The good learning environment - Trondheim 2018

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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 pÃ¥følgende tall 

What's Possible? or Hva er mulig? 

Think mathematically:

Tilted Squares - Teaching Using Rich Tasks 

Stringy Quads

Charlie's Delightful Machine or SlÃ¥ pÃ¥ 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).

 

 

 

 



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