Numbers as Language

I spent a couple of hours today having quality time with my dentist. He was doing some salvage work on my 3-6 using a 10 long and a 23 mesial clamp. As I lay there staring at the ceiling, I began to wonder about the use of numbers in language.

And then I realised, numbers are language.

We use language to communicate - and numbers do the same. Just as my dentist was communicating with his assistant to pass information and tools.

And we do that everyday in the classroom. Maths is part of our language. As I often tell the kids, the numbers came when we needed to do something like count, measure, record, compare or score. Before we had numbers, our language was deficient, it failed to communicate some really important ideas. 

If we didn't use numbers, what else could we do?

Well, we could use comparative language, like big, bigger and biggest. This would work if we were comparing three things but any more than that and we would be stuck. Imagine the dentist trying to get the correct tool by saying, "I need the one that is bigger than the big one but not as big as the biggest one." Great, if he only has three tools to work with.

What other elements could we use to distinguish between a variety of objects? Well, the dentist could colour-code his tools but once there are more than seven or eight colours, it starts to get a bit subjective. Have you ever looked at one of those giant tins of coloured pencils? How do you tell the difference between aqua and teal? Or look at paint charts. Can you honestly see any variation between Antique White and American White?

Or maybe the dentist could name all his tools. Perhaps they could be named after Prime Ministers of Great Britain or his friends at school or 70s pop stars. But that would mean learning a whole system specifically for his set of tools. And if his assistant was ever to be sick, take a holiday or resign, he would have to teach his system to a new person.

No - numbers have universal appeal because we can bring some prior knowledge with us when we use them. We know that 23 is bigger than 21, therefore the 23 mesial clamp is going to bigger than the 21 but smaller than the 24½. And if they are all lined up in order, you could probably work out their relative positions.

And the dentist won't have to retrain every assistant that ever works with him.

At least not to the extent of teaching them how to count.

Why I Don't Use Food in Maths

I was tweeting with Stephanie Adan @stephyadan last week - she is an enthusiastic education student on prac in Sydney - about some ideas for lessons on fractions. The issue of using food as a teaching tool in maths came up - seems every book you pick up suggests using pizzas or cakes or lollies or M and M's etc. 

In the past I have done the same - cutting up pizzas for fractions and measuring out rice for activities with mass - but in reflection I think I have a problem with using food this way. 

Here are some of my reasons:

1. Allergies

Not sure if your school is the same as mine but we have a number of students with food-related allergies. Many of these allergies are life-threatening. If I was to bring in a cake to cut up for fractions work, it would need to be nut free, lactose free, gluten free and egg free. Or I could exclude the kids who had these allergies from the lesson. I don't think this would be fair - or safe. 

2. Religion and Culture

We are currently in the middle of Ramadan in Australia. It would be pretty insensitive of me if I was to bring food into my classroom to use for maths. There are children who would not be able to participate and it would put them in a difficult position. There are other cultures and religions that have specific requirements with food preparation and handling that I could inadvertently offend by using food in my lessons. 

3. World Hunger

There are people around the world who do not get enough food to eat each day. Can I ethically justify using food as a maths resource while they are starving? I want the children I teach to have an awareness of their global responsibilities - by respecting the needs of others' and by not trivialising significant world problems.

4. Hygiene

My classroom is just that - a classroom. It isn't a food preparation area and hygiene standards are not what would be required in a restaurant kitchen. I don't want the responsibility for any sick children who cross-infect others as a part of a maths lesson.

5. Sugar

I've mentioned my feelings about sugar elsewhere in this blog. I don't think children need to be given more sugar by teachers who are using jelly beans or Skittles as part of a maths lesson. I need to be making responsible choices on behalf of the children that I teach.

6. There are other ways

Be creative - think of another resource that you can use to demonstrate and practice the skill. Coloured plastic counters may not taste as good as sugar covered treats, but what the kids really crave is affirmation and recognition from YOU - the teacher. If they only want you for your chocolate, then that's a pretty shallow relationship.

Am I a hypocrite?

Probably.

I did write about a lesson we did with our buddies last term when we cooked muffins to teach measurement. Wasn't that food? Wasn't that what you just said not to do?

Well, yes and no.

The purpose of lesson was social as well as mathematical. We were having a celebration party to end the term and thought we could prepare the food as a bonding activity with our buddies. 

The ELC has a kitchen that we used - it wasn't a classroom as such - so we were able to keep things pretty clean. 

Yes - we did consider children with special dietary needs. We were able to accommodate them with variations in the recipe. The boy with the most critical allergies was provided with an alternative food by his mother but he was able to participate in some of the measuring and mixing of the muffins.

We didn't waste the food or play with it - it was part of our end of term party. 

Rainy Day Maths

It was raining at school this morning so I let the kids into the room to stay warm and dry - what a nice teacher!

Some kids sat in front of the heater and chatted.

Some kids got out a game of monopoly.

And some kids got onto the white board....and started doing maths!

One decided to calculate the value of 10! - that's 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10.

Here's his working:

And another chose to calculate 3^10. 


Here's the working for that one:

Think we got a bit carried away with that one but the thought was there

What a great way to spend 10 minutes on a rainy morning!

Sugar in Your Cereal

I have a pracky working with me and the class for 8 weeks. She's 3rd year and has some really good ideas that we have been trying out.

One of the things that she has provoked us to think about is sugar. We were all amazed at some of the foods that contain added sugar and the vast quantities involved.

She also found a youtube clip for us to look at about the sugar content found in a certain fast food brand. (Click here to find out more...)

Maths for Breakfast

Which got us to thinking about other foods. Breakfast cereals are also very high in sugar, a fact that we confirmed when we researched inside our pantry cupboards for home learning.

To make it visual, we decided to spoon out the sugar content of some popular cereal brands and measure them on the balance scales.

I didn't really want to go and buy sugar for this purpose, so we used sand from the sandpit - it probably has a different molecular weight and density so it was never going to be a perfect substitute for sugar, and yes it tastes different too.

But it served as a satisfactory sugar substitute for our purposes.

Data summarised from http://www.sweetpoison.com.au/atp.pdf 


Using data from David Gillespie's website "Sweet Poison", the students completed measurements by converting teaspoons of sugar (or sand) to grams.

Starting with a cup of sand and a spoon

Carefully measure the sand out.

Lots of interesting discussion about spoonfuls.

Should it be level or heaped?

Do all people have the same sized spoon?

Is a spoon a good measure of mass?

Balance out the sugar with the weights.

So what?

It was:

- really visual

- really hands-on

-really fun

And we got a bit of an idea as to what a gram is like, and 5 grams, and 10 grams....

The Convertameter

I had a good idea the other day. 

It's quite simple. 

I call it "The Convertameter".

It looks like this.

That's it. A simple piece of paper with a few words on each side and a dot.

But what can this little baby do?

Let me show you.

You start with a line of zeros and some digits 1-9.

Place the digits to indicate what the value is you want to convert - in this case 1250 grams.

Simply flip The Convertameter over and hey presto!

We have the answer in kilograms.

I gave this little treasure to the kids a few days ago.

They didn't believe I'd thought of it.

"You must have got it off Google!" they said.

Well, no I didn't.

Anyway, we used it for 10 minutes to convert a few grams to kilograms and back again. Here's a few other things that the kids had to say:

This is becoming too easy.

You just move the decimal point three spots over.

When you want to convert grams to kilograms you move the decimal point three spaces left.

If you want to convert kilograms to grams you need to times the kilograms by 1000.

There’s three zeros in a thousand which is how many 1kg is.

1.654 – on this one you just take off the dot.

And with a bit of prompting, they soon realised 

the beauty of The Convertameter.

Well, you could use this for meters and millimeters

Or litres and millilitres

Or kilograms and tonnes

Or.....

I retain all rights to this idea, the name "Convertameter" and the design BUT if you want to use it in your classroom, you can as long as it is not for any financial gain, profit or benefit. Just for educational purposes in your own class okay?

Report Wordle

I've just finished writing the half yearly reports for my class.

It's always interesting to reflect back on what I have written. Here is a Wordle I created of the comments that I wrote:

Interesting to see what words I use a lot - "good" seems to feature pretty frequently, as do "knowledge", "work" and "understanding".

I'm pretty happy to see words like "learning", "enjoys", "discussions" and "inquiry" up there as well.

A feature of our reports is the student comment. Each student gets to write their own reflection on the front cover, giving their own perspective on their learning over the semester.

I did a Wordle of their responses as well:

I'm really glad that "enjoyed" is the most used word in their comments. "Maths" is in there - along with "fractions", "dance", "art" and "inquiry". All positive signs.

Give it a go. See what your kids come up with.