Linear and non-linear learning
Obligatory pic of horrific looking 19th cen school that should add impact to the post.
In a previous post, I talked about what language learning 2.0 meant to me. In the coming weeks and months I’ll try to elaborate through examples from projects that I’ve been involved with. I begin with a description of a key concept in learning 2.0 - its non-linear nature. I’ll try to outline my thoughts on this before showing how it has affected the design of ChinesePod and SpanishPod in the next post.
Linear learning
Textbooks, curricula, and our educational system itself are the products of a mechanistic past. School knowledge is pre-determined by a centralized authority, and delivered in a linear format to a mass audience. The system is standardized, mass produced, scheduled, etc. In the classroom, the emphasis has been on teaching - it is expected that the learning will simply follow. The act of teaching, then, is seen as transfering information in a controlled sequence, a process that eliminates context - all learners receive the same content in the same format - but fails to accommodate variations in learner needs.
At the individual level, traditional learning is also ‘linear’. Most textbooks stagger information - you can’t proceed to Unit 2 until you’ve learned Unit 1, type of thing. Let me give you an example: English languge textbooks for decades, have begun with present tense (aspect) verbs with an emphasis on the 3rd person. It’s always the first lesson. Thereafter the books invariably proceed with simple past tense, then past continuous, and so on. In fact, however, most learners of English do not ‘acquire’ the earliest items until they reach an advanced stage of fluency. It’s obvious that these sequence of items are presented out of expediency. The question is, however, whose expediency - the teachers’ or the students’? (There is no natural order of language learning that can be described as a linear set of morphemes.)
Non-linear learning
In nature, linear learning doesn’t exist. Children learn their mother tongue through random exposure and make sense of the language by identifying patterns. Our brains are designed to work/learn this way, but it is a subjective process because each individual experiences distinct social and psychological phenomena.
If there is a metpaphor for learning in the natural environment it may be the network rather than the line: our neural networks forms the basis of memory/knowledge and even the brain itself. Which is interesting because all networks come down to two elements: links and nodes. (This is as true for the internet as it is for the human brain.)
The internet is changing the way we learn and that’s because of its network qualities. I believe we’ve moved beyond the Mechanical Age, and beyond the Information Age, to the Age of Networks, and therefore to the Age of Networked Learning. Networks are every where and, as Jay Cross persuasively argues, they are changing everything, including how we learn. The last time that happened we had the Enlightenment on our hands.
In the next post I’ll try to show how we’ve applied these insights in the real life design of our learning programs. In the meantime, feel free!
Ken Carroll
December 13th, 2007 at 8:11 am
Hi, Ken —
I enjoyed our brief conversation on the topic this last Monday. In addition to my own language-learning experiences inside and outside the classroom, I’ve a bit of secondhand experience with the subject, as my mother homeschooled my younger brother after seeing all the fun I was having in the Philadelphia public school system. She was very heavily influenced by John Taylor Gatto, whose work isn’t really so much related to theories of education as it is to the social destruction wrought by institutionalized compulsory education, and by E.D. Hirsch’s “Core Knowledge” ideas and the “What Your [N]th-Grader Needs to Know” books, which relate somewhat to the ChinesePod model in that they posit a body of knowledge necessary for “cultural literacy” at various levels of development, but argue against prescribing any single way of acquiring it.
Language acquisition among children is a fascinating field of study, and one I wish I knew more about, but Mark Rosenfelder over at Zompist.com has an interesting piece on language acquisition as it relates to immigration debates — though I think it’s worth a look for anyone interested in the topic, at least if they’re as ignorant about it as I am.
December 13th, 2007 at 8:58 am
Are those really dichotomic concepts?
When you visit a large city there is no way a “linear” approach can guide you to every place that might be possibly interesting. What do you want to see? A geeky little museum? A second-hand music shop? An alternative dance club? The medival fassades in the older parts of the city? The pubs serving freshly brewed local beer?
However, when you first enter the city you will be lost and probably miss the important stuff with a non-linear approach because you do not even know what is there and where to find it. Or worse: You run into dangerous areals late at night.
A good guided tour (appealing to your taste) that takes you to the vantage points and introduces you to the specialities of the city + tells you the do’s and don’t is gold. And the guided tour is of course a more or less “linear” approach.
After the tour you can explore the city according to your own interests, hobbies, and demands.
Oh and there might even be short linear phases coming up later, e.g. when you decide to explore the insect life of the city and do not know where to start.
The same is valid for other forms of knowledge acquisition:
When entering a new domain, nothing beats a good textbook that gives a structured (=linear) overview of the field, provides you with frameworks and maps, and warns you of the pitfalls. From there on a non-linear course is the way to go.
December 13th, 2007 at 3:56 pm
There are plenty of subjects that cannot be tackled with a non-linear approach, the most obvious being mathematics. There may be a variety of fields within maths, but without a rigourous attitude towards the basic principles, you will never master the subject. Indeed, most fields of mathematics can only be understood fully by starting from first principles. Maths will never be a subject where you can pick and choose what you want to learn and when.
December 15th, 2007 at 1:22 am
Brendan,
Language acquisition (though I think the term ‘acquisition’ is starting to look suspect) in kids is definitely a fascinating field and one I used to stay in touch with. Having read the Rosenfelder link, I think it’s time to revisit the topic.
Henning,
I just learned a new word - dichotomic! In fact, the two things are not mutually exclusive and your metaphor for visiting a city is entirely valid in certain contexts. The issue for me is control. Textbooks don’t act as brief intros to the cities of learning in most cases. They are the cities! Too often they are seen as the be-all and end-all of the learning. Far too many school kids just stick to the script and fail to discover the rest. This is my point.
Secondly, you and I probably have different tastes, preferences, needs, and learning styles. Who says there is to be only one guidebook to a vast city? Too often that ‘one-size-fits-none’ approach kills the interest of the learners, im my view. Fundamentally it robs the learner of choice and without some element of choice, I beleive learners will feel a lesser degree of commitment to the learning.
Natalie,
I disagree entirely. If your point was true then there would be only one way to learn math. Is there only one way to approach the basic principles of math? What are those principles and what is that one, true method? Has everyone in the world who learned math successfully taken the same route? Not at all, some of the greatest mathematician’s have been total mavericks who approached the subject in an entirely sujective and original way. Notice too that he greatest thinkers in these fields tend to work independently - not by following a script. My whole point about learnign is that the brain is designed to enable a wholly subjective approach to any subject as long as you have the motivation and the choice to choose, control, and direct the resources with some autonomy.
Ken Carroll
December 17th, 2007 at 7:47 pm
Ken,
A few semesters ago I helped create a Spanish language course for our nursing program here at UT Austin. It was amazing to see the different needs of the learners. Some worked with elderly, others with children. Some needed Spanish to talk to the parents of their patients, others worked in clinics, while some made home visits, etc. In the end we were able to give the students a lot of flexibility in how the class was structured. This was only possible by not forcing the issue of following a text book and a traditional syllabus. So I totally relate to your comments about the non-linear nature of learning.
On the other hand, I usually try to go cautious when comparing child L1 acquisition with adult L2. Even if we don’t totally accept brain lateralization, etc., there are still significant differences between how children and adults learn.
BTW, I’ll be in Shanghai in a couple of weeks. I already have an appointment to get with JP at SpanishPod, and I’ve also been talking with Steve Williams (I believe those are scheduled for Jan. 2). If you are in town, it would be a pleasure to talk shop with you too.
Orlando
December 18th, 2007 at 2:51 am
Orlando,
Fantastic. I’ll make time for it. I look forward to meeting.
Ken
January 1st, 2008 at 5:09 am
I seem to find people who can learn under their own steam and people who can’t (a generalisation).
People who can are self-aware learners, they understand their own strengths and weaknesses and have spent sometime thinking about the learning process itself, basically they have aquired learning skills. Approaching a new learning problem they map previous experiances in learning to it and think about any unique issues. When they come to learn something they are looking for content, examples opportunities to practice and feedback etc.
People who can’t are looking for a course, a system, a map to an end point, a series of steps to take, a good teacher (nice, but how do you know how good your teacher is until you have spent sometime with them). If they fail they will blaim the course, system, map, teacher, etc.
Motivation is important but a motivated person may not know how to learn.
Depressingly even in the West, a lot of the people who know how to learn don’t seem to have aquired this ability at school, they aquired it afterwards. Surely by the time the majority of people leave school they should know how to learn (even if they choose not to).
This learning life-skill should be a major focus of schooling.
January 2nd, 2008 at 3:38 am
Ken, I find myself at odds with some of the things you are saying here. Perhaps it is just a question of terms; we mean the same thing but say it in different ways. At times it may be because I am, in my own subjective way, hearing things you probably never meant to say. But now, belatedly, let me take a swing at what you had to say.
First, I get the feeling that you are saying that order and linear organization are the same thing. If so, I see that as a mistake. I find it hard to read, or to learn without some kind of apparent order (the first place I look in a book is the table of contents). Sometimes the order is a smoky link, sometimes it is an iron chain. But in looking at something we time-bound, social beings naturally try to discern an order or a meaning to things. As I see it the true opposite of order is random chance and I am sure that very few people wish to let wild chance alone govern what they learn.
Secondly, I feel the very best examples of learning opportunities are also wonderful examples of supremely ordered experiences or, shall we say, linear thinking (where a mind takes us in steps from one experience to the next). Literature and film follow a linear order in the sense that if you were to take out all the pages in a book and throw them in the air, by chance the result that lands on the table would almost certainly be much less satisfying than the original.
I see linearity as a journey. I see linearity as an order. And I see linearity as progression. I am entranced by each of these and how to use these to further learning. I hear nothing of these wondrous things in your musings and it “bugs” me because it is almost like you are trying to pull a Wizard of Oz and claim that what we are experiencing with web 2.0 is akin to magic when all along it is nothing but the wizard behind a new “networking” machine.
The opposite of linear order is chaos, chance and disorder and I don’t think you are serving any of these things up with Chinese-pod.
January 2nd, 2008 at 12:17 pm
@micheal I am sure Ken has his own answer, but here is my take. I think there may just be a misunderstanding of terms but just in case.
I don’t think Ken is advocating total chaos and neither is web 2.0. I have seen an overly linear approach in education and it sucks, although of course there is always some level of progression (even if it is just that we will all age) otherwise how can you say you have learnt something.
If I wish to give directions to someone to visit me I can send them detailed instructions for every road and turning and distance they need to take. Great, unless they happen to make a single mistake or the route is changed by a diversion or something.
I can take a more holistic approach and start along the lines of “head for the West of the city first (there will be signs) then …. “. This is more robust
There may be variability in how people perform but most should be able to use the simple instructions to make their own way.
Finally I can recognise that technology is changing everything and knowing they have GPS in their car just send them my postcode and house number. Even if they want to internalise the information rather than just blindly follow the GPS I know they can go onto to Google maps to do this (they can even use the arial photos there to work out the quickest shortcut to pop out to a local shop for something whilst they are staying with me).
All of the above describe a journey and course of events that precede from start to finish (yes in some kind of linear fashion).
To my mind Ken is taking a shot at the education systems that are firmly embedded in example one, an approach that will work, so long as the students behave as predicted, so long as they think the same way that the person who writes down the instructions does and so long as the infrastructure does not change so that what I write today will still serve them well in five years time.
There is another point I would like to make, a more nebulous one, but yes there is a certain element of chaos, however in some chaotic systems you can still make assertions that something will happen depending on the probability of its occurrance and the size of the sample. In the traditional classroom I will interact with X number of fellow students, on the Web I can potentially connect with many more. I cannot gaurantee quality interaction either way but with the right tools I know which one my money is on. The same applies to the people that teach me etc. etc.
There are dangers, and in my poor attempt at an example they are probably best represented by the GPS system alone (in which the only only learning is to learn how to operate the equipment).
January 2nd, 2008 at 7:26 pm
Chris,
There is something new happening. Of I that I have no doubt. But can it be organized under the general rubric of non-linear? Of that I am profoundly sceptical.
I think Ken is an artist of sorts and that what he (and others at Praxis) is accomplishing is an art form. His artistry partakes of many disciplines but again I am profoundly sceptical that the “deep” organizing principle behind the Praxis educational experience is “non-linear” (whatever that means).
January 3rd, 2008 at 12:50 pm
Michael,
I am not an educationalist, but learner who feels I should spend more time looking at the learning process in order to learn better.
After a quick run through Google and the various materials I have gathered Ken’s use of “non-linear” seems to be entirely appropriate in this context (the earliest reference I found to non-linear language learning via the Web dates back to 1998). It seems that there is a strong precedent of the use of non-linear in Education to mean something like “not a single prescribed linear path” but rather a choice of many paths (which is not the same as chaos). This pleases me no end as that is exactly what I assumed and I was getting a little worried there for a minute.
As for the “deep” underlying organizing principle behind Praxis well I assume as a commercial organisation that is to make money (how deep do we want to go?). All I can say for sure is that I observed the original newbie lessons on Chinesepod (I know that is just a part of Praxis) originally start building in a linear, progressive manner and then delibrately switch to something that was much errr… is it safe to say “less linear” approach. There was also disscussion about this in the blogs and forum. I think we can therefore credit Praxis with some deliberate non-linear thinking.
So I guess for non-linear and its meaning we just need to follow and read some of those Google links and in this context it just means what most people think it means.
January 5th, 2008 at 12:33 pm
I’m sure my comment will sound rather uneducated and in layman’s terms compared to the others’ but I’ll have a go anyway. I would just like to say I know what you’re talking about Ken, with Chinesepod I have learned more in months than I ever have in 8 years of manadtory school French lessons! Keep up the excellent work.
January 11th, 2008 at 5:57 am
Hi Ken,
I absolutely agree with you, but it strikes me that the success of ChinesePod depends not only on the structure of the lessons, but on the personal chemistry and charisma of you and Jenny Zhu. I’m a Newbie, just beginning to dip my toes into the Elementary level, and the few lessons I’ve listened to that don’t feature you and Jenny have lacked the spark that keeps me attentive otherwise.
Which leads me to that old chestnut: it’s not the method, the materials, the content—it’s the teacher. As a teacher myself, I would put it this way: if the teacher is inspired, he or she has a chance to inspire students. An inspired lecturer can thrill an audience of 300; an uninspired constructivist can kill the best designed lesson in a class of 15. Inspiration is the key—everything else is secondary.
Thanks so much for ChinesePod, which keeps me inspired to continue improving my Chinese!
Eric
January 14th, 2008 at 11:02 pm
Great comments here. I’ll have to get back to Michael. He has a habit of asking questions that can’t be answered easily - and long may he contiue at that!
I’ve been off the scene for a while but I hope to get back into the big debate soon.
Ken Carroll
January 15th, 2008 at 7:40 am
Ken, while ChinesePod seems pretty good, I am not sure it is that revolutionary, or optimal, as you seem to think. I think it suffers from the same problem many other new-fanled methos of self-study suffer from. namely that it is too non-linear. That’s right, I said non-linear. But I mean it in a slightly different sense. The point is simply that the more linearly you progress from unit to unit, the easier it is to keep studying. In a classroom setting, it makes sense to have a textbook, tapes, quizes, conversations etc because you always have someone telling you what to do. Now in self-study, the biggest enemy is always, always your inherent lazyness. With enough motivation, you could learn any language with aid of just a dictionary, they are usually filled with phrases, rudimentary grammar and of course lots of words. The problem is that you don’t know where to start, so you probably give up before long. If instead you always have someone telling you what to do next, staying motivated (the one prerequisite for success) is so much easier. IF you supply the user with, say, five different ways to study and reinforce what they learnt, they will just get lost if they have to navigate between them on their own.
On the other hand, while I am personally very interested in theoretical grammar, I don’t think that teaching grammar is conducive to learning a language, other than indirectly. As long as you consciously decline and conjugate in your head before opening you mouth, you don’t really speak the language. The actual task you need to undertake is to reinforce patterns of speach, subconsciously associate certain tempora and grammatical persons with certain endings etc. But going by way of consciously learning and understanding (the simplified rules that we call) the grammar of the language is taking a long and completely unnecessary detour. Just look at children.
January 15th, 2008 at 7:53 am
Gustaf,
I didn’t make the claim that ChinesePod is either revolutionary or optimal. Not sure where that came from.
I think we’ve been all trained to ‘always have someone telling us what to do’, but I most certainly don’t think it has to be like that. Being told what to do isn’t very motivating for many people. But even more importantly, learner autonomy isn’t a nicety - we all have to become independent, autonomous learners in a future where there are terabytes of the data coming at us daily. We simply don’t have the luxury of waiting for the authorities somehwere to map out what we should be learning and then to push us into doing so. Those days are coming to and end.
Ken Carroll
January 15th, 2008 at 8:15 am
Ah, I didn’t mean that you should be told what to do, rather how to do it. You have probably heard of Pimsleur and simlar courses on tape. While perhaps a bit boring at times, they have the very important advantage of not giving the learner an excuse to linger or get lost on the way, beacause you there is no room for choices at all. It is like weight training, the hard part is not lifting the weights, but being motivated, overcoming the psychological barriers. If you always know what comes next, it is much easier to keep going. Some people with particularly low motivation use personal trainers that tell them what to do.
Now I am not saying that the flow of the course should be predetermined, or not take the individual learner into account, I am just saying that you shouldn’t be presented with too many choices at each point. Ideally it should be like having a personal trainer, or a personal language coach. “So now that we have read this text, let’s practice writing the characters”. The user will otherwise be at loss, he will not be sure of how much time to put into each particular exercise, in which order to do them etc. This state of mind is very tiring, and will eventually lead to him quitting the course.
By the way, I don’t think that the vast majority of people are even interested in becoming autonomous, and I am not sure how a society of millions of creative bohemians would work. Certainly all societies to date have been based on a very large base of ordinary workers that don’t ask too many questions. But be that as it may, the question here only concerns how to produce an effective learning tool.
January 15th, 2008 at 8:39 am
Gustaf,
I see where you’re coming from but you’re kind of putting words into my mouth, as it were. I’m not aksing that we all become bohemians, or anything else. I’m suggesting that we have to become more autonomous, given the future that awaits us.
I totally agree that too much choice is overwhelming. That’s why w’ve tried to create learning ecosystems with ChinesePod/SpanishPod. These are designed to give guidance and context but also with as much freedom and choice to explore the language as possible - learning on your terms. The community, the practitioners, and the experience of others all provide guidance and motivation for the learners. I believe this works quite well over there and I beleive we will see more of this type of approach in the future.
Ken Carroll
January 17th, 2008 at 3:42 pm
To me, learning and teaching English (to my mainly Mexican ESL 4th graders) was somewhat easier than learning Hangeul (Korean). Many of the phonemes needed breif practice because it was a Roman alphabet, the spelling rules took 10 minutes, and we were able to review the grammar book 3 times before the year was over. I did not take the book approach of teaching all of the verbs first, then nouns, etc. For me personally, I did not see a system that way and it confused me. So I taught lesson one of each chapter (verbs, nouns, adj., etc) within the week in present I. Then we went back and discussed the simple forms and variations that could happen to each. The third time around we did the entire chapter. I got this method off Nihouse and I don’t know if to call it linear or circular but it made sense because I could see structure right away. Meaning had to be derived from reading (2 hour block) and practice was in the form of writing (1 hour block).
On the other hand, the Asian languages started rough. There was no way I could discern anything but the last word that they spoke and that was hard to commit to memory. Nothing like the Romance languages. I had to start with phonemes and learning how to “read.” If I could relate the sounds to a system than felt better situated. I don’t watch the lesson in sequential order, but according to the needs of the day. Overall, you have to put some work in so that a language becomes acquired and usuable,
February 26th, 2008 at 5:34 pm
I have recently proposed a non-linear model of language learning at the Japan Association of Language Teachers Conference. My paper paper is available at http://docs.google.com/Doc?id=df8mx5rb_78g755hr
February 27th, 2008 at 12:15 am
Bill,
I just read your paper and it’s excellent.I particularly liked the points about the Emphasis on Individual Learning Processes, and Teachers as Resources and Models. Your observations certainly square with my experience and they could apply in most any learning scenario. I would also be tempted to add some thoughts regarding the use of technology, and particularly the principles behind connectivism. (Since so much of our future learning will migrate to the web, I believe we need a pedagogy that tackles it.) My second instinct here is to ask how you apply this stuff. For me, it’s about embedding what we learn into the ecosystem, Community of Practice, or ‘learnscapes, whichever term you prefer.
March 11th, 2008 at 4:57 pm
I couldn’t understand some parts of this article Linear and non-linear learning, but I guess I just need to check some more resources regarding this, because it sounds interesting.
July 27th, 2008 at 9:11 am
Thanks a lot Carroll: I m an English teacher who positively believes in the non linear approach. I ve been a chaos theory researcher and so far I ve been applying non linear techs to facilitate the learning of Enlglish. Guess what ! after a five months English training period my students learn more , faster wihtin a non-squared and non book based learning than those of other teachers.For exmple, I may start a beginners class by helping students to learn the days of the week and maybe ,I may be starting talking about the weather and from that learn the time and from there to another kind of related topic and so on.