**Mathematical Olympiad Problems in the Regular Classroom**

*Connections, Visualization & Metacognition
Yeap Ban Har
National Institute of Education*

**Introduction**

One of the characteristics of the Singapore education system is that average students in the system are high-achieving. This characteristic is important in producing a general population and, hence, workforce of high calibre. A high calibre workforce is essential for a knowledge-based economy such as Singapore’s. In this lecture, we discuss one of the ways to bring about this outcome – the opportunity for every student to experience high-level thinking through mathematics problem.

Problem 1

A small hamster sits at a corner of a square with side 10 m. The hamster runs 6.2 m along a diagonal towards the opposite corner. It stops, makes a 90o right turn and runs another 2 m. A scientist measures the shortest distance between the hamster and each side of the square. Find the average of these four distances.

What if the hamster moves to a different spot?

*Adapted from 23rd Annual American Mathematics Competitions for Grade 8 (AMC8) 2007*

This problem illustrates how our minds are encouraged to go beyond the details to see its essence. The ability of the mind to monitor and manage information is metacognition. Well-selected problems can be used to help students develop metacognition.

This problem also requires students to visualize to find the total of the four required distances

* Read more here from NIE. More questions included in his discussion. Perhaps our education system do favour more non routine questions in the coming years. What do you think ?
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