PISA 2012 problem-solving answer to question level 6 (robot cleaner)



The CORRECT answer recognises that the vacuum cleaner pushes the yellow block until it meets a wall or a red block AND that it turns 180 degres.



At Level 6, students can develop complete, coherent mental models of diverse problem scenarios, enabling them to solve complex problems efficiently. They can explore a scenario in a highly strategic manner to understand all information pertaining to the problem. The information may be presented in different formats, requiring interpretation and integration of related parts. When confronted with very complex devices, such as home appliances that work in an unusual or unexpected manner, they quickly learn how to control the devices to achieve a goal in an optimal way. Level 6 problem-solvers can set up general hypotheses about a system and thoroughly test them. They can follow a premise through to a logical conclusion or recognise when there is not enough information available to reach one. In order to reach a solution, these highly proficient problem-solvers can create complex, flexible, multi-step plans that they continually monitor during execution. Where necessary, they modify their strategies, taking all constraints into account, both explicit and implicit.



Fully describe the logic governing an unfamiliar system. After observing the behaviour of a (simulated) robot cleaner, the student identifies and writes down the two rules that, together, completely describe what the robot cleaner does when it meets with a certain type of obstacle.

The problem is static i.e. all information is disclosed at the outset. The setting is technology because the problem involves a technological device and the focus is socialbecause the problem involves the community or society in general.



The process is representing and formulating because it involves building a coherent mental representation of the problem situation. To do this, relevant information must be selected, mentally organised and integrated with relevant prior knowledge. This may involve: representing the problem by constructing tabular, graphical, symbolic or verbal representations, and shifting between representational formats; and formulating hypotheses by identifying the relevant factors in the problem and their interrelationships; organising and critically evaluating information.


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