Object Oriented Mathematics

[Dave Fashenpour]

Hello forward thinking math instructors,

I would like to propose a new and different approach to mathematics. A non-intimidating method which starts with Pictures and leads to Numbers, instead of the other way around.

Objects are used in Object-Oriented Software: Smart Phones, Robots, Drones, Space Stations, Satellites, Rovers, Self-Driving Cars-Trains-Airplanes, Facial Recognition Systems, Alarm Systems, Video Games, Social Media, Dating Matches, Smart Refrigerators/Microwaves/Dish Washers, etc. etc.

It is called the Internet-Of-Things (IOT) and it is the world that we are living in; right this minute. Google's Assistant, Amazon's Alexa with Dot/Echo, Apple's Siri with Homekit Devices, Samsung's SmartThings, and the Nest-Compatible home devices - to name a few.

In Object Oriented Mathematics, you perform the same type of data modeling accomplished in Object Oriented Programming -- working with Objects, not numbers! Concentrating on Properties like size, shape, color, and texture, etc. Defining Classes and Subclasses, of points, lines, planes, & solids; not to mention Sine Waves, Hyperbolics, and Heat Dissipation Patterns, and even the Mandelbrot Number Set graphics. Modelling mathematical data and categorizing the many similarities and differences into Classes/Subclasses of Objects, each possessing their own Methods of manipulation. 

I have an Introduction Video - a generic overview to the Object-Oriented Approach to Mathematics: https://youtu.be/rSUXbvzEFgg which is also available on my website:

http://www.OO-Math.com 

If anyone would like to see actual example of lessons using Object Orientation,

see Lesson #1-Triangles to Lesson #5-Multilaterals:

Lesson #1: https://youtu.be/wLxG_1vcbbI

Lesson #2: https://youtu.be/QyJr6NRuADw
Lesson #3: https://youtu.be/ETJw9Zbt0io
Lesson #4: https://youtu.be/lQlZVKCPq-g
Lesson #5: https://youtu.be/OKUwrd-yWN4

Would like feedback -- Negative or Positive. Would also appreciate mew ideas that could possible advance the teaching approach currently being used. Thanks for your time and interest,

Dave

281-380-2159

[Alexander Bogomolny]

Hi,

This  reminded me of a talk at a conference in 2000. http://www.cut-the-knot.org/Mset99/math.shtml

Mathematics is definitely object-oriented.

Alexander Bogomolny

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[michel paul]

I completely agree, thinking of mathematics as the description of certain kinds of objects, like rational numbers, complex numbers, matrices, polygons, and sequences, efficiently unifies mathematical and technological literacy.

Too often math education sees the mathematics and the technology as two different things, limiting the technology to the role of a device, to the role of a 'tool' that helps us do or 'apply' the math. 

This attitude is understandable, but it perpetuates a limitation that keeps the mathematics on one side and the technology on the other. What makes all this technology possible in the first place is a way of organizing ideas, and this way of organizing ideas in itself constitutes a new kind of mathematical reasoning. I believe we should teach this unity.

We developed this form of mathematics to help us conceptualize computational processes, but we can use it to shed light on ideas in traditional school mathematics. When we do so, new insights emerge. I've experienced that for myself over and over. In programming math concepts that I've long taken for granted, I've ended up seeing old ideas in new ways.

​For example, ​

I have said, "Fractions are objects, not unfinished division problems."

​ Simple fractions are an excellent vehicle for introducing some of the ideas of object oriented thinking.​

Our education makes students think of

​ a​

fraction as

​ an 'unfinished' expression​

 that still needs to be turned into a decimal

​, but fractions themselves are mathematical objects, composed of two pieces of information, and these two pieces are important. 

​We can think of a fraction

 as an ordered pair bundled with a set of functions

​ describing its behavior​

. 

​The s​

ame is true for a 2d vector - it can also be represented as an ordered pair, but the functions

​that ​

describ

​e​

its behavior differ

​ slightly​

from that of a fraction.

​The current goals in math education that we have students write more, think critically, use modeling to test their ideas, etc. are all effectively addressed in programming.​

- Michel

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--

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

--

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

[Dave Fashenpour]

Michel Paul's opinion is fantastic -- we need to rethink what our kids are interested in -- I used the "low-hanging-fruit" of geometric figures as objects. Michel mentions fraction (for example) which is perfect -- they are what they, not a connection to a continuum of division and multiplications -- but objects in and of themselves, with properties (and methods of solution). Any other forward tyhinkers out there? Dave.