Whether we ‘flip’ a classroom, use an online homework system, or refer students to Khan’s Academy … our students are using task-oriented videos. In addition, students have a tendency to see ‘look it up online’ as a substitute for learning something. As we become immersed in (and dependent upon) the digital age, can we still work on problem solving or critical thinking?
One of the sessions at this year’s AMATYC conference dealt with the topic ‘stop the assault on critical thinking’. In the session, they played the roll of a short video on subject (related rates in calculus, maximizing a function in pre-calculus, or unit conversions in a liberal arts math class). The audience experienced something like a typical 3 minute video on that topic, and then we talked about how this supported critical thinking (or not).
The next session was one by Jim Stigler on ‘using teaching as a lever for change’, though he talked more about the futility of identifying specific teaching activities as being ‘effective’. Dr. Stigler did include 3 aspects of teaching that are connected to improved learning — productive struggle, connections, and deliberate practice. Learning is a complex process, and the presence of these 3 factors in the learning environment are connected to improved learning.
So, there is a connection between this research-based observation and the concern about critical thinking, I think:
Discrete learning experiences like short videos focused on successful completion of a task, based on clarity and being easy to follow, are guaranteed to limit both overall learning and critical thinking.
Mathematicians hold critical thinking as a goal to be valued; we want students to be able to flexibly apply knowledge to novel situations and interpret results. This seems to be a basic problem. Our students expect math to not make sense, that they could not figure something out; task-oriented videos support this self-defeating belief.
We can not hide from the digital age, even if we wanted to. However, we can improve our understanding of the factors that contribute to the learning opportunities for our students. A balanced approach appropriate to each course can help students through the learning process — including the struggle, the connections, and the deliberate practice. We might even see these digital resources as just-in-time remediation to be used occasionally, rather than seeing the digital material as the basic course.
We need a more subtle understanding of how our teaching can contribute to student learning. A single belief or methodology will not succeed for our students, no matter how good of an idea we might have.
To see a presentation by Dr. Stigler similar to what he did at the conference, see http://www.salesmanshipclub.org/downloadables/scyfc-Stigler.pdf
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