Friday, 17 April 2015

Maths in Science - George Whitesides



Professor George Whitesides of Harvard University is one of the most significant chemical scientists in the world today. He is well known for advances in NMR spectroscopy, nanotechnology and physical and organic chemistry. He has been the recipient of many prestigious awards for his work, including the AIC Gold Medal, the Priestly Medal, the National Medal of Science, the Benjamin Franklin Medal, the IRI medal, the Othmer Gold Medal and many other national and international awards.

Professor Whitesides is also a prolific writer and has produced hundreds of articles for scientific journals and magazines. He took time out of his very busy schedule to answer some questions for me about his experience with mathematics.



The Questions:



1. Describe what maths lessons were like for you at school. 

   I loved algebra, geometry, and calculus; I was not so fond of arithmetic and trigonometry. I prefer abstraction to numbers

2. Was the maths that you learnt at school useful to you later in life?

Absolutely.  I’m a scientist, and I use mathematics all the time.  Also geometry (and drafting) were very useful in developing the ability to visualize things in 3D.

3.     How good do you need to be at mental arithmetic to do calculations in your head?

I can’t answer. I don’t think of myself as being good at mental arithmetic, but I estimate numbers all the time (in my head, on paper, wherever).

4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?

Again, I’m not sure of the question.  A combination of two things—in math, in physics, in art, in music—is often a new thing.

5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?

Both.  One tests for a pattern, and if that does not work, one tests for another pattern.  Sometimes you don’t find one.

6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?

If you mean here that “=” is equality and balance, of course. All the time.

7. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?

Constantly.

8. Is estimation good enough or do you need to measure things accurately?

Both. Estimation helps to follow the course of experiments, to design them, and to look for trends.  Accurate measurement and analysis is critical  to quantitation of prediction, and for both confirming compatibility of result and prediction, and maybe more importantly for showing incompatibility of result and prediction.

9. How do you use statistics to analyse your results?

Constantly in some programs.  Understanding what a number or a result means is absolutely crucial to any experimental program; statistical analysis is the best chance we have to answer that question.  Statistics is a hard subject to get excited about until you actually care (for whatever reason) about the meaning of data.  Simple questions like “Are these two numbers—with different numerical values—distinguishable or indistinguishable?” are core questions in science.  If I had one subject that I wish were better taught (I don’t know how) to students who would go on to work with data in any form, it would be statistics.   

10. Do you have any other insights to offer into how you use maths in your work?

There are areas of science that are purely qualitative, and for which math is not necessary, but not many.  I, most scientists, and all engineers use math all the time.  The more you know, the more you can do. 


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Thank you so much Professor Whitesides for your participation in the "Maths in Science" project. I certainly value your contribution.






Wednesday, 15 April 2015

Maths in Science - Professor Ian Frazer




Professor Ian Frazer is best known, particularly by Year 7 students around Australia and probably other parts of the world, for his work in developing the Human papilloma virus (HPV) vaccine against cervical cancer. 

Professor Frazer grew up in Scotland and moved to Australia in the early 1980's. His dedication to his work has resulted in many significant awards, including the Prime Minister's Prize for Science, The Howard Florey Medal, the Balzan Prize, the Australian Medical Association Gold Medal, the CSIRO Eureka Prize and the William B. Coley Award. Professor Frazer was elected as a Fellow of the Royal Society in 2011.

It is a great honour to have been able to ask Professor Frazer 10 questions about how he uses maths in his work and I have chosen him to be the first scientist to introduce the "Maths in Science" project.




The Questions:


1. Describe what maths lessons were like for you at school. 

We were the guinea pigs for a new curriculum focussed on sets and matrices - it was exciting to see the power of these tools to solve problems.

2. Was the maths that you learnt at school useful to you later in life?

Mostly I use the statistics and probability theory I learnt – sometimes calculus.

3. How good do you need to be at mental arithmetic to do calculations in your head?

I was lucky enough to find a book that had a series of “tricks” to do quite complex arithmetic calculations in your head – however they did require good mental arithmetic.

4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?

Inferences from independent observations are at the core of research hypothesis formation.

5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?

Pattern recognition, and outlier recognition, give rise to new theories for testing.

6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?

Systems analysis requires understanding of homeostasis maintenance – which is all about balance and equality.

7. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?

We measure and compare numbers routinely as part of bioinformatics.

8. Is estimation good enough or do you need to measure things accurately?

In biological systems significant changes generally occur in half log steps so estimation is often good enough – more than single digit precision is hard to achieve in my field of science.  

9. How do you use statistics to analyse your results?

Virtually everything in biological sciences is about demonstrating that differences observed between control and test measurements are (a) statistically and, if so,  (b) biologically significant. 

10. Do you have any other insights to offer into how you use maths in your work?

It would be fair to say that 98% of the interpretation of our work relies on mathematical tools. 

   ---------------------------------------------------------------

Thank you so much Professor Frazer! I am so grateful for your participation and generosity with your time. Your answers were thoughtful and will give us all something to contemplate.






 

  

Tuesday, 14 April 2015

Maths in Science - Introduction


I am interested in talking with people who use maths in their daily lives - that is all of us, isn't it? 

Last year I wrote two series of interviews with different groups of people, the first with world champion, world record holding or Olympic gold medal winning sportspeople and the second with world-reknown dancers and choreographers. The results were astounding - the insight and  wisdom these generous people shared with me was overwhelming.

You can read these interviews on this blog - Maths in Sport (January 2014) and Maths in Dance (July 2014).

After the second series, a friend from my pln (@stephygslalzar) suggested I look at Maths in Science.

So, here goes…





It might seem obvious - maths is a science, scientists use maths all the time, don't they? All those geeky kids at high school did lots of maths and science remember?

I started to think about this a bit. If I could ask some high profile scientists 10 questions, what would they be? I wanted to have some correlation with the questions I had already asked athletes and dancers but I realised that there would be some issues that would not be relevant across all three groups.

Here are the 10 questions I came up with:

1. Describe what maths lessons were like for you at school. 

This is a question I have used in the previous interviews. I think it is interesting and important to get a picture of school experience with maths.


2. Was the maths that you learnt at school useful to you later in life?

Another question from the previous interviews. I want to know if we actually teach anything useful in class or if most of it can be discarded.

3. How good do you need to be at mental arithmetic to do calculations in your head?

A third question that I have used with athletes and dancers. Is it important to be able to do mental calculations? Do people really need to be able to do this?

4. Mathematics teaches us that you can put two things together to make a new thing. Is this important in what you do?

A new question that I haven't used before. I am thinking about the nature of creativity and creative thought. It is a very mathematical idea - creating a new thing from two existing things.

5. Mathematics is about finding patterns. Do you need to look for patterns, or exceptions to patterns, in your research?

As Marilyn Burns said, the password of maths is pattern.

6. Mathematics also teaches us about balance and equality. Is this idea useful in your research?

You may have seen my ideas on the "=" sign being like a tightrope walker - whatever is on one side needs to be balanced by what is on the other side.

7. Mathematics helps us to represent quantities and measurements numerically. Do you do this in your work?

We do a lot of measurement in maths.

8. Is estimation good enough or do you need to measure things accurately?

I'm really interested in estimation - how does this fit in with a scientist's need for accuracy?

9. How do you use statistics to analyse your results?

Of course, I am expecting scientists to use stats to analyse their results but I what to hear it from them - HOW do they use maths to analyse ideas?

10. Do you have any other insights to offer into how you use maths in your work?

Always end with an open question - give the student input into the lesson, give the interview subject opportunity to provide insights that you may never have considered.



Well, I'm excited. I googled the top 50 most important scientists in the world and got replies from several of them. I also found a list of Australia's top scientists and wrote to most of them as well. Then I found a few other scientists who I thought might be interesting - people involved in industry and engineering. I would like to thank up front all of these people for their generous contributions of thought and time from their busy schedules. I really appreciate what they have all done.

Here's part of a reply I got from Professor Don Kinard, senior technical advisor at Lockheed-Martin:

Interesting questions Mr. Ferrington; they made me think and allowed me to philosophize a bit.  I am pleased that you are taking the time to collect information on how math is used in the real world to better impress upon your students that math is fundamental to all science and engineering advancement and is literally the key to the future for your students as well as for society as a whole. 

So starting tomorrow I will be posting the full responses.

This will be interesting...











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!