The second full week of school has been a very meaty one. The kids seemed very eager to learn after the first few unstructured socializing/cohort retreat days. And I am starting to see the various personalities starting to emerge, which is both wonderful and more challenging because now it is real teaching and real learning.
In my Algebra 2 classes, we had our first quiz, which challenged all the students in different ways. My vision for the start of Algebra 2 had been to lay down a solid tech foundation alongside review or re-teaching of linearity skills, so that kids realize that a corner stone of Algebra 2 has to be using technology flexibly in order to self-monitor accuracy. I told the kids that I don't want them to ask me, "Is this right?" but I would be very happy to hear them ask, "How can I check this using the calculator?" So, on the first quiz they needed to demonstrate this skill throughout the algebra problems, in order to earn full points on reflection. (I gave separate points for: Communication, Approach, Accuracy, and Reflection.) In the end, my two groups were challenged differently; the Grade 10 native-speaker class had holes in their algebra skills and couldn't complete all problems, and the Grade 9 largely non-native speaker class generally showed stronger algebra skills (even with less in-class whiteboarding practice), but struggled with using the calculator flexibly. But, some of the kids shared their effective studying strategies in class, and some of the other kids are planning to see me on Monday for a requiz, so I feel quite hopeful that this first quiz is just the start of a learning dialogue.
By the way, my relationship with the international kids is developing in an interesting way. Because I speak Chinese, I am able to help the kids in my class without watering down the level of tasks I am asking them to complete. But, at the same time I can carry some weight when I see them being off-task and I offer to call their parents in China to have the dialogue directly about their efforts, in Chinese. What an interesting situation for me and them. Interestingly, they are better-behaved for me, and they try hard to speak English in my class, except when they need to help each other translate something. I am curious how they are going to do on their first big writing assignment, which we will be doing next week...
In my Precalculus class, kids are wrapping up the rough drafts of their first big project on special (triangular and stellar) numbers. I had to be very explicit in helping them to format their writeup. (I had to say at one point, "Take out a sheet of paper. At the top, write, 'In this task, I was asked to...' Now, complete that thought in your own words. I give you 30 seconds to do that. ...Now, write down, 'In order to accomplish that, first we had to...' and go ahead and complete that thought, make sure you insert a diagram here." But, after about 5 minutes of modeling, I think they all got the idea and were able to continue the rest at home, because all the drafts that they brought back to me the next day looked pretty coherent. So, it has been a tough project for them, for sure, but I still think it had tremendous learning value. We also had a quiz, and the kids are doing fine with function identification, interpretation of f(3)=7, and writing both recursive and explicit equations for arithmetic sequences. Some of the more clever ones were able to write formulas for quadratic sequences already, based on their learning from the Special Numbers project. So, I am pretty happy so far. As we wrap up our project (meaning, as I read over their drafts), the kids are doing mixed lines review and checking all answers via their calculator. They use either the Table or Trace to check all equations that they write from given info, and they use [2nd][Math] to verify equivalent expressions after simplifying. So far, so good, because kids in this class seem to be quite independent.
In my Calculus class, I had one student come forward to say that he really enjoys the exploratory nature of our class, and two others who came to ask me to do more examples followed by practice. I thought over this carefully and decided that although I think it is awesome that kids are being advocates for their own learning, and I really wanted to acknowledge that and to encourage that, the issue is really much more complex than their individual learning styles. I ended up describing to the class two contrasting learning models, direct instruction and inquiry-based learning. I said that in most math classes they have had, they probably experienced the former (intro, example, guided example, individual practice, closure, and eval), and that that is fine. It is comfortable, you know what to expect when you come to class. But, that way only reaches the top half of the class, the half that is fortunate enough to maintain focused attention and to comprehend at the speed of material presentation. Then I showed them a diagram of inquiry-based learning, which is a cycle of asking questions, investigation, creation of model or new knowledge, discussion, reflection, and back to asking questions. I explained to them that what we do in class is NOT true inquiry, because true inquiry would be like me saying, "Go. Find out how much universal health care is going to cost our country, both in the short run and in the long run." The problem would be entirely open-ended, complex, and vast, and we would learn all the necessary math skills as we move along. I explained to them that what we do typically in our class is a smaller version of this; within the individual topics of Calculus, I try to think about ways to structure our class so that they can create their own understanding. I ended the class with showing a little clip from Sir Ken Robinson's tedX talk (the animated one), and saying that teaching creativity is hard, and that our traditional schools have been doing a good job killing creativity. I told the kids that, yes, I think even in math there is room for creativity in the classroom, and unfortunately we don't get that by me doing an example and then handing out 25 problems that look the same. So, although I will try to find a balance between direct instruction and exploratory learning, I want the kids to keep an open mind and to appreciate opportunities for creativity in any discipline.
After this talk, I heard from another student in this class who said that she really enjoys math this year, and that our chat helps her to understand and appreciate my philosophy even more. So, one point for being authentic with kids and treating them as intellectual equals.
Good second week. Our school is awesome, by the way. I love that kids clean the school three times a week, and I adore my colleagues!!!!!