginia!

Thanks for this amazing contribution. As usual you enrich the discussion and further my thinking. I am currently taking a course in Te Reo Māori.

For some reason I have never been good at learning a (2nd) language. I am 'reverting' to rote by simply going over and over and listening to the DVD over and over. I have a theory that sooner or later some of all of this will stick :-)

Catchya later

Tips & Tricks In Learning English as Foreign Language said...

that's quite nice way in learning language.