Days where I have important exams usually become days where I do a lot of reflection about purpose and identity. Today I took an exam whose result decides what undergrad program I get into. It's called the ”mathematics and physics test", a test Swedish students take every year. It’s important because if you get 30/75 points or above, you have a guaranteed place at many prestigious programs at top universities. After looking through the answer sheet, I think I'll get about 27-31 points, and it all comes down to if I can get some partial credit from some questions.
Immediately after taking the test, I usually end up being a bit annoyed, and it’s hard knowing where that irritation comes from. It's not really a feeling of "I did not do well enough on the test! I could have done better!". It's more about feeling a certain misalignment between who I am and what we measure in these tests. And every time, after these "post-exam reflections", it all sets in a feeling of both relief and sadness. A somewhat lonely feeling in which you find both acceptance and disappointment.
From an outside perspective, if someone "likes math", then they should do well on math tests. I thought it would be this way. But it all depends on who you are. When I studied for this test, a simple high-school geometry puzzle where you're given 6 minutes could turn into an inner reflection on category-theoretic connections to the problem or axiomatic views on geometry. A simple integral could turn into a review on properties about the integral itself or an exploration about what measure-theoretic assumptions are being made, or what would happen if those assumptions are tinkered with! In a timed exam, these things–explorations–are sadly punished. Exploration takes time, and it should take time, but you never have time for that during an exam. Today's tests train muscle memory and ones ability to quickly manipulate syntax according to some rules. These tests don't aim at improving understanding.
It’s hard being yourself during these examinations when you strive for depth and understanding, rather than ”getting the right answer” or "using the right mathematical trick". I don't want to "get the right answer" if I don't understand the solution and the structure behind it. But under time pressure, you can’t afford pondering about the structure beneath seemingly simple questions. Why? Well, probably because they are just that! Simple questions! So grow up! You just have to memorize, think strategically to maximize points, and work from muscle memory.
That environment forces me to disregard my way of thinking. It forces me to disregard the very things I believe in, such as the idea that mathematics is fundamentally about exploration. When you feel like the world around you measure your ability in a misaligned way, and especially when those measurements dictate big parts of your life, you feel disappointed. Not disappointed in myself, not disappointed in the teacher. Just disappointed, irritated, in general.
I feel a grief for the beauty of the subject. In a perfect world, a "test" would be windows into our vibrant, and very different minds, and how we understand the subject. But practically, this is pretty much impossible, since it would require unreasonable amounts of resources, time, and money. A test needs to be reliable and scalable. Having thousands of students across a country take a test, then automatically grade it, is much less resource-intensive than it would be to sit down with those students and audit their understanding through, for example, conversations.
I hope we can come up with better systems to test not only problem solving under pressure (which is a crucial part), but also deeper understanding. I think there’s an imbalance between the two today. I hope we can find resource-efficient ways to create a better balance between measuring someone’s ability to apply calculation rules and retrieve results from memory, and their actual understanding of what they are studying.