Manipulate, Experience and See & Talk

Manipulate, experience and see. Forms of scaffolds or prompts, available to support learners, are resources that pupils can manipulate, experience and see. The use of tangible and visual resources in mathematics cannot be underestimated.

Resources need to be visible in the classroom. The children need to be encouraged to look to use them independently rather than wait to be given them by adults. The use of multilink cubes, poly-dron, digit card, nets etc should extend through the whole primary age range. Year 6, Level 5 pupils need to Manipulate, experience, see (mathematics) just as much as foundation children.

Haylock and Cockburn (1997) stressed the need to encourage through all year groups the idea that practical equipment and visual stimuli come first and then alongside they never disappear. Whilst mathematics can become abstract, it is not where it starts. It is the educator’s role to ensure that supports are in place to allow the transition from concrete to abstract (Haylock and Cockburn 1997). Individuals will eventually use these experiences to process mathematics when the supports are removed (Delaney 2001).

Manipulating, getting a sense of and then articulating (The MGA Cycle, Mason et al. 2005), further proposes that by using a resource to create a visual image learners gain confidence and that by moving through the MGA Cycle several times, the learner may develop a generalisation and be able to articulate their mathematical thinking further (Mason et al. 2005).

Engage in Talk: The value of talk is paramount to mathematical thinking and cannot be exaggerated (Merttens 1997, Thompson 2003). Mason et al. (2010) suggest that through talk you can identify where the pupils’ understanding is: “Give me an example, show me.”

They refer to ‘the helix’ stages of understanding: manipulating, getting a sense of and then articulating (The MGA Cycle). By extending the talk process, the teacher can encourage the pupils to articulate their thinking further. This encourages meta-cognition; thinking about one’s own thinking (Arthur, Granger and Wray 2006). Via dialogue the pupil has the time and support needed to modify their initial problem solving strategy; they are able to adjust their thinking and improve their method and so gain confidence through success.