Quantitative Problem Solving

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What is "Problem Solving"?

This is a form of learning based on discovery: to solve the problem, you must both think and compute systematically.
It is different from both "exercise solving", in which past routines are applied to solve similar problems, and a "trial and error" approach is used to match correct formula for the problem.

A central idea in problem solving is the use of "concepts", which are the fundamental general ideas on which other notions may be built. In any subject, there are usually only a few basic concepts (sometimes expressed as formula), which are applied in a variety of ways or situations.

For example, basic concepts include limit of function in math, and t- test in statistics, Newton's 2nd Law in physics, mole in chemistry, and liability in accounting. Identifying and deeply understanding key concepts, and developing an organizational structure to allow you to recall how they relate to each other are essential elements in expert problem solving

The "spiral of learning" occurs when basic concepts are used repeatedly to solve a variety of problems. The central concept is the core of the spiral, and various applications spin out from, and loop back to, that concept. Frequently re-visiting those basic concepts allows you to firmly fix them in your long-term memory, where they can be quickly recalled and applied.

People learn in different ways, and have different preferred styles of relating to their world, seeking sensory input, making information meaningful, and patterns of learning. It is very helpful to understand your own preferred learning style, and use methods that both mesh with and challenge your style. See the free "Index of Learning Styles" by Felder and Silverman. www.ncsu.edu/felder-public/ILSpage.html and refer to the "Learning Style" module.

Self-Reflection Questions

Do you:

1. understand your own approach: strengths and weaknesses?
2. focus on concepts to increase understanding, and as an organizational framework?
3. learn material sequentially?
4. look for the "spiral of learning": repetition and expansion of basic concepts?
5. develop a systematic, methodical approach, to talk yourself through each step?
6. compute accurately, and eventually... quickly
7. persist?
8. get help when needed?

What is YOUR Approach to Quantitative Problem Solving?

Awareness of your own attitudes and habits is a good starting point to see your strengths and areas to change. Click on the "Evidence Based Components" questionnaire to assess your approach.

Evidence Based Components (55 KB)

Themes

1. Characteristics of Expert Problem Solvers
2. Characteristics of Novice Problem Solvers
3. Strategies to Improve Problem Solving Skills 

 

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