Balancing equations

This was a mental starter recommended by our previous maths consultant. Begin with a simple equation such as 5 =5 and ask for their initial thoughts. Is it wrong or just unusual?

The children were initially puzzled but then decided that it was not wrong, just different to what they expected. I then asked them to change one side so that the sentence stayed correct. They suggested 4 +1 so I changed the right hand side which surprised them as they had expected me to change the left to make a normal calculation.

                                                 5 = 4 +1

I then asked for suggestions for the left hand side. Initially they suggested other single numbers so the equation could not be correct. Then one child asked if it had to be a single number. Once they realised that they could substitute another calculation they began to see what I was after.

I asked what the = symbol stands for and received the quick reply that it tells you where the answer is. Anothe child then pointed out that it really stands for ‘the same as’. There were several intakes of breath and whispers of ‘I get it now’.

We quickly moved through a range of calculations to make 5, changing one side at a time. They moved into decimals as they ran out of simple addition sums they could make. I asked if they thought there would be more possible addition calculations or subtractions. They worked out that there were only a few whole number addition calculations possible but an infinite number of subtraction ones. There were so few addition sums because 5 was such a low number.

Then a child asked if they  could use negative numbers and the ball started rolling again as they found a variety of calculations that would satisfy the statement.

In 10 minutes we had done mathematical reasoning, decimals and negative numbers. I felt it was a really successful mental and oral starter. We could have extended it further by moving into algebra eg 5 = (n + 5) – n.

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Network meeting 3

The third meeting of our network group led by the LA consultant was as lively as usual with lots of joking and humour as well as lots of work being done and ideas being shared. Apparently we are the only group to have this much fun at our meetings, the other two groups are more serious. Not sure what that says about the 10 of us!

The session was on Representation and continued to stress the need for concrete examples and images to support all children, not just the younger and less able.

There was lots of sharing of ideas and favourite resources being looked at in the light of a quote from Kev Delaney ‘It’s not the resource that’s important, it’s what you do with it that matters’. The message was definitely to show children, don’t just tell.

I think that this is definitely the single most important message I have gained from my course so far. I think that I had really fallen into the trap of using physical resources for the less able and not really thinking about how they could be used to help understand more complex ideas.

As expected, there was also a lot of discussion about the assignment which is now due in 2 weeks time. There seemed to be a wide range of stages that people are at, I am slightly ahead of a lot of people but that’s because I need to have mine sent off by next Saturday!

We were also given details of the school visit that will be done by the LA. This is apparently to judge the current impact of the course on schools rather than assessing our individual progress. It’s still one more thing to worry about though.

Proportionality !

I spent yesterday afternoon at NTU for our latest 3 hour session which was all about the third of the course’s big ideas ‘Proportionality’.

We had the first session on this topic at the residential and I found it really hard going. I don’t know whether it was because it was the third session on the Saturday and I was pretty much brain dead, or whether it is just a hard concept. Most likely a combination of the two I expect.

Yesterday’s session took us deep into the mysteries of fractions, especially methods of multiplying and dividing them, something that I never really got to grips with at school. For me at any rate, it seemed to be the session that has concentrated most on improving teacher’s subject knowledge. There were ideas for us to use in our teaching but the focus seemed to be very much on getting us to understand why the rules that we learn about fractions work.

I have to say that I left the session with a lot more understanding about multiplying and dividing fractions. As with most things, it all seemed so simple when the tutor demonstrated it.

I had always been able to deal with multiplication of fractions, the idea that it’s really half of or a third of something. Dividing was something that I hadn’t really got to grips with though. Taking it back down to a basic division calculation where you simply ask how many times can you get x out of a given number seemed so obvious that I don’t know why I never saw it before.

We had an interesting conversation with the tutor who was actually from Northampton university who are running our particular MaST course. It was all about the desire to teach well and allow our children to discover things for themselves and the opposing pressures of demands that so many children achieve level 4 or 5 or whatever by the end of the year. There was no real agreement, just a sharing of ideas. Interestingly, those who taught younger age groups were more in tune with his point of view that you shouldn’t be pressured by outside influences such as targets.

I still try to teach for understanding to as great an extent as possible but sometimes I feel that you do just have to teach ‘how’ to do something rather than why.

As always, the session was interesting and thought provoking. I then headed off to the library to continue to research useful ideas for my essay.

Assignment part 3

I actually managed to get quite a lot done yesterday. I had felt really depressed about the whole thing on Saturday night as it seemed impossible to find research that had anything to do with what I was talking about. However yesterday things seemed to fit together better. I began to see how I could tie in some of the articles that I had already read. I also managed to find an article about representation being vital in maths which isn’t on the course reading list so hopefully i may get some credit there for independent research.

I managed to get up to about 15oo words out of 2000 but I’m sure that a lot of it is too based on narrative rather than analysis. I decided to send the draft off to my tutor just to check that I was on the right lines as I didn’t want to waste hours on something that was totally off topic.

I was really surprised when I found today that she had replied to me last night. Brilliant service I have to say. She was quite nice about the essay but did agree that it was too narrative based. However she also gave me an idea of how I could change one of the paragraphs so I will see if I can use that for the rest of it. I do feel a lot happier now about the essay and the possiblity that I might be able to write something that will pass.

My main research focuses have been on representation and also the role of talk, especially in problem solving. I have a book on order from Amazon and there is another in the university library which I will hopefully look at on Saturday and then it will just need redrafting to make sense.

All I will have to do then is write 33 reports!

Assignment Part 2

I finally got down to work yesterday and made a start on the actual essay. Having actually done something I now feel a bit better about being able to complete something that might possibly be on the right lines.

We were asked to write about what learning we used during the activity and link that to research. As I was writing, I found that I was being reminded of things that I had read and was also able to think of other possible avenues that I could explore.

At this point I have written 1300 words of a 200o word essay. I am sure that it is still too heavily based in narrative and not analytical enough but I feel that I now have something that I can possibly work on.

MaST Assignment

Now Die Fledermaus is over I really have to get my head around the first assignment for this course. We had a tutorial two weeks ago at the university where we were given details of what was expected of us. The actual assignment doesn’t sound too bad. We have to take a mathematical activity that we have explored at one of our meetings and write a critical reflection of the processes we went through whilst doing the activity. Then we have to use the same activity in the classroom and evaluate the children’s learning, pedagogic strategies used etc.

That doesn’t sound too daunting but the main problem for me and several others at the meeting is the sheer level of research that is involved. We were told several times that it should be a critical analysis of the activity and not a narrative about what we did. We are expected to research ‘widely’ and include our thoughts on this research in the activity. I left the meeting feeling very out of my depth and without any idea of where to start.

Two weeks later I have at least got a starting point as I have decided on which activity I will use and have carried it out with the children. We have investigated Trapezium numbers (like triangular numbers but without the number 1) and from working with the children I have a couple of ideas of areas that I can research.

A lot of the books and journals that we need are available online so we don’t have to physically visit the library. However the online catalogue is not as easy to navigate as they made it appear so I anticipate a lot of time being spent in trying to find suitable material to use.

I have four weeks to complete the assignment. That sounds fine until I remember that I also have to write all my reports and go on a week’s residential. May is going to be a very busy month!