Recording at Ashburton Primary School
Years 4 & 5
In the process of renovating the school, staff found a set of tasks that had been put away and not used for some years. Teacher change over time and other curriculum pressures both within and without schools can cause that sort of thing to happen. Julie Gilbert, Assistant Principal, who has extensive experience is mathematics support roles, saw this discovery as an opportunity to add new vigour to the school's mathematics program. This article records student responses to the request to keep a mathematician's journal which is an essential component of working with tasks.
Ashburton Primary School, Melbourne, Australia
Note: There are ways to lessen the possibility of tasks being 'put in a cupboard' never to be seen again. See: Principles of Continuing Use.
Click any photo to see a larger version.
- Sample journal pages below begin with pages from the first task lesson in each of three Year 4 classes. They show the children are very willing to see recording as part of the process of working like a mathematician.
- The next set of photos is from the same classes, and in some cases the same students, a term later. The teachers (Cathy Wright, Liam Purdy, Lori Giannaris and Kate Geddus) have consistently encouraged purposeful recording and the results are clear.
- The third set of photos comes from the first task lesson in Year 5 classes. This was part of a phase in across the school and occurred a term after Year 4. An ability to record in more detail the first time is evident in these photos, no doubt as much due to the school's literacy program as its mathematics program.
Year 4: First lesson
These first lessons began with the statement that school mathematics is about learning to work like a mathematician. Children were then asked what they thought a mathematician's work was. After a brief discussion of responses, the tasks were introduced as invitations to work like a mathematician. As students began investigating in their chosen task in pairs, the CRTRA system was introduced as appropriate, usually in a 'fishbowl' situation:
(This process and other wisdom from experienced task teachers can be found at: Principles of Daily Management.)
- Count - to check the materials were all there
- Read - through the card to make sure they understood what was being asked
- Try - what the card was asking, guided by the Working Mathematically process
- Record - significant information as they tried
- Ask - their partner, a colleague, the teacher if they needed help
These girls worked together on Task 2, Cars In A Garage,
but they chose different ways to present what they had learnt.
Similarly with these boys working together on Task 58, See-Saw.
Remember, these photos were taken during the first 50 minutes task lesson. These examples and the one in the photo at the top of the page in which the two girls were working on Task 192, Keith's Kubes, show that recording can be introduced in a way students accept as a natural part of a mathematician's work. It also offers an opportunity to encourage and value individual presentation skills.
Year 4: Through the term
Here, the girls who worked on Cars In A Garage above show that they returned to it at another time,
completed the their recording of the first challenge and extended the problem to more cars.
One more way to record Cars In A Garage, this time from Chloe,
and recording where the mirror is placed for each Mirror Patterns 1 challenge.
A week after Mirror Patterns 1, the same student was working on Task 17, Truth Tiles 2.
Julie introduced the idea that near the end of the lesson, in the time for 'making sure you record your work so far',
thought bubbles could be used to show 'what to do next time'. The students are gradually learning to make good use of them.
Oliver had an aversion to recording in the beginning, as evidenced by his effort for Task 196, Cross & Square (formerly Maltese Cross), even though he could have traced the pieces. This was March 18th. Later in his journal he records working on Task 183, Pizza Toppings, on both June 2nd and 13th and details three pages of possible pizzas. Whether or not he is correct in every aspect, the effort is clearly monumental in comparison to his first try.
Chloe working on Task 118, Ice Cream Flavours and showing the mathematician's strategy of learning from a previous problem.
Year 5: First lesson
Hugh and Harrison worked on Cars In A Garage and made some sophisticated calculations.
Blair & Alexander worked on Truth Tiles 2 and also made a video which can be viewed from Cube Tube.
Bella & Annie worked on Ice Cream Flavours and Isabelle and Hannah worked on Farmyard Friends.
Congratulations to all the teachers and their students for learning to work like a mathematician!