Summertime: Recharging

School’s been out for over 3 weeks now, and I’m starting to feel like thinking about it again. :) So I’m ready to post now.

Next year will be different for me. Two of my classes will be middle school courses, which will be new to me, and one of the high school courses will change from trig/analyt to precalculus, so not new material exactly but a different emphasis and course layout. Geometry and calculus will remain in my schedule (with a new text for geometry), and statistics will not.

Also, I’m expecting baby #2 in late December or early January, so I’ll basically be taking the 3rd quarter off. That means preparing for a long-term sub. I’m a bit worried about the SBG aspect of things there.

Speaking of SBG, here are some thoughts I’ve had relating to assessment…

• I need to get better about spiraling feedback for all students on all topics. I ended up with a “keep trying until you get it right, but then it’s okay to forget it” attitude among my students, and that’s not my goal.
  
• I’m going to be using ActiveGrade this year, which I think will be great for my students. My school is going to online grade reporting as well (I know, we’re waaaay behind the times there!), but I think I can reasonably just keep the ActiveGrade updated and then enter scores in the official gradebook when I need to for report cards. ActiveGrade will give the kids (and their parents!) access to so much more information about their scores than a traditional gradebook.
  
• A big problem I had last year was that as midterms or end-of-quarter approached, I would have large numbers of students in my classroom wanting to reassess. The rest of the time, not so much. It was a last-minute effort for most of the kids. (There were exceptions, naturally – this is just the general pattern.) I would also have kids who would say, “I want to reassess these three learning targets tomorrow. Can you tell me what they were over?” It was really, really painful to hear that, because it showed me clearly that it was still all about the grades. The kids were looking at their scores, finding the ones that were the lowest, and not even going back to their marked-up work to figure out what those were about, just asking me to tell them. Then they’d come in and, surprise!, not do well on the reassessment. Lather, rinse, repeat. I am working on how to remedy this, though I do think the previous two bullet points will help, but I also need to implement a better process for allowing reassessments, along the lines of Sam’s form email.
  
• In the fourth quarter, I stopped keeping track of student homework completion. This was not a good idea. While I still think homework should not factor into the students’ grades, I also think that knowing they have to report what they’ve done is good accountability. And I think I need to start taking up homework for feedback purposes at least some of the time.
  
• My students need to get better at knowing how to help themselves understand concepts. With some of them, I don’t know if they never bother to read my comments, or if they read them and think “okay, I’ve got it now” when they really don’t, or if they read them and think “I still have no clue what she’s talking about, or what to do from here.” I need to help them learn how to evaluate their own understanding better.

Other thoughts, not related to SBG…

• I started out last year with some great, fun activities for the students, plenty of active uses of the mathematics they were learning. Then I got bogged down and into a rut of mostly class discussions. I want to get back to the way I started out. Discussions are great things, but not when they’re the only thing happening.
  
• I want to continue working on incorporating the history of mathematics into my teaching.
  
• I had a “math fair” as part of my students’ final exam grades for the second semester last year. I believe it was a worthwhile endeavor, and I plan to do it again, though it will not be part of the exam grade in the future. However, with my maternity leave planned for the 3rd quarter this year, I’m not sure if it’s something that can happen, as I don’t want to place any part of that burden on a sub. So it may be 2012-2013 before I do it again.

Seems like I had more things rolling around in my head than that, but some of them must have escaped. ;) Anyway, those are things I’m thinking about with regard to next year. Hopefully, I’ll be back with further thoughts on how I plan to improve as the summer goes on.

Warm-up Follow-up

We’re in week 2 of doing daily warm-ups like I mentioned in my last post. One class had 4 days of them last week, and the other four classes had 3 (we spent one day going over the exam and one day reviewing what we’d been doing just before the break). What I told the kids is that my New Year’s resolution is to give them better and more frequent feedback, so that they don’t end up surprised on the quiz when they don’t know something as well as they thought. I also told them that I want them to improve their ability to self-assess, and the way to do that is by practicing it.

Here’s an example of what they look like, the final version (split into two images – they just have blank space in the middle to work the problem):

I have it set up so that I’ve got a Word document mail-merging an Excel file where I enter the variable information. (I <3 mail merge.) The only problem I have so far is that I can't enter both text and an equation into the same cell in Excel, so I sometimes have to write an equation on the worksheet before making copies. The same thing would apply if I wanted to add a figure. But that's not a huge deal.

I feel like it's working well. I've been able to get the papers marked from the previous day with no problem (I know that's just an issue of discipline, but marking papers quickly is something I have struggled with in the past). I am seeing where the kids are making errors and addressing them sooner rather than later. I get to see how well they feel like they're doing, and they've naturally started adding comments by the faces to explain why they're confused or don't feel completely confident with something. That is GREAT, because they are thinking about their thinking, which is a skill they need to continue practicing.

Today's warm-up says this:

We’ve been doing these warm-ups for a few days now. Do you feel like they are helping you understand the concepts more clearly? Why or why not?

Their feedback is almost entirely positive, and they’ve made some thoughtful comments that are helping me consider how I can improve things. If you’d like to see their responses, I’ve typed them up here (yes, I have small classes, though I was missing 3 kids in 1st period).

Trig Functions – a w00t and a help request

First off, a “hey this went well,” and then a “help me out.” :) These are both about my trig class.

Hey, This Went Well
I started today talking about amplitude and period of sine functions. They’d already understood that the period of sin(x) is 2pi, and they got pretty easily that the amount it goes above and below the x-axis is 1; I just had to add the word “amplitude” to their vocabulary. Check.

So then I put a GeoGebra window up on the projector and entered f(x)=sin(x), and I asked them what I should change about the equation in order to make the amplitude different. They weren’t quite sure what I meant, so I said, “Should I multiply sine x by something? Should I multiply the x by something before I take the sine? Should I divide instead? Should I add something at the end? Should I add something to the x before I take the sine? Should I subtract instead?”

Then they started conjecturing. I made them explain why they thought their particular change would effect the desired transformation, made them convince each other before I would type it in so we could see what it actually did. After we saw each change, I went back to f(x)=sin(x) before making another change, so we were always comparing our changes with the plain ol’ sine function. They were really pleased with being able to see the changes immediately.

It was also cool because we’d looked at what happened when we used f(x)=2sin(x) and f(x)=0.5sin(x), and then somebody said, “What if we used a hundred?” So I changed the coefficient to 100, and a couple of them said, “Whoa! It’s just straight lines!” Others said, “No, it just looks like that because it goes so far up and down.” The magic of the zoom feature allowed us to see that it was, in fact, still curving like we expected it to, just with really skinny humps. :)

So I think that using GeoGebra like that was a good way of looking at these transformations – they can make a guess, and we can see whether it’s right immediately. We can also use crazy big (or crazy small) numbers if we want to.

Help Me Out
I’ve got an idea, but it’s only partially formed right now. I don’t want it to flop like the last one (which involved kids spinning in circles and then releasing a stuffed animal – it was supposed to be about linear velocity, but it was a Fail, though they did enjoy going outside). So…here goes.

You know how when you walk, your body moves up and down? Walk across the room now. When your legs are side by side, you’re at your full height, but when one leg is in front of the other, the distance from the ground to the top of your head is less than your height. If you hold an arm straight out with a marker held to a long piece of paper, and you walk normally, the mark you make on the paper will be sinusoidal. (I remember my instructor showing us this in the health class I took in college…I don’t have a clue what his point was, but I thought it was cool.)

So I want to let my students do this. I want them to ask questions about what will be different for the curves formed by the tallest person versus the shortest person; what will be different between a girl and a guy; what will be different if a person is walking versus running; what changes if a person is on crutches (okay, I’m not sure if we could pull that one off or not, but it’s an interesting question, right?); what will be the same in each of these cases as well.

But I don’t want to get out there (I have an idea for where we can do this) and then just be wasting time with questions we won’t be able to answer. So I need to figure out how to structure this thing. Suggestions?

Math Department Identity

Our principal has challenged us (me and the other two math teachers) to articulate who we are as a math department. I’m trying to consider what that means in order to work on answering it. So far, here are the questions I think we need to address:

1. What are our overall mathematical goals for our students?
   
2. In what ways does our department work toward the goals of the school as a whole?
   
3. What is distinctive about our math program?
   
4. What is our perspective on the nature of mathematics, and how does this perspective influence our instruction?
   
5. What is our perspective on the purpose of mathematics, and how does this perspective influence our instruction?

What other questions should I add to the list?

Have you gone through an exercise like this in your own department? Any additional thoughts?

Water Tower Exploration

There’s a water tower right next to the building I teach in. Naturally, I had my trig students figure out how tall it is.

They were lying on the ground and measuring angles.

They were borrowing tools from other teachers (the science teacher has something she uses to see how high her 7th graders’ rockets go; the PE coach has a long tape measure for when he makes lines on the field).

They were mad that I wouldn’t let them climb the fence so they could get to the base of the water tower. (Dude, that’s not our property!)

They were making estimates before they took measurements.

They were recognizing when an answer they came up with wasn’t reasonable, working to figure out what went wrong, then trying again to correct it.

They were enjoying the nice weather.

They were noting that the ground isn’t completely level and trying to compensate for that in their measurements.

They were drawing pictures to represent their work.

After they’d gathered measurements and performed their calculations, I let a student call the city to find out the actual height of the water tower. Most of the students were within 8 feet of the right answer (which was 216 ft). One group was way off, but they realized that they hadn’t done a good job of determining the angles of elevation, so we got to see how much accuracy matters.

I love doing things like this. It seems to me like the students really feel like they own the mathematics when they tackle a problem like this and reach a solution.

However, I’m thinking about Dan Meyer’s recent post on pseudocontext. If we can just call the city to find out how tall the water tower is, what’s the point?

Well, it’s fun. It’s a chance to go outside. I think it’s significantly more engaging than the example in the textbook where you have to figure out how long the rope is that’s holding the tent up (the example is labeled as “Real World Application: Entertainment” – really? entertainment, because it’s a tent? yeesh).

But is the water tower activity flawed because there was an easier way to get the answer? My gut tells me no, but I’m still working on why.

SBG Question: Keep Moving Along?

I went to the school today, met with the person who’s taking on 7th grade social studies to give her my resources, met with a student to try to determine math placement, moved some stuff from my old room to my new, told one of my principals that I’m going to be using standards-based grading.

He had some questions.

The biggest thing he was worried about was this (and this is me trying to reword the question):

What about the student who doesn’t get these first few concepts? In a context where you are allowing for reassessment on those learning targets, does it make sense to keep moving along in the curriculum?

One thing I said in response was that in my experience, later math can illuminate earlier math. Sometimes you don’t truly understand a concept until you’re a few steps down the line and you see how it fits with other concepts.

Another thing I thought about since I left his office was that this isn’t an issue particular to a grading system. You’ve got kids who get left behind conceptually in a traditionally-graded classroom, too – more so, I’d argue, because of the whole “you didn’t learn it by Thursday’s test, too bad for you” approach. I think SBG encourages kids to go back and learn, or to get help learning, much more than the traditional system.

What thoughts do you guys have on this question?

Lessons from Statistics

(Refresher background info: I am taking a statistics class at the local community college, since I will be teaching statistics in the coming school year.)

I’m finding the content in my statistics class to be interesting and logically intuitive, and I’m really looking forward to teaching it. The class itself…well, I kind of feel like a spy in there, gaining insights for teaching as I play the role of student. So here are some things that I have learned (or have had reinforced)…

1. Don’t take over. Allow students to build the connections for themselves.
   
2. If someone asks for clarification on how to do something, make sure you understand which part they’re struggling with. If they can’t articulate it for themselves, listen as they continue to ask questions while you go through the process again.
   
3. If someone asks a question about application, extension, etc., do not dismiss it as “not what this class covers.” Encourage thinking! It’s even okay to say, “Let me think about it / look at some resources / etc. and get back to you,” or, “I would love to discuss that with you, but can we talk about it after class so we don’t lose our train of thought here?”
   
4. Be willing to admit when you could change a question, example, etc., to make it better for the students. Value feedback.
   
5. If you tire of hearing from a particular student (or of answering questions in general), don’t let it show. Not all students are concerned enough about their learning to make sure they keep asking questions anyway. Care about student learning.

There may be more to come…three more weeks of the class.

SBG and cheating

I have another SBG question. At my school, in general if a student is cheating on an assessment, the student receives a zero as well as a disciplinary referral. How does that work with SBG?

Do you refuse to allow that student to reassess the LTs addressed on that quiz/test? That seems inconsistent with the goals of SBG.

I expect that the knowledge that they can reassess will probably reduce the temptation to cheat, because the student knows that if he doesn’t get it he can try again later. So it may be that it’s never an issue.

However, thinking about that brings me to a related question – students who are suspended are supposed to receive zeros on any work from the day(s) of the suspension. Again, it’s hard to know how to follow this policy and still use SBG. Suspensions are not something that happen frequently at my school, but they do happen. (Edit: Same goes for cheating incidents.)

Thoughts on these issues?

(By the way, I am loving reading everyone’s discussions over on Twitter, where I am @praxisofreflect. I am just a little hesitant to jump in myself. Blogging is already pushing me outside my comfort zone, so I’m working on it!)

SBG and different course levels

I’m getting more and more excited about implementing SBG in my math classes in the fall. I’m finding ideas from others; I’m considering how I would deal with issues they raise when they arise in my own setting. I’m working on how best to communicate the idea to students and their parents.

And then I thought of an issue I hadn’t considered before. Because my school is small, we have different course levels in the same class. Overall, the understanding is that the different levels will indicate different volumes of work, and that the students in Honors & AP courses will be asked to do correspondingly more critical thinking work than those in General courses.

I can reasonably expect that my two sections of Geometry will each include a mix of Honors and General students. My Statistics class will probably have both AP and General. Calculus *could* have AP and General, but knowing the kids that will be in that class, I don’t expect any General students. The other class I’ll have is Trigonometry & Analytic Geometry, which only has one course code, so it’s all General.

So…what does that mean for using SBG? Should I just eliminate certain learning targets from the General students’ grades? That’s the first solution that’s coming to my mind, but I don’t know if there are other ideas that may be better. What would (or do) you do to differentiate between two course levels within the same class using SBG?

Going back in time?

I’m taking a class that started today. I’ve never taken statistics before, but I’ll be teaching it (one section that will probably have both AP and General kids) in the fall. So I thought that taking it would probably be a good plan.

I’m still processing the reasons why, but it felt somewhat surreal to be in a 2000-level course again. I’m looking forward to learning statistics, definitely; I have thought for a while that I would like to take a course like this. But actually sitting in the class just feels strange. It’s very different than the classes I’ve been in over the last 3 years as a master’s student, and it actually feels much more like I’m back in high school (except the part where the homework is all online).

I’ll have to continue mulling this over. It feels like there are things I can learn through this about becoming a better teacher, but I’m not completely sure what those things are yet. Maybe it will become clearer to me as the next few weeks go by.