My Response to an Assignment Question on Discovery Learning

The assignment question:


Write between 1/2 page and 1 page discussing your approaches and feelings towards "discovery" in the mathematics classroom. For example, you could discuss: 

• In what situations do you deliberately use this or not use this approach?
• Where do you find that you have the most success using this or least success using this?
• How do students react to this approach?

Relate this to your learning through the M.M.T. so far.


My response:

Minimally guided learning, as defined by Kirschner, Sweller and Clark, is an environment in which learners discover or construct new information for themselves instead of being presented the new materials. Discovery learning is simply another term for minimally guided learning. In my position at the University of Winnipeg, I teach math content courses to pre-service education students and we rarely - if ever - use discovery learning. I would like to explain further my reasoning for this, but I must explain briefly the interactions of the long-term memory and the working memory.

The working memory is quite limited in capacity, only able to hold 3-7 pieces of information at a time. As certain items are flagged as important, these ideas move to the hippocampus where memory formation begins; and later to the neocortex where they are eventually stored in our long-term memory. The interesting part of the relationship between working memory and long-term memory, is that new information that has not been encountered before takes up a lot of space in the working memory; while information that has been stored in the long-term memory takes up relatively little space. If a student's working memory is "too full" we often say that this student is in a state of cognitive overload.

As a mathematics teacher, I have to be aware of this cognitive architecture. As I present new material in my course, such as computations in base-5, I need to respect that my students are novice learners of this material and support their learning by discussing worked examples. Allowing them to discover the operations on their own, without any help or base-knowledge (no pun intended), may put them at risk for cognitive overload.

Carey states that "the harder we have to work to retrieve a memory, the greater the subsequent spike in ... learning." This quote, I believe, ties into the current ideology around discovery learning - if the students undergo some struggle, then this type of learning is "better" than other learning. However, prominent figures such as Christodoulou have mentioned that discovery learning often leads to shallow results, especially if the learner does not have a solid foundation of factual knowledge to build upon.  Without a foundation of factual information to build upon, students' working memories may become quickly overloaded due to the complexity of the task. This, to me, is the main problem of discovery learning as it pertains to elementary school. All students are novice learners and most material is new. Asking students to discover their own way through mathematics without any assistance is not only bad pedagogy, but it feels unethical in light of current research.

This is not to say that all discovery learning is bad - I believe that discovery learning has its time and place. Take the Master of Mathematics for Teachers (M.M.T.) at the University of Waterloo, for example. Students entering this program have a very strong foundation in mathematics (a B.Sc. in mathematics, or a B.Math). These students have also been teaching mathematics at the high school level for several years, which means their retrieval strength of math facts and properties from long-term memory is high. With this framework, minimally guided instruction through the M.M.T. program works well, since students are able to bypass cognitive overload (for the most part) and make meaningful discovery.

References

Carey, B. How We Learn, Random House, New York, 2014.

Christodoulou, D. Seven Myths About Education, Routledge, New York, 2014.

Kirschner, P.A. & J. Sweller & R.E. Clark. (2006). Why Minimal Guidance During Instruction Does Not Work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.