||It is not appropriate to offer students tasks in an unsupported way. If they have had no experience with working independently in maths we need to provide scaffolding to help them dig into the investigation. Otherwise they may see tasks as some form of game where the objective it to 'get as many done as possible'. One approach to getting the class started on the tasks and giving it a sense of direction and purpose is to start with a whole class problem.
I was apprehensive about using tasks when it seemed such a different way of working. I felt my children had little or no experience of problem solving and I wanted to prepare them to think more deeply. The Clinic proved a perfect way in.
View the Task Cameo for Eric The
A version of the text below
also appears in theTask Centre Manual
and Section 3 of each Maths With Attitude manual.
Usually a poster with a mathematics problem is displayed where all can see, perhaps in a Maths Corner or on the electronic whiteboard. Another approach is to print a copy for each person. A Poster Problem Clinic then fosters class discussion and consideration of problem solving strategies.
Starting a task-based lesson this way also means that just prior to liberating the students into the task session, they are all together to allow the teacher to make any short, general observations about classroom organisation, such as to remind them about Daily Management Principles, or to celebrate any problem solving ideas that have arisen.
A Clinic in Action
The aims of the regular clinic are to:
The following example illustrates the idea.
- provide children with the opportunity to learn a variety of strategies
- familiarise children with a process for solving problems
For each session teachers need:
Also organise children into problem solving teams of two or three.
The How To Solve A Problem/Strategy Board can be prepared in advance as a reference for the children, or may be developed with the children as they explore problem solving and suggest their own versions of the strategies. It can be used in any maths activity and is frequently referred to in Maths300 lessons as it is a component of the Working Mathematically Process.
The problem can be chosen from
- your task collection
- a book
- a web site
- Professor Morris Puzzles (see opposite)
Professor Morris Puzzles
- The Task Centre Teachers' Handbook is freely available on site from this link, or the Documents link on the Mathematics Task Centre page (see Link Box above). The Handbook has a section on Poster Problem Clinic which includes scans of more than 20 posters found in various classrooms.
- Based on Professor Morris #49, The Farmer's Puzzle, Lesson 14, describes a Poster Problem lesson in detail.
This example from one classroom is based on the task Eric The Sheep above. The teacher copied it onto a large sheet of paper and asked some children to illustrate it. The teacher also changed the number of sheep to sixty to make the poster a little different from the one in the task collection.
Step 1 - Read & Understand
Step 2 - Plan a strategy
- Tell the children that we are at Stage 1 of our four stage plan ... See & Understand ... Point to it! Read the problem to/with the class. Discuss the problem and clarify any misunderstandings.
- If children do not clearly understand what the problem is asking, they will not cope with the next stage. A good way of finding out if a child understands a problem is for her/him to retell it.
- Allow time for questions - approximately 3 to 5 minutes.
- Tell the children that we are at Stage 2 of our four stage plan ... Planning. In their groups children select one or more strategies from the Strategy Board and discuss/organise how to go about solving the problem.
- Without guidance, children will often skip this step and go straight to Doing It. It is vital to emphasise that this stage is simply planning, not solving, the problem.
- After about 3 minutes, ask the children to share their plans.
Sharing strategies is invaluable as it provides children who might feel lost in this type of activity with an opportunity to listen to their peers and make sense out of strategy selection. Note that such children are not given the answer. Rather they are assisted with understanding the power of selecting and applying strategies.
Well we're drawing a picture and sort of making a model.
Can you give me more information please Brigid?
We're putting 60 crosses on our paper for sheep and the pen top will be Eric. Then Claire will circle one from that end, and I will pass two crosses with my pen top.
Our strategy is Guess and Check.
That's good Nick, but how are you going to check your guess?
Oh, we're making a model.
John's getting MAB smalls to be sheep and I'm getting a domino to be Eric and the chalk box to be the shed for shearing.
We are doing it for 3 sheep then 4 sheep then 5 sheep and so on. Later we will look at 60.
Great so you are going to try a simpler problem, make a table and look for a pattern.
Step 3 - Get started
Step 4 - Checking & learning more
- Tell the children that we are at Stage 3 of our four stage plan ... Doing It. Children collect what they need and carry out their plan.
- Tell the children that we are at Stage 4 of our four stage plan ... Check It. Come together as a class for groups to share their findings. Again emphasis is on strategies.
We used the drawing strategy, but we changed while we were doing it because we saw a pattern.
So Jake, you used the Look For A Pattern strategy. What was it?
We found that when Eric passed 10 sheep, 5 had been shorn, so 20 sheep meant 10 had been shorn ... and that means when Eric passes 40 sheep, 20 were shorn and that makes the 60 altogether.
Great Jake. How would you work out the answer for 59 sheep or 62 sheep?
Sharing time is also a good opportunity to add in a strategy which no one may have used. For example:
Maybe we could've used the Write an Equation strategy, for example, 1 sheep goes to be shorn and Eric passes two sheep. That's 3 sheep, so perhaps, 60 divided into groups of 3, or 60 ÷ 3 gives the answer.
- Round off the lesson by referring to the Working Mathematically Process. It will provide many opportunities to compliment the students on working like a mathematician.
More from the Mathematics Task Centre