Pre-conceptions challenged: Letting go of chalk and talk

After writing in my last post about being reluctant to let go of chalk-and-talk style teaching with certificate classes I've gained a significant piece of evidence to suggest that letting go and being creative in terms of teaching methodology can very productive.

I have a little S2 bottom set who are generally quite low ability.  I opened the course folder last weekend to see that I had to teach them negative numbers.  Hmmm - how can I teach these kids negative numbers in an interesting, visual and tactile way?

The answer was a two part lesson.  The first part was a powerpoint I found from somewhere which I could put on my smartboard.  It was the user interface of an ATM machine.  The bank account had £50 in it.  I had kids come up and "withdraw" certain amounts of money.  We then investigated what happened when people withdraw sums of greater than £50.  This led is onto the idea of over overdrafts and negative numbers in context.  The calculations of the overdrawn amounts seemed to come to the pupils very easily. Next we took a look at another powerpoint, this time we had a virtual thermometer and discussed temperature rise and fall.

So far, all very well.  But what about doing calculations proper, so to speak?  I always favour having a number line from -20 to 20 on the kids page and then they can do the "steps" method of counting along.  In a bid to break free of jotter work I printed out all of these numbers and lay them along our corridor.  I then got kids to answer quesitons such as -5 + 7 and - 2 - 4 by standing on a number and then moving the correct number of steps to get the answer.  We then had a girls v boys challenge quiz.  With the scores tied at 4-4 and first to five being the winner I opted to throw a spanner in the works, just to see how they would handle it.  I asked the girls 5 - (-4).  I got all sort of answers some of which were more contrived than others.  The girls didn't manage to get the answer, although at this point I didn't explain how to do the question.  The boys too didn't get the answer. However, upon me revealing the answer to them some interesting discussion took place.

Kid A: "Hey, does take away not mean difference?"
Me: "Yip". (Although I'm thinking to myself - where is he going with this?)
Kid B pipes in: "Difference, what's that?"
Kid C: "The distance"
At this point I gasp in astonishment as the kids point out that to get the answer of 5 - (-4)
all you have to do is count the number of "hops" between 5 and -4,  thus giving the required answer of 9.

Startling as it may be, this was a completely new concept to this particular mathematics graduate.  I suppose I'd always just accepted that two negatives next to each other become a plus.  The kids on the other hand had no preconception of this and as such were a blank canvas!  They made be really think that yeah, by old school definition take away is difference, so getting the answer 9 is perfectly logical!  I told my colleagues, some of whom are very experienced, and they had to admit this was something they too had never properly considered.

With some more questions answered, by using our corridor number line the kids managed to spot that the two negatives do indeed become a plus.

I have to admit this lesson exceeded my own ambitions as to how it might go.  It gave me a whole new insight into this particular area of maths and how to deliver it in future.  It's always been a dry area of the subject for me, with little scope for doing nice problem solving lessons leading to conclusions, like this lesson did.  However, in future, I will always be doing this lesson rather than just telling them the rule!

Some of my own preconceptions of the kids have been challenged and that is no bad thing.

In the spirit of the moment - I've planned lots of nice investigative lessons on the straight line next week for my S4 credit class.  I don't intend to stand at the board for very much at all other than explaining how to fill in a table of values for (x,y) coordinates given a formula. My hope is that they will discover and understand the gradient and y-intercept concepts by themselves based upon the task sheets I've designed for them do in their small groups.  Hopefully the outcome will be some nice posters by the groups detailing the key points of the straight line.  I figure that by doing it this way I may not need as much textbook practice, and maybe, we might get through the topic quicker than normal - with a better than average comprehension.

I'll let you know how I get on in my next post!

Embracing Chalk and Talk

The following is a loosely edited post I made on the Tes wesbite this morning.

I'm a young maths teacher - just starting my fourth year in the job. I agree that for some pupils lots of repetition isn't needed and for others a big page of examples is an effective way of helping pupils to commit a technique to short term memory. For recall of this knowledge lesson starters and homework's have their place. By recalling the facts fairly regularly the aim is obviously to commit them to medium term memory.

It is easy to think of practical activities for pupils to do when teaching perecentages: use a catoluge, get on the internet and look at ebay, amazon, finance websites etc. If I'm being honest I find teaching lower school far easier as the topics lend themselves much more freely to "interesting and practical" lessons. I'm not saying that it isn't possible to do interesting things with credit and higher material but it is more of a challenge. I am only teaching higher for the first time just now so at the moment it is the classic "here are the notes, here's how it connects to the previous lesson, these are some questions about it for you to try" all mixed in with some good questioning technique etc and lots and lots of homework. But it is very traditional and not revolutionary at all.

With this in mind I find it easier to comment on credit as I am teaching it for the second time through now. My fourth year set are doing algebraic fractions just now (they are the third out of four credit sets in ability terms). My question to fellow posters is am I wrong to just stick with the good exercises in the 4B textbook mixed in with some "challenging ones" I put on the board myself? I feel to deliver something like this I need to introduce the ideas at the board and "help the pupils to make the connections between exisiting knowledge and what we are doing now". They all know how to add fractions but do they know how to do it when denominators are (x+2) and (x +5) respectively? We could faff around and do this by means of a worksheet etc that leads them to the same conclusions as our class discussion at the board would do. My lesson just now would be a big discussion of various problems as a class and we'd try to solve them together. I woudln't just say "this is what you do". I'd ask them to apply existing knowledge while I write what individuals are contributing at the board. Once we have got this sorted as a class we then get it down into our notes for future reference. I think at the moment - they get to articulate what they are thinking - I try to vary who I get input from and they can inspire each other. If I were to try something more modern and fancy like a group trying a worksheet on the topic and with the worskeet leading them to the same conclusions; we'd get there eventually - only it would take longer and inevitably some pupils still wouldn't be able to get to the correct conclusion. After we've all understood a few examples at the board (by holding up between 1 and 5 fingers to indicate confidence levels) we'd move onto the text for the remainder of the period. By this means they can encounter lots of examples with a good gradient of difficulty and thus improve their own understanding and knowledge. Of course I could use loop cards or another sort of "primary or lower secondary" idea such as that - but I don't see why any other way of delivering the practice questions would be any better for the pupils than just using the text. I don't see an immediate flaw with this style of teaching for this class. It's very effective - my results have been continually good in final exams, prelims, homeworks etc. Also the kids do get to enjoy it - some of them are really relishing the challenge of the maths at the moment - plus we always get directed banter and class jokes when the teacher leads from the front - something that helps to create a nice atmosphere for pupils entering the room. What would other posters do differently? We have time constraints which mean we need to get to the correct conclusions fairly quickly so that we can practice them. I've thought a lot about content delivery at this early stage of my teaching career and know I've got lots to learn - but at the moment I don't see many more effective ways of doing it than that which I employ just now.

For a top set, it would be a very different scenario. When the kids are generally much brighter then it is more of a "sink or swim" scenario. I'd be more prepared to let them experiment and stuff. My top s2's manage to discover indicies lawys, pythagoras and all other sorts of stuff on their own - but I know the same lessons wouldn't have worked with less able pupils - I've tried before!

Basically - what I'm saying is that for more complex maths issues sometimes a traditional teaching methodology seems to be very effective with pupils who are good but not great. Only when you get a right good top set (and in our school we are fortunate that the top sets really are top notch) have I felt that the kids can "step on the shoulders of giants" by themselves, whereas other classes need a shove-up onto the shoulders from me! Any ideas, reactions, thoughts etc much appreciated. Feel free to criticise my naive attitudes - I share my own thoughts purely because I want to improve for the sake of the kids. Cheers.

First Post

I've often read blogs by other teahers and found that they invoke a variety of responses from myself including laughter, sage nodding of the head and contempt. I'm a regular reader of the Tes forums community.tes.co.uk, especially the Scotland-opinions area. There are often some good aritculate posts expressing lots of interesting ideas which are good to read. However, there is a lack of content specifically for scottish maths teachers. With this in mind I have googled a few times for "scottish maths teacher" to see if I could discover a blog by somebody with wonderful ideas on the teaching of my subject. I would love to read from people who have lots of persepective on the not just maths, but scottish secondary education as a whole and who have innovative and thought provoking ideas to consider. Sadly, however, I haven't found any such place.

With this in mind I decided that I, with my long and illustrious teaching career now entering it's fourth year should start a blog. I don't know what I'll gain from this. Maybe it'll be theraputic - but I think most of all I'd like to make connections with other teachers out there who do the same job as me on a daily basis and who really care about what they do.

Here goes. By the way, I forgot to mention my literacy is terrible, so apologies in advance.

Fiona Hyslop would not be happy.