Discovery Learning in Math?

Unbelievable! Discovery based learning – a huge failure in the wrong context – is the latest fad in teaching math to children in Canada.

Discovery-based learning is the idea that someone is given a problem to resolve, and they will explore ways to solve the problem. Brilliant idea, but problematic to the core. Problem-based learning (e.g. used in medical education) is a form of discovery-based learning, and when used right (like in a medical school), and with a massive amount of support (I’ve supported a class moving to problem-based — huge amount of prep and work), is the most effective method of preparing medical practitioners for working in the real world.

How is this related to learning math in elementary school?

One of the things needed for discovery-based learning to work is that the foundational knowledge needs to be in place. Elementary school math, by its very definition, is where children acquire their foundational skills in math. The basic academic skills necessary for doing academic work – reading, writing, and arithmetic – are rarely learned through discovery. If this were so, there would be little illiteracy in te world. People would have figured out these skills, on their own, as soon as the brain was evolved enough to have these capabilities. It didn’t happen.

A very few individuals had the interest, time and inclination to discover these basic skills on their own, and then they taught these skills to others. The earliest foundation of civilization. There were never masses of people who discovered these skills for themselves. There are still millions today, who do not have access to basic education who do not discover these skills for themselves.

Some things just have to be taught!

This is another example of educators having a good idea and then implementing it with no research whatsoever to see if it will work. The research HAS BEEN DONE! and discovery-based learning DOES NOT WORK! for the fundamentals. People do not learn that way, but with no background in how people learn, teachers will rush from fad to fad, ruining generation after generation of children and their learning.


4 thoughts on “Discovery Learning in Math?

  1. I disagree very strongly.

    While discovery based learning is more difficult for th teacher, more demanding of the teacher, it is deeply effective. It is true that simply adopting “discovery based learning” as some magic pill can lead to a disaster, but that has nothing to do with the fundamental idea. See Lockhart’s book “Measurement” if you want to begin to understand how it can be done correctly. You should also read the same authors “Lament” you can find circulated on the web.

    I can tell you that the “teach them the facts/algorithms” methods can generate people that can count, crank a crank, etc, but not people that really understand, can innovate, really think for themselves.

    And, what we need are people that have been taught to think for themselves, to discover.

    On the other hand, teachers that do not understand the subject themselves, cannot begin to teach the students to explore and discover for themselves. Those teachers are lucky if they can teach the students just the algorithms, rules, etc. What you are really pointing out is the failure of the discovery based method because the teachers to not have a deep enough understanding, have classes that are too big, etc.


    1. You disagree strongly. So you simply dismiss the evidence and go with your gut feeling and follow a “great idea”.

      Discovery learning has never been shown to be an effective way of learning fundamental principles. It is a useful tool, once the fundamental learning has taken place (then it is called “problem-based learning”). However, if it were effective for learning fundamentals, there would be no illiteracy (either reading or math) in the world, because the need to learn it would result in everyone discovering the fundamental principles. If you know anything about history, you will see that the discovery of the fundamental principles is a rare event that has happened only once or twice.

      Why do teachers insist on ignoring research for following a good idea. We know how people learn…


      1. This is not about following a gut feeling.

        It appears you are using the term discovery based learning differently than I am though, which might matter a bit. (But maybe not) It depends on what you mean by fundamental principles. I strongly suspect that much of the research you refer to is skewed by ineffective teaching. Mathematics in particular is dogged by enormous amounts of ineffective teaching as well as a culture that delivers students handicapped in many ways.

        If you are acquainted with Lockhart’s approach … and you dismiss that approach, then we will have to agree to disagree.

        I know that — whatever you want to call it — moving students into a discovery mode from the very beginning, with pieces and ideas added along the way (maybe that violates your idea of discovery-based learning) is both what students needs and more challenging.

        The way students are being taught mathematics (at all levels) is destroying much of what is needed to make them true masters of the ideas and able to discover and innovate on their own.


      2. Rereading your comment again, I see that you appear to use the term “discovery based learning” in a very extreme way: do nothing at all and expect the student to discover all of mathematics completely on their own, expect them to discover the alphabet and words and etc etc completely on their own.

        I am referring to the part where you say:

        “However, if it were effective for learning fundamentals, there
        would be no illiteracy (either reading or math) in the world …”

        I would never use the term that way … but I know that one can guide students to a mastery of mathematics and reading using a discovery mode, in which the thrill of discovery can be harnessed


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