A week of maths.

Over at the
4 real learning forum, I am a moderator for the maths section – Living and Loving Numbers.

We have recently been discussing maths without a textbook.

I’ll be up front – my children do have maths workbooks. Of their choosing, with discussion and input from me.

They do not, however, work in maths books every day.

Okay, they don’t work in any book every day!

This is the essence of unschooling. Seasons of unschooling.

We have had seasons of no maths books and seasons of books.

I love keeping maths journals with the kids.

I like to often just see how maths will come up in every day life, without me manipulating things for a “maths lesson.” Keeping a (maths ) journal for myself of these daily/weekly things has enabled me to see learning.

And I also like going to the library to the children’s non fiction and pulling out a different fun maths book or maths picture book on each visit, for us to borrow.

We have used games books, maths cooking books, history of maths books, maths for real life, “all the maths you’ll ever need” books for teens – you name it!

Over the last week, I have kept a log of our unschooly maths activities, for the purpose of sharing at the 4 real learning forum. I am sharing it here, too.

Here is the log of some of our maths activities this last week.

As you can see, we have some workbook stuff and non workbook activities.

1. Collaborative and internet computer games followed by discussion on problem solving and strategies.

2. Plan routes for delivery of newspaper, using street directory and co-ordinates.

3.Work on budget and wish list, check savings record and bank statements.

4. Written maths – workbook pages on fractions, patterns, probability, money and written problems.

5.Fractions and double recipes for cooking.

6.Mental calculations while playing board games and rpgs – Rum Rebellion, Tunnels and Trolls.

7. Probability and calculations – card games – Bridge, 21s, Up and Down the River, etc.

8. Play with our geoboards and discuss making another geoboard.

9. Mathematical thinking – game of RISK.

10. Maths journals – mathography – when and how did you learn to count? How old were you when you first counted to 100? When you were younger, what did you think about maths?

So we are doing “things mathematical” ( very Gilbert and Sullivan ~ The Pirates of Penzance) . Sometimes this is formal and sometimes informal. Sometimes suggested by me ( the written maths, the maths journal) ~ sometimes initiated by the dc.

“The best way to meet numbers is in real life, as everything else. It’s embedded in the context of reality, and what schooling does is to try to take everything out of the context of reality. So everything appears like some little thing floating around in space, and it’s a terrible mistake. You know, there are numbers in building; there are numbers in construction; there are numbers in business; there are numbers in photography; there are numbers in music; there are fractions in cooking. So wherever numbers are in real life, then let’s go and meet them and work with them.” John Holt in an interview for the Natural Child Project.

“Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas…which should quicken the imagination. How living would Geometry become in the light of the discoveries of Euclid as he made them!” (Charlotte Mason Study Guide, p. 107-108)

Charlotte Mason also said, “The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders…” (Charlotte Mason Study Guide, p. 106)


Feast of the Archangels

September 29.

Traditionally, I make a Devils’ Food Cake on this day – well, when we have time, that is.

You can see the connection can’t you? – St Michael fighting the devil.

This year, I looked for a lower fat version of the cake.

I found a recipe for lower fat devil’s food muffins, in the
Calorie Queens book.

Here is my adaptation. Makes six muffins but the recipe can be doubled/tripled.

One muffin is definitely enough!

Devil’s Food Muffins

2 tablespoons Nutella
1/2 cup sugar
2 eggs
1 cup self raising flour
1/2 cup skim or no fat milk
1/3 – 1/2 cup chocolate chips

Preheat oven to 180 C. Lightly spray muffin cups with cooking spray.

Cream together the Nutella and sugar. Stir in eggs and beat until smooth.

Stir in the flour. Stir in the milk. Fold in the chocolate chips.

Divide the batter between the six muffin cups. Bake for 20-25 minutes or until muffins spring back when pressed.

Serving – two muffins, 240 calories, 6g fat.

But I only had one!


Homeschool learning.

I have been inspired by the blogs of Julie,
Cindy and Maria.

I enjoyed their sharing of homeschool learning.

I thought I’d share our homeschool learning – burned popcorn ! I will try to post some pics.

A chemistry experiment that failed. I burned the microwave popcorn ~ we were experimenting with different methods of cooking popcorn. The effect of heat.

Well , cooking is certainly not my forte ( I haven’t found my forte yet).

But – mistakes and burned popcorn are learning experiences.

Homeschool learning.

Julie’ s blog describes relaxed homeschooling.

She writes – The chief difference between home education and school is the word “home.” School happens in a building with teachers and dozens of other age-mates who must work through a set curriculum for each subject so that the school system can measure its effectiveness in achieving goals and standards of education. Fair enough.

Home is a whole other animal and that’s why we have such difficulty figuring out if what we’re doing is working, or whether or not we are producing comparable results to school. Let’s just admit right up front: we don’t do a good job of duplicating what school does. In point of fact, we signed up for this homeschool gig in order to not produce all the things school does.

But that admission needs to make us brave, not cowards. If the conditions of education at home are not the same as school, then Pysch Reseach 101 teaches us that the results will be different.

Read all of Julie’s post. It is a good discussion of what homeschool learning can be. Is.

Then read these other blogs.

Cindy shares her history learning with her sons.

Maria writes about classical unschooling in her home.

And, apart from burning popcorn, what sort of learning experiences are going on here in our home?

The popcorn was inspired by our attendance at Group Learning today. We have been undertaking activities in Chemistry with the other Group Learners ( homeschoolers) this term. Our focus has been kitchen or food chemistry.

Today, I am working with the Juniors ( ages 6-11). The topic is Eggs and Starches.

We are looking at the denaturation of the protein in eggs and making meringues ( which I will probably burn! lol! Typically, my meringues turn out to be shapeless blobs of an alien nature).

We are looking at the moisture content of carbohydrates and making popcorn. The reason for the (burnt) experiments above.

Here are my notes, in case you’d like to try these activities yourself. Hopefully, your food chemistry activities will not set off smoke alarms.

Meringue and the properties of egg whites

*To demonstrate how the protein in egg white can be denatured by mechanical energy.

*Observe the egg white in different stages of preparation, with and without sugar.

4 egg whites
pinch salt
250g. caster sugar
1 1/2 dessertspoons cornflour
1/2 teaspoon white vinegar


1.Pre-heat oven to 130deg.C. Lightly grease biscuit trays and then
dust with cornflour – shake off excess.

2.Beat egg whites and salt until frothy (at the mouth). Gradually add sugar, a spoonful at a time, until all the sugar is incorporated and the granules
have dissolved – test by rubbing a small amount of mixture between thumb
and forefinger. Add cornflour and vinegar and beat to mix in.

3.Using a spoon, place small amounts of mixture
on the prepared trays. Place in the oven and bake for 40 minutes. Turn oven off and leave door ajar until the oven is cool.

1. Egg white is made of water and protein.
2. When the egg is whipped, the structure of the protein is changed by the beating.
3. Is it possible for the egg white to return to its non whipped state? No, when protein is denatured, it is a permanent state of change.
4. How else can protein be denatured? By heat – cooking meringues, cooking meat or eggs.

Popcorn and the effect of moisture on seeds.

To determine the effect of moisture content on the ability of popcorn to pop.

1. Observe the difference between wet and dry popcorn.
2. Observe the difference between cooked and uncooked popcorn
3. Why is some popped corn big and some small? It depends on the differences in moisture content in the kernels.
4. What happens to water when you boil it? The liquid will convert to steam and the steam takes up more space than the liquid. So, the liquid or moisture content of the popcorn helps the corn to rise and pop.
5. Moisture inside the seeds affects the size of the popped corn.
6. The application of heat also causes the corn to pop.
7. Carbohydrate in popcorn helps the corn to expand.

½ cup popcorn
A bit less than ¼ cup canola oil
In a mixing bowl, add canola oil and popping corn.
Rest a paper plate on top of bowl (it is fine if it is resting in the bowl on the corn, it will rise up with the popping and keep kernels from going everywhere). NOTE: put the plate right side-up or upside-down depending on how it is resting in/on the bowl. The idea is to avoid dripping oil steam in your microwave if you can.

The tricky bit is how long to microwave. Set it for about 5 minutes ( probably less, in my experience!) and listen for the popping to slow. Add more time if needed. If you go too long then you get some burning. ( Some burning? )


Sharing my reading and thinking.

I am currently reading four books.

One is Scott Hahn’s “The Lamb’s Supper.”

Can I share a quote? I read this during my prayer/reading time this morning.

“We offer ourselves and all that we have. Not because we’re so special, but because we know the Lord can take what is temporal and make it eternal, take what is human and make it divine. The Second Vatican Council spoke powerfully of the offering of the laity: “Their work, prayers and apostolic endeavours, their ordinary married and family life, their daily labour, their mental and physical relaxation…all of these become spiritual sacrifices acceptable to God through Jesus Christ. During the celebration of the Eucharist these sacrifices are most lovingly offerred to the Father along with the Lord’s body. Thus as worshippers whose every deed is holy, the lay faithful consecrate the world itself to God.” ( Lumen Gentium 34)”

Hahn also writes, with regard to the Mass, that
~ ” Homilies don’t have to entertain us.”

Ouch. Father’s homily yesterday, on praying well, was an example of this.

Not entertaining but requiring me to question myself. Another ouch.

Am I praying for God’s will or for what I or dh want?

Is my work and life a spiritual sacrifice?


Home is for self expression, not good impressions.

“Home is for self expression, not good impressions.”

So says the mother in the 2006 re-make of the film “Yours, Mine and Ours.”

I like this comment. Home is where we get to be and to explore – we don’t have to try to make a good impression on others. We are ourselves – learning and growing, yes, but ourselves.

Anthony’s current exploration at home has been triggered by the movie “Troy.”

{ Aside – it is too funny to see how much of our learning is inspired by movies! }

“Troy” is not super movie and it is not historically correct and you may have to FF through some scenes. It, was, however interesting to watch.

Anthony , since watchng “Troy”, has been reading re-tellings of “The Iliad” and “The Odyssey” by Barbara Leonie Pickard. We have all been discussing Greek myths and legends.

All learning, all tastes of learning and of life, all our expressions and explorations at home are valid learning experiences.

It all counts.

This is not, by the way, a postmodern view that “anything goes” or that all perspectives are societal constructions or even “only” culturally relative.

It is a view of learning as one thing leading to another. It is a support of both pop culture and “high” culture.

I have seen this one thing leading to another in my own home – my sons can read Garfield comics and Shakespeare stories in one day. Can enjoy Vivaldi’s Four Seasons and Good Charlotte.

James Paul Gee, in “What Video Games Have to Teach us About Learning and Literacy“, discusses a canonical list of books which one must read . He discusses learning and video games and “high” and “low” culture.

Gee writes – Right wingers and left wingers who argue over the canon ( of books) tend to act as if people…will read books realizing and accepting their “inferior station” and either want to emulate their “betters”..or passively accept their inferiority as dupes of the elites in the society…. The Mary Smiths of this world need do no such thing. They already know that they are thinking, worthy beings. They sometimes see in canonical literature examples of who and what they could be ….

But schools have, by and large, tamed the canon ( of books). They have made it into the stuff of tests, of multiple-choice answers, and standardized responses. Everyone, now, finally has access to the canon at a time when schools have rendered it toothless and the left applauds ignoring it as a historical vestige of old, dead, western, aristocratic elites……

I am not pleading for the canon here, least of all, as a list…I am claiming that elites can use anything – canonical literature, the Bible, biology or any other sort of text – to attempt to dupe people by trying to force them to read it in the elite’s way. I am claiming, as well, that there are plenty of Mary Smiths who are more than capable of saying ‘No, thank you’ and reading it both their way and intelligently.

Video games are a new form of art. They will not repace books; they will sit beside them, interact with them, and change them and their role in society in various ways , as, indeed, they are already doing strongly with movies…We have no idea yet how people ‘read’ video games or what meaning they make from them. Still less do we know how they will ‘read’ them in the future. It won’t do to start this investigation by assuming they are dupes of capitalist marketers – though, of course, some of them very likely will be. But there will always be Mary Smiths out there who use cultural products, whether ‘high’ or ‘low’, for good purposes.

The self expression and exploration of learning in our house tends to be such a mix of high or low cultural products. An eclectic mix . A learning mix. Hopefully for good purposes.

From “Troy” to “The Illiad”.


Hello from Jonathon!

Hey!!! Jonathon here.
Been a while since I was last posting here, so I thought there’s no time like the present!
I’m not doing much right now. Just finished work on a new painting. It’s called “Escape”. Basically, it shows a kid walking through this field, away from his old life and into his new. I’ll see if I can post pictures this week. Sadly, it’s too big to scan and I’m currently not on speaking terms with our digital camera. It just doesnt understand me.

Tomorow I have youth band again, which should be fun! The members of the band came ’round on friday night and we all watched Back to the Future. I’ve been practising Michael J Fox guitar playing ever since….

Anyway, I’d better head off to bed. But first, I just want to say thankyou to mum and dad for being the best parents anyone could ever ask for. I know you’re going to read this mum, so thankyou!! 😉 I really am lucky.

Goodnight everyone! Hope you had as good a week as I did.



A shopping spree.

Have you seen the film “Clueless” ?

The main character in the film goes shopping when feeling down.

I am avoiding a decision 🙂 so, while the kids were at a movie this morning with Homeschool Teen Group ( they watched Stormbreaker) ~ well, I went shopping .

At Borders.

Above are two of my finds.

I sat and read , sipping coffee at the Borders coffee shop.

Then met the boys and friends for lunch at the Food Hall.

I think Teen Group is just as much fun for mums and younger siblings.

Shopping therapy is pretty good, too.


Turbo Jam again.

Turbo Jam is my happy workout. Lets me have fun while working out – and I want happy right now. lol!

It also gets results – down 500g this week and a mum at Kumon asked if I’d lost weight – said she really noticed I was looking thinner. WTG!

You can check out the cover of one of the new TJ workouts .

Can I ask for more TJ for Christmas?