Thursday, June 30, 2011

Day 9

Today's opener reviews Order of Operations, solving a one-step equation involving multiplication, and a Dimensional Analysis problem. While they are working on the opener I'll be walking around checking to make sure they have at least the Self-Check problems from the video they were supposed to watch for homework.

Then today's lesson is to learn about Inverse Variations in the context of speed (d = rt). First, we take a look at this.

I solicit guesses but am not counting on them guessing - at least not until I pick up a tennis ball and start tossing it in the air and catching it. Then, perhaps. Then I'll show them this:

Again, they won't see this entire slide at once. I'll show them the top two images and ask them what question(s) we could ask. Hopefully they will come up with at least "how fast is it moving" and perhaps "how high was it dropped (thrown?) from. I'll then ask how do we figure out speed (based on last year, most students don't seem to really know this). I'll then display the equations and the additional pictures (and, with the picture of the meter stick, I'll open the original so we can zoom in on it to see the markings on the meter stick better).

After we figure out speed, then we'll work through these questions:

I'll then display these pictures for context and to see whether our answer seems reasonable.

Assuming that goes well (that may not be a good assumption, the students struggled with this last year), we'll move on to another rate problem. Using an excerpt I've edited from this video, we'll see if we can figure out Rich Eisen, Tim Tebow (bonus, since he's a Denver Bronco and a hot topic around here), and Jacoby Ford's (average) speed (again, borrowed from Dan Meyer). We'll then do a quick table of values and sketch the graph to (hopefully) notice this is not a straight line, and then define inverse variation.

If we have time, we'll then do a couple of skill practice problems (if not, we'll pick up with this tomorrow).

I'm not sure at this point whether I'll give them any homework or not, depends on how it's going. Most likely their homework will be to review their notes and determine what areas they are feeling comfortable with and what areas they need some extra help on.

Wednesday, June 29, 2011

Day 8

Today's opener reviews Order of Operations, integer operations, and Dimensional Analysis.

We then move into a lesson on Direct Variation, attempting to connect it to our work with rates and proportions (with a touch of measurement and dimensional analysis thrown in). First we do some converting between kilograms and pounds, write an equation for that relationship, and graph it.

Then we see if we can apply what we've learned to a unit rate (price) problem.

Their homework is then to watch the Solving One-Step Equations Video. This is something they theoretically already know how to do, so it should be a review for all of them.

I don't feel great about today's lesson. It's okay, but I feel like I have to lead them through so much that I'm not sure it's that helpful in terms of their learning process or the actual content, and perhaps just 40 minutes of skill practice might be more effective. What do you think, would it be better to can the semi-interesting problems and just practice a bunch of dimensional analysis and then direct and indirect variation problems?

Monday, June 27, 2011

Day 7

Today is our first assessment over new material (the initial skills' assessment was theoretically over knowledge they already had). On assessment days last year when students entered the room they would see something like the following instead of an opener:

My thinking was to have them to begin to focus on the assessment as soon as they walked into class, giving them some scaffolding in terms of what I think they should be thinking about as they prepare. Then once the bell rings and everyone is settled, they begin the assessment (more on the assessment in a minute). The time it takes them to do the assessment, and for us to then go over it on the board, should be roughly equivalent to the time it takes to do a normal opener. This way we still have a "full" day of instruction even on assessment days.

While I like this plan, one thing I discovered last year was that some (many?) students really didn't prepare for the assessments. I've thought of switching to giving a short opener on assessment days, knowing they would do much better on the assessment, but I'm not sure that contributes much to their long-term understanding (and it would also reduce instruction time for the day). So I think I'm going to stick with just giving them the assessment without the opener, but I'm open to hearing your thoughts.

A very brief aside to describe my assessments just to give you an idea. My assessments are an imperfect implementation of standards-based grading. Instead of giving them a test over "chapter 3" or whatever, each assessment is over a specific skill(s). This allows both me and the student to get a better handle on what the student actually knows how to do (not "I got a 73 on Chapter 3"), and what they need more work on. It also keeps the assessments very short (usually only 2 or 3 questions) and very focused, which has the added benefit of making re-assessments take less time. (I've previously written about assessment here and here, so I won't repeat all of that.)

After the students take the assessment, I (or sometimes students) work through the actual problems on the assessment on the smart board, which then gets posted to the class blog (so students have the exact assessment, including worked out solutions, to look back at if they need to review and re-assess). To give you an idea, here's last year's (pdf).

Then we begin today's lesson with a measurement activity that will lead us into dimensional analysis.

Then I get a little more explicit about the vocabulary (rate, unit rate, dimensional analysis), and we do some unit conversions that are hopefully somewhat relevant to the students. The "Vehicle Stopping Distance" at the bottom is a link to a website that talks about average stopping distance to give a little more perspective.

We then do a couple more conversations based on track records at my school, then watch a two-minute video from Discovery Education about dimensional analysis using the cost of gasoline in Australia. I'll then have the students figure out today's cost of gasoline in Australia (in U.S. dollars per gallon). I provide them with links to the current exchange rate and average prices per liter in Australia.

While I anticipate we'll be out of time, I have one more slide where we figure out how much Steven Spielberg made per second he was awake in 2009 that we'll go to if we do have extra time.

Their homework tonight is to check their grade on the assessment on our online portal and, if necessary, make an appointment to come in and re-assess (or get help first, then re-assess) if they did not do well. Tonight is also our Back To School Night, so I'll ask them to remind their parents to come tonight.

Thoughts on today's plan?

Saturday, June 25, 2011

Day 6

Today's opener reviews proportions and percents and integer operations, and also gives them a more open-ended estimation problem.

As they work on the opener I'll walk around and ask each group if they had any questions about how the online pre-assessment worked last night (and I'll also talk briefly about it after we finish the openers as a class).

Today's lesson is designed to solidify their understandings of ratios, proportions and percents. We'll start with a quick skill review, with students working in groups and then coming up and explaining their work at the board (or possibly on their group-sized whiteboards, I'm not sure which yet).

Then we'll look at an example with the chemical formula for TNT and one with the stock market. (Again, note that I'm displaying the entire slide for you, but I would use the window shade function to reveal only parts at a time.)
Then, thanks to Dan Meyer, we'll watch about a minute of The Bone Collector and then I'll turn them loose (with printouts of the footprint/dollar bill and rulers handy - bottom image is hidden until we discuss it).

Their homework will be to prepare for the Solving Proportions and Percents Assessment that they will take first thing tomorrow. They can do that however they'd like: review the video, review their notes, review everything that's been posted to the blog, review the online pre-assessment, do some practice problems online or from the textbook, work with a friend/parent/sibling, etc., as much or as little as they think they need.


Wednesday, June 22, 2011

Day 5

As a reminder, this is day five of my class, but it will be Monday of the second week since my class only meets four days a week.

The opener today is designed to build off the work we did on Friday as well as the video they watched for homework.

As they are working on the opener I will be walking around and looking at their notebooks to make sure they have the "Self-Check" problems from the video written down. This is somewhat of a philosophical dilemma for me. Last year I made the philosophical decision to not check whether they had watched the video. I explained to them that I expected them to watch the videos and that they needed to watch the videos in order to be successful, but that I wasn't going to look over their shoulder to make sure they did it. I continued to talk about this throughout the year, and it worked well for some students, but unfortunately other students had real difficulty completing these videos without me "checking up on them." So this year I've decided to backtrack a bit and check that they're watching the videos/completing the self-check exercises, at least at the beginning of the year. Then hopefully gradually back away from that throughout the year as they internalize that the videos are helping them. We'll see.

After they work on the openers individually, and then in their table groups, we'll discuss them as a class. Then today's lesson is to look at ratio, proportion and percent in the context of a sampling problem. We'll begin with a 3.5 minute video from Discovery Education on the Capture-Recapture Method of estimating animal populations. After watching the video we'll simulate the capture-recapture method using paper bags and two colors of beans (in the context of sampling fish at a nearby reservoir).

After working through the simulation, we'll then see if it took hold by completing three sample "application" problems. Assuming that goes okay, we'll then talk about how we could sample our class to try to predict answers for the entire school (or a class across the hall). The "freshmen" question is designed to get them thinking about what a good sample might look like (since my class is majority freshmen, this is not a good sample for the school, but might be for an Algebra class at the school). (Note: On all these images keep in mind that they are on a smart board and I'm using the window shade to control how much is visible at one time.)

If we have time, we'll then conclude with a quick skill review..

We'll then talk briefly about their homework for tonight, which is to complete the Solving Proportions and Percents Online Pre-Assessment. My plan is to use these in a very similar way to the way I did last year. Usually two class periods before an assessment I'll have the students complete a sample online pre-assessment. This gives them an idea of how they'll do on the actual assessment and gives them some time to get help/figure it out before the assessment that "counts." I ask them to write down the problems in their notebook and work them out, then click on "Check Your Work" to see how they did (and correct if necessary). I'll also give them an optional link if they'd like more practice, but it is completely optional.

A second piece of homework, but one that's not due until Friday (four days from now), is their first reflection piece:
Looking back at your first week in Algebra (and, for some of you, your first week at AHS), how are you feeling? What's going well or you're excited about? What's challenging or are you concerned about? Then I want you to set three goals for yourself for this semester. One goal specifically related to Algebra, one goal related to AHS in general (can be related to classwork, sports, activities, or something else at AHS), and one goal outside of AHS. Make these goals fairly specific, not just "I want to get a good grade." I'll be asking you to revisit these goals toward the end of the semester and evaluate how well you're doing on them, so make them be worthwhile and achievable.
Last year we did this in Google Docs, but this year I've decided to go ahead and have them blog them. I debated about whether I wanted these private (in Google Docs, so that they could perhaps be more honest and share more information), or public (Blogger, where they might feel somewhat constrained because it's public). Last year I really didn't have anything shared that I think wouldn't have been if they'd been public, so I want to open this up for all the usual reasons for why blogging can be powerful. I'll also let the students know that if they have anything they'd like to share but not publicly, to just let me know.

I'm a little worried that's too much homework, but I figure the pre-assessment only takes 10-15 minutes and the reflection isn't due until Friday (and they have Thursday "off" of Algebra), so I'm hoping it's not too bad.

As always, I'd appreciate your thoughts/suggestions on any of the above.

Monday, June 20, 2011

Day 4

As a reminder, my Algebra class meets four days a week (MTWF), so day four is going to be a Friday but it will be two days after our day three meeting on Wednesday. Today is really the first day that is my "own" in Algebra. The first semester of Algebra at my school is basically all about linear equations, and I start by taking a look at proportional thinking - more specifically, ratios and proportions.

My opener today is designed to build off the skills review/assessment they just had and help front-load some ideas for today's lesson. At the moment (assume that phrase for all planning posts on this blog), this is what it looks like:

As a reminder, students are expected to begin the opener by the time the bell rings. They then work on it for a little while individually, then discuss with their group members, then students come up to the smart board and explain them to the class (with that getting saved to PDF and posted to the class blog).

We then open the lesson with a bit of vocabulary.

Then I try to lead them into solving proportions by starting with something they hopefully can do somewhat intuitively: "When you divide some number N by 2 you get 12. What's the value of N?"

From that we move slowly toward doing the inverse operation, to "undo" dividing by 2 we would multiply by 2; to undo dividing by 4 we would multiply by 4.

But then what happens when we throw a fraction into the mix? Hopefully they'll see that the same principle applies. From there they work through several examples with the variable in the numerator, then we try to extend to having the variable in the denominator.

At this point I really want them to focus on inverse operations, so I'm not showing them to "cross-multiply" to solve proportions.

Assuming things are going reasonably well at this point, I then introduce a hopefully somewhat interesting application of proportions.

In my head we still have about 10-15 minutes left in class (but often my head is very, very wrong), so we'll try to make a quick geometry connection. (If we don't have the time, we'll skip this - perhaps taking a look at it the next day.)

How ever much we get through gets posted to the class blog as a PDF.

We will then talk briefly about how I expect them to work through (and take notes on) the videos, as their homework will be to watch/work through the Solving Proportions and Percents video.

While I'll probably tweak it, this is what I wrote last year on the blog to follow-up what we talked about in class.
We previewed the Solving Proportions and Percents video that you're going to watch for homework tonight and talked about the different pieces in it, how you should use it, and what you need to write down in your notebook. There are three main parts to the video: an Examples and Explanation part, a Guided Practice part, and a Self-Check part.

Examples and Explanation: Just what it sounds like. I explain how to do the problems and work through some examples. You don't need to write anything down (unless you want to), just watch, listen and learn. Pause the video and replay parts if you need to.

Guided Practice: I give you a problem, then ask you a series of questions with about 5 second pauses between questions for you to think about it and answer it for yourself. If you need to, pause the video to give yourself more time. Again, you don't have to write anything down here (although you can and it may be a good idea to).

Self-Check: I give you a problem, ask you to write it down in your notebook and solve it, then I show you the solution in the video. Once the problem is on the screen you need to pause the video, write it down and solve it, then play the video again to check your work. You may need to pause the video again to view the solution if you need more time. These problems you definitely need to write down in your notebook.

Remember, you can always replay any part of the video you need to go back over something.
I would love to hear your thoughts/feedback/suggestions for improvement on any/all of this.

Saturday, June 18, 2011

Day 3

Day three is when I give the common assessment over the Math Skills (this is the only thing all year where they are not allowed to use a calculator). I plan to start with an opener that has several problems that involve the four skills areas on the common assessment. The basic structure of my openers is that they are projected on the smart board as the students come in to class. I ask them to be in their seats and either start them before the bell rings or be ready to start as soon as the bell rings. They work on them individually for a certain amount of time (varies depending on how many and the complexity of the openers), writing them down in their notebooks. Then I ask them to take a few minutes and discuss their results with the other members of their groups (again, typically four in a group, with one or two threes to make it work out even). Then I ask for volunteers to come up and work them out on the smart board (which I then post to the class blog - sample from last year) and explain then to the class. (I go back and forth whether to ask for volunteers or just pick randomly making them all responsible for being ready and "forcing" them to come up - your thoughts?)

After we work through the openers, I'll then give the common assessment (roughly 15 minutes, although I remember last year it took some students significantly longer than that). Then, based on Dvora's comments on the previous post, I'm considering shifting some of the culture/class expectations piece to today. I'm thinking that after the assessment I may take them to the computer lab (assuming MAP testing hasn't started yet and I can get into the lab) to help them get into their Google Accounts. All of our students have Google Apps accounts, and for students that were in my district last year they may remember how to login, but I also have three students who are new to our district. Once they get logged in I'll help them with their basic Blogger setup (mostly display name and creating a reflective blog for my class), then have them read (and eventually comment on, although we may not get that far) a post on the class blog talking about culture and expectations. This may enable some of a conversation online even if they aren't quite comfortable enough yet to engage in a face-to-face discussion.

Their homework will be to check the online portal for the results of their assessment and, if necessary, make plans to re-assess over any of the areas they did poorly on. (While I'm probably going to tweak it some, here was my assessment plan for last year.) Students sign-up online to re-assess (again, here's last year's sign-up form), and they only need to re-assess over the area(s) they did poorly on (so I'll divide the assessment grade into four portions: adding and subtracting fractions, multiplying and dividing fractions, integer operations, and order of operations). In addition, depending on how far we get in class, I may ask them to comment on the class blog post about culture and expectations (perhaps not "due" until Friday as we don't meet on Thursdays).

We would then be setup to really begin "Algebra" on Friday.

Friday, June 17, 2011

Day 2

Day two is really my first day of class due to the freshmen class meeting on the first day. When the students come in they'll find a handout with their name on it (to again help them find their desks) with a suggested layout for how they organize their notebooks.

I'll also explain that we will typically start with an "Opener" that they are expected to begin working on by the time the bell rings. (I may have a brief opener this day as well, or the opener might just be explaining how the openers are going to work, I'm not sure yet.)

Then my natural inclination is to jump right into the content. While I value class culture tremendously and I admire teachers who can generate a great discussion on day one (or two), I've never been successful with that. I can barely get my students to talk at all the first couple of weeks of school. So, let me put that part on hold for a bit, then return to it later in this post.

As I mentioned previously, my math department asks students to complete a Math Skills Assessment over the summer. These are prerequisite skills that the math department feels enable students to be successful in Algebra at Arapahoe. Consequently, the first thing we're supposed to do is assess our Algebra students over those skills (a common assessment). Last year my class didn't meet on Tuesdays (Algebra only meets four days a week at my school), so I asked students to review on their own during the two days between the first day where we really didn't meet and our second day (in addition to the review they hopefully did over the summer), then gave the assessment after a very quick opener reviewing the skills.

This year my class meets on Tuesdays (and not on Thursdays), so I think I will devote some class time to reviewing these skills (adding, subtracting, multiplying and dividing fractions; adding, subtracting, multiplying and dividing integers; and Order of Operations), and then assess on day three. While my "stand and deliver" gut response is to dazzle them with review, my initial thought is to have the students work in groups to develop the review themselves. I've purchased a set of 8 large whiteboards (roughly 24" by 32" from here, thanks to Frank Noschese) to use this year. Last year I grouped students into groups of four (with one or two groups of three to make it work out evenly), and I anticipate doing that again this year (currently 31 students, so probably 7 groups of four and 1 group of 3). I'm thinking of giving them one skill at a time (adding and subtracting fractions; multiplying and dividing fractions; operations with integers; order of operations - may break it down further than that), and asking them to work in their groups to explain the skill. I'd have them use the whiteboards to demonstrate what they know, then pick one or two groups to share with the whole class. (I'd also capture the whiteboard images and post to the class blog.)

I think that sounds okay, but things always take longer than I expect and I'm worried that with 8 groups and only one or two being able to share on each skill that they others will feel like they're wasting their time. So, alternatively, I'm considering giving each group their own skill (probably adding fractions, subtracting fractions, multiplying fractions, dividing fractions, adding integers, subtracting integers, multiplying & dividing integers, and order of operations - to make it work out to 8 groups) and that way each group is responsible for something on their own and reviewing for the entire class. Two concerns with this approach. First, some of those skills are easier (and quicker) than others. Second, I could by chance have a group that's not capable of generating a review on the skill they get.

So, which approach would you favor? Or do you have a different idea altogether?

Now, back to the culture piece. While I still don't feel like I can lead/generate a good discussion this early in the year (and that early in the day - my class of teenagers meets from 7:21 - 8:20 am), I feel like I need to do something to address the culture of our classroom. So I'm considering spending a little time talking with them about my philosophy and thoughts about this class. That's still very much one-sided, just me talking at them, but perhaps it's better than ignoring it altogether (and maybe a few brave souls will join in). Last year it wasn't until about three weeks in that I shared some of that with them and perhaps sharing it sooner will help.

Thoughts on that? Or anyone want to try to convince me of another activity surrounding culture I should try?

The homework for day two would then be to spend as much or as little time as they think they need to review the skills (by using the skills assessment website and/or the whiteboard images captured in class that will be posted to the blog) in preparation for the common assessment on day three.

Day 1

The first day of class for me is kind of a wash. My class meets first period and during first period on the first day of school the freshmen have a class meeting in the theater. Since 22 of my 31 (my numbers right now, anyway) students are freshmen (9 are sophomores), and I'll only see them for about 5 minutes, we can't do much. (Last year I went with the freshmen and the sophomores stayed with another Algebra teacher and their sophomores - we'll probably do something similar this year.)

So this is what I did last year. As the students came in there was already a slip of paper on their desks with their name on it (telling them where their seat is) and the URL for the class blog, as well as our Algebra textbook. When the bell rings I do a very quick "hi" and let them know that the freshmen will be dismissed shortly to go to the class meeting. I ask them to write their names in their Algebra textbooks and that they should visit the class blog tonight to see what their assignment is. I also have the class blog up on the screen and, if I have time, I briefly go over what that assignment is.

Before I talk about that assignment, I need to backup briefly. Right now (in June) I'm in the process of contacting all the parents to verify that they have high-speed Internet access at home (if they don't, then we'll switch them into another Algebra section - last year they all had it.) As part of this I make sure I have the parent's email address and I share some initial information about the class with them, and then let them know that I'll be contacting them - and their student - in early August. I also share with them the Incoming Freshmen Math Skills Assessment and Resources that my math department asks our incoming students to work through before August.

In early August I then send some additional information to the parents, and also ask them to share some information with their student. This includes reminding them about the Math Skills Assessment, and Resources, asking them to read through the course expectations (here's last year's) and completing an online form indicating they've read them, and asking them to write an "About Me" and, if possible, emailing it to me before school starts. I also ask them if they are called something other than their given first name and ask them to bookmark the class blog.

So, back to the first day's assignment. On the blog that night I'll ask them to read the course expectations and submit the online form (if they haven't already done it), complete the About Me writing assignment (if they haven't already done it) and get it to me by Wednesday, and I ask them to take their textbook home, place it wherever they study, and take a picture of it there. Then they need to email the picture to me (or they can just show me on their cell phone) to show that the textbook made it home (if any students just have no way to get a digital image of the textbook, I tell them they can draw a picture). We don't use the textbook day-to-day in my class, but I still give it to them as another resource that I want them to keep at home in case it helps.

So, while I am giving "homework" on the first day of class even though we really didn't have class, for most of the students the only thing they need to complete is taking their book home and taking a picture of it. (But it does allow for those students who chose not to do the other two things before school started to do it now.)

Given the restrictions of my "first" day of class, what do you think?

Take Two

Well, okay, that didn't work so well. I started out with the best of intentions but, for a variety of reasons, I just couldn't keep up with it. So, a new plan for this coming year.

What I'm going to try to do (at least for a while, we'll see how it goes) is begin to blog about my plans for next year. This summer I'm going back over my lessons from last year and trying to figure out where I should tweak a lesson, where I should do a major overhaul of a lesson, and where I need to come up with a completely different lesson. I hope that by sharing that process here that some of you will help me become a much better teacher (my students thank you in advance).

Obviously you won't know my students or my school and, like all teachers, I'll adjust on the fly as the lesson (unit, year) goes along based on what's happening in the classroom with my students. But by front-loading my planning process I'm hoping to come up with even better ways to help my students learn and understand Algebra, as well as try to model what being a transparent teacher looks like (at least for me). So, for anyone still out there, I'll periodically be posting over the summer (and throughout the year) as I begin to work my way through an entire year of Algebra 1 plans.