A curious programmer

Math help, theory

April 28th, 2015 by Derrick

Is there a need for Math help? Countless parents and High School teachers think so. The problem seems to be an inadequate grasp of Math basics.

As a programmer, I wanted to help. It would be an easy matter to provide computer assistance for Math help and Math basics. I can pick a theory that appeals to me and just do it. But what would be the best and most efficient way. The literature was awash with theories and cognitive models. A popular quip : “A theoretical model is like a toothbrush – everyone has one, but no one wants to use anybody else’s.”

So I started to research the topic. Many of the theories have considerable intuitive appeal. But do they work? Sadly the answer is ‘sometimes’ or ‘it depends’.

Many of us will remember some of these theories, from our youth. A theory gets rolled out in the school system. After a few years – failure. Another theory then takes its place and again after a few years – failure. After a few cycles the old theories (with new names) gets repeated.

Minimally guided approach
I set about looking at some of these failures to make sure I don’t repeat any of them. I relied on research by educationists but followed the arguments that followed to make sure it made sense to me. The popular theory amongst ‘experts’ is minimal guidance or Constructivism. This approach has been called by various names including discovery learning, problem-based learning, inquiry learning, experiential learning, and constructivist learning.

Some quotes from ‘Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching – Paul A. Kirschner , John Sweller & Richard E. Clark’

  • The minimally guided approach says “that people learn best in an unguided or minimally guided environment, generally defined as one in which learners, rather than being presented with essential information, must discover or construct essential information for themselves.”
    However, “The past half-century of empirical research on this issue has provided overwhelming and unambiguous evidence that minimal guidance during instruction is significantly less effective and efficient than guidance specifically designed to support the cognitive processing necessary for learning.”
  • A conclusion: “After a half-century of advocacy associated with instruction using minimal guidance, it appears that there is no body of research supporting the technique. In so far as there is any evidence from controlled studies, it almost uniformly supports direct, strong instructional guidance rather than constructivist-based minimal guidance during the instruction of novice to intermediate learners.”

Should Math help follow the popular Constructivist theory in any of its various forms? The answer is NO.
Math help will definitely use directly guided instruction over minimal guidance.
Two excellent ways of guiding instruction:

  1. A worked example is a perfect example of strongly guided instruction. It directs attention to learning the essential relations between problem-solving moves.
  2. Process worksheets provide a description of the phases one should go through when solving a problem as well as hints or rules of thumb that may help to successfully complete each phase.

Looking forward to seeing how to use this in computer aided instruction.

Till next time.

This is part one of the Math help series. To be advised when the next in the series is published, fill in the ‘Follow’ form.
Please leave a comment below and tell me what you thinkā€¦


3 responses to “Math help, theory”

  1. Derrick says:

    Another angle to getting to know the basics first. http://www.scotthyoung.com/blog/2015/04/15/too-original-lessons-china/
    I have seen this happening: copy the original, use the knowledge gained to make a better product, add spin offs.
    Same as guided instruction. Guide the basics, build on the basics, go on to bigger and better things.

  2. Lonnie says:

    Such a forum fills a need that has existed for a while and, with other such sites that are available, can only help to improve mathematics understanding and performance.
    Good luck with your venture.

  3. […] stated previously – Math help, theory, Math Help will stick with direct instruction but will use all methods to help with […]

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