Discovery Learning in Developmental Math

Compare these two situations:

You are placed in a laboratory with 12 objects of varying shapes and matching openings on the wall.  The learning goal is for you to discover which opening goes with which object.

You are placed in a room with 3 sheets of paper, 3 pencils, and two other people.  The learning goal is for you to discover the properties of a good drawing of a rose.

Really, take a minute to see yourself in each situation.

When we design a class to depend on discovery learning, we often assume that the students will experience a good thing.  We’ve listened to the sages say ‘guide on the side’ (rhyming makes right!!), so we have stepped out of the way.  If students discover the math, they will own it and learn it better (or so the story goes).

Like other people doing reform courses, I have been using discovery learning more.  From that point of view, the most important thing to say is this:

Discovery learning is very difficult to design and implement for positive results.

Two problems routinely come up with discovery.  First, many students have a difficult time seeing the idea that we want them to discover; this is primarily a communication issue.  The second: students come with prior knowledge, some not so good; the ‘discovery’ process often activates erroneous patterns, and the student ‘discovers’ initially that they had a great thing — which then needs even more effort to re-direct to better ideas.

The instructional materials being developed for the emerging models (Math Lit, Carnegie Pathways, Dana Center Mathways, commercial texts) tend to build a discovery process in every lesson, centered around a sequence of questions.  In general, the materials insert ‘check points’ for the instructor to assess the quality of the learning.  The developers work hard to create these materials that can be used by a variety of faculty.

The research base for discovery learning has not been consistently positive, and I think we sometimes confuse the motivational impact with learning mathematics.  I did some searching for a productive analysis of the issues with discovery learning, and found something that might help us.  The article is by Kirschner, Sweller, and Clark; called “Why Unguided Learning Does not Work …”, and is available at http://www.ydae.purdue.edu/lct/hbcu/documents/Analysis_of_the_Failure_of_Discovery_PBL__Experiential_Inquiry_Learning.pdf

This article is not a quick read.  However, I think you will find useful information which will impact your work in the classroom.

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4 Comments

• 

  By Brenda Shepard, June 24, 2013 @ 9:34 am

  Jack: the link didn’t work for me.

  Also, I wanted to comment, I do think guided discovery has merit, but sometimes textbooks that try to promote this format are too guided and don’t take students prior knowledge into account.

• 

  By Jack Rotman, June 24, 2013 @ 9:54 am

  Brenda: The link should be fixed now — it’s
  http://www.ydae.purdue.edu/lct/hbcu/documents/Analysis_of_the_Failure_of_Discovery_PBL__Experiential_Inquiry_Learning.pdf

• 

  By Sue Jones, June 24, 2013 @ 9:43 am

  Thanks — the link to http://www.ydae.purdue.edu/lct/hbcu/documents/Analysis_of_the_Failure_of_Discovery_PBL__Experiential_Inquiry_Learning.pdf has some extra characters in it that need to be trimmed to get to it, though.

• 

  By Jack Rotman, June 24, 2013 @ 9:53 am

  Thanks, Sue … I have fixed it (or *tried* to).

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