We are working on sequences and series in PreCalc (and I'm using Sam's stuff which is awesome, but this post isn't about content, I promise to share how I adapted it later). Last class I had kids exploring visual patterns and then for homework they were supposed to find general form equations for a bunch of numerical sequences. I knew that students would have varying degrees of familiarity with the sequences included (from linear to perfect squares to factorials to alternating 1 and -1) so the homework instructions specifically said "if you cannot come up with an equation, describe the pattern." As a warm up today I asked students to list "sequences that are important to recognize" and we came up with a really useful table (name, first five terms, nth term) based on all the patterns they had recognized in the homework or looked up in the back of the book. After we were done (and I'd given my spiel on how important this was to record and keep since it would help them to Look For and Make Use of Structure), a student commented "You know, this list would have been really useful to have before we did the homework." I immediately felt myself getting angry. At the time I couldn't pinpoint exactly why this comment made me so angry, but I tried to keep my cool and explain once again that the homework had been to recognize patterns and figure things out, I certainly didn't expect them to know all the formulas already. She continued to argue, my blood continued to boil, I recommended that she come after school if she didn't know how to analyze patterns and the class all jumped in to take my side. I wish it hadn't come to the point of everyone vs. this student. I wish that I had acknowledged her frustration and ended the conversation, talking to her privately later if she wanted to. But most of all, I realize now, I wish that she trusted herself to think. The comment made me so frustrated because it's the very last day in May and I have yet to convince this child that she can figure things out for herself. I'm running out of time to reach her, and this thought is devastating.
I know I should be happy with how many students I have reached. And there are many. And I know that I've made progress with this student; even if I haven't made her believe in her own abilities, I am paving the way for someone else to do it. Life long learning and all that. But right now I'm just upset that the circumstances all to often lead to high schoolers who won't play with math, who think they need to be taught before they can do anything, who demand a method because they honestly don't believe that they are capable of coming up with one on their own. In my department we have an essential question that runs through all of our courses: "Is mathematics invented or discovered?" If students leave with nothing else, I hope that they leave with the understanding that mathematics isn't arbitrary, it's not something someone made up to torture them with and the rules should make sense. And, if all those things are true, math is something they can experiment with and make their own discoveries. Because, dear child, you can think.