This is an exciting time of great experimentation by many people to seek out a variety of good active learning teaching techniques for mathematics. What I can contribute is an evolutionary process of my own questioning, experience, reaction, and adaptation leading to a philosophy and long-term implementation.

-D. Pengelley, From Lecture to Active learning: rewards for all, and is it really so difficult?

In May of 2018 David Pengelley, of New Mexico State University and Oregon Sate University, presented a paper detailing his struggles and subsequent success with “flipping” his lecture experience.⁠1 He discusses why the traditional lecture doesn’t work and goes deeper into how his alternative does. 

As a secondary school teacher I’ve been hearing about flipped classrooms since I began training. A flipped classroom is one where students do the learning outside the classroom – usually by way of the internet: youtube, khan academy, etc. – and practise in class, rather than learning in class and practise at home (hence the flip). With all the “talk” Pengelley’s outline should be a golden cloud on the horizon. Unfortunately, when you get your meteorological pince-nez out of the draw you see that it’s probably somebody else’s horizon and not yours. Let me explain: Pengelley meticulous lays out his procedure and for the most part any maths teacher could follow his methods. The main sticking point is that Pengelley has control over how the students are summatively assessed: that is, what their grade is for the  course. Now, we secondary teachers could follow the same procedures to assess formatively but the summative assessment will always be externally constrained. This is the gap between Pengelley’s horizon and mine. It demands caution. 

Is the gap between control of summative and formative control a knock-down objection? The number of times I hear “is this on the test?” would suggest that it might be. Personally, I don’t think it is. Rather, it’s just a bloody big gap that would require a lot of structural, systematic work to properly implement. This work would probably have to happen across the department and maybe even across multiple departments. You would have to institute a system where students are taught how to problem solve and the language and practises of problem solving remain the same from day A to Z. Students understand situations of inequity and if they’re being made to work hard, consistently, whereas their friends in other classes are enjoying the hands off learning of the lecture then you can bet buy in will be low. You couldn’t just do it sometimes. If the system is working and your students are engaged then traditional teaching will get in their way and will cause frustration. If they are not engaged with the process then reverting to traditional pedagogy will give them resolve that if they’re just obstinate enough you’ll buckle and they won’t have to worry about working hard,

To answer Pengelley’s title question: yes, it really is so difficult. If a way to flip a classroom in a high school exists it isn’t going to be as simple as putting a youtube link on google classroom. Even if we don’t do exactly what Pengelley does we must approach it in the same way: namely, with “an evolutionary process of [our] own questioning, experience, reaction, and adaptation leading to a philosophy and long-term implementation.”⁠2 



2 From Lecture to Active Learning, 2.

Flipped Classrooms in Secondary School: Mind the Gap
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