Do we Confuse Good Pedagogy for Good Teaching?

Our professional organizations (both MAA and AMATYC) have published references related to good pedagogy within the last two years. MAA had the Instructional Practices guide (https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide), and AMATYC has IMPACT (http://www.myamatyc.org/). Lots of good ideas. References to decent research. What could be wrong?

Let me use an illustration from the other side of our ‘desk’. When a student uses procedures without understanding them, we uniformly provide feedback that this is not sufficient. When a student has some understanding of procedures, but can not understand connections between topics … we tell them that the connections are important. If a student gets those connections to a reasonable level but can not transfer the knowledge to a slightly different context, we tell them that their learning is not good enough.

However, we tolerate — or even encourage — corresponding misuses of teaching pedagogy. We see a pedagogy at a conference and ask questions about what to to in the process but rarely a question about WHY does it seem to work. Very seldom do we even reach the low standard of minimal understanding of the procedures. Rarely do any of us reach the expert level of knowing how to transfer our understanding to a new situation.

Now, it’s true that ‘good pedagogy’ (like good procedures) create some correct answers … ‘learning’, even if performed without much understanding. However, the same can be said for some ‘bad pedagogy’; certainly bad stuff has worked reasonably well for me (though I try to not do that stuff anymore). How do we even identify a method as “good” for teaching?

Sadly, we seem to have only two standards we apply to the process of identifying good pedagogy:

It’s good if the method feels right to us.
It’s good if somebody has seen good results with it (either better grades or some ‘research’)

Of course, our students do a lot of bad learning by the first standard (such as ideas about fractions or percents). Students don’t generally use the second standard, and the second standard is actually not a totally bad thing when the results are solid research comparing two or more treatments with somewhat equivalent students. I don’t expect us to use a gold-standard for research prior to using a pedagogy; I do expect us to do a better job of judging elements of a pedagogy based on understanding the process and the validation of those elements in research over time.

We also fall in to the trap of saying that diverse teaching methods are good. Now, it is reasonable to assume that a given pedagogy might be well matched to a certain situation; we might even believe that a pedagogy is especially suited to a given mathematical topic (though this is difficult to justify by research).

What should we do differently? My advice is to keep the classroom pedagogy simple from a student point of view. I’ve seen teachers use multiple complicated methods over a semester, which requires students to learn our methods which will necessarily have a reduction in their learning of mathematics. [Students have a finite supply of ‘learning energy’.]

My teaching methods are very simple. Every day (besides tests) are team based with two activities for learning (start and end of class). We don’t have assigned roles, and we don’t create artifacts to share with the entire class. There is only one criteria for measuring the value of our teaching methods:

Every student learns the most possible mathematics with the highest level of rigor possible every day.

Making this simple method work depends upon my understanding of learning processes as they relate to each topic and concept we explore. I have studied the learning process for my entire professional career (it’s what my graduate work was in), and what has been shown by research supported by theory is:

The amount and quality of learning are functions of the intellectual interaction of the learner with the material to be learned.

In other words, maximize a quality interaction for each student in order to impact their learning every day. The learning needs vary with the individual, so the pedagogy must provide a structure for my intervention (based on instant interviews) during class. My assessment of my methods involves global and individual progress in learning mathematics (including how much rigor is achieved).

One of my students commented last semester: “We could not help but learn.” I have had more dramatic comments (usually good 🙂 ). However, this ‘we … learn’ comment is the most valued comment I have received.

My concern involves the frequent copying of teaching methods (often based on the ‘seems right’ criteria). If you don’t understand how it works … you don’t understand who you will harm with the method. Although we don’t take a professional oath about this, seeing ourselves as a profession suggests a ‘do no harm’ standard of practice. Any specific pedagogy has the capacity to harm students; some pedagogies have a decent chance of helping students.

We should not settle for “it works for most students”. We certainly should not settle for “this generally works, but I do not understand how it works”. Our lack of understanding will cause harm to students. Being an expert means that we see simpler solutions that produce broad benefits; using complicated ‘solutions’ means that we don’t understand the problem.

Resist the temptation to copy ‘methods that work’. Copying methods is not productive for our students; it’s harmful to students if we copy methods without understanding the processes involved. Your best bet is to keep it simple and interact with students constantly.

cognition, Learning math | Jack Rotman | September 3, 2019 9:40 am

2 Comments

By Susan Jones, September 3, 2019 @ 2:08 pm

Have you seen the book _Routines for Reasoning_? It’s got structures for building ideas and skills and concepts so there’s consistency across the course.
By Jack Rotman, September 5, 2019 @ 10:13 am

Nope, had not seen that book. Thanks for mentioning it.

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