# The Good Learning Environment - Trondheim 2018

### Curiosity doesn’t always kill the cat

“… a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.”

Polya, G. (1945) How to Solve it

We know that good mathematicians are not only good at answering questions - they are good at asking questions, experimenting with examples, conjecturing, looking for connections, and finding new ways of applying familiar ideas.

Slides

Here is a selection of NRICH starting points, including links to translated problems available at MatteLIST, which are intended to surprise, intrigue, puzzle and engage your students, and may lead them to:

Develop fluency:

Cryptarithms
Subtraction Surprise
Cuboids
Generating Triples Pythagorean slides
Factors and Multiples Game or Faktor og multiplum
Sticky Numbers or Kompistall

Gain insights:

Five Steps to 50
Mind Reader here or here followed by Always a Multiple?
Make 37 followed by What Numbers Can We Make? or Hvilke tall kan vi lage?
Keep it Simple

Make discoveries:

Pair Products or Produktpar
Summing Consecutive Numbers or Summer av påfølgende tall
What's Possible? or Hva er mulig?

Think mathematically:

Tilted Squares - Teaching Using Rich Tasks
Charlie's Delightful Machine or Slå på lysene!
Reflecting Squarely followed by a discussion of Andrei's strategy in the solution
What's it Worth?
Almost One or Nesten 1

To create a better society, first we must imagine it.  But then we must act.
"A tiny act is worth a million thoughts" (Ai Wei Wei).

Links to resources to support teachers:

Posters for the classroom.

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“I don't expect, and I don't want, all children to find mathematics an engrossing study, or one that they want to devote themselves to either in school or in their lives. Only a few will find mathematics seductive enough to sustain a long term engagement. But I would hope that all children could experience at a few moments in their careers ... the power and excitement of mathematics ... so that at the end of their formal education they at least know what it is like and whether it is an activity that has a place in their future.”

David Wheeler