Problem Solving, Learning and Assessment Session 2.

Problem Solving, Learning and Problem Solving, Learning and AssessmentAssessment

Session 2

Some rules for Some rules for doingdoing maths maths Think about when to talk, ……and when to listen Think about how you choose to

represent the situation Think about your emotional response, ….the emotional response of others in

the group Think about ‘having’ problems…

Golden ZerosGolden Zeros A new hotel is to be built in Las Vegas with

no expense spared. There will be 1000 suites, numbered from 1

to 1000. All suites are to be numbered using solid

gold numerals. How many golden zeros will be needed?

Golden ZerosGolden ZerosRooms with two digits and one zero:

* 0 9x1 zeros Rooms with three digits and one zero:

* * 0 9x9x1 zeros * 0 * 9x1x9 zeros

Rooms with three digits and two zeros: * 0 0 9x2 zeros

Rooms with four digits and three zeros: 1000 1x3 zeros

9

8181

18

3

Total Zeros 192

Golden ZerosGolden Zeros

More questions:

•What if there were more rooms?

•What about other digits?

•Do some numbers cost more than others? (Maybe a different way of ordering rooms would be cheaper?)

•Are there any ways to predict numbers of zeros for any number of rooms?

……

Mathematical behavioursMathematical behaviours Solve problems Investigate Collect data Work systematically Search for patterns and links Specialise Generalise Conjecture Convince yourself, a friend, an enemy

BilliardsBilliards

Strange table: only 4 pockets at the corners table divided into squares ball always struck from one corner,

diagonally ball bounces round table

Making Assessment Making Assessment MeaningfulMeaningful

Assessment is for Learning

What there is to learn about learnersWhat there is to learn about learners

conceptual understanding perceptual understanding directional awareness maths/philosophical awareness number knowledge operational skills maths literacy

ability to strategise decision-making skills

Who can do the assessing?Who can do the assessing?

the learner the tutor an external agency

Assessment is about learningAssessment is about learning … … what others see how they think what they do what they know how they see themselves

and not simply what they don’t know, don’t understand, can’t do!