Saturday, September 28, 2013

Week 3 Teaching - Setbacks and Triumphs

We are in the thick of it now, the part of the semester when I see how kids handle setbacks and challenges. This is one of the ways I really get to know a kid, because I truly believe that how you handle setbacks defines your character. I tell the kids that they can keep reviewing and re-quizzing, or re-submitting drafts of a writing assignment, until they decide that their score is good enough to stop. No one is going to disallow them to keep working to get better, because I think that training kids to keep tackling something long after the class has "moved on" is how we can teach them to develop a persevering character.

For me personally, I've always viewed myself as a second-try kind of gal. If I weren't, I would have given up the first time a teaching program told me that I wasn't their ideal candidate, and I would never have ended up doing what I do, and loving it. Too many adults give up on their goals too easily, and let other people decide for them what they can and cannot achieve. I don't want that to happen to my students.

Anyhow, enough philosophizing. More about teaching. My Calculus kids are entering a very interesting phase of the course. We had our first quiz, which was quite tricky and conceptual, even though it did not involve many numbers. To my delight, about two-thirds of the class did quite well on this quiz, and the top three or so scores were all girls!!! I cannot help myself but feel gleeful about that, especially because 1. the girl who did the best on the quiz (missed actually none of the problems, including the bonus ones which we had only briefly seen during class) had previously said to me that she always felt a little behind in other people's math classes, and 2. our school has been having some conversations surrounding issues of diversity (mainly ethnic and socioeconomic), which has been making me wonder a bit about the role of "male privilege" in the math classroom, similar to the issues of "white privilege." Anyhow, the fraction of kids who didn't do so well on their quizzes are seeing me on Tuesday for a re-quiz, so as of now it is still too early for me to say whether they just had a bad day, or they are still learning how to study effectively, or they really need some serious intervention with the topics that we have covered. In this class, unlike the other classes, I have not been collecting/grading homework past discussing the answers as a group, since thus far we have been building up introductory concepts and there are not a lot of nitty-gritty skills checkpoints for me to look at and respond to. I think that contributed to the lack of individual feedback before the first quiz, which I will remedy in the coming unit by being more hands-on with grading their homework assignments, once we step into the realm of manual differentiation techniques. Overall, I have been very happy with the way that my kids have built their conceptual understanding around derivatives and instantaneous and average rates. We take every second Friday to review algebra skills from the past, and then I assign a review homework assignment for the weekend following. So far, we have reviewed: 1. factorization techniques, 2. how to solve for a parameter within an equation, and 3. when to use their calculators to solve complex equations; and already I can see their independence growing inside the classroom from these mini skills reviews. We just wrapped up a great worksheet (if I may say so myself), because every problem in this worksheet is anchored in something very real. Problem 1 was about investment, and I had talked to the kids about how my husband does real-estate investment and how he uses this type of math to calculate mortgage rates and monthly expenses on a rental property, in order to compare those fees with his rental income to make sure that he will clear a profit every month from his investment. (Related to this I talked to the kids about why they should invest, and why investment does not mean that they cannot be contributing productively to the society.) Problem 2 was about carbon-dating, but the kids needed to read the initial C14 levels out of a graph of atmospheric carbon levels to use in their carbon decay model. This is very realistic, and we got to talk a little bit about the science behind your body equalizing with the atmospheric carbon levels while you are breathing/alive, as well as about how cow-farming is causing historic carbon levels to rise (connecting this to what they see in the graph of historical atmospheric levels). Problem 3 on the worksheet is an ad that I actually found on the web for Gap Inc's credit card offers, so although it is another review problem for interest rates, it is steeped in real world context. I am trying to make my Calculus class as inter-curicular as possible on a day-to-day basis, so that kids can see the reason/motivation behind studying what we study. Interestingly enough, a couple of the faster-moving kids have already started on our end-of-unit economic mini-project (Part 1 and Part 2), and the first question they asked me before even starting the math was, "Why would anybody care about marginal costs?" --Aren't my kids fabulous? I want them to ask me questions like this, so that Calculus can come alive for them.

Anyhow, Precalc is also going swimmingly. I heard feedback from one 11th-grade advisor that her advisee loves my class, and thinks that all the math we do thus far is very clear and very understandable. The students are in the process of finishing up their first big lab writeup, which was very exciting because when I took them down to the computer lab, I got to show them how to 1. enter and format equations properly into MS Word or Google Docs, and 2. how to connect their TI-84s to the computer via TI-ScreenConnect to prove that they are doing the tests of their formulas. Some of the kids, in fact, didn't even know how to construct tables or write subscripts, so there was lots of tech education there, besides helping them out with the mathematical language. The kids thought that typing up their revisions to the rough drafts was going to be easy, but it did in fact take them two full (45-minute) class periods, and many still had to go home to take some time this weekend to re-read through it to make sure that they have hit every part of the project rubric. Anyhow, I prepared a graphical organizer template so that sometime next week, we can discuss how this idea of approaching and analyzing math sequences is going to be the big idea through the entire first Quint. (We have 5 Quints a year, as opposed to 4 Quarters.) Also, something quite cool that I tried recently was to put kids into groups and let them do mixed analysis of linear and quadratic sequences, and instead of me telling them whether they were correct, they got to check using the web interface of! The kids were super into it, and I think seeing the two types side by side really helped them to clarify mentally the different strategies for each type. Alongside the writeups, the kids have just about finished reviewing all the algebra skills for lines, so I will give another quiz next week before moving on to reviewing quadratic and transformational skills.

My Algebra 2 classes are moving pretty slowly through their regression project, because I have discovered that they have some holes in their Algebra 1 knowledge and am taking some daily class time to discuss homework problems before assigning new review assignments. In class, we are doing white-boarding practice about once a week, because it is a great time for me to make sure that everyone is doing some algebra practice together and getting instantaneous feedback/help as needed. Following our fairly difficult first quiz, which I had written about last week, lots of kids came to see me to do re-quizzes, which I loved. Although they didn't all get 100% on their re-quizzes, it started a very productive dialogue with kids about how they are studying, what study tips I can recommend, and why things always seem easier when you do a re-quiz. One international student in particular had an 180-degree shift of attitude towards me after the re-quiz. I think she's the kind of student who thrives particularly on positive feedback, so the fact that she had failed the first time but got 100% on the second try, really boosted her confidence and her feelings towards math (and I guess, me). So, although it had been a challenging/"discouraging" week last week, I think it was a necessary reality check for many kids and now they are much more focused and strategic in their learning. My 10th-graders, for example, took a lot of photos yesterday during our white-boarding practice, because the one student who had done that last time and who had practiced with those problems later at home, had done very well on the quiz and had offered that up as a study strategy to her peers. So, we are a growing community of learners, moving in the right direction, slowly but surely!

For both Algebra 2 classes, on Monday we will go and test out the kids' predictions for the bungee drop. They will build the cords, name their rubber chickens, take a photo with their chickens, and then we will go out to the balcony. It'll be a very fun day, but the hard work that is yet to come is to write the lab reports coherently. I am a little nervous about getting their rough drafts on Tuesday, and what those will look like, especially for my international kids....

But, I cannot complain. I love this time of the year!


  1. Just seeing this as I'm going through your Algebra 2 posts :) can you say more about how you do lab reports? That is something with which I have always struggled with.

    1. Hi Anna! Sure. I typically follow a fairly strict format. They have to: introduce the task, identify and name their independent / dependent variables, describe their procedure for collecting data, present their data in table and in graph, justify their choice of regression model, record regression results and interpret all parts of equations / meaning of all parameters in the context of the problem, make prediction for future behavior, test their prediction, and analyze result of test and generate a list of possible sources of error. I give them a sample write-up from a different topic to help them see the desired structure, as well as a checklist for what to include and a rubric for how much detail they should have. They always give me a rough draft, I mark it up, and then they get graded on the final draft. Does that help? This model I find to be very flexible for a variety of content.