Ender’s Math

1 / 13

# Ender’s Math - PowerPoint PPT Presentation

Ender’s Math. Ian Underwood 2010 Numeracy and Financial Education Summer Institute. Suppose you're looking at some problem, P. A small hummingbird flaps its wings 78 times per second. Estimate how many times the hummingbird would flap its wings in one minute.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Ender’s Math' - kenyon

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Ender’s Math

Ian Underwood

2010 Numeracy and Financial Education Summer Institute

Suppose you're looking at some problem, P.

A small hummingbird flaps its wings 78 times per second.

• Estimate how many times the hummingbird would flap its wings in one minute.

2. Estimate how many times the hummingbird would flap its wings in one hour.

[PoW #9235]

What is the abstract problem, A?

It's about accumulation at a constant rate,

with a change in units.

Total

| . total = rate * units

| .

| .

+---------- units

How about an account with regular deposits?

Or the cost of some commodity (gasoline, cans of tuna)?

Or the cost of an item, with inflation?

P -> A -> Q1: rate is deposit per week,

unit is months

Q2: rate is price per ounce,

unit is gallon

Q3: rate is change in price

of burger per year,

• and presto! We have some 'finance problems'.

Note that this is reversible.

and turn it into a problem that is 'about something different’,

but still really the same problem.

It's a 'scenario' until you ask a question.

Then it's a 'problem'.

We can identify the abstract scenario, S, and generate a cluster of related problems by changing the unknown,

P -> A -> Q1: rate is deposit per week,

| unit is months

v Q2: rate is price per ounce,

unit is gallons

S Q3: rate is change in price

| of burger per year,

Qa: Given rate and total, find units

Qb: Given total and units, find rate

• and we end up with 2*3 = 6 separate problems, all about 'finance'. Or, we can just work with the scenarios directly.

Why do this?

There are lots of problems out there already.

Why re-invent them?

This approach reinforces the idea that abstraction makes math

powerful as a tool.

If done properly, it could ameliorate the usual difficulty

of cross-domain transfer.

And if done correctly, the students can do the heavy lifting.

Ender's Math?

"Knocking him down won the first fight.

I wanted to win all the next ones, too.

So they'd leave me alone."

Conclusion:

There's no such thing as 'financial math'.

There's just math, applied to finance.

Shall we give it a try?