Math Strategy Poster 2

Here’s a large map with strategies, tactics, tools and tricks for math problem solving.
The basic ideas behind this map are of course massively influenced by the works of George Polya, Arthur Engel and Paul Zeitz. Several important ideas come from Christian Hesse’s book “Das kleine Einmaleins des klaren Denkens”.

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A New Problem Solving Method

The impact of reflective thinking on problem solving is impressive.
Here’s an article on how general problem solving may profit from this.

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Solving Math Problems

The following article presents a number of key concepts for successful math problem solving.
From the introduction:
“This paper describes a method for solving math problems.The basic idea is to combine two things:

• First, a simple method for making handwritten notes while thinking about a problem.This method is aimed at supporting
  – a step-by-step approach to problem solving and
  – reflective thinking: Better understand and control what you do while solving a problem.
• Second, a densely packed cheat sheet with broad advice on math problem solving. At present, this sheet focuses on general methods for problem solving. Later versions may contain material on specific domains like calculus or algebra.

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Problem Solving With OneNote

My enthusiasm for software that supports human thinking and problem solving is unchanged.
After several articles and videos on mind mapping software, here’s a new approach:
Using notebook software (here: OneNote from Microsoft).
OneNote provides a number of features that are very useful for problem solvers:

• outlining text,
• very flexible tables,
• diagrams and
• freehand notes.

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Problem Solving: How Computers Can Help

The following article is an Englsih translation of something I’ve written for the 2010 Mind-Akademie.
From the introduction:
“Solving problems is one of the most important things we humans can do. On
the other hand, computers are one of our most useful inventions.
So it is not surprising that computers are used for countless aspects of problem
solving. (Moreover, they make invaluable contributions to the field of problem
creation.)
But helping people immediately with the job of thinking, of creating and
evaluating ideas – that’s where computers are much less often used.
This article shows how it can be done.”

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Computer Aided Problem Solving – a no-cost approach

The following article describes how to use mind mapping software for computer-aided problem solving and thinking.
It provides links to

• a problem map tool map template and
• a tool map, with a large repository of problem solving tools.

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Video: How to become a better problem solver

Here’s my new video – enjoy!
(And don’t forget to choose full screen viewing mode.)

The video shows how to use mind mapping software for computer-aided thinking and problem solving.
You can use the free mind mapping programs FreeMind or Freeplane.
The music comes from Arnaud Condé, a French composer born 1990.

Mentor Mapping – how your computer can help you think

Here’s my new video on computer aided problem solving and thinking.
All you need is the free mind map software FreeMind. Alternatively you can use Freeplane.
The basic idea is to make your computer your mentor, using a “Mentor Map”.
Like a friendly mentor, this map will provide advice on

• how to start,
• how to make good plans or
• how to deal with obstacles.

Editing branch images in mind mapping software

It would be nice if mind mapping software would not only allow to show images in branches, but also allow editing these images.

Here are some details.

How could it work?
In the context menu for a branch, you choose “Edit image”. An editing window pops up, similar to the window for text notes.
You start with either an existing image from a library or from the internet, or with an empty canvas.
In the image editing window, you edit the image – add, erase or move parts etc. This works especially well in combination with a graphic tablet.
The changes made are shown in the branch image immediately afterwards.
(It may be tricky to find a reasonable scope of functionality – from elementary line drawing to full-fledged image editing software…)

Why is this a good idea?
The feature will strongly support the visual thinking aspects of mind mapping. The benefits of visual thinking have been emphasized often enough, but simply chosing an image from a library or the internet is not nearly enough if you want to use images, diagrams and scribbles for developing ideas and plans.
On the other hand, editing images with a separate piece of software and then putting them into a mind map is by far too clumsy.

Who could use it?
The function will be especially useful for all people working with images, diagrams and formula in their work – e.g. engineers, scientists, and, with a decent scope of image editing functions, designers, artists and advertising experts.

Combining handwritten math notes and the internet

I’m looking for information on how to combine handwritten math notes and computers and the internet.
My basic idea is to use a graphics tablet and an online canvas that supports collaborative works.

I have few relevant experiences myself, but a number of advantages of combining handwritten notes and computers are obvious:
- Handwritten notes are natural for doing math.
- They are much quicker than TeX etc. and avoid disruptions from coding formulae.
- It’s easy to add simple diagrams etc. in handwritten notes.
- Via the internet, collaborative work with all its benefits becomes possible.
- The material can be made available for a large audience.
- Adding audio streams etc. makes the written material easier to understand.
- An electronic canvas or blackboard can be made much larger than a physical one.
- It’s easy to manipulate elements on the canvas: remove parts, move them, highlight them, change their size, zoom in and zoom out, add comments (written or audio) …
- It’s easy to keep track of different versions.
(I know there are a number of severe shortcomings – messy handwriting being a major one.)

So – any ideas on this?