The Typical Student in Year 2

We are currently inquiring into "Who We Are". It is a opportunity to learn a little bit more about life and our central idea is:

Birth, growth and death are part of 

the natural cycle of living things.

To find out about ourselves, we decided to collect some data. We wanted to know what things we had in common and what our differences were. Some of our questions were about physical features, some about our personal preferences.

Here are our 5 questions:

1. Are you a boy or a girl?
2. How old are you?
3. What sport House are you in?
4. What is your favourite colour?
5. What is your favourite school subject?

All students in Year 2 were surveyed. Here are our results:

Now that we had some data, it was time to start playing with it. 

Our "Typical" Year 2 Student

We found that we had one student who was in the highest scoring category for each question.

She was a girl, currently aged 7, in Acacia, liked blue and her favourite subject was PE!

We had found a typical student - she was very excited!

Our "Atypical" Student

We also found we had a student who was in none of the highest scoring categories.

He was a boy, aged 8, in Kurrajong, liked red and loved doing maths!

An atypical student - he was equally excited.

We showed our data about ourselves…

…compared to the typical student…

…and then recorded this in a table and made a statement based on our data.

Discussion

Much discussion followed once we started playing with the data. Lots of questions started to come from the kids.

Boys could never be the "typical" student in our data set because they were eliminated by the first question. Similarly, girls could never be the "atypical" student, since they would always have their sex in common with our typical student even if they disagreed on everything else.

Interestingly, our "atypical" student has a twin brother but they could be differentiated by their favourite colour - the other twin liked the colour blue - but all their other answers were the same.

We ended up producing a large graph showing how many of the responses each student had in common with our "typical" student.

An interesting distribution and one that brought on more questions. Prior to representing the data in this way, we asked the students to predict which group they thought would be the largest. Most opted for 2 or 3 things in common, agreeing that it might be expected for people have a few things similar but that there was plenty of option for differences.

The kids were engaged, focused and ready to take it further.

I wonder what they will come back with tomorrow once they go home and reflect on what they have done?

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...

Maths in Year 6 Exhibition 2014

Last week our Year 6 classes did their PYP Exhibition. It was amazing. Such a great opportunity for the kids to celebrate their journey through the PYP.

I am always keen to see how they will use mathematics. They never disappoint me with the creative ways they look at things.

So here are a few precious examples from last week.


The first thing I noticed was some clever use of infographics. The kids had been shown the Piktochart website and ran with it. Here are a few nice examples:

This group used an infographic to present results from a survey they did to find information about technology use and addiction.

 This group used their infographic to present information they found in their research

Other groups used "live" surveys to ask visitors to answer a question. They found some great ways to present their results that they built up over the Exhibition period.
 

This group was asking a big question about racism in sport...

 

 ...and they got respondents to place a pin with a football into the pitch to show their answer.

 The question of what to do with refugees - voting by marbles.

 I really liked this one. You got to put your vote in the balance scale and each ping pong ball had a positive message written on it.

This was a fund way to vote - and the kids loved it.

This called for a tough decision - which is a more significant problem: child soldiers or post traumatic stress disorder in returned service personnel?

The votes were cut into leaf shapes to represent a "tree of hope".

 

 

So once again I was very impressed. I hope you enjoyed seeing what the kids came up with.

 

 

  

Maths in the Year 6 Exhibition 2013 - Part 2

It's been a few days now and the Exhibition has been and gone. I have reflected on what we experienced and have identified a few more ideas relating to Maths that came out of the kids' inquiries.

Here we go....

Timelines

Quite a few groups used timelines to present information - after all our transdisciplinary theme was "Where we are in place and time." Lots of them were fairly traditional timelines but there were a few that showed some excellent creativity.

Here are a few:

One of the "Fashion" groups did a really good timeline using miniature dresses that they had made to demonstrate the changes to fashion over time.

Another (different) "Fashion" group used shoeboxes for a timeline. Inside each box was a pair of shoes that represented the fashion of that decade.

The "Women's Rights" group (ironically) used a clothesline to display their timeline of significant events in the history of the women's movement.

Voting and Polls

Several groups decided to ask their visitors questions about their inquiry and were able to represent their data in interesting ways.

The Women's Rights group asked a question about the Suffragette movement.

Then people were asked to place a gold (wedding ring-like) ring into a jam jar. (Irony again?)

Gold rings laid out on a beautiful silver tray.

Visitors got to put their "vote" into one of three jars.

Another group, inquiring into developments in medicine, conducted an activity that asked visitors to place a small coloured bead into empty medicine boxes if they thought that the product contained penicillin.

Results were tallied to see which products were most easily recognised as containing penicillin.

Another group looked at "Body Image" and the influence of Barbie dolls on young children. They asked people to decide which doll they preferred, Barbie or "Emme" - a doll with "real" proportions.

Vote by placing a picture into the correct box.

Representing Data

There were several other interesting ways that data was managed and presented.

A group that was looking at Post Traumatic Stress used plastic soldiers in a sand tray to demonstrate the percentages of soldiers who would experience PTSD.

Presented with this data, visitors were asked if they could model the percentages using the plastic soldiers in the sand tray

Showing that 1 in 5 veterans get PTSD - 4 soldiers on the left out of 20 on the right.

Another group was looking at sweatshops and sporting clothes manufacturing. They wanted to show different perspectives so they constructed a Venn diagram using hoops suspended by fishing line.

There ideas were organised to show their understandings of the issues involved.

I was impressed! I thought they had demonstrated their understandings in very creative ways. 

It's always good to give the kids some room to do things their own way - they will always come up with things that you don't expect!

Maths in the Year 6 Exhibition 2013 - Part 1

What a week - I am exhausted! I imagine the kids are too after an amazing PYP Exhibition. This is a culminating activity  for students who reach the end of the Primary Years Programme where they get to develop their own inquiry into an area of interest. 

Being transdisciplinary in nature, I am always keen to see how the kids will use maths in their Exhibition presentations. How will they display data? How will they analyse data? What creative ways will they find to use maths to make sense of what they are doing?

It will probably take a few posts to get all the information up about the different inquiries the students engaged in.

Here's an example of how one group inquired into the use of transport by people coming into our school each morning...

Displaying Data

The "Transport" group decided to collect some data about the makes of cars that come into our school each morning and also how many people were in each car. So they got to school  about 45 minutes early and set themselves up near the front entrance.

When they collated their data they decided to display it as a picture graph because the audience for exhibition was going to include a wide age range, from pre-school to pensioners. 

They made a second graph based on the fuel consumption of the most popular cars to come into the school each morning. At this point they realised that their initial data collection only included the make of car, not the model as well. Consequently, they decided they would calculate what the fuel consumption for an "average" Toyota etc would be by getting the fuel consumption of all models of each make of car and finding the mean. 

They also distributed a survey via Survey Monkey to all the staff at the school to see how they commute. The first graph shows that the vast majority drive cars while only a few walk, ride bikes or catch buses. 

The second graph asked how many people came in the car with you. This question was a bit ambiguous as there was no option for zero - did it include the driver or not? Anyway, the most overwhelming response was "1" - which might mean none or one.

The final graph asked for the age of the car that was driven. They asked this question to explore the idea that older cars produce more pollution. It also showed that not many teachers have new cars, in fact many have cars that are 10 years old or older.

Data Analysis

The data for this group was well displayed and easy to read. The really exciting part was reading their analysis of what they had learnt.

Here are a few of their comment:

Well, I'm not buying a Lexus then - I think I'll get a Land Rover.

Or...if you can afford a Lexus, do you worry about the cost of petrol?

Australia is very big on 4x4 cars. Interesting to see some data.

Can you get this from the data or would you need to ask a few more questions?

This one makes me ask a few questions - where are they driving? City? Country? How fast are they going? Does it matter? What type of Toyota do they have? How big is the bucket?

Like all good learning, it made me want to ask more questions. Hopefully, the "Transport" group feel the same.

The Human Graph

As our culminating activity for a Week of Maths and to celebrate National Maths Day, the whole school got together to create a human graph and to answer the age-old question...

What Fruit Did You Have For Breakfast?

Very sneakily, this combined maths (data collection and representation) with a healthy diet.

Here are a few pics of what it all looked like:

Getting ourselves organised - yes, it took a bit of time. 560 kids to organise.

That's the "apple" line disappearing into the distance - very popular with the kids. "Bananas" is the next longest and the one you can see further across coming in third place is "strawberries" - they're very cheap at the moment.

Yep, that's the "strawberries" group with "apples" and "bananas" on the far left of the picture.

I got some Year 6 kids to design the data categories. They chose:

1. Apple
2. Avocado
3. Banana
4. Fruit Salad 
5. Grapes
6. Kiwi fruit
7. Mandarin
8. Orange
9. Peach
10. Pear
11. Rockmelon
12. Strawberry
13. Tomato
14. Watermelon 
15. Other
16. None

Results

 1. Apple was the most popular fruit for breakfast, followed by banana and then strawberry.

2. Only 25 children had no fruit for breakfast.

3. Only 1 person had tomato for breakfast and 1 had avocado. These were the two smallest categories.

4. There was a protest that bananas are a herb. 

5. There was an interesting selection of fruits in the "Other" category  - star fruit, cherries, pineapple, etc

6. Everyone had some fun.

So what?

Over the week, have we achieved anything?

I think so.

• We have focused the kids' attention on data collection. 
• We have got them to think about some of the issues behind working with data.
• We have constructed graphs.
• We have made statements based on information represented in graphs.
• We have made some sound generalisations about how to handle data.
• We have participated in an activity across the whole school P-6.
• We have had some fun.

Can't wait till next year...

More Data Handling

Day 3 of our Week of Maths and we got to look a bit more closely at some data that compared the average intake of various food groups in four countries - Australia, Italy, China and Ecuador.

The data was presented on the AAMT website in graphs produced on an Excel spreadsheet. It looked a bit like this:

You could enter a value from 1-4 and the data for each country would appear.







The students were asked to get the data from one category and compare it across the four countries.

Comparison of grain consumption as a percentage of total

Comparison of drink consumption as a percentage of total.

Do they really not drink anything in Ecuador?

Comparison of average meat consumption in $US per week.

Naturally, once we started playing with the data, the questions started flowing and we were able to make some important generalisations:


1. Garbage in, garbage out


You can only work with the data that you have. If you collect poor quality data, you can't improve it by manipulating it. So, if the data provided says Ecuador has no expenditure for drinks, does that mean:
a) they don't drink anything?
b) they don't pay for anything they drink?
c) the data hasn't been collected properly?



2. Your scale needs needs to have all the numbers up to your biggest quantity


The scale need to be cover the range from your smallest value to (at least) your largest value. It also needs the have graduations that are useful, that make the data accessible and that inform the reader.


3. Say the exact amount for each category

When dealing with data, it is important to be as accurate as possible. It was difficult for students to read exact money values off the graph provided. They resorted to estimating which meant that they ended up with different numbers. This made it difficult for them to compare their information.


4. Spreadsheets can give an exact number - roll overs

At this point, one of the bright young things discovered that if you hold the cursor over the individual data column, the exact dollar amount was shown. Now, that's something you can't do with a piece of paper.


5. Zero is data and we need to show all data

And so the conversation came around to the question of "zero". Ecuador had 0 for several categories of data. Students began to realise that if we leave out zero it will change the meaning of the graph. Zero values need to be included in data sets to show that the question was asked, the measure was taken, the observation was made but the result was zero.