Discovery Learning versus Good Learning

As people look at improving mathematics courses in college, we tend to look at some methodologies as naturally superior to others; we often fall in to the trap of criticizing faculty who use “ineffective” methods (traditional ones).  Some of my discomfort with the current reform efforts in developmental mathematics is the focus on one category of teaching methods … discovery learning.  #CollegeMath

At the heart of the attraction for discovery learning (and it’s cousins) is a very good thing — an active classroom with students engaged with the material.  It’s no surprise to find that research on learning generally concludes that this type of active involvement is one of the necessary conditions for students learning the material (in any discipline).  We can find numerous studies that show that a passive learning environment results in low learning results for the majority of students.  One such study is “The Effects of Discovery Learning on Students’ Success and Inquiry Learning Skills” by Balim ( In this study, the control group was (perhaps intentionally) very passive; of course, discovery learning produces better results.

It feels good to have our students engaged with mathematics.  By itself, however, that engagement does not produce good learning.  Take a look at a nice article “Correcting a Metacognitive Error: Feedback Increases Retention of Low-Confidence Correct Responses” by Butler et al (’s/Butler%20et%20al%20%282008%29_JEPLMC.pdf) The role of feedback is critical to learning, but most implementations of discovery learning suggest that the teacher not intervene (or even correct errors).

Good learning does not happen from constantly applying one teaching method; teaching needs to be intentional, and modern teaching tends to be diverse to the extent that our work is research based.  I can see the benefits of incorporating some discovery learning activities within a class, along with other teaching modes.  See a study of this for college biology “The Effects Of Discovery Learning In A Lower-Division Biology Course” by Wilke & Straits (

I use some discovery learning activities in my classes, and have found that I need to be very careful with them.  Here is my observation:

When students are asked to figure something out, they tend to apply similar information they have (correct or erroneous) and the process tends to reinforce that prior learning.

For example, I use an activity in my intermediate algebra class to help students understand rational expressions at a basic level — focusing on the fraction bar as a grouping symbol and on “what reduces”.  The activity provides a structured sequence of questions for a small group to answer.  Each group tends to use incorrect prior learning, even when the group is diverse in terms of course performance.  Even the better students have enough doubts about their math that they will listen to the bad ideas shared by their team; the only way for me to avoid that damage is to be with each group at the right time.

So, I have taken the discovery out of this activity; I now do the activity as a class, with students engaged as much as possible.  Even when done in small groups, students tend to not really be engaged with the activity.

I notice that same self-reinforcing bad knowledge in our quantitative reasoning course.  I use an activity there focused on the basics of percent relationships — percents need a base, and percent change is relative to 100%.  Many students do not understand percents, and the groups tend to reinforce incorrect ideas.  I continue to use that particular activity, as the class tends to be a little smaller; I am able to work with each group, during the activity.

Some of the curriculum used in the reformed courses are intensely discovery learning (often with high-context).  We need to avoid the use of one methodology as our primary pedagogy.  Do not confuse the basic message of replacing the traditional math courses with the pedagogical focus used in some materials.  To achieve “scale” and stability, our teaching methods need to be more diverse.

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