WEBVTT 00:00:02.250 --> 00:00:05.469 Hi. For most of my life, I thought mathematical 00:00:05.469 --> 00:00:08.650 ability was something that a person either had 00:00:08.650 --> 00:00:12.810 or did not have. Some people were, quote, math 00:00:12.810 --> 00:00:16.449 people. They understood it quickly. They could 00:00:16.449 --> 00:00:19.250 remember the right formulas, and they could produce 00:00:19.250 --> 00:00:24.050 correct answers. Everyone else stood at a distance, 00:00:24.269 --> 00:00:27.550 looking into a world that they were not equipped 00:00:27.550 --> 00:00:32.259 to enter. This, my friend, is a fixed mindset. 00:00:32.820 --> 00:00:36.560 The belief that our abilities are largely permanent. 00:00:37.159 --> 00:00:40.920 If I struggle with something, the struggle reveals 00:00:40.920 --> 00:00:44.679 who I am and what I will always be able or unable 00:00:44.679 --> 00:00:49.060 to do. Learning mathematics has gradually changed 00:00:49.060 --> 00:00:54.079 that belief. Mathematician and teacher Joel Bowler 00:00:54.079 --> 00:00:57.219 writes about the importance of approaching mathematics 00:00:57.920 --> 00:01:02.799 with a growth mindset. Mathematical ability is 00:01:02.799 --> 00:01:07.599 not a fixed gift granted to a fortunate few. 00:01:08.319 --> 00:01:13.299 It can develop as we explore ideas, make connections, 00:01:13.599 --> 00:01:16.760 try different approaches, and learn from our 00:01:16.760 --> 00:01:20.239 mistakes. Now, this does not mean that everyone 00:01:20.239 --> 00:01:23.280 has the same background or learns at the same 00:01:23.280 --> 00:01:28.200 pace or finds the same things easy. A growth 00:01:28.200 --> 00:01:32.019 mindset is not a promise that every problem will 00:01:32.019 --> 00:01:36.959 yield if I simply try harder. It is a refusal 00:01:36.959 --> 00:01:41.180 to treat my current understanding as the final 00:01:41.180 --> 00:01:46.239 measure of my capacity. And that distinction 00:01:46.239 --> 00:01:51.239 has changed me. When mathematics is treated as 00:01:51.239 --> 00:01:55.000 a performance, every question becomes a test 00:01:55.000 --> 00:01:59.680 of identity. A correct answer proves that I belong. 00:01:59.819 --> 00:02:06.260 A mistake suggests I do not. Speed becomes confused 00:02:06.260 --> 00:02:10.879 with intelligence. And struggle feels like evidence 00:02:10.879 --> 00:02:14.960 of failure. But when mathematics is treated as 00:02:14.960 --> 00:02:19.900 learning, a mistake becomes information. It can 00:02:19.900 --> 00:02:23.319 reveal an assumption I did not know I was making. 00:02:23.960 --> 00:02:27.469 A difficult problem. problem can expose the boundary 00:02:27.469 --> 00:02:30.710 of my current understanding and show me where 00:02:30.710 --> 00:02:36.550 growth might begin. Okay, sure, I still prefer 00:02:36.550 --> 00:02:39.969 the satisfaction of getting the answer correct. 00:02:40.610 --> 00:02:44.050 And I still become frustrated when understanding 00:02:44.050 --> 00:02:48.750 does not arrive quickly. But mathematics keeps 00:02:48.750 --> 00:02:52.990 reminding me that confusion is not a verdict. 00:02:54.090 --> 00:02:57.009 Often it is simply the place where I am standing 00:02:57.009 --> 00:03:02.289 before I see something new. The small word yet 00:03:02.289 --> 00:03:07.849 creates room for change. I do not understand 00:03:07.849 --> 00:03:14.069 this yet. I cannot see the connection yet. I 00:03:14.069 --> 00:03:19.810 have not found an approach that works yet. This 00:03:19.810 --> 00:03:22.370 way of thinking has reached beyond mathematics. 00:03:23.599 --> 00:03:27.280 I am less willing to define myself by what I 00:03:27.280 --> 00:03:31.740 can do today. I want to remain teachable. I want 00:03:31.740 --> 00:03:34.919 to be willing to revise my thinking and be patient 00:03:34.919 --> 00:03:40.400 enough to let understanding develop. Mathematics 00:03:40.400 --> 00:03:45.159 has not taught me that everything is easy. It 00:03:45.159 --> 00:03:49.240 has taught me something more hopeful, that difficulty 00:03:49.240 --> 00:03:54.919 does not get the final word. My mind is not a 00:03:54.919 --> 00:03:58.840 finished object. It is still learning, still 00:03:58.840 --> 00:04:03.319 making connections, and still capable of change.