4-Digit Multiplication -- the proof is in the Montessori pudding!

Rocky is just now 8, and though she should be in the 2nd grade (year 3) if she went to school, she's in the 3rd grade (Year 4) Shillermath book.

Rocky, the (not always) model student!

Some of you may be thinking: "Oh, that's all right for you!  She obviously has the genes/the talent/the instruction/(insert explanation here", but let me tell you, this is the most free-wheeling, doll-playing, coloring-book-addicted child I've ever seen.

Yet, somehow, she picks things up.

(I've just deleted the phrase "just by listening", because I'm not sure she even does it by listening -- when we do our read-alouds, she can rarely muster up a decent narration beyond "There was this guy ... and he rode his chariot to this other guy ... and he shot him in the head or something" -- Rocky's version of 2 Kings 9 where Jehu shoots Joram in the back with an arrow. Kudos to her -- there WERE two guys, and there WAS a chariot, and someone did some shooting.)

Maybe she picks things up because she's a thinker behind all that cloud-cuckoo-land exterior.  I mean, usually, she's the kind of child who does things like choosing the alias "Yellow Rocket Ship Plane" when the other kids chose Phoenix, Killer, and Timmy.

Last year, though, she surprised me by saying, "Your grandma must have been pretty young when she had Grandma."  And I said, "Why do you say that?" She replied, "Because Great-Grandma has just had her 90th birthday, and Grandma is going to be 70, so she must have been 20 when she had her."

At that time, her maths books were still only doing addition up to 5. Yet, we were working with the decimal materials like 1000s cubes, 100s "flats", etc, so I'm guessing she just had a really good visual picture of what it means to subtract one number from another regardless the place-number it is.

Anyway, two days ago I introduced simple multiplication to her a la Lesson 3 of Shillermath's Book 3.  We had out the 1000s cubes and the 100s "flats" and the 10s "bars" and unit cubes. We practised multiplying 3 of the 1000s cubes and got 3000. We practised 4 of the 10s bars twice, and got 8 10s bars, or 80.

Then today, she did this:

4-digit multiplication with exchange

I'm flabbergasted. I'm astounded.  And it's not Rocky so much I'm amazed by (though maybe I should be), it's just this Montessori-based maths curriculum that teaches everything SOOOO carefully, SOOOO visually/aurally/kinesthetically, and SOOOO well!

So if anyone asks me what's the best purchase I've ever made in all my 8+-years of home educating, Shillermath would be at the top of my list. (Ambleside Online is also brilliant, but I haven't had to purchase it!)

I wish Mr Shiller had continued his math adventure beyond primary school (there are rumors that middle- and high-school version are on the cards), but that discussion will lead me into a review of Life of Fred, so I will just sign off instead.

In the meantime, you might want to look at my review from a few years ago when the curriculum was still new to us.  It gives a bit more detail, and compares it to other hands-on math options.

AMAZING resource -- Montessori printables -- a $3000 value!

If you want a great resource for your Montessori school, homeschool, co-op, or even just for your primary-school aged kids in general, then this is it.  Hundreds and hundreds of .pdf printables at your fingertips.

Bought separately, you'd spend over $3000, but the CD-ROM is available for just under $600.  Once purchased, you can continue to purchase future files that she makes for 50% off. Visit the Montessori for Everyone website.

I tended to use the 3-part cards.  These are brightly coloured pictures, words, and a third card with pictures and words together.  Once you print them out on card and laminate them, then your child can practice matching the pictures and the words together, and then check them with the "control" card to make sure the answers are correct.

That makes these items self-correcting, which is great for a child's learning and independence.

BTW, I've had to withdraw the offer to give my copy away free: it infringed Lori's T&C's.

Why do (most) boys hate writing?

One of the most common complaints I hear from parents about boys -- whether they're home educated or at schools -- is that they don't want to write anything.

Why do (most) boys hate to write so much?

The short answer is that boys develop later in that area of the brain. In fact, research has shown than girls' brains develop in the region of language and fine motor skills about six years earlier than boys!  On the flip side, boys develop their spatial memory areas about four years earlier than girls.

Unfortunately, our expectations as educators are geared more toward writing than spatial memory, and so the boys get labeled or pushed too hard too early.

 Is it any wonder they can develop a hang-up about writing?

Logic states, therefore, that boys should be allowed to develop more slowly in this area, and in the meantime, be provided with opportunities and strategies that can help them achieve as writers at their level!

Here are a few ideas based on experience with my own boys, aged 3 and 8:

• Use the computer.  Because boys develop earlier in their spatial skills than their literacy skills, they might find it easier to write using a keyboard than trying to form letters with a pencil.  Further, writing on a word processor is less permanent and easier to correct, so boys needn't be too worried about mistakes (and who hasn't had to deal with a tantrum when something didn't work out just so??!!).  An ICT educator recently told me that the schools in her district were going to explore this link in a bid to improve boys' literacy, so it's an idea that seems to be gathering some momentum.
• Handwriting practice.  "Killer" has rejected most handwriting programmes, some with violence and/or chucking books into the rubbish bin.  Getty-Dubay italic book A was thrown across the room.  Draw, Write, Now has the right idea -- drawing pictures and writing a two sentence caption underneath.  Unfortunately, that was still too many words as far as Killer was concerned, so I got many well-drawn pictures and no writing.  Our success story has been Write from the Start by Teodorescu -- a handwriting programme that's more about connecting dots, drawing circles around triangles, and practising curves.  Killer and Timmy both get their respective books out in their spare time.  You might ask if a handwriting programme is necessary at all, and I would probably say it isn't; however, the Teodorescu book allows us to tick that box without ticking each other off.
• Let him dictate. We're eclectic homeschoolers who err on the side of Charlotte Mason method, so I check on the children's comprehension of our reading materials by getting them to "narrate", or tell back, what I've just read.  This is primarily oral narration from the age of 7-11, or until a child is fluent enough in writing that his/her skills in handwriting won't disadvantage the thoughts making it to the page.  Phoenix, for example, is capable of writing her own narration.  Killer, on the other hand, will dictate his narration to me, which allows me to save some of his work on paper without coming to blows about the way in which that work gets processed.
• Copywork. This is another hallmark of the Charlotte Mason method.  Some might argue it's an unnecessary battle, but I like how it helps a child learn well-written sentences, good vocabulary, and complicated spelling, in a natural way.  Any Charlotte Mason book or website will tell you more about it, but here's an example.  My advice when it comes to boys? Keep it short.  Keep it large.  Offer a reward such as some computer time when he completes this along with three or four other topics, or break up the writing skills with a game, some dancing, some outdoor play.  

• Use movable alphabets.  These are individual letters cut out of thick card, usually with the vowels in blue and the consonants in red.  They're excellent for training young children to read, but also useful for the reluctant boy to practise spelling and writing without having to use fine motor skills which he may find difficult still.  Here is an article about using movable alphabets, and also a very good Montessori book about teaching reading and writing which includes more detail and exercises for the younger child.
• Diagram, or draw first.  If you think about it, this is common sense.  In their shoes, you would want to draw something with a great deal of detail and action and excitement, everything happening at once, rather than write a word-by-word, sentence-by-sentence explanation.  Think map rather than a list of directions and you may see what I mean. 
• Read Michael Gurian's book "The Mind of Boys" for more excellent tips and the science behind them.

The bottom line is that we're wrong when we think boys aren't that good at writing.  They certainly *can* be good at writing, but maybe not when we want them to be.   It's a matter of being patient with them.  Remember, Charlotte Mason, the Victorian educator and theorist, didn't have her children write their narrations till they were at least 11.  

Perhaps we shouldn't either.

Teaching with Thomas the Tank Engine

He's only a little blue wooden train with a number 1 on his side and a fairly jolly looking expression on his front, but Thomas the Tank Engine seems to be one of the few toys amongst our mountain of plastic that is a perennial favourite.  I mean, my kids really do play for hours with their trains.

Did I say "play"?  I meant to say "work", because that's what a child's focussed attention is with any object or in any activity.  It's their work, and should be respected as such.  In fact, if you look at this article here about child development and Montessori theory, you will see a list of bullet points about learning through play, all of which a good session with Thomas and friends will satisfy.

Let's take for example the second point in the list, "creativity expanded using problem-solving skills".  If you've ever tried to make anything more than a simple figure-8 or circular track with the Thomas railway, then you know that this activity is all about problem-solving skills.  Just how can I get one more bridge into the scheme, how can I make this bit of track match up to that bit of track, and how can I make that shed hook up when I've run out of little pieces with two sticky-out ends?

Then there's the point about building muscle control and strength.  This article here lists how delicate an operation it is to push along an engine and its trucks without losing the back cars, but even the youngest of children will enjoy passing the tactile pieces from one hand to another, turning their wheels, tapping them (bashing them) against the floor.

Rocky and Killer pose with their collection
(notice how they've grouped all the square faces together)

Perhaps most interesting of all is the connection to Thomas and a child's emotional education.  Countless articles are written about children on the autistic spectrum and how Thomas makes an important developmental connection for them.  In conjunction with watching the short little films, an autistic child benefits from a relationship with Thomas, ranging from language skills to facial expressions.  A very helpful article about this can be found here.

I can personally vouch for the way that Thomas the Tank Engine served a purpose in emotional intelligence for Killer when he was about 2.  He's not on the autistic spectrum at all, but we both derived great pleasure from his learning to imitate the different facial expressions used by the engines on the show: angry, happy, surprised, snooty, sad.

I'd like to hear from other readers about how they've perhaps used Thomas or other wooden trains in a "work" capacity.  We have done all kinds of things mathematical, like sorting and grouping.  I made copies of all the engines with numbers, from 1 to 12, and pasted them into a file to be part of a "math mini office", and I also trawled old Thomas magazines to cut and paste pictures from A to Z as a sort of alphabet primer (hint: go for a kite for "k" and a queen for "q").

Above all these suggestions, however, are those which emphasize the enjoyable, the sociable, the imaginative work which is more than child's play -- it's just plain purposeful fun!

Different Homeschooling Methods

If you’re new to homeschooling, then sooner or later you’re going to want to explore the whole issue of different methods to try.

Here’s a short explanation of the main methods in a nutshell.

First, there’s the school-at-home option.  This is where you try to imitate the kind of schooling you probably grew up with: desk work, worksheets, workbooks, perhaps computer-based lessons, schedules, grades.  Some people try to cobble together a version of this with different curricula, while others might opt to purchase a comprehensive curriculum such as Sonlight or the Bob Jones University Press materials.  Pros: it’s all done for you.  Cons: it’s expensive, and sometimes, it’s difficult to pinpoint the right level for your child.

At the opposite end of the spectrum is the un-schooling method.  Perhaps it would be better labelled as the child-led method since un-schooling smacks of doing nothing.  Most educators and parents come to realise that children are naturally curious and cannot help but want to learn things (think about how keen a toddler is to learn to walk or talk or feed himself).  This method is about trusting children to do just that. 

If you have withdrawn a child from school, then un-schooling can be a way of de-schooling a child; that is, letting a child regain confidence or self-esteem by dropping anything that seems related to school, especially if the child has had a bad experience.

John Holt is sort of the “father” of un-schooling (see How Children Learn (Classics in Child Development)). 

Pros: child-led, spontaneous, everything comes under the learning umbrella. 

Cons: justifying the method to others, worrying about “holes” in your child’s education, pin-pointing achievement.

In between these two methods are a lot of other options.  In no particular order, they are:

Unit Studies: basically, this is an inter-disciplinary, topic-based approach.  You pick something like bats, borrow a lot of books from the library, find multi-media resources on the web, go to some places of relevance to serve as field trips, and then choose some way to document your work: maybe a journal, a notebook, a lapbook (see http://www.squidoo.com/lapbooking-vs-notebooking for an explanation of lapbooking v. notebooking).  

Here’s a link about how to plan a unit study: http://homeschooling.about.com/cs/unitstudies/ht/unitstudy.htm).  Konos is an example of a character-based unit study curriculum.  The picture to the right comes from the unit on Honour, when we studied Japan.

Pros: comprehensive, multi-disciplinary; flexible to teach wide age range. 

Cons: often there’s lots of preparation, and it’s sometimes difficult to juggle the wide age range.

Charlotte Mason method: Charlotte Mason was an educator living in England during Victorian times.  She was a pioneer in child-led learning which was a new concept back then.  Her method is characterized by reading “living” books – that is, written by one author who loves the subject rather than dumbed-down readers or textbooks; by nature study; short, sharp lessons; and narrating, or telling back, what’s been read as a way of “testing” what the child has learned.  Charlotte Mason described education as “an atmosphere, a discipline, a life,” showing how wonderfully it meshes with the homeschooling environment.

Catherine Levison's book is a brilliant and practical summary.
 







Karen Andreola's website http://www.charlottemason.com/ and books are also recommended. You can find a free, ready-made curriculum from Ambleside On-line to help guide you.

Pros: living books are wonderful; can be an inexpensive option if you use the library a lot; emphasises fresh air and observation of nature; can be light on writing if you need it to be.  

Cons: not every child is good at listening to stories read aloud; not every child is that keen on nature; some children are actually more tired when changing quickly from lesson to lesson than if they’re left alone to work and concentrate for long periods of time.

Montessori method: Maria Montessori was another educator from the turn of the 20^th century, this time in Italy.  She worked with deprived children and discovered many amazing, ground-breaking observations about the way that children learned.  Her books are still fascinating, and most beginners do well to read the The Absorbent Mind.  Other good beginning books are Montessori Read and Write, Montessori Play and Learn, and Elizabeth Hainstock’s Teaching Montessori in the Home.  One word of caution with this method: there are thousands of dollars to be spent on proprietary Montessori equipment, and there are hours of angst to be had in trying to imitate a trained Montessori directress.  Don’t panic.  You can achieve many of the same aims by using basic household items – just have a browse for Montessori blogs like those listed in my “other good blogs” section for more details.

Pros: very hands-on; encourages concentration and self-discovery; advises order and neatness in the whole home environment.  

Cons: can be very expensive if you try to buy the proper equipment; can be very time-consuming to prepare all the laminated cards; probably needs more space than other methods; may seem overwhelming if the parent tries to imitate a Montessori school in the home.

Classical education: based on the education systems of ancient civilizations, and mirroring children’s natural ways of learning, classical education breaks down learning into three distinct stages, or Trivium: the grammar stage, where children absorb facts and exercise their memory;  the logic stage of junior high, which is characterized by questioning and arguing; and the rhetoric stage of high school when the child focuses on explanation, persuasion, and debate.

 Susan Wise Bauer’s book, The Well-Educated Mind, is probably the best introduction on the topic.

Pros:  well-ordered and disciplined; prepares children well for further education;
highly enjoyable for children who like to read or who love history.  

Cons: can be teacher intensive; requires daily discipline and consistency; may not
be of interest to a child who’s not keen on history or reading a lot.

Finally, there’s the eclectic method.  This is the one that picks a bit from one method and mixes it with a bit from another, to make one’s own, unique brand of homeschooling.  It’s the one that comes together depending on priorities, personnel, and resources (such as money and space), and offers the most flexibility when it comes to the ebb and flow of children’s maturity and interests.

Pros: can pick and choose the best on offer from any method; flexible; adaptable.  

Cons: easy to lose one’s way in the jungle of options out there.

I hope you found these definitions helpful.  If you have any questions about them, or want to know further resources, then drop me a comment below.

Homeschooling 101 -- Three Steps for the Start

Are you thinking about homeschooling?  Or, are you just starting out?

Either way, you're probably full of questions right now: what curriculum should I use? what kind of schedule should I have? what equipment do I need? how do I convince my friends/family that it's a good idea? should I go see a psychiatrist?

As a homeschooling veteran of seven years, I have three simple pieces of advice for newbies: first, don't rush into anything, especially not curriculum purchases.  Mistakes on this front can be expensive, and it's also likely you'll change your mind a lot as you get more informed and get to know your children better.  If you're desperate to get started, then just use the library for a while.

Second, read anything you can get your hands on with regard to homeschooling.  Terrie Lynn Bittner's book, "Homeschooling: Take a Deep Breath -- You Can Do This", has a lot to recommend for itself as a good beginner's book.  Its reviews on Amazon are outstanding.

But don't just limit yourself to books.  Blogs and Yahoo! groups (like Homeschooling Boys) offer a wealth of up-to-date, hands-on information.  Some of my favourites are listed in the sidebar to the right.

Finally, sit down with a pencil and paper so that you can brainstorm what your aim is for homeschooling your children.  This step may seem a bit underwhelming, but I believe it's one of the most important stages in a homeschooling journey.  Times will come when learning at home gets a bit bumpy, or diversions arise, or distractions appear, and then you'll be glad to have a sort of philosophical satnav to keep you on course.

Some possible aims are: providing an atmosphere without bullying, focusing on character-building traits, strengthening family ties, seeking flexibility, letting a child enjoy innocent freedoms for longer, providing an appropriate environment for a child with special needs, accelerating your child's learning, or any number of other goals.

Setting goals will help you decide what method or style of homeschooling you'll adopt for your home: unit study, lapbooking, Charlotte Mason, Montessori, principled, classical, unschooling, or a combination of these (called "eclectic").  This will, in turn, lead you to make wise curriculum choices, that is, those that support your goals rather than something that just looks slick, is popular, or is on sale.

Setting goals will also keep you from straying when "the grass looks greener".  Last year, for example, a friend of mine was looking into a school that specializes in foreign languages for her daughter who's the same age as my #3.  I feel I'm particularly weak in this area, so I was tempted to enrol my children in the same school.  However, as I investigated its total package more carefully, I realised it was far more restrictive and generic than I wanted in the individualized, child-led system I've adopted as my goal.

Of course, your goals may change over time, but don't let that stop you from defining what you're wanting right now.  So get that cup of coffee or tea or can of Coke or whatever, grab a pencil and some paper or your journal or your calendar, and start making some notes about why -- right now and this minute -- you want to homeschool.

When you've reached the stage where you sort of like what you've written, then why not tell me in a comment?  I'd love to hear from you about the goal you've set for your own home-learning journey.