A look back at MEP Primary

One of the big disadvantages of having only one child is that I only get one chance to get it right.  I will only ever do AO1 once; I will only ever do one AO7.  I will never be an Über-homeschool Mum, with twenty years under her belt and another two kids of ten yet to graduate.  I have one go through and then it's quits.

All of this means that just as I've finally got the hang of MEP Primary, Jemimah has moved into Secondary, and I'm having to learn all over again.  Poor guinea pig of a kid.  Actually, it was starting MEP7 that helped consolidate it all for me, and since it is all too late for Jemimah, I thought I could at least share my new found cleverness with some of you.  Sound good?

The thing I want to talk about most, is how much of each lesson you should get through.  Through the last six years, I tried most permutations and combinations with my guinea pig daughter, and only now do I think I have it right. Now that we're finished and mucking up Secondary.  So here is my wisdom, such as it is.

First, let's look at a few different statements from the MEP website:

• Challenges or extension work set for able students…no one is inactive. (a)
• The 5th lesson each week is for practice and revision. (b)
• The first few weeks provide introductory activities to help you assess the capabilities of your class and to bring them together at a suitable starting point for the systematic treatment which follows. (b)

So, what do these statements say?  First - that some of the work is for more able students.  Second - the fifth lessons are for revision and practice.  Revision.  If your child totally understands the work on these sheets he does not need to do the fifth lessons.  In that case, these sheets would be mere busywork.  On the other hand, we all know that practice makes perfect.  If your child needs more practice, then do use these sheets - that's what they're for. Third - If your child is new to MEP then the introductory revision lessons at the beginning of each year will give you a pretty good idea of what gaps your child might have in coming to MEP from a different programme.  Do the lessons and observe your child closely.  If, however, your child has been doing MEP right through, then he probably doesn't need to do these lessons.

Okay.  In one paragraph we've tossed out about 30 percent of the year's work.  What do we do with the extra time?  Just this - we use it where we need it.  Some MEP lessons are really quick and easy (if they're too easy, then just skip them); there are other MEP lessons that are not easy at all.  In fact, they're downright difficult.  If your child struggles in a lesson, split it in two.  If your child needs more revision in a concept, then revise for a few days.  Go on, you have the time.

Which brings me to my next point.  Don't slow MEP down too much.  It's spiral.  The material will be covered again.  Over and over again. If your child really doesn't get it, then it probably doesn't matter.  For some reason, Jemimah really struggled to learn to tell the time.  The lessons moved much too fast for her.  She needed practice on 12 o'clock and half past two, not 2335 and 1342 on the 24 hour clock. When we reviewed Time last week in MEP7, however, she did fine with all the work.  She has jumped her road block and moved forward easily.  It was not worth beating her over the head with the kitchen clock in MEP2 after all, and it has probably left her indelibly scarred for life and up for thousands in counselling bills.  Poor child.  Anyway, I say aim to get one year's worth on MEP work done within a a year.  If you split a lesson in two, the you need to skip a 5th lesson to make up.  A MEP year is 35 weeks; aim to be done in 36 or 40 or whatever your school year is.  You may even get done more quickly, although sometimes you run into trouble if you reach something like long division too early before your child is developmentally ready for it.  Then you'll need to take a break. (Been there; done that - we did SCM's Business maths for a term just to slow down for long division and to renew Jemimah's love for maths.)

Moving right along.  Next, have a look at the lesson plans, and at the top you'll find something that says something like this:

R: Place value

C: Extending numbers to 10 000; counting, reading, writing, ordering

E: Vocabulary

This is from MEP4 Lesson Plan 31, and what it tells me is that in this lesson we hope to revise place value, cover numbers to 10 000 as our core work, and if the work is done in time, then we can learn some new vocabulary.  In my own case, Jemimah finds maths fairly easy, and so we almost always looked at the extension work.  On the other hand, she rarely needed the revision work. If I was unsure, I set her a few questions to check.  You know your child.  Does he struggle?  Would he benefit with lots of review of earlier work?  Perhaps he is more average.  Some things he does really well, and would benefit from some further extension, other work needs lots of reviewing.  Or perhaps you, too, have a Jemimah. When you only have a class of one, you should at least ensure that you are tailoring the work to that child's level, yes?

Looking again at Lesson 31, I would consider Activity 1 to be introductory and for all students.  It is good, because it is visual. Question 2, I would consider to be revision, and Activity 3 to be extension (although it looks pretty easy, in fact). Q1 of the Practice Book is Revision also, and I would at most set one for an average student to ensure he remembered how to do them. If the student gets it right, move on; if he gets it wrong he does some more. Question 2 is revision too.  For an able student, leave it out.  Also leave it out for students with a pencil allergy.  Have those kids do it orally instead. Have them sort them into increasing order, though, if they needs that.

That leaves Q3 and Q4.  Set half of the exercises.  Alternate questions works well, because often they get harder as you go through.  If he gets them all right then he is done.  If he needs more practice, he does the rest.

Pronounce a sum wrong, or right––it cannot be something between the two. That which is wrong must remain wrong: the child must not be let run away with the notion that wrong can be mended into right. The future is before him: he may get the next sum right, and the wise teacher will make it her business to see that he does, and that he starts with new hope. But the wrong sum must just be let alone. Therefore his progress must be carefully graduated; but there is no subject in which the teacher has a more delightful consciousness of drawing out from day to day new power in the child.
Charlotte Mason Home Education pp 260-261

Miss Mason reminds us to set problems that are within the child's grasp.  He is not to be frustrated by question after question that he already knows, but similarly, he is not to get answer after answer wrong. By setting every second question, then the child has an opportunity to demonstrate that he either knows the work…or he doesn't.  If he gets them all correct then maths is done.  If he gets one wrong, then set him another one.  Only this time sit over him and make sure he gets this one right! A child that struggles may need to do all the examples, but this is not a punishment, and shouldn't feel like one.  It is just more practice. Reassure, encourage, give positive feedback.

Over and over again I hear that MEP is too long, or too complicated.  I hear that mums take hours over each lesson, or that they split each lesson in two and do one year's work over two.  I say don't!  Look at the lesson plans - be prepared, and Know Thy Child.  Does he need revision?  Is he average?  Is he advanced?  Is this just busywork, or does he need more practice and to linger over a particular concept?  Is the thing he doesn't understand part of the core work that he will need to advance, like knowing numbers to 10 000, or is it something he can learn next time - like the 24 hour clock, or Roman numerals.  Is there something that particularly interests him, or he would understand better with some concrete examples and some manipulatives? Could you make up some play $10 000 notes and play shop and buy a house or something?

MEP is a fantastic tool, but it is a programme designed for a classroom of students all of different abilities and skills.  Your classroom consists of one, or at most two students in a level.  Mould the lesson plans, make them fit your child. Use them for your purposes.  Don't make your child fit into a classroom that doesn't even exist.

Recently, a friend was telling me about her daughter who was struggling with maths.  I listened, but then I asked my friend who she was comparing her daughter to.  A classroom?  The fact is, that young lady is absolutely average for her Year 8 class, because she is the only student in it.  There is nobody worse than her, but equally, there is nobody doing better, either. When you use MEP,  remember that you are not teaching a UK curriculum; you are teaching your own precious son or daughter.  And then make the curriculum work for you.  Chances are, MEP will work just how you always dreamed a maths programme could work for your child.  It did for mine.

Even if I did make lots of mistakes along the way.

Traditional counting songs

In the early years, the MEP lesson plans call for 'counting songs'.  These interludes are there to prevent brain strain - remember that MEP in a classroom takes 45 minutes, and that's a long time for a small person.  But a well chosen song can have value for another reason too - to practice counting backwards and forwards.  Counting backwards is harder than you think.  If you consider yourself mildly proficient in a second language, try counting backwards from numbers other than ten.  It is pretty hard!  That's what it is like for our youngsters as well.

Here are some of our favourite counting songs.  There are lots of modern ones as well, but this is most of the traditional ones.  Hopefully you'll find something that you and your kiddos like!

For obvious reasons, the ones counting forward and backward are probably best.  Have fun!

(Also, singing counting songs in your foreign language is also great practice...even in the middle of maths!  That's probably another post.)



Once I Caught a Fish Alive

1, 2, 3, 4, 5,
Once I caught a fish alive,
6, 7, 8, 9, 10,
Then I let it go again.
Why did you let it go?
Because it bit my finger so,
Which finger did it bite?
This little finger on the right.



Ten Green Bottles

Ten green bottles
Hanging on the wall
Ten green bottles
Hanging on the wall
And if one green bottle
Should accidentally fall
There'll be nine green bottles
Hanging on the wall

Nine green bottles
Hanging on the wall...and so on.

Finish with:

One green bottle
Hanging on the wall
One green bottle
Hanging on the wall
If that one green bottle
Should accidentally fall
There'll be no green bottles
Hanging on the wall.



There were 10 in the Bed

There were ten in a bed
And the little one said
'Roll over, roll over'
So they all rolled over
And one fell out

There were nine in a bed
And the little one said...etc

Finish with:

There was one in a bed
And the little one said
'Good night!'

There are many variations to this song. We love the one with the following sung between the verses, so if you have just sung the 'There were seven in bed' verse it would be:

Bumped his head,
And gave a shout.
Please remember,
To tie a knot in your pyjamas,
Single beds are only made for (then shouted) Ten, Nine, Eight, Seven, six in the bed and...

(Anyone know a YouTube video for this variation?)



10 Little Indian Boys

1 Little, 2 Little, 3 Little Indians,
4 Little, 5 Little, 6 Little Indians,
7 Little, 8 L9ittle, 9 Little Indians,
10 Little Indian Boys!

Then count down again!



One, Two, Buckle my Shoe

One, two, buckle my shoe,
Three, four, open the door,
Five, six, pick up sticks,
Seven, eight, lay them straight
Nine, ten, the big fat hen,
Eleven, twelve, dig and delve,
Thirteen, fourteen, maids a-courting,
Fifteen, sixteen, maids in the kitchen,
Seventeen, eighteen, ladies waiting,
Nineteen, twenty, my plate's empty.




This Old Man

This old man, he played one,
He played knick-knack on my thumb;
With a knick-knack paddywhack,
Give a dog a bone,
This old man came rolling home.

This old man, he played two,
He played knick-knack on my shoe;
With a knick-knack paddywhack,
Give a dog a bone,
This old man came rolling home.

This old man, he played three,
He played knick-knack on my knee...etc.

This old man, he played four,
He played knick-knack on my door...etc.

This old man, he played five,
He played knick-knack on my hive...etc.

This old man, he played six,
He played knick-knack on my sticks...etc.

This old man, he played seven,
He played knick-knack up in Heaven...etc.

This old man, he played eight,
He played knick-knack on my gate...etc.

This old man, he played nine,
He played knick-knack on my spine...etc.

This old man, he played ten,
He played knick-knack once again...etc.



Ten Little Ducks

Ten little ducks went out one day,
Over the hills and far away.
Mother duck said
'Quack, quack, quack,'
But only nine little ducks came back.

Continues with:

Nine little ducks went out one day,
Over the hills and far away...etc.

Finish:

No little ducks went out one day,
Over the hills and far away
Mother duck said
'Quack, quack, quack,'
And all those ten little ducks came back.



One Bottle of Pop


This is a great song!!

One bottle of pop, two bottles of pop,
Three bottles of pop, four bottles of pop,
Five bottles of pop, six bottles of pop,
Seven, seven, bottles of pop, pop!

Fish and chips and vinegar, vinegar, vinegar
Fish and chips and vinegar,
Pepper, pepper, pepper, salt!

Don't throw your trash in my backyard,
My backyard, my backyard.
Don't throw your trash in my backyard,
My backyard's full!



Five Speckled Frogs

Five little speckled frogs
Sat on a great big log
Eating some moist delicious flies (Yum, yum, yum!)
One jumped into the pool
Where it was nice and cool
Now there are four speckled frogs! (Ribbit, ribbit!)



Five Little Monkeys

Five little monkeys jumping on the bed,
One fell off and bumped his head.
Mama called the Doctor and the Doctor said,
"No more monkeys jumping on the bed!'.

Four little monkeys jumping on the bed,
One fell off and bumped her head...

Finish:

One little monkey jumping on the bed,
He fell off and bumped his head.
Mama called the Doctor and the Doctor said,
"Put those monkeys straight to bed!'.



One Man Went to Mow

One man went to mow, went to mow a meadow,
One man and his dog - Woof! - went to mow a meadow.

Two men went to mow, went to mow a meadow,
Two men, one man and his dog - Woof! - went to mow a meadow.

Three men went to mow, went to mow a meadow,
Three men, two men, one man and his dog - Woof! - went to mow a meadow.

Four men went to mow, went to mow a meadow,
Four men, three men, two men, one man and his dog - Woof! - went to mow a meadow.

Five men went to mow, went to mow a meadow,
Five men, four men, three men, two men, one man and his dog - Woof! - went to mow a meadow.

You can count as high as you like!

Enjoy!  Have I included your favourite counting song?  If not. leave me a link in the comments.  I'd love to listen.

PS There are as many variations to the lyrics of these songs as there are songs.  The lyrics here are my family's personal favourites.  They're the right ones, of course. Heh.

Here's a playlist for all these songs if you like them like that.

More fractal fun

If you love Vi Hart - we do
And if you love fractals - we do
And if you've just read Maggie and the Abacaba Genies - we have
Then I'm thinking you'll love this video as much as we do.

If not, you may not like it at all. It takes all kinds.

Vintage maths

My mum recently passed on to me my old Cuisenaire rods. They were much loved and used and are missing many pieces - lost, no doubt after making fences for paddocks or walls for houses or some such activity not related to mathematics - which I can't ever remember doing with them. Rods, like blocks are all useful, but along with this universal usefulness comes an attrition rate that is to be expected with children and building activities.

Still, enough of the rods remain for me to be able to use them in Jemimah's geometry lessons this week, and she and I have found it rather special for her to be using the very same rods that I had used oh...so...many...years before. Well. Yes. They're not quite antique, but they're certainly vintage, and their age brings with them a sort of desirable designer style that is missing from Jemimah's plastic 10 year old version. Have a look. Old on the right; new on the left.

Invented by Belgium school teacher Georges Cuisenaire, who wrote a book about them in 1952, Les Nombres en couleurs, the coloured rods have long been helping children learn maths...and build houses. They're amongst the most useful maths manipulatives in this house. We still use them occasionally, and Jemimah is in MEP6!

I'm glad that now my daughter will have fond memories of this set too.

Timez Attack

I purchased the deluxe version of Timez Attack yesterday, and I've been struggling to get access to the computer ever since.  Yep.  Jemimah's been practice her multiplication facts most of this morning.  Bit weird, really, when she could have been outside in the pool.  She also had a bit of a go at her division facts, but they're really hard.  Take a look:



See? How do you think you'd go doing your maths facts the other way around? I did really poorly, to be honest.  Don't tell my daughter.

We first loaded the free version of Timez Attack onto our computer back in January 2009.  Sometimes over those almost four years Jemimah has played regularly; at other times it has been quietly neglected.  That's fine.  In general she thinks it is fun.  Maths - Fun.  Yep.  As a consequence of playing, her multiplication facts are pretty good.  Now we're back into it for division.

The free version of the game offers you the ability to practice all your maths facts - addition, subtraction, multiplication and division up to 12x12.  The $60.00 deluxe pack is so far only available for multiplication and division, but offers a whole heap of extra worlds and playing environments, and since Jemimah has demonstrated a lasting interest in playing the game, I thought I would treat her a bit and buy the multiplication upgrade.She was delighted.  Apparently the game is Awesome!

You can download the free or paid versions of Timez Attack here.  Now we're waiting on the iPad version to be released!

Math(s) Week

I'm guest blogging this week at Afterthoughts, the blog of my dear friend and fellow AOer, Brandy Vencel.  This week at Afterthoughts is Math(s) Week, and Brandy has put together a great series of Charlotte Mason maths posts for us all to ponder.  I am especially interested to learn about Euclid.

Here's the table of contents:

Welcome to Math Week! {Series Introduction}

Teaching Maths the CM Way {by Jeanne}

Five Strategies for Teaching Mathphobics {by Tammy Glaser}

Teaching Euclid in the Homeschool, Part I {by Willa}

Teaching Euclid in the Homeschool, Part II {by Willa}

While you're there, be sure to read some of Brandy's other posts.  She's one of the deepest thinkers I know, and I respect her immensely.  Actually, I am rather in awe of her, but that's a secret.  Don't tell her, please! ;)

Testing time

Jemimah is sitting the IPMA Level 5 test today. It is hard to believe that she has completed Level 5 of MEP. Where has the time gone?

She is working on the computer and the house is very quiet. It's strange. My job is to supply the busy worker bee with hot cups of milky tea and chocky bikkies, but I find myself wandering in and out of the room and feeling generally superfluous. I will not like it when my girl does all her work independently, that is for sure.

I still have nothing but praise for this free maths programme. It supplies a complete, rigourous maths education in a simple and interesting format. There are no gimmicks, no coloured workbooks, no fun manipulatives. What there is, though, is sensible explanations, little busywork, interesting applications, good teaching materials for mum, sufficient repetition and adequate practice, and plenty of variety.

We've used MEP from the beginning and think it's great. I'll be interested to see the results of the test today.

Now what should I do? More biscuits perhaps?

Pet Shop Maths - the verdict

So the Pet Shop made a profit. $6884.98 profit to be exact. Which isn't too bad over the 'year'.

I last spoke to you about Simply Charlotte Mason's Business Maths Pet Store on Day One of the course - right back at the beginning of term. We were pretty excited. Now that we're at the end I thought you might like to know what we think now.

And we're still happy. For us, this programme was a perfect choice. Let me remind you that I was becoming concerned that Jemimah was moving too far ahead in MEP maths. At the beginning of term three of AO4 she was more than half way through MEP Year 5. I could see her love of maths waning, and I really didn't want that. A term of maths practice seemed a perfect solution.

That's what Pet Shop Maths was for us - maths practice. Now at the end of term Jemimah's adding and subtracting of columns of decimals has improved dramatically. She is able to calculate a percentage by changing it to a decimal and multiplying. She can calculate a percentage increase. She can maintain a ledger and knows what one is for. Most importantly, she has regained a love for maths, and has some idea of how it is used in every day life. The programme was fun and quick. Most days we could get the work done in five minutes, allowing time for some multiplication practice in a quick game of Timez Attack, or to just relax.

In case you're wondering, Pet Shop Maths isn't a full maths curriculum. The skills I mention above are pretty much all it involves. It is best regarded as an adjunct to a regular maths curriculum - or a break from one - rather than as a stand -alone maths programme.

Each 'month' the tasks are the same. By the end of the book Jemimah was bored by them, but by then it didn't matter, she had mastered them and we were done. What she most loved was the random Chance cards that added an element of risk to each month. Would the card be a goodie or a baddie? Would it put us into debt or increase sales? Jemimah loved picking Chance cards.

For me the best bit was removing the angst that seemed to be accompanying maths lessons. I loved the way the books were set out, and I loved how quickly we could get things done.

For us, Pet Shop Maths served its purpose very well indeed.

Slow down, you move too fast

I guess you all know by now that I'm not a curriculum switcher. I make my decisions based on thorough research, and that's pretty much that. I then I spend my valuable time thinking about other things. Like where to go on holidays, or what books I absolutely need this week. Important stuff.

The other thing I do rarely is change my mind mid term. Actually, I don't think I've ever done that.

Until now. Let me elucidate.

I've been becoming increasingly concerned about Jemimah's maths. Now before you leap to your feet in alarm - or worse, in glee - let me reassure you that I still love MEP maths. I think it is a great fit for our daughter, and I have been incredibly impressed by her progress in this subject.

And that is precisely the issue I've been grappling with: My nine-year-old Grade 3 daughter is halfway through MEP Year 5 maths.

She is going too fast.

I am beginning to see her enthusiasm wane as she gets into more and more complicated concepts, and I really, really don't want her to start disliking a subject that she is so very good at.

Which led me to Simple Charlotte Mason's Business Maths Series - something that I've been looking at for a while. In this programme, kids use their maths knowledge to run a virtual sports store, pet shop or book store. Of course in Jemimah's case it just had to be a pet store!! They practice addition, subtraction, multiplication and division. They learn about budgeting, making sound financial decisions, paying accounts, balancing a ledger, and about managing a profitable business. And hopefully at the very same time, they have fun!

And so yesterday, I bought a virtual pet store. It's called 'Jemimah's pet paradise', and it is owned by...well...Jemimah. Obviously.

Today, she developed a logo, printed promotional stickers and posters and decided on her inventory. Keeping within budget, of course. Tomorrow she'll decide on a mark-up and make price stickers. Pretty soon she'll be open for business.

Today she spend her whole afternoon doing maths. I wonder how long that amazing state of affairs will last! So far, so good. Actually, I don't think she really believes that it is real, that this is what she's doing for mathematics.

I'm really excited. Having looked through the teacher's book I can see practice in a significant number of the maths skills she's mastered in MEP up to now. I can see application. I can see that Jemimah will begin to see the relevance of maths to every day life.

I haven't decided yet how we'll incorporate the programme into our term. You've heard of the term de-schooling, I guess? Where you do no school to sort of recover from being at school? Well, for a short time we're demathsing. During this period our Pet Store is all we'll be doing. Later, MEP will return. Maybe once we've finished the whole kit and caboodle; maybe before. I don't know yet.

I like this programme because it's giving maths practice in a relaxed but realistic way. It's rigourous but in a very different way from MEP. It's exciting and challenging.

I think it will slow my girl down in just the right way.

MEP Reflections

Yesterday Jemimah completed Year 4 of MEP. Hurrah!

(She is nine years old and is in Year 3 (Her 4th year of formal education in Victoria)).

The initials MEP stand for "Mathematics Enhancement Programme" - a maths programme (obviously) developed by the CIMT - Centre for Innovation in Mathematics Teaching - at the University of Plymouth in the United Kingdom. It is the curriculum I've be using with Jemimah since the beginning, and today seemed an opportunistic time to touch base with you about how we are liking the course four years in.

Is it comprehensive in scope?

Firstly and importantly, it is a rigourous curriculum effectively covering most of what Jemimah would be studying at public school. Today as I write, Jemimah is tucked up in the room we currently use as a store room (you can see her above) completing examination papers. At the end of each term MEP has students complete an IPMA test - yes, the course is jargon and acronym heavy - short for International Project of Mathematical Attainment. According to the Coordinator's Manual:

The tests are designed to assess progress on key mathematical topics and concepts over a yearly period of time. Further questions are added each year to the original questions. In this way we hope that there will be sufficient new and relevant questions to assess progress, whilst having at least some questions on the test paper for children who are progressing slowly.

The test covers only the key mathematical concepts covered in the previous year of study, and as such I have found it reasonable to expect Jemimah to attain 100% each year. This expectation has proved achievable each year so far - including today. Go Girl!!

(The test is only moderately useful as placement test for parents who look to use MEP in place of another curriculum choice in their homeschool, since the course itself is far more comprehensive than the test indicates. Still, it could be used as a placement test if parents give the whole test and look at the stage at which their pupils baulk at the questions. A summary of the number of questions relevant to each year level and age is included in the Coordinator's Manual.)

In addition to the IPMA tests, Jemimah is today also sitting Australia's NAPLAN tests for Years 5 and 7 (Remember, she is in Grade 3 here.).

National Assessment Program - Literacy and Numeracy (NAPLAN) testing commenced in Australian schools in 2008. Every year, students in Years 3, 5, 7 and 9 are assessed on the same days using national tests in Reading, Writing, Language Conventions (Spelling, Grammar and Punctuation) and Numeracy. Many of you, I know, use homeschooling curricula that regularly test your children's progress in major subject areas. Those of you who like me choose the Charlotte Mason method of educating and testing will be less sure where their children fit in relation to their State educated peers, especially since MEP only tests using the IPMA test once a year. There is no obligation for me to use these tests with my homeschooled daughter, but it is always encouraging to me to see that her mathematical learning level is at or above that of her peers. I chose the Year 5 and 7 levels rather than Year 3 because I am confident that she is familiar with the vast majority of the material included in both of these year levels. That gives me incredible confidence to continue using the MEP course in the future.

(As an aside, she also sat the Year 3 Language Conventions paper. Her English grammar and punctuation were perfect; her spelling was 'atroshus' - as usual. Sigh - what more can I do?)

After all that testing, this is her brain food reward of choice - Kool Mints.

Is it teacher intensive?

Those parents using lower levels of MEP will be reassured, I am sure, to learn that the level of daily parental input into the programme decreases somewhere through Year 3. During this past year I have spent only a few minutes at the commencement of each lesson covering the material contained in the Lesson Plans before Jemimah completes the Worksheet for that day. She is free to come to me for help, but often all I do is go through the sheet with her after she has completed it alone.

How long does it take?

Lessons at this level take between 20 minutes and half an hour. This is in line with Charlotte Mason's guidelines, since her students spent 30 minutes on arithmetic in Years 4-6. Do not allow procrastination!! Generally we cover all questions on all worksheets, but if a lesson is taking far longer than usual we may hold a question or two over to the next Friday's lesson. Friday's lesson is worksheet based only and takes less time. We like this at the end of a busy week.

Do you still use manipulatives?

At this level manipulatives are used far less often, but we still use counters and Cuisinaire rods occasionally. Dice and coins are used for probability at this level. Sometimes it is fun to use lollies as manipulatives. Smarties are fun. Maths is far more interesting when you can eat the answers!!

Do you print everything?

We continue to print all paperwork including all copymasters. Jemimah prefers to use the larger sized copymasters when they are available, even when they are reproduced on the worksheet. Each Year Level is divided into a and b. Each of these is further divided into three sections. We print one section at a time and put the sheets into a folder. At this level she completes most of the sheet in pencil with a rubber available to correct mistakes, but she always has a few textas to brighten up her day a little!

Do you prepare the lessons?

Aside from pre-printing the materials I do very little lesson preparation. I generally glance over the lesson plans in the morning before school starts to see if any manipulatives are required so that I can gather them together. This takes no more than a minute or two most days. (Well, unless somebody has borrowed the dice for a board game, that is.)

Does Jemimah like maths?

Maths is not Jemimah's favourite subject, but nor is it her least favourite - studied dictation takes that ticket! Generally she just gets on and does it.

Generally if she doesn't understand a new concept the first time, MEP's continual cumulative review will give her many more opportunities to master a process later on. This removes much of the stress that children can often feel with mathematics as a subject, in my experience.

MEP Maths is not an issue either way to Jemimah.

I like it though, four years in. Does that count?

Feel free to let me know if there is anthing else you want me to cover. I'd be happy to oblige! There are plenty of other posts on MEP in the archives as well. You'll find them under Mathematics in the right sidebar.

If you have had experience with MEP how did you find it? Are your experiences similar to mine?

Do tell.

Yay, Jemimah!

I suppose we really ought to include deportment and lady-like posture as classes for next year, shouldn't we? At least we're working on flexibility though...and lolly eating... and getting our daily dose of Vitamin D. All while doing maths. Multitaskers extraordinaire, we are.

This is Jemimah completing her final lesson of MEP Book 4a. It was last week actually, but I forgot to show you, and she had asked me ever so nicely if I would tell you that she was up to her new book that I really had to rectify that omission as soon as I realised it.

We're working on fractions and decimals at the minute. They're a nice break from written calculations of numbers up to 10 000, which it seemed like we'd been doing forever. A few weeks of geometry were a pleasant reprieve as well.

We're still loving MEP. That doesn't mean that every day is fun and easy. A lot of the time maths is the subject that Jemimah chooses last - so that when it's done school's over for the day - but the spiral form of the programme means that no topic is around for long. "If you don't like what we're doing then just wait for next Monday" is our philosophy, and mostly it works.

Amongst my likes are MEP's emphasis on mental maths, and its use of precise and correct mathematical terminology. I love the variety of exercises. A lesson might include setting up a shop to practice using money; measuring weights and capacity; or using manipulatives like Cuisinaire rods or number cards. We might have a mental drill type exercise practicing multiplication facts, followed by a couple of practical applied maths problems and a puzzle. All this keeps boredom to a minimum - in our peaceful home, anyhow.

You hear of mums changing maths curricula nearly as often as they change their clothes. Personally I see little value. For me a maths curriculum is merely a tool that reassures me that I've not left too many gaps. It is not necessary to follow it slavishly, and, in fact, it seems foolish to even attempt to do so. As homeschoolers, we are in the enviable position of being able to tailor the education process to fit our children's unique learning requirements. It would be crazy to not take advantage of this. To me this is not a matter of changing the curriculum, but rather tweaking the one you already have to ensure that it fits your child's needs. MEP's presentation makes this easy.

Unless you insist on sitting like this while you're doing it, that is...

Well done, Jemimah.

Are MEP and CM compatible?

...and what do they spell?

Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination.

How living would Geometry become in the light of the discoveries of Euclid as he made them!

...Mathematics are a necessary part of every man's education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of 'subjects,' a knowledge of which is his natural right.

Charlotte Mason A Philosophy of Education p233

I'm not really qualified to talk to you about very much except the genetics of blotchy and brindled mice. If you want to know about murine mottled mutants - brindled, Mo br, and blotchy, Mo blo, - and why they play a valuable role in the study of mammalian copper metabolism, then I'm your girl. Otherwise, you'll probably find a better expert than me to tell you about almost anything.

I certainly can't tell you much about homeschooling. Don't look to me for advice on whether your kids would be better off using an unschooling or Montessori or Thomas Jefferson or Enki or Waldorf method in your homeschool, because frankly I don't know a thing about them. To be honest I only know their names because I plugged 'homeschooling methods' into google and up they came. I read The Well-Trained Mind: A Guide to Classical Education at Home by Jessie Wise and Susan Wise Bauer, and the amount of work required for the Classical Method of homeschooling terrified me, so don't ask me about homeschooling using the Trivium either.

It's probably providential then that the first book I read about homeschooling was Susan Schaeffer Macaulay's For the Children's Sake: Foundations of Education for Home and School. A quick google one day introduced me to Ambleside Online and my path was set. Jemimah was three years old.

It was through Carol Hepburn's posts in the Ambleside Online yahoo group that I first heard about the Mathematics Enhancement Programme, MEP developed by the CIMT - Centre for Innovation in Mathematics Teaching - at the University of Plymouth in the United Kingdom. I respected Carol's opinions, but the real reason I first looked at MEP was that it was free online.

Apart from the Math-U-See demonstration CD, this is the only homeschool curriculum I've ever seen. So don't ask me about homeschool maths programmes. I know next to nothing about Saxon, Singapore, MUS, Miquon or Horizons math. I can't compare spiral and mastery learning either, for the same reasons - I've never seen nor used a mastery system.

Can you see why I'm not qualified then, to talk to you of such things?

What I do feel qualified to talk to you about is our journey through a Charlotte Mason education using MEP maths and how they fit together. In answer to the question, "Are MEP and CM compatible?" I believe the answer is 'yes'! I'd like to tell you why.

Mastery or spiral?

Firstly let's tackle the mastery/spiral question. I'd like to start here because this is most commonly cited as the reason that MEP is not in line with Miss Mason's recommendations for a maths programme. So what is the difference?

As far as I see it, and remember that I am far from an expert, teaching to mastery is based on the idea that learning is sequential and that each new idea builds upon ideas that are already fully understood. Rather like in a staircase one stair is built upon the stair below, the child must master the subject the first time it is presented because that particular topic will not be presented again, and the next topic is dependent upon the knowledge gained before. Not only mastery of the skill but also the reasoning behind the topic are expected first time round.

With a spiral programme a subject is presented over and over again with increasing complexity each time. If a fact is not understood first time then it will be covered again in subsequent passes in a few weeks or a few weeks or even a few years.

Silvia's reviews here and here of mastery versus spiral programmes are worth a sticky if this topic interests you.

MEP is a spiral programme. Negative numbers are covered for the first time only a six weeks into year one by introducing a thermometer. Certainly my daughter looked at me as if I had horns when I told her at 5 years of age that the number after 2,1,0 was 'minus 1'. At this stage we were only working with numbers between 1 and 10, remember. A child living in Alaska where the temperature regularly goes below zero might have understood this concept at that age, but not my Australian daughter. No matter, nothing hinges on this understanding - it was merely incidental knowledge. Jemimah knew then that there were numbers below zero, nothing more.

They're covered again in year two, but it is only in year three that the children are expected to understand how negative numbers work. In year three children learn to add and subtract numbers below zero on the number line. Whole lessons are spent on explaining and practicing this difficult concept, and most children will understand. If they don't then no doubt it will be covered again in year 4.

MEP lessons move fast, and each day contains one or two new concepts and several of cumulative review. Even if the child doesn't understand something when it is first introduced, then they generally will after much review.

Okay. This is all well and good, but what does Miss Mason say? Of course she doesn't use the terms 'spiral' versus 'mastery', so what does she say even obliquely about this subject?

Engage the child upon little problems within his comprehension from the first, rather than upon set sums. Care must be taken to give the child such problems as he can work, but yet which are difficult enough to cause him some little mental effort.

Subtraction is worked out simultaneously with addition. As he works out each line of additions, he goes over the same ground, taking away instead of adding, until he is able to answer quite readily, 2 from 7? 2 from 5? After working out each line of addition or subtraction, he may put it on his slate with the proper signs, that is, if he have learned to make figures. It will be found that it requires a much greater mental effort on the child's part to grasp the idea of subtraction than that of addition, and the teacher must be content to go slowly until he knows what he is about.

When the child can add and subtract numbers pretty freely up to twenty, the multiplication and division tables may be worked out as far as 6x12.

Now he is ready for more ambitious problems: thus, 'A boy had twice ten apples; how many heaps of 4 could he make?' He will be able to work with promiscuous numbers, as 7+5-3. If he must use counters to get his answer, let him; but encourage him to work with imaginary counters, as a step towards working with abstract numbers. Carefully graduated teaching and daily mental effort on the child's part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind.

When the child is able to work pretty freely with small numbers, a serious difficulty must be faced, he must be made to understand our system of notation. Introduce him to the notion of tens and units, being content to work very gradually.

Let the child work with tens and units only until he has mastered the idea of the tenfold value of the second figure to the left, and would laugh at the folly of writing 7 in the second column of figures, knowing that thereby it becomes seventy. Then he is ready for the same sort of drill in hundreds, and picks up the new idea readily if the principle have been made clear to him, that each remove to the left means a tenfold increase in the value of a number. Meantime, 'set' him no sums. Let him never work with figures the notation of which is beyond him, and when he comes to 'carry' in an addition or multiplication sum, let him not say he carries 'two,' or 'three,' but 'two tens,' or 'three hundreds,' as the case may be.

On the same principle, let him learn 'weights and measures' by measuring and weighing; let him work with foot-rule and yard measure, and draw up his tables for himself. Let him use his judgment on questions of measure and weight. The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child. While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a 'fraction,' half a pound, a quarter of a yard, etc.

If the child do not get the ground under his feet at this stage, he works arithmetic ever after by rule of thumb.

The fundamental truths of the science of number all rest on the evidence of sense but, having used eyes and fingers, the child has formed the association of a given number with objects, and is able to conceive of the association of various other numbers with objects. In fact, he begins to think in numbers and not in objects, that is, he begins mathematics. Therefore I incline to think that an elaborate system of staves, cubes, etc., instead of tens, hundreds, thousands, errs by embarrassing the child's mind with too much teaching, and by making the illustration occupy a more prominent place than the thing illustrated.

Dominoes, beans, graphic figures drawn on the blackboard, and the like, are, on the other hand, aids to the child when it is necessary of him to conceive of a great number with the material of a small one; but to see a symbol of the great numbers and to work with such a symbol are quite different matters.

I need to encourage you here to read Miss Mason's own words on this subject. The quotation above is summarised from a long section of Home Education beginning on page 253.

So what does she say? This is how I read it:

1. Single digit addition and subtraction
2. Multiplication and division up to 6x12
3. Introduce place value.
4. Work all four operations as each new place is introduced.
5. Practice place value using money, weights and measures.
6. Introduce fractions.
7. Begin to phase out concrete manipulatives by encouraging virtual manipulatives instead as a preparation for real 'mathematics'.
8. Beware the trap of over-using manipulatives and making them more important than the mathematical concept being illustrated. (As an aside, Miquon and Math-U-See may be guilty of this perhaps?)

Now the big question: How does MEP measure up?

Pretty well, it seems to me. MEP covers addition and subtraction of numbers from 1-20 in year one. In year two the number line is extended to 100 with money as an example. Addition and subtraction followed by multiplication and later division are covered in year two. Weights and measures are introduced. Gradually over year three the number line is extended to 1000, with a brief foray into larger numbers near the end of this year. The four operations are revisited using these larger numbers, and length, capacity, mass and time are extended as new mathematical concepts are reached.

Despite being a spiral programme , the basics that Miss Mason discusses are covered to mastery at each stage before a new place value is introduced and the four operations are covered again. I think this is exactly what Miss Mason recommends. You can read my post on why I like MEP's spiral approach here.

Demonstrate everything demonstrable

The next point is to demonstrate everything demonstrable. The child may learn the multiplication-table and do a subtraction sum without any insight into the rationale of either. He may even become a good arithmetician, applying rules aptly, without seeing the reason of them; but arithmetic becomes an elementary mathematical training only in so far as the reason why of every process is clear to the child. 2+2=4, is a self-evident fact, admitting of little demonstration; but 4x7=28 may be proved.

A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to 'do sums' on his slate.

This is MEP's position as well. From the Notes on the Lesson Plans:

Visualising mentally and through the use of models and manipulatives, and relating concepts to real life situations where relevant, are important aspects. Children should be encouraged to build up their own set of manipulatives eg shells, pebbles, beads, buttons, lolly sticks, marbles, used match sticks etc in a container so that their maths becomes more meaningful to them. In each lesson, children should work with manual aids, number cards, counters, sticks, rods, dominoes, items from their collection etc wherever possible.

Problems

Now he is ready for more ambitious problems: thus, 'A boy had twice ten apples; how many heaps of 4 could he make?' He will be able to work with promiscuous numbers, as 7+5-3. If he must use beans to get his answer, let him; but encourage him to work with imaginary beans, as a step towards working with abstract numbers. Carefully graduated teaching and daily mental effort on the child's part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind.

MEP begins with mental maths in year one where they say:

Children should count and carry out operations mentally, sometimes as a class, sometimes individually...Also, we have planned some thought-provoking logic problems to form a basis for the development of problem solving skills and creativity.

Notation

Let the child work with tens and units only until he has mastered the idea of the tenfold value of the second figure to the left, and would laugh at the folly of writing 7 in the second column of figures, knowing that thereby it becomes seventy. Then he is ready for the same sort of drill in hundreds, and picks up the new idea readily if the principle have been made clear to him, that each remove to the left means a tenfold increase in the value of a number. Meantime, 'set' him no sums. Let him never work with figures the notation of which is beyond him, and when he comes to 'carry' in an addition or multiplication sum, let him not say he carries 'two,' or 'three,' but 'two tens,' or 'three hundreds,' as the case may be.

I think we've dealt with this above. MEP spends some significant time ensuring that a child understands a place value before moving onto operations. Once the child has been introduced to 'hundreds' for example, the four operations as well as related examples of measurement, time and the like, are reviewed using the newly extended number line.

MEP expects correct mathematical vocabulary and terminology. I do not recall whether they refer to carrying 'two tens' or not, but a parent can use this terminology with any programme. (I have written a reminder to myself to ensure I am doing that with Jemimah.)

Weighing and measuring

Let him learn 'weights and measures' by measuring and weighing; let him have scales and weights, sand or rice, paper and twine, and weigh, and do up, in perfectly made parcels, ounces, pounds, etc. The parcels, though they are not arithmetic, are educative, and afford considerable exercise of judgment as well as of neatness, deftness, and quickness. In like manner, let him work with foot-rule and yard measure, and draw up his tables for himself. Let him not only measure and weigh everything about him that admits of such treatment, but let him use his judgment on questions of measure and weight. The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child. While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a 'fraction,' half a pound, a quarter of a yard, etc.

From MEP:

It is very important to use pupils' knowledge, customs and information from their home and 'out of school' lives and to build bridges between that life and what they have learned in school. Use the playground, park, woods, market, shops, railway station, airport, countryside etc as contexts whenever possible.

You should demonstrate the discussion with real-life models...

The MEP lesson plans detail the way measuring of capacity, length and mass should be demonstrated. I'm afraid they do not explain the perfectly made parcels - you will need to do that yourself!!

Putting Mathematics in its place.

Mathematics are a necessary part of every man's education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of 'subjects,' a knowledge of which is his natural right.

Miss Mason was frustrated by the - to her - excessive amount of time that mathematics consumed in a child's education.

In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary! Lack of proportion should be our bête noire in drawing up a curriculum, remembering that the mathematician who knows little of the history of his own country or that of any other, is sparsely educated at the best.

But... why should a boy's success in life depend upon drudgery in Mathematics? That is the tendency at the present moment to close the Universities and consequently the Professions to boys and girls who, because they have little natural aptitude for mathematics, must acquire a mechanical knowledge by such heavy all-engrossing labour as must needs shut out such knowledge of the 'humanities' say, as is implied in the phrase 'a liberal education.'

The claims of the London Matriculation examination, for example, are acknowledged by many teachers to be incompatible with the wide knowledge proper to an educated person.

Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination.

How living would Geometry become in the light of the discoveries of Euclid as he made them!

If were are going to spend time on mathematics when we could be studying more edifying subjects then at very least we need to make it come alive. Much like we have living books we need living maths. I'm not convinced that this means the unorthodox approach to mathematics seen in such sites as Living Math!, however, although maths literature and history certainly bring out the excitement of great minds like Euclid's in a way that a study of Pure Mathematics never will. We have used many of the books included in Living Math's excellent book list as part of our maths programme over the years, and I recommend a judicious use of a few of these books regardless of which curriculum you eventually settle on.

And so, in conclusion and from the website, what of MEP? Let's finish with their words shall we?

• MEP aims to make all pupils mathematical thinkers and to make mathematics lessons challenging and fun for both teachers and pupils.
• It has very high expectations of both teachers and pupils.
• MEP continually revises facts and concepts.
• Lessons anre highly interactive and have many activities.
• It stresses the logical foundation of mathematics and correct consise mathematical notation and language are used at all times.
• Visiualising mentally and through the use of models and manipulatives, and relating concepts to real life situations where relevant are important aspects.
• Above all, MEP is fun.

I think Charlotte Mason would have approved of MEP, I really do. But then again, I don't really know. As I said at the beginning, I'm not an expert. I do know that in our homeschool, MEP dovetails neatly with the philosophies and aims of our Charlotte Mason education. More importantly, as my 8yo daughter reaches the end of MEP year three in the next few weeks, she continues to thrive. Her approach to mathematics is positive and she continues to enjoy what for many children is a much disliked subject. I am so glad that I found this programme, and I encourage you to give it some consideration.

This post is written for Kathy and Phyllis. I do hope it is what you were after, ladies. If not, do yell. I'd be glad to answer your questions...for what my opinion's worth!! Heather has also tackled the topic of MEP and CM here, for more on this topic. You can read my article MEP 101 here if you are interested in MEP and would like to give it a burl.

Now anybody want to know about blotchy and brindled mice? Anyone? Coz I'm your man.

Talking of numbers

My maths teacher used to try and make the learning of multiplication tables into a competition. Each morning he would point to a random fact written on the blackboard, and we were to see how many of the following problems we could complete before he called 'time'.

The process did two things for me. Firstly it made me wonder why none of the other kids realised that all you needed to do was find where you'd written this answer most recently and then copy all the answers that followed straight into your maths book. Secondly it made me into an incredibly fast writer.

I invariably used to win maths drill - but I never learned my tables. To this day I skip-count my 7s and 8s instead of knowing the answers by heart, because despite spending 15 minutes every school-day doing exercises like the one I've just described, I couldn't see the reason for knowing this stuff and so I didn't bother to learn it.

Nowadays there are proponents for and against rote learning of maths facts. Relaxed types say that you'll learn them by using them. They're probably right. My 7s and 8s are better now that I'm teaching them to Jemimah then they've ever been before (and can I remind you that I did University maths?). More formalised classical educators say that rote learning works and committing stuff to memory works better when you're younger so why not begin teaching maths facts to your four year old? They're probably right as well. We've had lots of success with early rote memorisation in our homeschool.

So which group to follow? Either, neither or both?

This dichotomy is not new. Back in about 1945 an Adelaide man called John Flanagan wrote a little book called Numbers - A Book of Figures. The forward, written by senior lecturer at Adelaide Teachers college, H H Penny, MA, PhD, Dip Ed (Pr), Dip Ec (phew!!) says this:

There was a time (wholly gone?) when arithmetic was the grimmest of lessons. Many will remember the dolorous chanting of "tables" day in, day out. And despite the massive weight of repetitions 9x7 would sometimes be 56 and 7x0 still oftener be 7. To the teacher of the old school every such error was an incitement to more and yet more rote work. Later came the view that children should learn their number facts entirely by experiment and use. "Away with the dulling drone of rote drill," said the New Educators. "Soft pedagogy," was the retort of the Old School-ers.

Today? Today we can see the right and wrong of both points of view. In a nutshell it is, I believe, this: Each new step, be it only the adding of 2 and 2 should be a conquest and a delight, but certainly should follow on the heels of conquest. There are so many "new steps" in arithmetic; they can be safely taken only if the child stands firmly on all the steps he has already been asked to take.

This as I see it, is the purpose and justification of Numbers - to give the child a firm grip of the basic number facts. From the very nature of the material there can be little that is new in the book. Its merit lies in the ingenuity with which the old, old facts have been grouped and displayed and in the thoroughness with which the ground has been covered.

Seems to me that in the past 65 years nothing much has changed.

Which is probably why I've found John Flanagan's little book as valuable in Jemimah's homeschooling as HH Penny predicted that it would be for kids back in 1945. To Mr/s Penny, "the aim of Numbers (was) that the learning and testing... (be)... 'thorough-going and comprehensive". I agree. To me, whether you learn your maths facts opportunistically or methodically by rote, the bottom line is that you must learn them. You can't do maths without them. First you need to learn your numbers. Next come your addition and multiplication tables, whether by rote all together, or bit-by-bit. The aim of this memory work is not an ends in itself, however. A child who can sing all of his times tables but not do a multiplication problem using these facts has learned nothing useful at all.

Second, the maths facts we learn need to build on each other. Our memory of a fact depends on how useful it is to us - and in how connected it is to other things we already know to be useful. My times tables were not useful to me during my school tables competitions, for example, so I didn't bother to learn them. I just wrote the stuff out mindlessly each day for a whole year with the sole aim of coming first in the competition.

"New steps...can be safely taken only if the child stands firmly on all the steps he has already been asked to take."

Some people will take this quote as support for a mastery based maths programme instead of a spiral programme. I disagree. I thing there are advantages and disadvantages to both of these approaches, but the thing that is important, regardless of which you chose, is that you need to ensure that the foundational skills are mastered befor you move on to something that requires that skill. Whether you learn all addition before subtraction and all multiplication before division or all basic skills in the four binary operations all at once is not the important thing here.

Understanding is what is important at each step - HH Penny called it a conquest - is the third thing. Conquer one step before moving up the ladder to the next. Got it?

Step one: Learn it. Step two: Know why. Step Three: Conquer it.

Which is where Numbers come in. As the author puts it so well,

Numbers is like your figures' gymnasium. This is the place to make your number memory strong. You have plenty of ladders to climb up and down. Be like the boxer with his punching ball. If you work you must succeed and will get your reward - speed and accuracy.

Yes, memorisation of maths facts is important to a child's later success in mathematics, but look at that memorisation as a means to an end. Look for real, relevant ways to use those maths facts repeatedly. Look for word problems that practice the maths facts. Over and over and over again.

And look to make the memorisation a conquest and a delight.

So what does your figures gymnasium look like? We use Numbers. It is worth looking out for this delightful little book during your second-hand book shop forays. Yours could be Maths games. Playing maths card games. Using Timez Attack. Making up fun and relevant word problems. The Living Math site is full of maths related activities as well. Perhaps you've discovered a way to make rote times table drill fun and exciting.

Look for ways to develop your gymnasium. Look for ways to exercise that number memory muscle. Then use your membership and don't let it lapse if the going gets tough. If your child still doesn't get it then be patient and try something else. All they may need is more time.

So finally, either, neither or both? Well it still doesn't matter much. Probably you'll use whatever works best for your students - or for you - or both! What does matter is that they learn their maths facts. Then they can move on to the good stuff that builds upon their foundation. That's what they're doing all of this for, remember, for what they can build on top!

Goodbye!

Well, every good thing comes to an end, so they say, and I have finished my explanation. I do hope you have been able to understand me. Would you mind if I told you one last short story? Two men had a saw. At the end of six months one man had a new table and some chairs; the other still had just the saw. Do you see?

Using the NAPLAN tests at home

I subscribe to the Department of Education and Early Childhood Development's email newsletter for parents of Victorian school children, Parent Update. I am always interested to hear what is going on in our local State schools, and generally find at least one article of interest. The October 16th edition was no exception and contained information on Victoria's performance in the NAPLAN tests.

Standing for National Assessment Program Literacy and Numeracy, the NAPLAN tests were (as the name implies) implemented Australia-wide last year for school children in Year 3, 5, 7 and 9. They test students in Reading, Writing, Language Conventions (Spelling, Grammar and Punctuation) and Numeracy. NAPLAN test results allow schools and systems to compare their students’ achievements against national standards and with student achievement in other states and territories. It also allows the monitoring over time. The National Summary Report: Achievement in Reading, Writing, Language Conventions and Numeracy 2009 is available online on the NAPLAN website. On the website you'll also find pdf downloads of the the Literacy and Numeracy tests for 2008 and 2009.

Now this gave me an idea.

Many of you, I know, use homeschooling curricula that regularly test your children's progress in major subject areas. Those of you who like me choose the Charlotte Mason method of educating and testing will be less sure where their children fit in relation to their State educated peers. Now this is not an issue per se. One of the main advantages of homeschooling to me is the opportunity it provides for me to tailor Jemimah's education to her academic needs, interests and, in particular, temperament, rather than having to accommodate the varying standards displayed by a class of 20 Grade 1 school students of varying abilities. Still, I was curious.

I administered the Year 3 numeracy test last Friday. You may recall that 7yo Jemimah is in Year 1, but is currently midway through MEP maths Year 3. I hoped that the standards would be similar. They were. Despite never having sat a test of any type before, Jemimah scored 29/35, or 82.85%. Her results placed her within the range of Level 5 or 6 (it is difficult to gauge precisely without the assessment tool), considerably above the majority of Victorian Year 3 students. I was very excited; her Daddy was very relieved. This was a concrete way for me to demonstrate her abilities.

This result gave me the confidence to administer the Year 3 reading test today. Well, my clever Grade 1er achieved 100%. Wow!! Imagine what Daddy is going to say about this one!!

Now before you dismiss this post as that of a proud and boasting mummy (which I'll admit I am, rather), please note that I won't be asking Jemimah to complete the Language Conventions or Writing tests any time soon. Don't forget, we're Charlotte Masoners. These things absolutely mustn't be attempted before year 4. That gives me a few years, doesn't it? Jemimah's spelling is appalling, dreadful, horrifying, dire, dismaying, terrible, ghastly and grim. I won't be showing you these results for quite some time.

Miss Mason assures me that good spelling comes with exposure to living books. I will be patient.

If you, like me are vaguely interested in where your child rates, hope over to the NAPLAN website and have a look around. You, like me, may be pleasantly surprised.

MEP minute-by-minute

...There is no subject in which the teacher has a more delightful consciousness of drawing out from day to day new power in the child. Do not offer him a crutch: it is in his own power he must go. Give him short sums, in words rather than in figures, and excite him in the enthusiasm which produces concentrated attention and rapid work. Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring.

Charlotte Mason Home Education p261

So this is for Phyllis. And this is her request:

I'd like to see a detailed description of how you do a (MEP maths)lesson. I loved what you have there already!

To be honest, Phyllis, I don't know how this post'll pan out, but let's give it a go, eh?

So, before we start, a review of where we're at, and what we're doing at the moment.

Okay. Today we're doing MEP Year 3 Lesson 18. If you look at the Scheme of Work, you'll see that during this week (Week 4) we're still revising Year 2 work. We're covering division with remainders and the four operations (addition, subtraction, multiplication and division). During this revision period Jemimah has really grasped the division process, so this additional practice will be good for her.

On the top of Lesson Plan 18 (you'll find that here if you want to follow along) you'll see that today we're Revising mental calculation and the four operations; the Core work is division with remainders, and Extension work covers problems in context, brackets and order of operations. This gives me an idea of which areas to focus on during today's work.

Today we started at 10 am. Generally we do maths at the end of our first block of work just before morning tea, or at the end of the morning. Doing maths at the end of a period of work discourages dawdling and procrastination - it is her own free time she is wasting!!

We work at the kitchen table. I used a kitchen timer to time the lesson for the purpose of this post. We just keep a vague eye on the clock normally.

10:00 We began with some skip counting and quick mental maths questions. Today we reviewed the 8x table. Generally this is included in the day's plan, but today's plan was different, so I just added this in as a quick fun introduction.

10:02 The first three activities are whole class activities. We work together on these and answer half each. We use the copymasters for this lesson. In a classroom a child would only be called on once or twice in a session, so it is reasonable to expect that she only be asked to do half of the questions. I note that Jemimah is having trouble with her 7x tables and ensure that she answers all of the questions relating to her area of weakness.

We cover the extension work at the end of question two together and then Jemimah elects to work at question 3 alone. You can see her above tracing out Robin Rabbit's walk. Notice that she is using a blue texta. We work all of our maths in coloured texta - makes it more fun, somehow. I use the time to unpack the dishwasher.



10:12 I pass Jemimah her Practice worksheet (pictured above)( it's page 18 here) and watch her commence question 1 alone. She shows a new and pleasing grasp of division and remainders, so I am able to leave her and make a cappuccino (did I tell you I love my coffee machine?) for me and a hot chocolate for Little Miss. She has these completed in 3 minutes - her exercises, not her drink...

10:15 We complete activity 5 together, but Jemimah is excited to have 'got it' and is keen to work all the examples herself. Together we complete the extension and she does well after I give her some examples.

10:18 Activity 6 is a mental maths problem. I replace the pence in the example for cents, and she writes the calculation in her exercise book, dated in the top right hand corner.

Activity 7 is a written example of the same type, so we continue on. Her calculation is rather odd, so we work it again together, and I show her an easier way to get the same answer. I again explain that the question uses £ and p, but we use $ and c instead.

10:22 Jemimah completes the table alone. She uses her toes when she runs out of fingers...a bit unorthodox and a little unladylike, but she needed to divide 99 by 5 and it seemed to work!!



10:25 I show her what to do with question 5 and she works it alone. This is her first introduction to letters representing numbers, but she has worked several questions with a blank box instead of the letters, so the new representation doesn't phase her.

We don't bother with the extension, since she has a grasp of the concept. We stop at exactly 10:30 - a coincidence, I'll admit, but maths generally takes us between 25-35 minutes in Year 3. In Years 1-2 we aimed to be finished in 20 max. If it takes any longer than this we just divide the lesson in two.

Sometimes I read of mums taking much longer than we do using MEP. I always wonder what the reason might be. Developing the habits that Miss Mason speaks of in the quotation above are certainly important. I find that Jemimah is more likely to dawdle if we do maths at the beginning of a block of work rather than at the end. I do not allow procrastination as a matter of course, and will act early to find a solution. Sometimes she finds the work too difficult and we work a few problems - or even the whole lesson- together. This helps.

It is important for me to remember that I have only one student and that I have the freedom to work at her pace. I do not have to worry that some students in a class are falling behind and that others are getting bored because of too much repetition. I have only her to worry about. She can gallop through a lesson like today's, which was easy for her, and slow down if she needs extra help. Sometimes she need only work half the examples; at other times I might make up a few extra. Sometimes we work together; at other times - and every Friday - she works independently. She never has to wait for the other kids to catch up. She never daydreams her time away.

Jemimah is working "above grade level" because we move on when she's ready, not when the whole class is. She's not at school; she doesn't have to do maths like she is.

MEP is perfect for us, right now, because it is perfect for her - and she's thriving on it!!

Smarties

MEP maths is even more fun when the counters are Smarties!!

MEP 101

So you're intrigued by the idea of MEP maths. You've read my blog posts and you've decided to take the plunge. After all, it's free - what've you got to lose? So far so good, but what do you do next?

In a departure from my usual blogging style, I'm going to walk you through the process. It seems so simple, but you can't believe how confused some people seem to get when things are simple...

So choose your starting point:

What is MEP anyway?

MEP stands for the Mathematics Enhancement Programme. It is a maths curriculum developed by the CIMT - Centre for Innovation in Mathematics Teaching - at the University of Plymouth in the United Kingdom. It is currently undergoing trial in British schools.

MEP is free for non-profit use and while not specifically designed for home schoolers, the programme works well with a little modification for a 1-on-1 teaching style.

You'll find the programme at their website.


What makes MEP different?

This is from the MEP website - adapted slightly for homeschoolers by moi. You can read the original on the Primary information sheet linked below.

• It has very high expectations of teachers and pupils.Maths is taught in an integrated subject in a spiral, ever widening curriculum through the Primary years, with continual revision of facts and concepts.
• Lessons are highly interactive and have many activities.
• The logical foundation of mathematics is stressed, with correct, concise mathematical notation and language used at all times.
• Visualising mentally and through the use of models and manipulatives, and relating concepts to real life situations where relevant, are important aspects.
• Creative thinking and critical evaluation and discussion are encouraged.

Most importantly, MEP aims to make all pupils mathematical thinkers and to make mathematics lessons challenging and fun for both teacher and pupils.

You're interested in learning more about MEP.

• Join the MEP-homeschooler's yahoo group moderated by the amazing Carol Hepburn and ask lots of questions.
• Read the Primary information sheet.
• Watch the video of how it's done in Hungary where the programme was first developed.

You don't know where to place your kids.

This is always a bit of a challenge. I just started Jemimah from the beginning. If you've already begun maths using another programme, then this is my two-bob's worth of advice...for what that's worth...

• Print off the Scheme of Work. This shows you exactly what MEP will be covering and when.
• It is better to begin at the start of a year. Which one suits, do you reckon? If you find your kids know many of the earlier concepts, you can always do two or three lessons per day until the work begins to challenge them once again. Then slow to one a day.
• Many people find that MEP is ahead of other programmes, especially those written expressely for homeschool like MUS, for example. I don't know - MEP is the only maths we've ever done.
• Once you've decided on a level, print off the relevant IPMA test. You'll need an access code to access the test, and the details on how to obtain one are on that page. .. Kids generally do this at the end of each year. You should expect your kids to get close to 100% on this test before you select a level. Clear as mud? What I mean is this: Say you've chosen to commence little Johnny at Year 3. Open IPMA the test for Year 2. These are not placement tests. They do not cover all the work that has already been taught for a particular year. If your child doesn't get close to 100% he or she will find the next year's work too difficult.
• Remember that is is okay to tweak your child's level. If it all gets too difficult, then just adopt the 'pin-the-tail-on-the-donkey method and give a year a go. You can always go back or forwards!

You've decided to give MEP a burl.
Congratulations. I don't think you'll be sorry. After all - it's free, right!
Now comes the fun bit. You'll be giving your printer a bit of a workout for a few hours - do you have enough paper and ink? Beetle out and get those before you start. While you're at the newsagents, pick up a folder - we use this one (pictured above)because it contains a pencil case as well as pockets for manipulatives; some dividers; an exercise book; some felt tip pens in bright primary colours; and a ruler. While you're gone, send your children outside to start a collection of counters. Shells, pretty pebbles, sticks, pretty much anything that interests them, really. We use the counters from our Go board game.


If you're doing Primary maths, on this page you'll find the entire MEP programme to print out...well almost all. There is a text book that is available for purchase. You don't need it - really - but if you want to buy one, here's the order form.
Regardless of grade, you'll need to print the following:

• Practice book - these are the pages that the children complete - the worksheets as it were. Warning - you can't do MEP with these pages alone. You'll also need...
• Lesson plans - these are your sheets. They tell you how to teach the programme; give the answers; and introduce new concepts. They also contain mental maths drills. You need to do MEP with your children.
• Copymasters - Some of the copymasters are contained in the practice book; others are not. I print them all, and don't use everything. Other mums only print out the pages they need. It is up to you. I need to be organised before I begin, and this way I only need to print at the beginning of a new practice book.

You'll notice that some files on the website have a small red P beside them. These are password protected files. Interestingly, if you use an older version of some software you may find that you can view the files without a password. For the rest of us, you'll find the password in the files of the yahoo group here.
I print off a section of pages at a time, not the whole practice book. There's about 30 lessons in each, and that amount fits well in my folder.

Label your dividers with something like these headings and place the relevant pages behind each:

1. Practice Book
2. Lesson plans
3. Copy masters
4. Mum's pages

I have a fifth divider that I call French maths. We do our maths bilingually using pages that complement MEP. If you are teaching Spanish, MEP is available in that language here.
Under Mum's pages I keep:

• The scheme of work
• Notes on the lesson plans Years 1 and 2
• The posters I only used these for Year 1. In Year 2 we found things around our schoolroom instead. Note also that the posters aren't in the correct order. You need to use your nouse a little to work out which poster the lesson plans actually refer to. at some stage I'll correctly number them and pop it in another post.)
• The OHP transparency collection. You'll need 1-5 for year 1 and the rest for year 2. You'll find reference to them in the lesson plans when you need them. I print them all off at once. Print in colour.

Finally organise your manipulatives.

You'll find most of the manipulatives you'll require supplied. Print all cards on cardstock. You can laminate them if your kids are hard on their things. I didn't bother but we did take care of them.

• Number cards Years 1 and 2. You'll need two sets.
• Number lines Years 1-3. Print on card stock, colour each line a different colour and laminate. You'll only need one, and it's very useful.
• Sign cards Year 1. You may use these in Year 2, but less often.
• Shape cards Year 1 and 2 (and maybe later years?)
• Shape cards with dots Year 2 (and maybe later years?)
• Purchase some cheap plastic dominoes - two sets preferably. Year 1 and 2
• Some cuisinaire type rods would be nice. Jemimah got some for her first birthday from an uncle with high expectations. You don't need them, but they beat cutting up strips of paper IMHO. Year 1 and 2
• A purse with coins of your own currency. Year 2
• A packet of toothpicks. Year 1 and 2
• Finally, you'll need the counters we discussed earlier. MEP says this:

Encourage pupils to collect their own materials for use in maths lessons. (eg pebbles, shells, buttons, sweets, trinkets) to make maths for relevant to them individually.

Getting started
Now it's time to start.

• Allocate a time early in the day when your mind is fresh (and so are your kids!!).
• The first few lessons may take a while. don't panic. Soon you should get finished in 20-25 minutes. Less sometimes, slightly more when a new concept is introduced.
• Don't allow procrastination. If you do find it occuring, investigate why. For us it happens when Jemimah thinks she can't do something (even if she can).
• If a lesson does take too long split it up. don't allow maths to become a hard slog that everyone dreads.
• Use coloured textas to answer questions and to liven up the page. colour things in if you like.
• Have fun!

And now folks, I think that's it. MEP 101. Do let me know if I've left something out. I'm happy to edit and make it useful. Also, don't forget this is MEP à la Jeanne. You may find it works differently in your home. Doesn't matter, really. There are no MEP police...not in Australia anyhow!!

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Post Script 12/08/09

There have been literally hundreds of visitors to this post. Some of you have come from the MEP or AO Yahoo groups, others from the Well Trained Mind Forums, and even others from an Aussie group. I hope you have found what I have written useful to get you started with MEP.

Be sure to read my follow-up post MEP minute-by-minute, which shows what an MEP lesson actually looks like in our home. You'll get to see Jemimah counting on her toes there as well!

Hey, you now know lots about us, but I don't even know who you are! Please leave me a comment to let me know you've visited!

Please do.