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Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
Analogue overheads (short)
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Analogue overheads (short)

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  • 1. Analogue thinking in mathsDavid Coulsondtcoulson@gmail.comSolving math problems in unmathematical ways
  • 2. Is this a form of maths?
  • 3. Is this a form of maths?(How would a robot do it?)(might not be maths but whatever it is, it solves a mathematical problem)(Birds and dogs can do it too)
  • 4. Analogue thinkingPrimitive brainNumbers represented as imaginedlengths, distances, etc.Lengths etc represented asnumbers: manipulate symbolsHigher brainDigital (Symbolic) thinking(algebra & arithmetic)(sensory representation)
  • 5. Analogue thinkingPrimitive brainNumbers represented as imaginedlengths, distances, etc.Lengths etc represented asnumbers: manipulate symbolsHigher brainDigital (Symbolic) thinking(algebra & arithmetic)(sensory representation)
  • 6. Analogue thinkingPrimitive brainNumbers represented as imaginedlengths, distances, etc.Lengths etc represented asnumbers: manipulate symbolsHigher brainDigital (Symbolic) thinking(algebra & arithmetic)(sensory representation)
  • 7. Primitive brain Higher brainAnalogue thinking Digital (Symbolic) thinking(videotape) (CD-ROM)Medium = senses (usually vision)
  • 8. Slow but precisePrimitive brainFast but rough(“ballpark thinking”)Higher brainAnalogue thinking Digital (Symbolic) thinking(fixed number of stepsregardless of size)
  • 9. Classroom thinkingPrimitive brainReal world thinkingHigher brainAnalogue thinking Digital (Symbolic) thinking examples
  • 10. What’s 90 percent of $400 ?(story)
  • 11. What’s 90 percent of $400 ?• how many of you do that? i.e., use size as a guide?• Would you teach it?• dirty shortcut?• Is it legitimate?• Do we encourage it, ignore it or unintentionally suppress it?
  • 12. How long is a metre?
  • 13. What’s the circumference of the pool?13 m
  • 14. What’s the circumference of the pool?13 mSymbolic thinking: 13 x 3.14 ...... But is the answer right?Decimal places?
  • 15. What’s the circumference of the pool?13 mAnalogue thinking: “Three-and-a-bit diameters ” forty-something metres
  • 16. What’s the circumference of the pool?13 mHow accurate do I need to be?And what am I doing this for?A lot of the time, all we really need is a rough answer.
  • 17.  Should we teach mathematical procedures for quick-and-easy approximations? If maths is quick and easy, kids will choose to use it. If there are choices, maths becomes a treasure hunt.Ask “How would YOU solve this problem?”
  • 18. Is the size of this number important?Symbolic thinking? NoAnalogue thinking? Yes! Is it big or small?
  • 19. 0.90.1Sin(x) ~ 0.1Visual representation:
  • 20. 0.90.1O5.7x( Correct value 5.48O )Sin(x) ~ 0.1Analogue thinking accelerated symbolic thinking!
  • 21. Is the answer good enough?If it isn’t then does it guide us towards a better answer?Should we let kids at school learn to do this kind of thing?If not, why not?
  • 22. Quick and easybut impreciseAccurate but tedious(requires sensory experience)(usually visualisation)Not one or the other but both working together
  • 23. Who’s good at analogue thinking?People with rich sensory experience of materials and objects(sportsmen, builders etc) Get kids outdoors playing sport and building things
  • 24. Who’s good at Symbolic thinking?People who process symbols on a page( linguists, musicians) Expose kids to other languages and (especially) music
  • 25. Therefore to make kids really good at maths...... teach them lots of things that have nothing to do with maths!philosophy:Maths should be one of those things that binds all the other subjects together,not that arcane stuff that sits out there on the edge of education, all by itself.
  • 26. [END]dtcoulson@gmail.com
  • 27. Earthquake experienceMagnitude. 7 1. 6 3. 5.5+ 10. 5.0+ 47 or more (sway)In all, 13,000+ earthquakes in ChCh since Sept 2010.Sensory experience leads to expertise.Can estimate an earthquake’s size by the seat of the pants.

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