analogue overheads (short)
TRANSCRIPT
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Is this a form of maths?
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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)
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Analogue thinking
Primitive brain
Numbers represented as imagined
lengths, distances, etc.
Lengths etc represented as
numbers: manipulate symbols
Higher brain
Digital (Symbolic) thinking
(algebra & arithmetic)(sensory representation)
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Analogue thinking
Primitive brain
Numbers represented as imagined
lengths, distances, etc.
Lengths etc represented as
numbers: manipulate symbols
Higher brain
Digital (Symbolic) thinking
(algebra & arithmetic)(sensory representation)
![Page 6: Analogue overheads (short)](https://reader035.vdocuments.mx/reader035/viewer/2022062312/555a025fd8b42aa8098b4f8d/html5/thumbnails/6.jpg)
Analogue thinking
Primitive brain
Numbers represented as imagined
lengths, distances, etc.
Lengths etc represented as
numbers: manipulate symbols
Higher brain
Digital (Symbolic) thinking
(algebra & arithmetic)(sensory representation)
![Page 7: Analogue overheads (short)](https://reader035.vdocuments.mx/reader035/viewer/2022062312/555a025fd8b42aa8098b4f8d/html5/thumbnails/7.jpg)
Primitive brain Higher brain
Analogue thinking Digital (Symbolic) thinking
(videotape) (CD-ROM)
Medium = senses (usually vision)
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Slow but precise
Primitive brain
Fast but rough
(“ballpark thinking”)
Higher brain
Analogue thinking Digital (Symbolic) thinking
(fixed number of steps regardless of size)
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Classroom thinking
Primitive brain
Real world thinking
Higher brain
Analogue thinking Digital (Symbolic) thinking
examples
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What’s 90 percent of $400 ?
(story)
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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?
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How long is a metre?
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What’s the circumference of the pool?
13 m
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What’s the circumference of the pool?
13 m
Symbolic thinking: 13 x 3.14 ...... But is the answer right?
Decimal places?
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What’s the circumference of the pool?
13 m
Analogue thinking: “Three-and-a-bit diameters ”
forty-something metres
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What’s the circumference of the pool?
13 m
How 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.
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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?”
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Is the size of this number important?
Symbolic thinking? No
Analogue thinking? Yes!
Is it big or small?
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0.9
0.1
Sin(x) ~ 0.1
Visual representation:
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0.9
0.1
O5.7 x
( Correct value 5.48O )
Sin(x) ~ 0.1
Analogue thinking accelerated symbolic thinking!
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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?
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Quick and easy but imprecise
Accurate but tedious
(requires sensory experience)
(usually visualisation)
Not one or the other but both working together
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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
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Who’s good at Symbolic thinking?
People who process symbols on a page
( linguists, musicians)
Expose kids to other languages and (especially) music
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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.
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Earthquake experience
Magnitude
. 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.