Was That a Good Class?

I have a class this semester (called ‘summer’, even here in Michigan!), and I have my normal worry about a class. Are students learning? In other words, was that a good class?

This cartoon is a bit oriented towards elementary school settings, but the ‘teacher’ comment applies to college settings … our teaching does not mean students are learning. This observation has resulted in huge increase of so called ‘active learning’ strategies. I use the phrase ‘so called’ because I see this is a redundant statement of the obvious … learning, by its nature, is active. I also say ‘so called’ because activity does not mean there is learning.

So, back to my class. I am using teams every day, with structured activities to support student learning. Most days, I leave class “feeling good” about how we are doing. Students are talking and doing, and everybody is engaged with the material. When a student needs help, their teammates contribute … as do students on other teams; I never know who will do the helping … there is a good level of support in the class. [I use the tag line in class “no student left behind”.] It’s clear that we have established a social structure in which students are comfortable.

However, this only confirms the ‘active’ part of learning, not the learning itself. I can take the easy way on this and look at test scores to see if learning is taking place. However, the starting point (what students already knew) is only known at the general level — not at the granularity of a test. It would be easy for me to conclude that students are doing well because the test scores are relatively good. (And they are.)

In the social sciences, there is an awareness that symbols are often confused with what they represent. Everybody wants the latest smart phone because it’s got a cool image, whether a given person has any need for the features (or not). The appearance of health is confused with the presence of health. In a classroom, I think we frequently confuse activity with learning.

I don’t have any magic to reconcile this quandary. I suspect that being continuously aware of the risk is the best strategy to avoid the pitfall. Perhaps we need to be less worried about visible activity and pay more attention to the cognitive processes within the learners. The best measure may be the direct assessment of a conversation with a specific student about a specific mathematical idea.

It’s nice (and fun) to have a very active class with students engaged with their team and the entire class. This ‘niceness’ likely has only a limited connection to the learning taking place. When I read articles … attend sessions … study presentations & reports … concerning active learning methodologies, I am left with the impression that these opportunities are very popular along with a perception that most practitioners will not do a good job implementing the ideas. In fact, I am not sure that I am doing a good job implementing them. Copying a pedagogy is dangerous practice; I seek to understand the process at a deep level, and look to my students for feedback on whether a pedagogy was successful. My class atmosphere certainly contributes to very good attendance, though I need to maintain my critical thinking about the processes and outcomes.

We need to have a complex understanding of the interaction between a pedagogy … such as team-based learning (or “PBL”, or “flipped”, etc) … and the needs of students related to the mathematics to be learned. In many cases, the only gain for implementing a pedagogy is that it reduces boredom for our students (and us); the lack of boredom is certainly not an indicating of any learning taking place. In fact, I think that many pedagogical ‘methods’ copied from others serves the purpose of fundamentally limiting the depth and rigor of learning: we focus on a sequence of steps in a process at the expense of understanding mathematics.

Effective teaching is not accomplished by feel-good methods, and learning is not measured by the level of activity visible in a classroom. Dealing with this complexity is the core issue of our profession as mathematics educators.

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