Tuesday, 10 March 2015

Sort it Out

I have taken an interest in how children sort things.

I want to know what things they use to organise groups of objects and how they can show this grouping and explain what they have done.

So we got out some stuff - every classroom should have bucket loads of stuff for this very purpose.

I have been collecting milk tops for a while now - they are all pretty colours and just end up in the bin. They are an ideal maths resource.





Step 1 was to discuss a question that could be answered by sorting out the lids. This was harder than I thought it would be. I was assuming that the idea of comparing one group to another or showing which group was the biggest would be pretty obvious - but it wasn't.

And here is where I think I started to influence the thinking a bit too much. Anyway, more of that later.





Once sorted, I wasn't happy. How can you tell which group is biggest? 





So they lined them up - but I STILL wasn't happy. Can you put them side by side to use length as the basis for comparison?





Now, is that really fair? They don't all start at the same base line. Don't you need to line them up?





This looks better - to me at least. But have I been influencing the process too much? In getting the kids to "do it my way" have I gone beyond gentle "challenging and provoking" to a very un-subtle "influencing and directing"? Have I forced my adult thinking onto their own creative ideas? And if I have, was it a good thing or a bad thing?

Certainly there were a few mathematical concepts that we needed to address in comparing groups - but because I stepped in, I may have killed the opportunity for the kids to discover them for themselves. 

So I tried to step back a bit and let the kids do their own sorting to show difference between groups. Here's how they did it - much more creative than my "line them up neatly" strategy.




So hard to sort! So many different categories! 
You almost need a different group for every marble.




Right! The counters make a number to show how many there are.



Just enjoying the shapes...




Note to self - step back a bit. The photographer doesn't need to be in the picture...







Friday, 20 February 2015

What direction does time travel?

We have started the year with a look at time - using clocks, calendars and diaries. It is a really interesting place to start and has given us some interesting experiences already.


Thank you, Father Richard

We have an extraordinary chaplain at Radford - Richard Browning, known as Father Richard. He has often spoken to the kids about our Western perception of past and future, where we think that the past is behind us and the future is spread out before us.


To demonstrate this he will get someone out the front to sit on a chair and point to the future (in front of them) and the past (behind them).

BUT

…he goes on to explain that other cultures see things differently. Some indigenous cultures think the past is in front of us and the future is behind.


We can see our past, what we have done, what we have experienced. The future is behind us and we cannot see it.

Considering these ideas, I wanted to hear what the kids have to say about time.

I wrote the months of the year out on different coloured cards and then asked them to organise them for me.

Here is what happened:



So here was the first idea. Very linear and a perfect display of the months of the year.

But then I asked, is there another way?

So someone suggested:



Ah-ha! The colours relate to the seasons, don't they? So we can use that as a guide and then arrange it summer-autumn-winter-spring.

But then I asked, is there another way?

And we got this:




Hmm, so time can be seen as a circle or cycle? Nice thinking.

Right, time to get personal and individual - get out there and draw your own representation of how the months of the year should be arranged.

And the kids never disappoint:


Yes - it's linear BUT this student has decided that the year can start and end with December.



This one looks rather random but the months are grouped into seasons.



The months and seasons as a brick wall.

What other shapes could we use?



A circle….


A triangle…



A raindrop…



And then this one - each season is represented as a separate circle but "it was really hard because I had to write some of the months backwards to show it was going around in circles."


Never under estimate the kids - they will think of things you never had.

And why don't we think of the year as being shaped like a raindrop anyway? 













Wednesday, 18 February 2015

Maths is… from Year 2

Well, we're back into it for another year.

This year, I am teaching Year 2 (that makes 5 different grades in 5 years - is that a record?) and I wanted to start the year with my favourite activity.

I gave the students a sentence to complete:


Maths is…


I'm always keen to get into their heads from the start, to see what they think about maths and to get some insight into their expectations.

Here's a few of their responses:



Good to see that numbers are a part of it.




And here is the idea of operations with numbers.




And a few more operations - subtraction, multiplication and division.




Addition, subtraction - and counting.




Now this is interesting! It's about questions and finding solutions.




And ultimately - FUN! Glad someone came up with that one.


Love the insight that kids have into some things. These guys are only 7 years old and they already have some pretty strong perceptions.


A Goal for 2015


Word is out in the school that if you end up my class, you are going to do a lot of maths.

Interestingly, a goal I have set for this year is to promote…

READING.



Yep - it's going to be a big focus. 

But yes - we will also being doing lots of maths. I don't think maths and reading are mutually exclusive. In fact, I think I can see ways to make them work together…

In fact, I've already been checking out a few blogs and websites that discuss literature relating to maths.

I really good one I found so far is:


Check it out!






Sunday, 28 December 2014

Bye bye 2014 - here comes 2015

So that was 2014. All done.

Lots of interesting things happened here at AIM, including the Maths in Sport interviews way back in January and the Maths in Dance series in July. I might go back and read through a few of them, they were good.

I have decided not to do a similar series this January but will be taking a break and having a family holiday, so things will be pretty quiet here at AIM.

My plan for 2015 is to change the look of this blog a bit. I'm ready for a bit of a new look so stay tuned for how it will evolve. 

I'm hoping to include more video and more student reflection - they are my two big targets for the coming year.

I will be teaching Year 2 in 2015 so there will be a noticeable shift towards that end of the teaching spectrum.

I also want to do some more of those interview series - perhaps looking at Maths in Music and Maths in Science.

Finally I am also hoping to engage with other classes out there and do some collaboration, particularly at the Year 2 level. I have one class in Melbourne lined up and ready to roll - the class of my (former) close friend and colleague Capitano Amazing (Richard Black) who has left the nation's capital and headed south. So if you are interested, get in contact.

My e-mail address is bruce.ferrington@radford.act.edu.au

Anyway, you all have a great holiday break and we will get back onto the blog sometime in late January.

Be good!





Friday, 14 November 2014

End of Year Reports Wordle

As is my habit now, I have completed a Wordle using the text from my end of year reports.

Here's what my comments about my kids looks like:





 I've posted it in "extra-large" size - I know it will go off the page a bit but it makes it easier to see.

I'm glad to see words like IDEAS and ABLE and GOOD coming across strongly. Good to know that these are the things I talk about most often in reports - especially the "ideas" thing.


Next level down we have INQUIRY and KNOWLEDGE and WORK and LEARNING and UNDERSTANDING and DISCUSSIONS. This is an interesting group - lots about the learning process. Glad to know that I am commenting about that.

A few maths words jump out - NUMBERS and MULTIPLICATION and DIGITS.

Something I do notice is that a lot of the Learner Profile words, that describe the individual and how they approach learning, and words that describe attitude are very small - something for me to reflect on. Next time I will...

Give it a go - drop your report comments into Wordle and see what comes up.

 








Thursday, 13 November 2014

Fractions Workshop

This afternoon I attended a Canberra Maths Association (CMA - check out our website or Facebook page) workshop on Fractions being run by Caroline Evers. 

Caroline is a Canberra teacher with a great breadth of experience from primary school up to college level. She had some great ideas that she shared. I want to show you one of them. It is beautiful in its simplicity but in the multiple layers of depth that you can uncover with it.

We chose some coloured A4 paper and had to fold it in half, then in quarters, then in eighths. I did mine like this:


We labelled the sections as we went along. 

"This is a half."

"This is a quarter. I made it by getting half of a half."

"A half is bigger than a quarter."

"This is an eighth. It is half a quarter. It is a quarter of a half."

See this conversation? We are already laying the groundwork for multiplication and division of fractions! 

1/2 x 1/4 = 1/8

But we could also compare and combine the different fractions to see which were biggest, smallest, equal etc.

The Caroline moved us on to thirds and sixths. Fold A4 paper in half, then into thirds. Label as you go:




Ah-ha! So, one third of a half is a sixth! 

1/2 ÷ 3 = 1/6


And then we did fifths and tenths:




You guessed it - a fifth of a half is a tenth. And there are 5 tenths in a half. Sounds like equivalent fractions to me.

And it is all so visual.

You could do this with early years classes to show what fractions look like and get that understanding of what a fraction of a whole is.

You could use it with upper primary classes to look at equivalent fractions, adding and subtracting fractions and even looking at comparing areas of rectangles (e.g. - all the different ways you make an eighth of a piece of A4 will have the same area).

And you can use it in high school when you start to multiply and divide fractions with different denominators. Or with fractions in algebra. Or with...

Ah! It looks so simple on the outside but this activity has lots of possibilities. Give it a go and see what you can do with it...



Monday, 10 November 2014

Playing with Probability

Having started the conversation about probability, I was keen to push on and get our hands dirty with a bit of investigation.

First thing we looked at was rolling dice. Each number has an equal chance of being rolled. How would this play out with 100 rolls? And then if we added the 100 rolls from 24 students?

So we got to work. Would the numbers come out evenly?

Here's some data recording:



 This one looked a bit random - the numbers are in a strange order -
but it works.





 A bit untidy but you get the idea.
So, did you record 100 rolls? Let's see if that adds up...
 


 Don't you just love girls? They are soooo organised!


 And once we had data, we needed to display it as a graph so that we could see our data clearly:




Yep - beautiful presentation, accuracy, colour, neatness...

So we then combined all our data and put together the results on Excel.

You will notice that 24 students rolling a dice 100 times each gave us a total number of dice rolls of .... 2419?



Much discussion followed about why we got these results. Why weren't they all even? Why was "3" so low? Why was "2" so high? How could we do it differently?


 Next we made some spinners. This was a bit of fun. Simple to make as well.

I printed off some hexagon shapes which we stuck onto cardboard, coloured in different ways (one spinner unequal chances, one spinner equal chances, one free choice) then stuck through a tooth pick.




You will notice that 24 students rolling a dice 100 times each gave us a total number of dice rolls of .... 2419?



Much discussion followed about why we got these results. Why weren't they all even? Why was "3" so low? Why was "2" so high? How could we do it differently?


Next we made some spinners. This was a bit of fun. Simple to make as well.

I printed off some hexagon shapes which we stuck onto cardboard, coloured in different ways (one spinner unequal chances, one spinner equal chances, one free choice) then stuck through a tooth pick.



 Here's the template we used





Here's what mine looked like



 The kids were so much more creative than me...


 And then we had to invented some games of chance. Here's a few action shots of games in progress:











And a lot of fun was had by all.

It's simple. It's easy. It relates to the Australian Curriculum:

List outcomes of chance experiments involving 
equally likely outcomes and represent probabilities 
of those outcomes using fractions (ACMSP116)

 All good.