Problematised Situations

A problematised situation has at it's starting point an everyday situation that the students are familiar with and which is likely to hold their attention. So, out of the window go word-problems such as "Joan had 5 apples, Jane had 3 apples. How many apples did they have altogether?" In their place come realistic situations such as the new puppies at my neighbours place. "Did you know, my neighbour's dog has just had a litter of nine puppies. (Everyone loves gossip) He told me that half were black and the other half were spotty, but I think he is fibbing! What do you think?"

As well as "true stories" situations in story books such as One is a snail, Ten is a crab provide brilliant situations around which a problem can be framed.

The Power of Narrative

Ann writes: One thing that I notice when I do demonstration lessons is the fact that students are very easily drawn into a narrative (another of the productive pedagogies) and engage very easily with problematised situations presented in the narrative form. Last week we drove to Rockhampton, then Mackay and onto Middlemount, back down to Rockhampton and then to Gladstone before returning to the Gold Coast. In Rockhampton I had the chance to do a quick demonstration lesson with some Grade 2-3s.

On the spur of the moment I decided to tell the students about the amount of time I had been spending travelling and that I bought some lollies at a Garage to help alleviate the boredom. I told them that I thought the shopkeeper had not given me enough change and asked them to help me see if I was short changed or not. I could have just told them what I bought and what I paid and then asked them what change I should have had but I don't think this would have engaged them in the same way as my narrative did.

The class was very sympathetic and did their best to solve the problem. It didn't seem like a boring maths problem to them and they really did want to help me out. For some students just using coins to make the amounts was challenging, for others finding the total amount spent was enough challenge but some students managed to get all the way and find out what change was required. Not bad really since it was quite a complex problem. I have used similar stories with students of other ages too and would urge you to try to create narratives to surround your problematised situations whenever possible. Age does not seem to be a barrier to narratives-all kids enjoy them. Perhaps it is because there is an element of gossip in them.

Innovating on a Theme

When students work on a problematised situation there are many opportunities to see a range of strategies and to reflect on them. Sometimes too it is evident that students need more experiences with similar problems. Innovating on a known problem makes it easy to create similar problems.

Ann writes: Recently I was working with a teacher called Stefan. His class worked on the problematised situation presented in Numeracy Blocks Level 3 as shown below.

As the students worked and then reflected on the problem it was evident that they needed more experiences with similar problems. Stefan chose frozen juice cups (hugely popular at the school tuckshop) as his context for a follow up problematised situation that would allow his students to reflect on and try out strategies presented in the earlier problem. Changing the numbers was deliberate to encourage use of the rule for multiplying by ten and possibly doubling and halving, aspects that Stefan noticed needed to be further developed.

Here is Stefan's innovated problem:

• Our school tuck shop ordered 5000 frozen juice cups from Cottee's Cordial Company for Term 4.
• Every box of cordial holds 160 juice cups.
• In the first delivery from Cottees there were 10 boxes of cordial.
• In the second delivery there were 12 boxes.
• In the final delivery there were 5 boxes and 200 looses Juice cups.
• Was the order properly filled?

Stefan ran this problem in his room within days of running the first one and was pleased to see his student's progress in terms of trying more efficient strategies than they had in the first problem. He also noticed less hesitancy in tackling the multi-steps and having a go rather than worrying about the answer.

Thankyou Stefan for allowing us to use your problematised situation.

Fix-up Strategies - Bags of Lollies

Ann writes: I recently drew a bag of lollies like the one shown below, blew it up to A3 size and took several copies (mine were laminated because I knew I would want to use them lots of times) into a classroom. I have found that students of all ages but particularly the younger ones engage with narrative and have begun wherever possible to create narratives to present problematised situations. The following is the narrative presented.

I began by asking the students to estimate how many lollies were in the bag and suggest ways of counting them. The first student to try to count began to double dip and to forget which lollies were already counted. This allowed the class to suggest strategies to overcome this. Strategies included marking the counted ones and given that I kept interrupting the person counting (which caused a lot of laughter) a strategy for writing numbers in each lolly so that there could be no further miscounting. When asked if there was a faster way of counting it was suggested that we should count by twos. Again this was problematic because the lollies are not neatly organised to make it easy to touch two at a time while counting. Eventually a strategy for joining pairs was arrived at and counting could take place. We briefly reviewed the earlier estimates and talked about why some estimates might have been closer than others and about what they could do next time the have to make an estimate.

Joining and marking the lollies seemed to prompt some new ideas and soon colouring in fives and later in tens gave new methods of counting. I had wanted this background because the problematised situation I had in mind could build on these ideas.

The children were asked to draw a bag like mine and to draw lollies in it until I asked them to stop. We reviewed the need for the lollies to be a reasonable size and spaced so that there were no overlaps and some space around each lolly. At a time when some students had still only a few lollies on their paper and others had more than twenty-five I stopped the class and asked them to put themselves in the role of the lolly packer and make sure that there were exactly 25 in their bag. The children were asked to change to a different colour to carry our their fix up strategy so that we could see how that went about it.

As mentioned previously, this activity provided a useful opportunity to demonstrate to the children that fixing up an error is not only okay but also part of everyday situations.