Practical Methods of Solving Math Problems – a Restart

December 19, 2013

Which practical methods could help me solving math problems?
I will approach this question by splitting it into two parts:

Q1: How can I make notes that support thinking about math problems in the best possible way?

Q2: How can I use thinking tools that are helpful in solving math problems?

In Q1, I find the following aspects important:

  • How can notes help me to develop ideas and to think straightforward?
  • How can I add reflections on my thinking, to see what works well and what doesn’t?
  • How can I deal with multiple approaches and chains of thought without getting lost?
  • How can I store sudden ideas for later examination?

In Q2, I’m puzzled by the following things:

  • How can I find useful representations of the problem?
  • How can I generate and exploit seminal ideas that eventually lead to a complete solution?
  • How can I deal with obstacles, mathematical and otherwise?

Answers to Q1 and Q2 are obviously closely linked, so I’m aiming at an “integrated method of math problem solving” – it’s not just about note-making and not just about thinking tools, but about combining both for good results.

This is the program for the following posts.

The next post is about note-making technique.

I’m focused on these topics for several years now, and I have written previous posts about them, see here or here. What I present now is a thoroughly revised version.


Math Strategy Poster 2

April 3, 2011

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

February 19, 2011

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

December 31, 2010

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

December 20, 2010

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

November 20, 2010

The following article is an English 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

July 14, 2010

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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