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!