On Ode To A Teacher
The person that taught me the power of questions in learning
This post is in remembrance of one of my professors in college Margarida Jacome. She passed away too early in 2007. I had two classes with her, circuits and algorithms. She was one of my favorite teachers at UT. But here’s the funny thing about me saying that, I learned a tremendous amount from her classes although I thought she was a mediocre lecturer. The key was her exams. Now I had many professors that created great exams with questions that required you to think, apply your learnings in new and creative ways. But her exams had a distinction. I didn’t walk away from her exams proud of solving a difficult puzzle. No, I walked away from the exams proud of myself for having learned the topic at hand.
I was reminded of her when I read this article about using questions to foster learning. Unfortunately I don’t remember any of the questions from her exams. I don’t remember much about Op-Amps other than you can set them up solve differential equations and to calculate integrals. Although I do remember NP, the knapsack problem, greedy algorithms, and Huffman coding. So I’ve been trying to recreate the magic of her exams. How to create a question, after answering which you have a stronger grasp of the source material even without any new info in the middle of an exam. Unfortunately, I don’t remember any of the questions she asked, so I’m going to have to rely on very vague memories, related experiences, and crowdsource the rest by inviting you all to participate with your thoughts. But here is my attempt at trying to reverse engineer her magic formula.
Use For Keystone Ideas
Sorry for the slight abuse of this word but I feel a keystone is the best analogy for the concept. A keystone is a wedge shaped stone put between two sides of an arch. This architecture technique was invented in Roman times and it holds the structure together by having the weight of the stones in each side pushback and keep the stones on the other side in place. The Newton’s 3rd law in action. The key to making it happen is the keystone wedged between the two sides, transferring the force from each side to the other. And that is why the expression means central idea that holds everything together.
What’s interesting about questions is they rely on the pre-existing knowledge of the learner. Similar to the arches that are constructed but they are not able to support their own weight. What I mean by keystone ideas are ideas that bring together different learnings from these different arches of knowledge, and join them together to create a stable mental model for the ideas. The idea may be something mentioned in passing or may be a completely new idea. But the amazing thing is the clarity it brings to both the ideas helps deepen your understanding to the varying ideas that led you to this point.
Explore The Limits
You have to teach a baseline amount of knowledge before someone can learn through questions. So the power of self-teaching questions is not in building a solid foundation. The foundation has to be there to begin with. Rather it is when you start to explore the limits of the ideas. And so much like how the keystone requires there to be the tall arches that it brings together, you need your ideas to explore the limits. Yes building the tall structure reinforces the position of the foundational blocks. But you can’t focus directly on the foundational blocks.
Cause Cognitive Dissonance
The idea needs to be extremely loud, and it should be obvious that it is challenging the preconceptions the learner may already have. You want them to think, no that can’t be right. Because that is how they’ll be forced to examine what is actually happening. If the answer is simple, they’ll just gloss over it, not realizing that they’re skipping over a learning moment. Remember, we are talking about questions that can be
Fortunately, I remember two examples that you most likely were also exposed to in the chapter for work and energy in Physics. The examples go along the lines of:
- A girl carries a handbag at a height of 1.5m with a mass of 2kg for 1km at a constant speed of 2m/s. What is the work done against gravity in carrying the handbag assuming g=9.8m/s²?
- A weightlifter tries to lift a mass of 200kg by applying a force of 1000N for 5 minutes. Even though he is not able to lift the mass he is tired from his strenuous effort. What is the work done on lifting the mass assuming g=9.8m/s²?
Both of these questions have the answer 0 Joules. In the process, they reaffirm a few concepts, the work done requires displacement in the same direction as the force. And while it is easy for us to associate work done with our own fatigue, we should not fall into that trap because we can feel fatigue for a lot of other reasons. And so while in both cases the person may think they’ve done work they haven’t. And in these examples the number 0 stares at you in how counter-intuitive it is. Although in my Physics book these examples were pre-cursor to an actual explanation. Which is part of why Dr. Jacome was so brilliant. Because it was just the learnings I had taken into the exam room that allowed me to extend the idea. I can tell you the first time I did the two examples above I didn’t get it.
Make It Self-Verifying
In creating these questions the teacher won’t be there to make sense out of the learning. So it is best if you can create the problem in such a way that there is a second way to verify it. This will help the learner to recognize the truth behind their solution and to link it with another concept.
So let’s take the example of the girl carrying the handbag again. As she’s walking, she walks side by side to a frictionless surface. On the frictionless a pedestal of a height of 1.5m is moving alongside the girl at the speed of 2m/s. The girl sets the bag down on the pedestal and walks another 1km. Afterwards she picks up the bag from the pedestal and continues to walk. How much work did the pedestal do? In this case it is a lot easier to accept the answer of 0 joules because it’s a lot easier to accept the pedestal did nothing. This example brings the dissonance we saw earlier into a more obvious contrast and prevents the learner from making the easy mistake of not recognizing the direction of the force.
So consider this rule as something you can use to force the learner to recognize the dissonance and to accept the reality of it. They have to reconcile the two different ideas that are opposing each other. And the only way to do that is to place the keystone in between to hold the two ideas together in balance in their opposition to each other.
Don’t Be Easy On Them
The work that has to be done is difficult. It is shattering pre-conceived notions. And that is never easy. Since it’s not going to be easy, don’t worry about making it easy. Just worry about making it accessible. Provide multiple routes to understanding and validating your thought process is one of them. Then there is the ideas coming together in an epiphany. But to get there, you’ll have to push ideas to their limit. So the difficulty is a given. Instead of trying to reduce it, figure out how to work with it.
I’m thinking over these points. And I’m still filled with awe for Dr. Jacome. I’ve been thinking about what can make good examples. And I’m struggling to think of original examples. And yet there she was, she did it in both the classes I had with her. The same level of brilliance twice. So in the end, I have to thank her for the impact she had on my life. When I found out about her passing away, I was confused. She was too young. Now after all these years, I can only thank her for the perspective she gave me. I hinted a week ago how education is compromised by the focus on exams. Yet she was the person whose exams showed me that testing can be just as much a part of your education and can be used to expand your horizons.
Also I want to thank her for the note she wrote on my SigBook. For a long time I felt inadequate in achieving the praise she bestowed upon me. Now, I am happy to have her in my life, and am sure she would be proud of me. When I’m able to I’ll share the note with you. In the meantime would love to hear your thoughts on favorite teachers, learning from questions, and how to honor those that are no longer with us.
