OF COMPREHENSION IN A LEARNING OF MATHEMATICS
Anne selected some activities focussing on these different representations, that are shown below.
The following key points were raised:
- use of colour as a checking device
- arrows imply from and to
- careful with 33.3% = 1/3, but 44.4% =/ 1/4
- pictorial representations of money on pink cards
- spatial representation is determined by the students
- may have been better to have physical piles of money
- money could have been replaced with weights
We then looked at a crossing the river problem.
Eight adults and two children need to cross a river. A small boat is available that can hold one adult, or one or two children.
The task was very structured, encouraging us to act out the scenario, then predict, plot graphs, explain, and generalise. The representations we used were:ENACTIVE: moving people physically across the river, moving objects around
ICONIC: drawing arrows to represented movement
SYMBOLIC: numbers (data), variables (expression), graph
It was noted that in this exercise using tracking arithmetic, i.e. writing 4 + 1 instead of 5 was useful as it could lead to the equation.
In terms of this detailed structure, Anne suggested that it was not required and more to the point unadvisable. We were encouraged to think about taking children to a high ropes course:
You want to help them feel safe, but they only need ad-hoc hints after that.The next activity was another matching activity, this time with graphs.
We were encouraged to find multiple representation software.
The final task was to consider the multiple uses of a number line.
