Thursday, 24 April 2014

Anatomy of a Self-Determined Education: an Overview

Most non-homeschooling people find the idea that we don't follow the National Curriculum, or indeed, any curriculum at all, to be incredulous.  To these people, the idea that there are those who actually know what is important and personally relevant to their own lives or circumstances is beyond belief.

The response I hear most often is, "Without using any curriculum or guideline, how do you know what to teach your son?"

The truth is, I don't teach him.  I stopped teaching him about 18 months ago.  My son basically teaches himself.

When I say that my son teaches himself, the only people who know how it works first-hand -- because they have seen the process themselves -- are Tortoise, my mother-in-law, and I.  It is certainly not a case of my piling a stack of textbooks or 'required readings' in front of Tiger and making him work through them -- although I'm sure this is what some people think happens in our homeschool.  For some reason -- maybe schooling has trained it out of most people -- many people find it hard to believe that anyone, let alone a young child, has the passion and motivation to learn widely and deeply without being told to do so by anyone.

I spoke briefly about the process as applied to maths, but I think it will be more clearly demonstrated by sharing how Tiger pursues military history, a topic that is neither examinable nor taught in the National Curriculum, GCSEs, A-levels, or in most universities around the world.  If we were to take the traditional curriculum route, we would have hit a brick wall very quickly because there is absolutely no guidance whatsoever for children who are interested in this topic.  Does it mean that Tiger is wasting his time learning about something that is irrelevant because it's not on any curriculum?  Well, try telling military historians or anyone who's involved in the military industry that their professions are a waste of time, and I'm sure some very interesting conversations will follow.

While a lack of specific guidelines (bad news) may deter some people from pursuing the topic further, Tiger is actually interpreting the situation to be a lack of boundaries (good news) so that he is free to decide how far and wide he wants to go with this. I suspect that his optimissm at learning may be attributed to the fact that he has never attended school and therefore has never had anyone told him where the limitations of learning (which often disguise as the "syllabus") are.

In my attempt to recording Tiger's self-driven education, specifically in the area of military history where the process is most obvious since he is 100% in the driver's seat, I shall be writing a few posts to record my observations.

My role these days has become less of a 'teacher' and more of:
  • an observer - who gets out of Tiger's way to let him teach himself
  • a consultant - who asks questions like "Do you think this book/event/workshop/lecture/article/programme is interesting or useful to what you're learning?"
  • a chauffeur - who takes Tiger where he needs to be for a related event
  • a P.A. - who organises Tiger's diary so that he can attend all the events that he wants to go to
  • a sponsor - who pays for all the books/events/workshops/materials that Tiger says he needs for his study

So, without a syllabus/outline/guideline to follow, what has Tiger covered in the area of military history, and how?

A Broad View
It appears to me that Tiger first gets an overview of the various aspects of military history by reading very broadly and widely.

The broad interest then extends to modern warfare, which Tiger then continues to read about and update himself on the development of battle tactics and weaponry used.

The information that Tiger learned from books leads him to search for more online, and often leads him to documentaries such as:

1.  Battlefield (he watched the entire six series)
2.  20th Century Battlefields (watched all eight episodes)

Leadership and Strategy
Names, places, and strategies (or mistakes) of all the battles are mentioned in the various sources from the "Overview" phase above.  Such mentions inevitably leads Tiger to want to know more about the men behind these decisions that shaped the world.

Tiger's research in this area often involve reading books, articles, and magazines.

He also often plays war games.  As in chess, he often plays different scenarios out on the board by himself before engaging either Tortoise or I in the games.

We started with Risk, but Tiger soon got the hang of the game and quickly moved on to the more complex game of Axis and Allies 1942.  The Axis and Allies board game is stretching Tiger's learning needs in many ways as he has yet to gain a consistent stream of successful campaigns when playing against Tortoise.  The game is set to keep him busy for a while.

In the next few posts, I will write about some of the details that Tiger goes into for his military history study and how I provide support when asked.

Friday, 11 April 2014

In and Out of the Twilight Zone

It's the first week of the spring term school holidays in the UK so Tiger and I have been out and about quite a lot, mainly to attend holiday activities at the museums.

Our encounters in the early part of the week can be summed up in one word: surreal.  To put it simply, our experience this week closely resembles the plot in this particular movie (caution: the movie contains adult language, so it's not suitable for youngsters)

John Taylor Gatto warned about this many years ago.  I didn't actually believe I would experience it in real life, until now.  Maybe we just happened to be hanging out at the wrong places......

Anyhow, sanity returned for the second half of the week as we remained close to home.

The early part of April marks the Qingming Festival where, according to the Chinese tradition, people visit the graves of their ancestors to honour and remember them.

Tortoise's side of the family is English so he has never heard of a dedicated time or any specific rituals associated with visiting graves.  Nonetheless, after I explained the significance and meaning behind this particular Chinese custom, he agrees that a tradition that encourages respect and reverence for the elders should be upheld, so we visited my father-in-law's grave to tidy it up and pay our respects.  What we did was a simple act of tidying up my father-in-law's grave and remembering him, nothing like the elaborate rituals of burning incense and paper offerings that typically take place for the Chinese people, but a full-blown Chinese ritual would have been inappropriate in this case, given that my father-in-law is English and is buried in an English cemetery.

This week our main food at home at a few cold dishes, such as the 'White-cut' Chicken and the Braised Duck, that are associated with the Qingming Festival.  The reason behind eating cold food during at this festival comes from a tragic historical event that took place over 2,500 years ago:

As with many traditional festivals that have been passed down through the generations, the custom of eating cold food actually came from another festival, the Cold Food Festival.  Through the years, the traditions between the two festivals (Cold Food Festival and Qingming Festival) have been amalgamated into one.

Other than the above, we haven't done much else.  Most of the time we were in the garden to make the most of the sun, with Tiger just enjoying being a boy and doing simple boy stuff such as playing with marbles,

reading while eating mango yogurt,

digging and gardening.

This post is linked up to:
  1. Hip Homeschool Hop - 4/8/14
  2. History and Geography Meme #112
  3. Entertaining and Educational - Games and Beading
  4. Collage Friday: It's Good to be Bored
  5. Weekly Wrap-Up: The One with the Movie and the Japanese Food
  6. The Homeschool Mother's Journal (4/12/14)

Friday, 4 April 2014

How to Be a Narcissist

Well, not really!

Although I have had some run-ins with a few narcissists in the past, I don't teach or encourage people to be dysfunctional.  This post is really about the next flowering plant Tiger and I studied together: the narcissus family which consists of the daffodil and the jonquil.

We used pages 549-552 of the Handbook of Nature Study to guide our observations.

The interesting part about nature study is that we learn to closely observe objects that we often take for granted.  For example, prior to studying the narcissus family so closely, we thought there are only different-coloured daffodils.  Little did we know that, at a basic level, the daffodil family consists of:

1) the 'normal' yellow daffodils that we often see -- either the smaller wild one, or the bigger garden-cultivated ones;

2) the mutant daffodil that has two or more layers of petals;

3) the Poet's Narcissus;

4) and the jonquil.  Funnily enough, Tiger and I had never thought of looking for the jonquil until we read about it in the Handbook of Nature Study.  We were very excited when we spotted them in somebody's front garden one day.

As we looked closely at the flowers, we noticed that the ovary of the flowers that had withered in our vase had swollen up to a size that was not observed in those that were left in the garden.

We are not entirely sure why the swelling occured but we think it was caused by self-pollination (since there are not insects in the house to facilitate cross-pollination) which resulted in the maturation of the ovules.  We then made a cross-section cut of the ovary to observe the triangular compartments that contain the rows of ovules.

After that, Tiger pulled the flower apart to look inside.  He discovered some liquid at the base of the style, just above the ovary and wondered whether it was nectar.  Both of us scrapped the liquid with our fingers and tasted it -- it was sweet!  Nectar!

It suddenly occured to me to ask Tiger whether he knew the Greek myth of Narcissus, who gave his name to this family of flowers that we were studying.  He said no.  Gasp!  I distinctly remember Tiger becoming somewhat of an expert on the Greek Myths in Year 1 after we spent a few months studying the topic, but I appreciate his honesty at admitting that he is not entirely sure about the subject.  As far as I'm concerned, it is better to acknowledge our ignorance than to pretend to be an expert when we really don't know something well enough to call ourselves that.  As part of his growing self-awareness, Tiger is learning to know what he doesn't know and be comfortable at acknowledging that to himself and to us.  Not knowing something is not a problem -- all we have to do is to get a quick review by listening to the story followed by watching a clip:

Along the way, I also realised that we had not formally learn the scientific names of the flower parts, so we watched the following clip:

I also printed off the Parts of the Flowers cards set and used it as a learning tool.  Being designed in the Montessori fashion, the cards set is very useful as a set of nomenclature to introduce, isolate, and reinforce learning about the different flower parts.

The set also provides opportunities for matching names to parts, as well as matching names to definitions, all of which reinforces the intended learning.  There is also a small booklet in the set that provides a summary of the reproductive function of the flower.  After reading it, Tiger identified a small error on page 3 of the booklet that needed correcting: where it is written "Pollen from the anther collects on the stamen.", it should be "Pollen from the anther collects on the stigma."

Labeling the flower parts in a diagram summarised everything we learnt in this session:

In the process of learning about the process of pollination and the flower parts that are involved, we found it fascinating to note how similar the process is to human reproduction.

This took us off our flower trail for a little while as we spent some time discussing the similarities and differences between:
  1. the male parts of the flower (stamen) and the male reproductive organs of a man;
  2. the female parts of the flower (pistil or carpel) and the female reproductive organs of a woman;
  3. the time frame of the reproduction processes of a flower and a human; and
  4. the process of fertilisation of a flower and a human.

Who would have thought that a study of flowers would lead to a study of the human reproductive system?  Such connections certainly would not have been made in the school curriculum.

We then decided to dissect the flower to see the various parts for ourselves.  In our effort to be a little less amateurish in our scientific pursuits, we watched the following clip to make sure that we dissected the flower properly:

The dissection video got Tiger so interested that he decided to take down notes on his computer while watching the clip.  It was interesting for me to see Tiger starting to develop the skill of note-taking of his own accord.

Once Tiger was happy with what he has learnt from the clip, we proceeded with taking the flower apart.  We first took apart a 'normal' daffodil flower.

We used a clear sellotape to stick the various parts of the dissected daffodil in Tiger's nature journal:

Dissected parts of a normal daffodil.

The details of the male part (stamen = anther + filament) and female part (pistil or carpel = stigma + style + ovary + ovule) are just too fascinating not to look closely in detail:


We then decided to check whether the 'mutant' daffodil flower is any different, so we repeated the process with the mutant flower:

We were not surprised to observe a number of differences in the mutant flower when compared to the normal flower:
  • there were more petals on the mutant flower;
  • the corona appears to have mutated into an extra layer of petals;
  • we didn't find the male part (stamen) of the flower;
  • the alignment of the ovules were different from that of the normal flower;
  • there were fewer ovules in the mutant flower

Dissected parts of a mutant daffodil.

I had Tiger fill in the worksheets from here based on our exercise.

During dissection, it would have been a perfect to observe the pollen grains and the various flower parts under a microscope.  However, since we do not own one, we resorted to looking up the relevant information in a book that provided us with superb photographs of what we would have seen under a microscope, along with detailed explanation of the subject.

To round up what we've studied so far, we played the matching games using the cards printed off from  here.  It is basically a slightly simplified game as the one we played earlier using the Montessori card set.

This is part of our flower study series known as:

This post is linked up to:
  1. Hip Homeschool Hop - 4/1/14
  2. Entertaining and Educational - West Africa Study
  3. Collage Friday: Como Se Dice?  Dad's in Honduras
  4. Weekly Wrap-Up: The One In Which Spring Sprang... or Is It Sprung?
  5. The Homeschool Mother's Journal (4/5/14)
  6. Science Sunday: Blood Type activity for kids

Wednesday, 2 April 2014

Maths as a Pleasurable and Sociable Pursuit

Can maths ever be a pleasurable and sociable pursuit for a normal young child?  The answer appears to be a positive "yes".

To start with, maths is done slightly unconventionally in our house.  Instead of following a specific curriculum, we tend to work on a certain topic that interest us at any given moment.  As it turns out, we have been spending a fair bit of time on simple arithmetic in the past few months, as I said we would.

The independent aspect of maths learning here takes place when Tiger reads maths-related books on his own, such as the ones pictured below:

He enjoys reading them repeatedly but he doesn't want me to get involved with his reading.  When I saw what can be done with these books, I offered to work through the problems with him but my offer was politely turned down.  Somehow, despite (or maybe, because of) very little involvement on my part, Tiger has found his own pleasure in maths and an inner confidence to put the following notice up outside his room:

Note the happy face on his selfie.

Since he became the self-appointed 'consultant maths guy' in the house, Tiger has been pestering me for "worthy" maths problems.  Sometimes I show him maths puzzles from this book, which he attempts to solve on his own before working collaboratively with me to find different solutions.

At other times, he sets himself the target of working through the problems/puzzles in the following book:

Once again, he doesn't want me to get involved in his work here.   The reason he gives is that he can check the answers at the back of the book, and since the solutions are also provided, he can figure them out by himself.  Fair enough.  Nevertheless, Tiger is happy to share his approach:  he raced through the "Easy" section within an hour and is a quarter of his way into the "Hard" section.  There are some concepts in the "Hard" section that he hasn't come across yet, which he wants to figure them out by himself so he is working on one problem a week -- he reads the question on Monday, thinks it through for the rest of the week, then solves the question on Friday.  When asked why he needs a whole week for one question, his reply is that he wants to "think through all possibilities and get it right" (his words).

Tiger will not have engaged himself in the above activities if he didn't derive some pleasure from solving mathematical problems, mostly on his own but sometimes collaboratively with me.  Recently he has progressed to sharing his mathematical discoveries (mostly applications of numerical patterns) with Tortoise and I by giving us mini lectures in the evenings.  Again, to give lectures as a way of showing what he has learnt is entirely his own idea; Tortoise and I are usually given a few hours' notice to attend a lecture in the evening.  It suits us fine since we are keen to know whether and what Tiger is capable of learning on his own.
When learning to learn is given a higher value than the learning of information, then the educational system will have made a big step in the direction of enabling children to be autonomous students (in the general sense) for life.  By encouraging the exploratory aspects of learning, its excitement and inherent satisfaction can be generalized into an approach to all life experiences; learning then is not associated only with school and the classroom, but becomes a part of living.
-- Joan Freeman, Gifted Children, page 272

Tiger's maths lectures so far have been very interactive and engaging.  He usually starts off with an example of how he applies his method to a problem, then he explains how he arrives at his method, which is followed by a very lively Q&A session where he is often challenged to defend his new-found techniques.   He is thrilled when his discoveries withstand the grueling challenges thrown at them from the floor, yet he is also able to find the grace and courtesy to accept that a few of his conclusions have been wrong due to careless calculation mistakes or a logical oversight.
Gifted children can jump to conclusions by a process of brilliant mental leaps, which are wrong because of lack of information.  In a reassuring 'safe' exploratory classroom, mistakes are part of the process of learning; they are not 'failures'.
-- Joan Freeman, Gifted Children, page 273

I find it interesting to observe that Tiger appears to be more receptive to learning maths in this way rather than in the traditional instructional way.  To my mind, the traditional way is a very quick way to learn something -- someone tells you the 'right' way to do things and you just practise until you master it.  However, that's not how Tiger likes to learn, at least where maths is concerned.  His preference for learning through discovery takes a lot longer, and can sometimes lead him down the wrong path where he has to back track and relearn some of what he thought he knew, but he won't have it any other way.  Luckily for him, being homeschooled gives him the time, space, and support to do just that.  Can you imagine how his approach to learning would be interpreted in the mainstream schools?  "Unteachable" is a word that comes to mind, but that applies only if the teacher has very fixed ideas about what teaching and learning look like.  A child like Tiger may appear to resist formal instructions, but that doesn't mean he lacks the ambition, enthusiasm or capability to master his chosen subject matter.  The challenge, then, is for the adult to get to know the child so well as to be able to provide the right kind of support at the appropriate level.
The teacher of the gifted child is in a particularly important position - not there to demonstrate her superior knowledge or to show what a good actress she is, but to enable children to grope and leap towards understanding.  It is important that the bounds of that understanding are determined by the characteristics of the pupils, not of the teacher or the school.
-- Joan Freeman, Gifted Children, page 273

Besides the in-house lectures, the more obvious social aspect of Tiger's mathematical pursuit comes in the form of maths circle.

We don't attend these very often due to their infrequency, but we enjoy them immensely every time we go.  The maths circle informs us of a number of things:
  • that mathematicians work both alone and collaboratively with others to solve problems;
  • that real maths problems are multi-dimensional and require an ability to connect various topics that are currently taught in segregation;
  • that it's fine to spend a long time on a single problem;
  • that sometimes the solution doesn't come even after a long time of thinking.

At the latest maths circle, Tiger spent the entire time there trying to solve one maths problem, and that was with the help of two maths undergraduate students.  I watched from a safe distance (far enough not to interfere) as the three of them racked their brains for nearly two hours, trying to grapple with that problem using various hypotheses, numerous discussions, and multiple experimentations.  Although he did not solve the problem by the end of that session, Tiger came away feeling exhilarated and asked to attend more of such events.

Between this and a method that produces children who "can't wait to be done with boring maths", I'd be happier to take the former even though it looks nothing like the time-honoured (although not necessarily successful), conventional way of teaching and learning maths.

The following documentary addresses directly the American public, but the issues discussed are just as applicable to the UK and indeed, to anywhere in the world that subscribes to the "standards" of mass schooling:

This post is linked up to:
  1. Hip Homeschool Hop - 4/1/14
  2. Entertaining and Educational - West Africa Study
  3. Collage Friday: Como Se Dice?  Dad's in Honduras
  4. Weekly Wrap-Up: The One In Which Spring Sprang... or Is It Sprung?
  5. The Homeschool Mother's Journal (4/5/14)

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