Calculus Fail

I’ve been beating myself up, and it’s only day 4 of school. It’s sad because I just want this year to be the most fantastic year ever, and I wanted it to start so positively. But I’m feeling sad about my classes. I am okay being a teacher centered teacher for my Algebra II class. I really am. We have a curriculum that we are following, and we don’t have too much time to dawdle. Also, the kids are younger, so I feel okay keeping them mostly reigned in. And my MV Calculus class is going to be relaxed, though more challenging to teach than last year, because there are only two students (gasp!). That is a nice combination of student and teacher directed.

However, my calculus classes are a different story. I don’t have a set curriculum, which allows me a lot of freedom. I want to make sure that these students leave understanding calculus. I want them to see what makes calculus cool. What makes math cool.

So I promised both sections of my calc kids on the first day that my goal was to make math understandable to them. And I secretly promised myself that day that I would make math more interesting than they’ve ever seen it before.

It’s day 4 of teaching, and I feel like I’m flopping already. My classrooms are depressing (no sunlight in one; loud sounds of recess floating through the window in the other). I haven’t made one interesting lesson or one group/partner activity. I’ve just been up at the stupid SmartBoard pointing, talking, asking questions, going over homework. We’re just reviewing. And honestly, I don’t even really know where the students are in terms of what they know and what they don’t know. I call on random people, I walk around when they’re working on problems practicing in class, and still: not much clue. That’s not good.

I want to feel okay letting go this year and shift from having a teacher centered classroom to having times when the room is student centered. Where I’m not the one talking for most of the class. And I feel if I talk about that goal here, it’ll force me to keep it in mind. And be slightly more accountable.

As Alison Blank (@pvnotp) said on Twitter: “Maybe just try to be student-centered a little more often – like set aside one class every two weeks where you switch it up.”

Baby steps. And I’m going to try that. Even if it means something as small as playing a review game with students, or having some sort of hard problem challenge we spend the whole period solving together (like I do sometimes in MV Calculus), or making a guided worksheet to lead students through a concept. I should also remember that I can mix things up by asking for different forms of homework, instead of book homework, worksheets, etc. I can ask students to write a letter to their math-illiterate uncle explaining a concept we’ve been working on in class, or create a quiz of their own, or write a formal solution to a challenge problem. I can have students each work on different problems and make a SmartBoard presentation of their solutions for the class — and grade their presentations. Or even have students research the practical applications of calculus.

My brain to itself: Okay, Mr. Shah, keep these things in mind as things you can do instead of traditional classwork and traditional homework. And you just came up with these in the last 5 minutes. Imagine what you could come up with if you gave yourself 10 minutes, or (egads!) 15 minutes?

So I’m going to try to experiment a little this year in calculus. Be slightly daring. Put my foot in the water.

Optimism! Glimmers of hope!

If you want to see why I’m so dejected at the moment, you can see my SmartBoard presentation for my calculus class.

Setup. We’re in Algebra Boot Camp and we’re learning about rational functions before we start on the Limits unit. Up to this point, these kids have reviewed holes and vertical asymptotes, and have just started thinking about the domain of rational functions.

View this document on Scribd

It’s not that the SmartBoard is bad, exactly. I actually think it’s pretty well thought out and organized. But you can see what my class would look like, by looking through it. (FYI, this particular lesson on domain, x- and y-intercepts, horizontal asymptotes, and sign analyses takes more than a day to go through. It will take 2 days to teach and 1/2 a day to pull it all together.)

I know I shouldn’t beat myself up too much. It’s only day 4. But I am. I’ve just been in a bit of a teacher funk. I’ll get out of it. All I need is some kid to say that they’re actually learning something in my class, and that they’re excited about it. I’ll get that.

Important Note. I don’t mean this to be a pity party. I don’t want pity comments – please. I only posted this because this is a place for reflection, thoughts, emotions, whatever. An archive of how I’m feeling today, so I can look back later and see how I’m evolving.

However if you have ideas on activities/games that work for you, things that break “the teacher introduces an idea –> teacher asks questions to develop idea –> teacher goes through example applying idea –> teacher asks students to practice a few problems –> start over” cycle, I would love for you to throw those in the comments below.

Google Forms

Tonight I got a call from my dear sister. She’s an amazing teacher, and I always forget that she’s starting her 7th year of teaching. That’s right, 7. But — dear blog — that isn’t what I wanted to write about today. I was talking with my sister about the best thing I’ve done so far, in my three days of teaching.

It was using google forms to get information from my classes. I needed some basic info from each student, and I didn’t want to hand out individual sheets for them to fill out. I hate keeping track of papers. So I created a google form and made filling it out homework.

Please, if you don’t know about google forms, click here and see a sample of the form I used. Fill it out! Put nonsense down! Play around with it! It’s a fake form. So do whatever!

If you want to see the responses to the fake sample survey, click here.

It took me less than 10 minutes to create this survey and email out to my students. What I got was a quick way to get information about each of my students — information that has already helped me see where my students are coming from and what they’re going to need from me.

Example? One student wrote about being nervous about math because s/he hadn’t done well in math for a while. I saw that and wrote an individual email to this student off on a positive place.

Hi [Student],

I am reading through the online survey, and wanted to respond to a few students. In one of your responses, you said

[student quotation]

I want you to know that it’s okay to be nervous. But I want you to know that I am here to help you, so you shouldn’t ever hesitate to meet with me. I would also recommend finding a few students to work with in this course — so that you can study with them or ask them questions, and so they can ask you questions too!

I’m here to help you! And I hope you have a great year this year in math. We will work hard, yes, but the reward is that I promise that you will leave knowing a heck of a lot!

Always my best,
Mr. Shah

I responded to a bunch of these.

A second benefit is that this form actually asks students questions about my course expectations and policies. I used to just assign “carefully read the course expectations” for homework. But I never really knew if my students did. Having them answer questions about my expectations shows me they know exactly what I want from them.

I can see me possibly using this in my classes throughout the year…

… when we’re collecting data and doing some basic statistics/regressions. I can say “For homework, find how many DVDs and how many books you have in your room. Enter what you find in this online survey.” Or when we’re in class, measuring the period of pendulums of various lengths, I could have them enter all their data in a survey and then we’d have a class’ worth of data on a single spreadsheet.

…I can also see this as a way for me to survey students to see how they’re feeling about a particular topic, or to write what they learned in a particular class. “What did you take away from class today? What did you learn? What questions do you still have?”

…I can see using this to administer an online “take home quiz” for students (on the honor system).

…I can see using this to find out what to focus on before I hold review days. I just create a survey with the various topics, and ask them to answer on a numerical scale how they’re feeling about each topic.

Just throwing a few of the ideas I have out there. I knew about google forms, but I didn’t fully see their potential.

PS. I was first convinced of the power of google forms when I created the homework survey for math teachers.

ack! disaster in 7-1!

On October 21, 2007, I sent an email to the other accelerated 7th grade math teacher. The subject: “ack! disaster in 7-1!”

I had only been teaching for about a month and half. I hadn’t learned the “mountain vs. molehill” principle, which — when I figured it out — changed my life. I was filled with insecurities, even though I had started gaining my sea legs. But the event conveyed in this email below kept me up all night. I was freakin’ out.

Wanna read the email?
Thought so.

[Other 7-1 teacher],

A total disaster! So the test that I gave right after the fire drill? The students were making ALL sorts of careless errors and conceptual errors. I don’t know what it is — either it could be that it was Thursday last period, everyone was crazy after the fire drill, or students felt rushed. I told them they could finish the next day — and so I gave them an extra 12 minutes…

But once you see the grades, you’ll see why I’m freaking out:

[list of all students’ names and grades]

I don’t know if I messed up teaching it, or if they were just all flustered, or what. Even the best students were really mucking things up. The mistakes ranged from sign errors to not simplifying to conceptual errors. What I’m thinking of doing is having a “make-up test” for them this Thursday during lunch or after school (whichever they can make it to). Is that sort of thing allowed? If they took it during lunch, when would they get a chance to eat? Or do you think I should give them “test corrections” for extra points on the test?

As for if they are totally missing the boat or not, I don’t know how to fix that since we’re starting on new things! Maybe each day my Do Now will be stuff from the last chapter?

Best,
Sam

I sound reasonable in this email. But internally, I was an absolute mess. How could I be such a bad teacher? It was one of those “take stock of things” moments. And I was coming up short.

What brought this back was misscalcul8’s recent tweet:

And it all felt so familiar. What’s great is that she has a support network with all our twitter buddies! Not that anyone can really help too much — I mean, we’re so far away from the situation we’re taking stabs in the dark on how to deal with it — but I can only imagine that the commiseration and advice was soothing.

I can just say that I didn’t have that on October 21, 2007. I was convinced that I was simply terrible, and that no other teacher had ever had a class bomb. No, seriously, I was so terrified that I believed that. (What a moron I was.)

I know I’ve grown a lot since those first few terrifying months, where I felt I was on trial — with the students, with the school, and most importantly, with myself.

As that first year went on, and I was exposed to some serious trial by fire, I found I slowly started to thrive. I dealt with a few (not many) challenging parent situations, had a few discussions with students who were acting out, actually sort-of yelled at a student when nothing else was getting through, coped with excessive absences of some students due to mono, and dealt with cheaters. A lot.

But as the year progressed, I got comfortable in my teacher skin. I gained my teacher voice. I learned to just lay my expectations and not try to justify everything or argue with students about them [1]. I learned not to be defensive.

But the only thing that does that is time.

So for anyone out there who might be new, and hitting their first major so-called-hurdle, just know that

(a) it probably isn’t as huge a hurdle as you think it is

(b) we’ve all probably gone through it too

and

If your teaching trajectory is anything like mine, I had a few bumps my first year, and my second year was smooth as silk. There wasn’t one major bump. I might have encountered the same problems again, but this time I knew what I needed to do when dealing with them.

Example? Last year my Algebra 2 students all bombed a take home quiz on quadratic applications. I knew they were going to. I rushed, taught it badly, and knew I was doing a bad job for the three days we worked on it. I wasn’t surprised by their (very low) quiz grades. So what did I do? I just fessed up. I told ’em I frakked up, and I knew it, and I couldn’t hold my mistakes against them. Quiz was wiped. We moved on from there. Not a huge deal. The previous year I wouldn’t have been nearly as mature as that.

[1] I’m requiring my Algebra II students to use a binder this year, and I got some pushback. “But I don’t like binders! Can I use something else?” “No.” “Why?” “Because I said so. But if you need, I’ll hold your hand when we use the binder, promise.”

First Day

My first day was underwhelming.

I could list all the things I would do differently, and all the things that were out of my control that affected things, and go on and on and on. But I won’t. I just don’t feel like it.

Instead I’ll just say that the biggest letdown for today was my own too-high expectations. I remember the community that we built in each of my four classes last year. By the end of the year, it was a crazy joy to go to each of my classes. I seriously cared about every single one of my students more than I thought I could. [1] That’s my last memory of teaching. I forgot that I don’t get that at the beginning of the year. The class clown hasn’t come out. Students don’t know how they’re allowed to act in class, what I expect of them. I still don’t know what they expect from me. I’m having a real hard time reading them. That stuff comes with time.

I totally forgot. I totally forgot that it takes time for a group of individuals to become a class.

Sam

[1] Ah, selective memory and the idealization and whitewashing that comes with time!

From whence this came…

UPDATE: Here is my Advice from Algebra 2 Students Past, in full glory.

Today I was compiling and typing up my “advice from Algebra 2 students past” to hand out to my kids this year. And I forgot about a striking passage from one of my students:

It will behoove you to understand going into class what exactly Mr. Shah wants from you, which is an attentive, honest, and interested student. It has taken me six months to realize what Mr. Shah really wants from you; he wants you to ultimately be a good person in the world.

Where that came from, I have no idea. None of my other students wrote anything like it. It rang so sincere and specific in the way it was written that I know it wasn’t just a casual, flippant remark. Of course I glowed when I read it — because the student hit on something even I hadn’t been able to articulate. My primary goal is to get my students to understand and be able to do mathematics, but these kids are in the process of learning how to be adults. And whether my kids remember completing the square years down the road is ultimately less important than the person they forged through trying to learn how to complete the square. Not that I ever say that to them, really.

Which is why I’m darn curious from whence this remark came from, though. Cuz I have no freakin’ clue.

Imagining the First Day of Calculus

At one point during my first class, I want to drive home a point. You guys know a lot, and I want this course to help it all hang together.

I’m going to ask them to spend a few minutes minutes solving the problem: $2x^2-56x+1=0$

Then I’m going to go around and have students explain how they got their answer, why they think they’re answer is the answer, what they know about the question, whatever.

Who wants to bet that 100% of them graph it on their calculators or use the quadratic formula?

I’m counting on it. I will then show them an example of their graphing calculator lying to them (there are a million of ’em), and then say “why does the quadratic formula work? why are we allowed to use it?”

We’ll then take a moment and say “what do we need to know to solve this problem? I’ll start by throwing something out: we have to know what a variable is.”

So we’ll throw a bunch of things on the board: variable, number, exponent, addition, square roots, etc.

Then I’m going to reveal the big secret to mathematics, the secret that all teachers have kept from them until now: all we’re doing to solve problems is to turn something we don’t know into something we do know.

This is the rant I have playing in my head…

So when we first learned quadratics we didn’t know how to solve ’em. We had only seen baby linear equations. But guess what? When we learned to solve quadratics two years ago, we turned these horrible grossities (quadratics) into beautiful nice-ities (linear equations). Watch!

$2x^2-56x+1=0$

$2x^2-56x=-1$

$x^2-28x=-\frac{1}{2}$

$x^2-28x+196=-\frac{1}{2}+196$

$(x-14)^2=\frac{391}{2}$

$(x-14)=\pm \sqrt{\frac{391}{2}}$

$x-14=\sqrt{\frac{391}{2}}$ and $x-14=-\sqrt{\frac{391}{2}}$

I didn’t know how to solve the quadratic, but I do know how to solve (two) linear equations!

This procedure is completing the square. I know y’all remember it — vaguely. I know y’all hated doing it. But why did we evil math teachers foist it upon you? Because what this lengthy, arduous, annoying process did was took something gross, and turned it into something nice. The process wasn’t super nice, I know, but taking a step back and looking at the forest for the trees, it did that magic little math secret: turned what you didn’t know how to solve into something you did.

And look at all you needed to know about in order to make this happen. Numbers, addition, exponents, square roots, positive and negative, linear equations, variables. In that one equation

$2x^2-56x+1=0$

is a whole universe of knowledge! And you KNOW that knowledge. And in this class, we’re going to time and time again see equations that we might not think we know how to solve. They’ll look scary and unfamiliar like

$\int_{-3}^{3} \sqrt{9-x^2}dx$

But we’ll turn it into something we are more familiar with. Just don’t lose the forest for the trees. Don’t get stuck in the muck and mire of the procedure and not forget about why we’re embarking on that particular path, or what ground the path is built upon.

Our mantra: take what we don’t know and turn it into what we do. Math is an art. The creative aspect of it is finding the right path to turn what we don’t know into what we do know. Therein lies the puzzle, the beauty, and yes, the frustration.

PS. This post is basically a recap of this previous post. I just think it will be fun to talk about on the first day.

A Vacation From My Vacation, or a Toast to High School Friends

I need a vacation from my vacation within a vacation. (Translated: I need a week to recover from going to a high school friend’s wedding at the very tail end of my summer vacation.)

I just got back from Seattle, spending 5 days with high school friends, going to a wedding. What struck me is that we’ve known each other for over 13 years, and that these particular friends have actually grown closer to me with each passing year instead of more distant. High school can be extraordinarily important, socially. Heck, when I moved from my first high school (few friends) to my second high school (lots more friends), I felt free to be whoever I was, without the weight of years and hardened opinions of classmates weighing me down. I was able to become who I became — a colorful, irreverent, independent, overly dramatic personality — in high school.

Even though I very rarely commit anything about my personal life to this here blog, I just wanted to give a visual toast to those friends who forged the backbone of who I am today in that crucible that was high school.

(And I just know all y’all were dying to know what I look like. Hot, right?)