Maths materials – tools or manipulatives? A walkthrough query.

Readers of my blog will know that we have Michaal Ymer, an educator with a focus on maths, coaching teachers in classrooms. Michael early on in his work with us presented three main messages:

  • students need maths materials to manipulate so that they get a better understanding of concepts – less abstract.
  • maths materials need to be organised in learning spaces so that students are responsible for getting the material they need and being responsible for packing it up.
  • teachers need to present clear instructions or pictures [birds eye drawings – photo 1] of what students need to set up for the lesson. The picture drawn by a year 1 teacher shows a table with two students and the following materials set up: tub of counters, a pencil, some paper and a dice. When students have this set up they join the class for the group instruction period. This means when the teacher instruction is over students can go straight on with the task rather than forgetting the instructions as they spend time setting up – simple but effective as I have watched younger boys sometimes spend 10 or more minutes locating the equipment before they start – and thus forget the purpose or strategy just demonstrated by the teacher.

When we were walking through the junior classes during maths lessons this week I noted lots concrete material being used in activities – however was the material really supporting them construct a mental picture of the operation they were performing?   Well it seemed lots of materials were being used for the activity – roll dice place counter over number on sheet – but not lots of material that students used to create the mental pictures of the operation, with some exceptions – the last picture has the student with some counters for the activity and different counters for manipulating the mental equation.

As we reflected after the walkthrough we began to pose some questions:

  • in a sequence of lessons students might first learn the activity before learning the skill or strategy to be practiced in the activity: e.g they might learn the roll and cover up game first before learning the strategy to count on from the first number instead of starting from 0 every time. How would we know the lesson sequence we were viewing unless we consulted the planner on the teacher table, desk or interactive whiteboard  – next walk through ask for planners to be on the table or board  so that we can get a quick picture, if needed – making feedback more specific. 
  • opportunities for assessment – the middle picture of a prep class showed students measuring a track using counters – some were counting to 60 or more, others counting on from numbers and some even writing the total – we need to devise simple strategies to record the observations and not detract from our incidental teaching as we move around the group. What a great task – all can start and many have different exit points of learning – caters and engages all – fantastic!
  • concrete materials that help students think or picture maths concepts might better be labelled manipulatives [I think this is an American term?] while others might be classified tools for the activity – students might need both?  

I wonder if other teachers and principals doing walkthroughs question similar instructional strategies? If so please comment as I’d appreciate the feedback.