# A guest lecturer…

Last year I had this student who struggled in Algebra II. And then, one day, he decided he hated struggling. He was frustrated and didn’t want to be frustrated anymore. He wanted to get math. And so… he did. To the point where he was getting almost perfects on assessments.

This was a student who I always thought highly of (I knew him both inside and outside of the classroom), and when he was frustrated, I felt for him. And when he made a dramatic turnaround, I couldn’t have been more elated. I have to say, there are some students who you just want to ask you to write college recommendations for. And these college recommendations just roll off the keyboard. He asked me, and I remember sitting down, and going at it. I think it ended up being two and a half pages, and I had to edit it down to be that. He exemplified the transformation that I hope all my struggling kids go through, but his transformation was the most dramatic of all my students last year.

Because I wanted my kids this year to know that they can struggle, and come through the other side, I invited this student to come talk to my class for a few minutes and talk about his frustrations. And how he made his transformation. I want to show my kids that they can be more successful, but there is no royal road to mathematics. The way to be successful is to work hard.

The key points that my former student made when talking to my kids:

• One day, one moment, he said “enough’s enough.” And he made a decision to do well in math. He was sick of that low grade on his report card, year after year. It was this moment that changed it all, because he changed his mindset to “I can’t do it” to “I will do it.”
• He said that doing well in math has a lot to do with confidence. He didn’t have a lot of confidence, but slowly when things began to turn around, he became slightly more confident. And then more confident. And now, this year, he is overconfident in math.
• He said that those annoying “explain this” questions that Mr. Shah asked were… annoying. But once he learned why I was asking them, that I was trying to get him to understand more than procedures, but to draw connections and see everything fit together, they made sense.
• He stopped looking at each test as something that needed to be crammed for the night before. Instead, each night he would work on understanding the material. And when doing this, he saw connections.
• He entreated my kids this year to try to draw connections between everything we’ve learned. Because that’s how it all hangs together. That’s what made everything click for him.
• He also said that even though he failed the first five binder checks, he finally figured it out. And he could be organized.

I don’t know if his message got through to any of my kids, but I do know that me saying these things isn’t going to do as much as a kid who went through the trenches and came out a hero.

So if you want to honor a kid who was awesome, and maybe (possibly?) get through to your class, think about inviting a former student to give a short guest lecture!

PS. I have former calculus students stop by all the time, and I always make them come to class. Sometimes I’ll leave the room and have the student talk to the class alone, about what recommendations they might have for my current students, sometimes I’ll stay, and sometimes I’ll have ’em talk about college life, and how everyone gets through the college application process, and how truly there is light at the end of the tunnel (even when it may not feel that way).

# Implicit Differentiation

Normally, I don’t have trouble teaching implicit differentiation. However, I’m never satisfied with what I do. I’m fairly certain that I have taught it four different ways in the past four years. But what’s common is that we do a lot of algebra. By the end, they can find $\frac{dy}{dx}$ for a relation like $\sin(xy)+y^3=2x+y$. Or something like that. But we lose the meaning of what we’re doing.

I realized we can do all this algebra, but it’s all procedure. And so there’s no real depth.

So today, after introducing implicit differentiation (including some visual motivation), I assigned 5 basic problems from the textbook. Each of the problems has an equation like $3y^3+x^2=5$ and students are asked to find $\frac{dy}{dx}$. My kids are going to go home today and struggle with it. We’ll spend about 20 or 25 minutes in our next class going over their solutions, talking about things, whatever.

And then… then… I’m going to hand out this sheet I wrote today.

[.doc, .pdf]
[if you’re wondering, the graphs were made by the fabulous winplot which I adore… it can do implicit plotting!]

My kids found $\frac{dy}{dx}$ for homework. Now in class, my kids are going to interrogate what that means.

I am not sure yet how I’m going to structure the class. I think I might have us all work together on the first problem (#9), and then assign pairs to work on two of the remaining problems. And then I’ll pick one problem for each pair to present to the class. But what I’m truly happy about is that each problem gets kids to relate implicit differentiation to a graphical understanding of the derivative. It forces my kids to look at the derivative equation, and make connections to the original graph.

Although I’m proud of it, I’m honestly just not sure if this investigation is beyond the scope of my kids’s abilities. It pulls together a lot of concepts. I think it’ll work for them. This year I have a really really strong crew so I have faith. However, it’s an activity I’m going to have to give my kids time to do, and room to struggle. I know me, and I’m going to want to rush it, and I’m going to want to help them in ways that aren’t good for them. The struggle is where they’re going to learn in this, so I have to give it time and stay out.

I am in the middle of a hellish week, but if I have time, I’ll try to report back how it goes after we do it in class.

# Next Semester

You know my philosophy about blogging… blog only when you want to blog. If you put pressure on yourself, it becomes a chore. And why would I make myself do a chore? More than that, it would be like a chore I created just to make my life harder. Like: every day, make sure you windex the windows to your apartment. (FYI: I have never windexed the windows to my apartment since moving in two and a half years ago.) (That’s what rain is for.) (And curtains.)

However, now that it’s been over a month since I’ve blogged, I wonder what’s going on?

We did have two weeks off, so it’s not like I could blog about school stuff when we didn’t even have school…

True. But that’s me rationalizing. Or how about…

I don’t have time because I’m just so busy…

I think. But this year I’m no busier than previous years. In fact, I might be less busy with school stuff. (However, I should say that I’m making good on my school year motto this year: “I’m doing me.“)

Actually, I think that is the problem. I wonder if I’ve gone stale, like that moldy bread in the back of my fridge? I only think it’s moldy, actually. I keep on putting things in front of it, because I’m scared to take it out, but I don’t want to look at it. It’s like smelling milk that might have gone bad. I don’t do it. I just throw it out, because the mere thought of smelling rancid milk makes me want to puke. Where was I going… oh yes, feeling stale. I’ve grown accustomed to having my SmartBoards that I slaved over years ago, and my worksheets and packets that I created ages ago. I’m tweaking. I’m not inventing. Or really even reinventing. I don’t have much to post because I haven’t been doing a lot of creation. And that’s always when I feel excited about posting. Invigorated about what I’m doing.

Now that I know this, I have an easy fix. Recreate. Invent. Reinvent. I’m also meeting with my department head on Friday to talk about course assignments for next year, and I’m going to ask to teach a course that will be new for me next year.

With all this mind, I’m going to keep a list (that I will update) with possible ideas/goals for next semester, which will be starting in a little over a week.

• In Algebra II, remember to do group work, and do more “participation quizzes” during that group work.  I did a bunch in the first quarter, and then the groupwork dropped off in the second quarter. Booooo, me! Keep it going, and strong!
• In Algebra II, remember to utilize the Park School of Baltimore curriculum, especially when working on Quadratics, Transformations, and Exponential Functions. It didn’t quite fit in with our 2nd quarter material, but it will align with our 3rd and 4th quarters.
• In Algebra II — since we don’t have a midterm for students to see a broad view and get a review of all the 1st and 2nd quarter’s material — have the 3rd and 4th quarter problem sets include “review problems” from topics from the first semester. Or if not, have review problem assignments, in addition to the problem sets.
• In Algebra II, do a written “final exam study guide” project again, to continue having kids work on their writing skills. Provide feedback, and an opportunity to do revisions, and fix errors. (Video study guides from years ago, paper study guides more recently.)
• Create this “pencils and eraser” station for kids who forget pencils.
• In Calculus, continue having kids work in groups on challenging problems every so often.
• In Calculus, do problem sets in the 3rd and 4th quarters, but make them shorter and give less class time than the 2nd quarter. Continue to make the problem sets have a “group” component and an “individual” component.
• I finally got large whiteboards for my students. I’m struggling to use them. So in the 2nd semester: use them. Even if it doesn’t go well, I need to keep using them. I need to have some practice and experience with them, even if to show me what works and what doesn’t work.
• Now that we’re starting the 2nd semester, have built in time to review the course expectations, and collaboration guidelines for all of my classes.
• Consider making changes with my Binder Checks in Algebra II? More frequent? Have kids leave their binders in class, and have time set aside for them to organize themselves? This year their binders are not improving much. It may be that I need to baby them. Some things might include: putting “correct the home enjoyment that we went over today” each day on the course conference (the place where I post the nightly work), having binder checks every two weeks instead of every five weeks (or random “homework correction checks” in addition to the five week binder checks), making test corrections a homework assignment (instead of just telling them they need to have it done by the binder check date), and showing kids how to create their own “checklist” to make sure they have everything in the binder done. I am a little surprised that sophomores and juniors are still finding this so challenging.

Some things I need to do regarding this blog:

• Blog about problem sets in Calculus and Algebra II
• Blog (briefly) about the change I made to Standards Based Grading in Calculus (scale is now out of 5). And also how this year is going compared to last year (read: better). And what still feels like it’s missing…