Day 26

Today's opener builds on what we did yesterday, as well as the slope video they watched last night. I'm trying to help them make the connection between slope and the graph, as well as between the slope, the graph, and the equation (eventually).

Today's lesson is a look back at some of the "application" problems we've done over the last few weeks, but trying to more explicitly tie them to the starting point/y-intercept and the slope/rate of change. I'm really trying to get them to think of the meaning of the y-intercept and the slope in these problems, as well as get them to begin to connect those ideas to the visual representation (the graph).

We'll work through the first 2 or 3 together, then they'll work on the rest by themselves. Depending on how far we get we'll save #6 for a later date.

 

Their homework will be to finish whatever problems we didn't get done in class (again, we may save #6 for later), to take the online pre-assessment over slope on the Moodle (assessment will be Friday), and (optionally) do some practice problems at CoolMath over calculating slope.

Day 25

Today's opener builds on yesterday's lesson to see if they can construct a slope triangle and/or use the slope formula to find the slope between two points. Then there are two problems seeing if they can figure out the y-intercept from an equation in slope-intercept form, then a dimensional analysis problem involving texting and driving.

Today's lesson was then an activity with bouncy balls where they compare drop height with bounce height. Each group got a bouncy ball and a meter stick and had to record the mean of 3 bounces from each of 4 heights, then plot those points, sketch a line of best fit, and then come up with an equation for that line. They then use that equation to predict drop height and bounce height for a couple of scenarios.

 

Their homework for tonight is watch the Slope video and, optionally, do some slope between two points problems at CoolMath (they can do none, some, or a bunch, depending on what they think they need).

Day 23

I had to miss today, but another math teacher covered my class. It was another shortened class period due to our Homecoming Pep Assembly. They worked through this review worksheet (below is the key, posted to the class blog for them to check their work over the weekend).

 

Their homework for the weekend was to finish the review worksheet if necessary and to prepare for their assessment on Monday over Graphing Linear Equations by Using Intercepts.

Day 22

Today's opener utilizes a hopefully interesting problem pulled "straight from the headlines" - well, okay, straight from the news, about the world's largest chocolate bar, which I then turn into a dimensional analysis problem.They then have two practice problems involving graphing using intercepts and finding the intercepts from a graph.

Today's lesson then provides an application problem to link recursive sequences to writing equations and to talk about the concept of y-intercept (we'll get more explicitly to slope shortly, but we talk a bit about it today as well).

Their homework for tonight is to review the notes from the lesson (as always, posted as a PDF to the class blog), and to complete the Graphing Linear Equations by Using Intercepts Online Pre-Assessment on the Moodle.

Day 21

Today is a shortened class period due to our Homecoming Royalty Assembly. So, the bell rings and we have about 4 minutes where I'll remind them that we're going to have an assessment and briefly remind them of some things they should think about while doing the assessment, then we go to the assembly. When we get back, they take the assessment over Graphing Linear Equations by Using a Table.

After the assessment we work out the key together (to post on the blog), and then due to the shortened class period we previewed the Graphing Linear Equations Using Intercepts video that they need to watch tonight so that we could go over, once again, some good strategies to utilize while watching these videos.




Their homework was check the portal for the results of their assessment and schedule an appointment to re-assess if necessary, and to re-watch the video.

Days 20-23

Okay, so clearly I didn’t get caught up on my blogging. Again, I’ll try to do a week in this post and then see if I can find time this weekend to do individual posts for this past week. Again, all links to the openers, lessons, assessments, and other stuff are contained in the class blog posts that are linked from each day.

Day 20
Today’s opener contained a problem about the world’s largest chocolate bar (used it for dimensional analysis), as well as some intercept questions. The lesson was an application of slope-intercept involving me, calories and a treadmill. I think the students appreciated the context, especially when I explained that the numbers were reasonably accurate, but I still feel like I’m doing too much of the work/thinking. I also gave them the background information for our next Skype session, with an engineer from NREL that’s working on a geothermal hvac system at a new IKEA store that’s going up in our city.

Day 21
Today’s opener contained another dimensional analysis problem, this time around texting and driving. Again, the students seemed interested in the context, and the fact that I can apparently find openers just about every day in the newspaper, but they still struggle mightily with actually completing them on their own. I’m wondering if perhaps I should start class by having them do jumping jacks instead.

The lesson for today involved weighing pennies and coming up with a linear equation to predict the weight based on the number of pennies (thanks to Frank who gave me the idea in a comment a while back). I had them place the pennies in a beaker before they weighed them so that I could manufacture a y-intercept other than zero, and I also made sure that each group had pennies that were either all pre-1982 or post-1982 (when the composition, and therefore the weight, changed).

This lesson went okay, but some of the groups collected such poor data that it was hard for them to get what I was hoping they would get. I think they more or less understood when we discussed it at the end, but I’m wondering if all the data collecting I’m having them do is perhaps getting in the way of their learning.

Day 22
We assessed on Graphing Linear Equations Using Intercepts today. Once again I thought I had prepared them well and had constructed a straightforward (and easy) assessment. Turns out I was wrong, as there was still a wide range of performance on this assessment. Some students are clearly not studying at all for these assessment but, even if that’s the case, I would hope they would still be doing better based on what we’ve done in class.

I thought the lesson today was pretty interesting, as we looked at – and graphed – data based on the current tax bracket rates, the rates proposed by the Obama administration, and the rates if the current tax policy expires. We worked with the data first, before I told them what it was. I then asked them to guess what the data represented, and one of my students did guess (surprising even himself). Again, though, I’m worrying that while I find the context of these investigations very interesting, I’m not sure they do. We then looked at some linear wind chill data as well.

Day 23
I’ve decided to try to make my openers take less time. For a while, at least, I’m removing the longer (and more interesting I think) problems in favor of problems that focus directly on the skills we’re learning. They just seem to be getting lost with the more in-depth problems, and then we also run out of time in class for our lessons, so I’m going to try this for a few weeks and see if it helps.

The lesson today gathered data on drop height versus bounce height for various types of balls (bouncy balls, tennis balls, etc.). This went okay, and they seemed to be getting the idea but, once again, at the end of the day I wonder if they would’ve gotten just as much or more out of it if I had just provided them the data instead of them collecting it.

Days 16 - 19

Sorry, I got kinda busy the last couple of weeks, so I’m going to try to cover all of last week in this post (obviously not quite as in-depth as usual), and then try to catch up with individual posts for the four days this week. To save time I’m going to simply start linking to the individual days on the class blog where you can find links to the openers, lessons and videos, instead of linking them individually. I hope that works for you. Here we go.

Day 16
Today we took the assessment for Solving Equations with Variables on Both Sides. I was concerned about giving an assessment on a Monday for all the usual reasons, but with a four-day-a-week class and the frequency of my assessments, there’s really no good way around it. (Plus, philosophically, I don’t think it should make a difference giving an assessment on a Monday, it they know, they know it.) The results were pretty much what I expected, which was slightly disappointing. They didn’t do as well as I had hoped and it was clear that many of the students hadn’t thought about Algebra since they walked out the door at 8:20 am on Friday. I’m really struggling with the lack of effort some of the students are giving outside of class (and this seems to be a common complaint among other teachers of freshmen at my school this year).

After the assessment we did a quick review of graphing an equation by making a table, and then moved on to the lesson, which was a distance/rate/time problem that we attacked using recursive sequences. Once again I’m worried that I’m scaffolding this too much for them, but whenever I try to back off and let them take more ownership they flounder. This is going to be a continuing theme for me I think. My other concern today was their continued difficulties with the concept of speed and how you figure out how fast someone is going. We have already done a few distance/rate/time problems and I know they’ve done some in science before, plus I thought that speed was somewhat of an intuitive concept for most students. Yet they can’t seem to translate “how far I’ve gone and how long it took me” into actually calculate a rate.

Their homework was to watch the Graphing Linear Equations by Using a Table video as well as finish the lesson for the day. This was a little more than I intended to give them, but we didn’t get as far in class as I had hoped, and they do have two days to work on this. I encouraged them to come in on Tuesday (the day they don’t have me) for help if they were struggling.

Day 17
This was a day I had high hopes for in terms of engagement, as I invited in several folks (two assistant principals and our media specialist) to be guest participants in an activity. We walked down to our gym hallway where there was a little more room, I setup a 50 m tape and then the guests performed eight ten-second “walks” as the kids noted their position at each second. I had given the participants written directions ahead of time (“Start at 0. Walk at about 1 m/s for 3 seconds, then stop for 3 seconds, then walk at about 1 m/s for 4 more seconds”) and then I counted out the seconds and the students wrote down the positions.

This turned out to be more difficult for the students than I had expected, and then collating the data took a long time (which I did expect), so we’re going to finish this activity on Friday.

Their homework was to take the Graphing Linear Equations by Using a Table pre-assessment and to make sure they had all the data we collected written down.

Day 18
This was another Carnegie Hall day (“How do you get to Carnegie Hall? Practice, practice, practice) to give them some repetition of some skills and hopefully prepare them well for their assessment tomorrow. My class seems all over the place on their ability to plot points (something they’ve done before in multiple classes), and they are still struggling mightily with simply substituting in values and evaluating expressions correctly. I told them today that I’d love for them to be able to do this without a calculator but, if they find themselves getting things wrong often, I want them to use the calculator to be sure. So, do it in your head first, then verify with the calculator. I don’t think I convinced many of them.

Their homework tonight was to finish the review worksheet if they wanted to (we did most of the graphing problems in class, but then there was a spiral review of earlier topics), or they could save the non-graphing review problems for the weekend if they wanted to. Then they also needed to review for the assessment tomorrow. I feel like I’m communicating well in terms of what they should do to review for assessments, but I’m not sure I’m getting through.

Day 19
The assessment over Graphing Linear Equations by Using a Table was today – and, overall, they bombed it. Several factors here I think: Homecoming Week, two assessments in one week, me not standing over their shoulder making them do the homework, their difficulties in substituting and evaluating, and perhaps too high of expectations on my part in terms of their readiness to take ownership over their own learning. Back to the drawing board.

After the assessment we then worked with the data we collected on Wednesday and they seemed to be getting the hang of it. We had a shortened class due to the Homecoming Pep Assembly, so I once again left them with more of the lesson to finish for homework that I would like (this is getting to be a bad habit on my part – I really need to fix my timing issues). They also need to watch the next video, Graphing Linear Equations by Using Intercepts over the weekend.

I felt like this week was a step back for me and my class, hopefully next week will be better.

Day 15

Today went well (I think). It felt much more relaxed, perhaps because I got the timing right for one of the few times this year. The students have also seemed more relaxed the last few days, joking around with me more at the beginning of class (although they still get too quiet as we move deeper into class and content).

The opener (pdf) was designed to reinforce some basic distributive property stuff, give them some practice on solving equations with variables on both sides (formal assessment over that is on Monday), and to remind them/introduce them to the concept of a sequence. They did reasonably well with these, although I’m still concerned with the number of students who can’t do problems like 1a correctly (with a calculator).

The lesson (pdf) was then an introduction to recursive sequences (this is leading to writing linear equations and the concept of slope). It was also an opportunity to show them one of the features of their graphing calculators – the ANS key. (Not all of the students have graphing calculators, but I made new groups this week to make sure at least one student in each group, and usually more, has a graphing calculator).

So they built the patterns out of toothpicks and pretty easily saw the rules for number of toothpicks and perimeter. I then showed them how they could build a recursive routine into their calculators using braces and the ANS key so that they could quickly generate results for additional figures. They then pretty easily came up with the number of toothpicks and the perimeter for figure 25. (As cool as this is, we’ll eventually transition to, “Well, what if we needed to know figure 125, or 1125? Wouldn’t it be nice to have a quicker way?” Bingo, let’s right an expression/equation.)

They fairly easily then replicated this process with a sequence of squares, although I did lose a few students who were more interested in creating artwork with the toothpicks. My favorite quote of the week was from a student who said, “Mr. Fisch, do you ever worry that parents are going to call you when they find out we were playing with toothpicks in Algebra class?”

Their homework was to prepare for their assessment over Solving Equations with Variables on Both Sides on Monday (and, yes, I’m a little worried about giving it on a Monday), and to plan how they might want to participate in Homecoming Week (pdf) next week.

Day 14

Today went better. It was a Carnegie Hall day.

How do you get to Carnegie Hall?

Practice, practice, practice.

They seemed more confident on the opener (pdf), even though questions 3 and 4 were something they just had last night in the video that was for homework. Now, that doesn’t mean they all understood how to do it, but enough of them did that it makes me think we might be on the right track. Then, as the students worked them out on the smart board and I then went back over them, I saw several more light bulbs go on for students. (And, later in the day, I had a student come in for help for the first time unprompted. I’ve had students come in before, but always prompted directly by me.)

We then attacked a series of problems (lesson, pdf), divided into distributive property (they did well on) and solving equations with variables on both sides (mixed results, but definite progress). I had hoped we would get through the third section (graphing on a coordinate plane), which would’ve just left review problems for homework, but no such luck. Still, they only had those two sections for homework, as well as completing their online pre-assessment for solving equations with variables on both sides.

I had this day planned well in advance but, in retrospect, it would’ve been better if I’d done this yesterday. I think the students would’ve been much less stressed, and I know I would’ve felt better about things. If I’m still in the classroom next year, this post will help remind me what to do differently.

If you’re kinda sorta following along with this blog, take a look at Jason’s thoughtful comment on flow on yesterday’s post. He makes some great points, and in my reply comments to him I try to explain why I’ve made some of the choices I’ve made. I appreciate the comments folks are submitting, as it’s helping me re-examine what I’m doing from another perspective and sometimes make changes (and sometimes re-justify to myself why I’m sticking with something).

Day 13

Today was . . . confusing. I’m pretty sure it was confusing for my students, but it was also confusing for me. We started with the usual opener (pdf) and they seemed pretty stumped again. At this point I’m expecting them to be able to do a straightforward order of operations problem, particularly because they have calculators. That wasn’t the case, as some of them struggled with 1a.

I knew they would struggle some with 1b, as I could tell when they did the openers on Friday that they weren’t very comfortable with distributive property. (Note to self: I need to find out for sure what they’ve had in middle school. I know in the past that distributive property was something they had been exposed too, but now I’m wondering if perhaps that’s not the case anymore). I wasn’t that concerned that they struggled with 1b, as this was another opportunity for them to see how to do it, and because I know tomorrow I’m going to give them more practice with it.

Question 2, however, was a little bit depressing. While I knew some students would struggle with it, I wasn’t prepared for the number of students who apparently had no idea where to start. I referred back to what we did on Friday (suggesting they look back at our work from Friday if they didn’t remember), and referred to the video they watched on solving two-step equations. I was anticipating that they would be able to do column 3, “undo the steps,” and struggle a bit with column 4, “The Algebra,” yet many were unable to even start the undo the steps column. I think this confirms my supposition that at the end of the day Friday they didn’t get it quite as well as I had hoped, but I’m also frustrated since I thought the video they watched should’ve helped solidify the idea of simply doing the inverse (opposite) operation. When I ask how to “undo” something they all seem to know, yet they can’t come up with what to ask on their own. I’m hopeful that when we do some more practice problems tomorrow (no new stuff) it will begin to click for more students.

Then the lesson (pdf) today was equally frustrating. (Note: image from Discovering Algebra from Key Curriculum Press). We did what I thought was going to be a quick and straightforward experiment, using their textbooks as a ramp and rolling pencils off of them, and then measuring how far they rolled. Then we were going to plot the points and see if there was a relationship (greater the height of the ramp, the farther the pencil rolled). I’m not sure if it’s just too early in the morning, or if I did a really bad job explaining this, but they moved through this so lethargically that it felt like by the end they had no idea why we did it. Again, I’m feeling conflicted about how much scaffolding I need to give them to be successful, versus my philosophy that they need to be problem solvers themselves.

Then we moved on to a data set from the U.S. Department of Transportation, showing the average fuel efficiency of U.S. passenger cars by year since 1980. I pulled the chart from the web and then started a table for them. I then asked them to copy the year and the mileage from the chart into the appropriate columns in the table, and then in a third column they had to calculate the years since 1980. I demonstrated with the first three points to make sure they knew what I was asking them to do, then asked them to complete the rest of the table (they did not have to copy the actual chart itself). That proved really difficult for some of them, so once again I’m questioning my assumptions about what is reasonable to expect 14 and 15 year olds to do. Should transferring information from the chart to a table, when I setup the table and help them with the first three data points, be pretty straightforward as I think it is, or is that unreasonable?

Either way, that took much longer than I anticipated (yeah, back to my poor timing issues that I thought I had resolved). As some students had finished their tables and others were still working, I revealed step 2 so that the students who had finished could start on their graphs. Again, I worried that I was scaffolding too much by telling them to scale both axes by 1’s. It turns out that that wasn’t enough scaffolding for many, as they labeled their x-axis 0, 5, 10, 11, 12, . . . Once again, my assumption was that they have done some graphing previously and that this wasn’t completely new for them. So, again, I need to find out for sure (in my own defense, I did ask the students if they have graphed previously and they say they have).

I then talked through steps 3 through 5 to make sure they knew what I was asking for, and then gave those to them for homework (as well as a few will need to finish the graph as they did not finish in class). I’ve been working really hard at not trying to play “gotcha” with checking their homework, but I think I may be wavering a little bit on that. Every day I talk about the importance of doing whatever I’m asking them to do outside of class, and the importance of coming in for help when they don’t understand, but the blank looks are starting to wear on me a bit. My philosophy of continuing to trust them and share with them the reasons I’m asking them to do things, and then giving them time to figure it out and start stepping up will eventually have to end if they don’t step up. As I said to someone I was talking about this with today, eventually if it’s not working for my students, then I’ll have to change something as I do have a limited amount of time with them (even if I think that’s detrimental to them in the long run).

Today felt like I stepped back about two weeks.

Day 12

So today seemed to go really well until right until the end, but then it seemed like maybe they weren’t getting it after all. Of course, it was the Friday before a three-day weekend, plus we don’t meet on Tuesday so I won’t see them until Wednesday, but still.
We started with our usual opener (pdf), but I tried something different today. As I’ve mentioned before, I’ve been surprised about how long the students are taking to do what I consider to be pretty routine stuff. So, each day on the openers I’ve been saying things like “I think these should take you about five minutes” or whatever, but then they take ten minutes and I’m not quite sure what happened.

So today I decided to make it a little more explicit, I put suggested completion times after each opener. Now, I want to be clear that I don’t believe that speed is the most important thing here. I don’t want to rush my students. Yet I also believe that students must have a comfort level and facility with the mathematics to do things at a reasonably good pace if they’re ever going to be able to move forward and work on more interesting – and complex – mathematics.

So at the beginning I told the students what I was doing, and that they shouldn’t panic if it took them longer – or shorter – to do each problem. I told them that those times were the times that were the target for them, where I would like to see them get. I also told them that the total time on the timer was slightly more than the sum of the times, so that I didn’t push them too much (I think I had four minutes on the timer in the upper right corner, even though the suggested times totaled three minutes). When the timer went off, I then said that if they were finished, or working on #3, they were in pretty good shape. But if they weren’t even on #3 yet, then perhaps there was some concern there and they might want to come in and get some help. They then had several minutes to talk over the openers in their groups before we worked them on the smart board.

I’m not sure how I feel about this, as part of me really hates doing this. But they did seem a little more focused today, and I’m going to try it for a few weeks and see what happens.

We then moved on to the lesson (pdf), where we approached solving two-step equations via the idea of working “magic” with numbers. So, here’s the scenario. I told them to pick a number between 1 and 25 and write it down. I then gave them one operation at a time (“Add 8” or “multiply by 4”). After each operation, they then wrote down their result. After about five operations – and keep in mind they have calculators for this – I then revealed the magic and told them what the last number they wrote down was (“5”, or “Your original number”).

Now, I knew this was going to happen, yet it still was somehow a surprise. A fair number of students didn’t get “5” or “their original number.” So, here’s my question to you, is it unreasonable to expect that students, using a calculator and taking one basic operation at a time, couldn’t complete five operations in a row successfully? I’m really struggling with this, because I think (perhaps naively) that they should be able to and that, if they can’t, they are going to struggle mightily in Algebra. Given the fact that clearly some of them are struggling with this, I’m not sure what to do to help them. Ideas?

After translating the “magic” to the algebra to show them why the tricks worked, we approached solving two-step equations by “undoing” operations. As we were working through this I was feeling pretty good, they really seemed to be getting it and understanding the concept, even if they were still a little shaky with the fourth column (“The Algebra”). But then I turned them loose (in their groups) on the last page of the lesson, and suddenly a whole bunch of them didn’t know what to do. Not just with the fourth column, but with the other columns. I had anticipated they would struggle with the last one (writing their own given just a result), but not that they would struggle so much with the first two.

Their homework for next week (again, I won’t see them until Wednesday), is to watch the video on solving two-step equations (in addition to completing their reflection/goals assignment from Wednesday), so hopefully that will help solidify the concept of undoing and what to write for each step.

So, overall, week three felt better, but still nowhere near where I want it to be. I did much better on my timing each day, and I think I’ve scaffolded things better for my students, but I still worry that I’m doing too much of the thinking. As always (at least until the end of the year), next week is another opportunity to do better. Let’s hope I do.

Day 11

MAP Testing today, so no instruction.

I should've mentioned in yesterday's post, however, that I did give them a couple of assignments after the Skype session and our conversation yesterday.

First, I gave them a short set of review problems (pdf), since I'm worried I'm not giving them quite enough repetition. Those are due tomorrow.

Then I asked them to write their first reflection piece, as well as set some goals. I'm asking them to do this in Google Docs (in our Google Apps installation), so I gave them a brief set of instructions in case they weren't comfortable finding it. I created the document for them (in shared folders that I've created between each student and me) that contains the prompt, they just need to open it and type in it. I've previously asked them to login and check their email, so theoretically at this point they all know how to access it - we'll see. I've told them to check before the weekend to be sure they can get to it, otherwise they should see me for help on that.

Here's the prompt:

Looking back at our first couple of weeks in Algebra, how are you feeling? What’s going well or you are excited about? What’s challenging or are you concerned about? Please answer in complete, thoughtful sentences.

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)
• One goal outside of AHS

Make these goals fairly specific, not just “I want to get a good grade.” For each one, answer with what, why and how – what is your goal, why is it your goal, and how will you accomplish it.

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 good. Please also use complete, thoughtful sentences for these.

Day 10 - What I Said Today

[cross-posted on The Fischbowl]

Today was our Skype session with Professor Garibaldi, and I thought that went well. After the Skype session we only had about twenty minutes left (shortened classes due to a PLC day) so I took that opportunity to talk with my class a little bit. I realized that I hadn't done a good job of conveying my thoughts and beliefs about the class, of sharing my passion, of explaining why I setup class the way I did and what I was expecting from them - and what I was hoping for them.

So here, more or less, is what I said. I'm sure it wasn't quite this smooth, as when I write I automatically correct and tweak, but this is pretty close to what I said (and definitely the spirit of what I hope I conveyed).

---

I wanted to talk a little bit about this class and why I’m doing the things I’m doing. Mr. Krause, one of our English teachers, is doing a project right now where his students are asking people how they define success. I answered that for several groups of students, but I wanted to talk for a minute about how I’ll decide if I’m successful with you guys in this class.

I won’t think I’m a success if you get a good grade in Algebra, although I certainly hope you do and I’m going to try really hard to help you do that. I won’t think I’m a success if you score well on tests like CSAP or ACT, although I hope you do, and even though a lot of well-intentioned people think that’s how I should define success. I won’t even think I’m a success if you go to a good college and then get a good job, although I certainly want you to do that because I’d like to retire someday and I need you all to have good jobs to support me.

No, I’ll consider myself successful if you turn out to be good, kind, caring adults. If you’re a good spouse, child and parent. If you contribute to the world and to your community and help those around you. If you participate. And learn.

And here’s the deal. The education that I received was a pretty good one. But it’s not good enough for you guys. Not anymore. You see, in a rapidly changing, information abundant world, the people who are going to be successful – both professionally and personally – are the learners. And by “learners” I don’t mean people who just learn what we teach you here at AHS.

Now, I want to be clear, that doesn’t mean I don’t think you should learn what we teach you here at AHS. I don’t want you to go to your second period teacher, raise your hand, and say, “Mr. Fisch said I don’t need to learn what you’re teaching.” Please, don’t do that. That’s not at all what I’m saying. Your teachers here work very hard trying to share important, meaningful and relevant knowledge and skills. And that’s important, but it’s not enough. Because to be successful in the 21st century you’re going to have to be a learner, you’re going to have to learn how to learn, and go after things on your own. You’re going to have to be independent, curious, passionate learners, who don’t just sit back and wait for someone to tell them what they’re supposed to know, but who go out and try to figure things out for yourself. Who pursue your interests, your goals, your passions with intensity, and who actively participate in everything you do. Who go out and find other learners who are passionate about what you are passionate about and learn from them – and alongside them.

To quote myself (sorry), the world has shifted. The world of school, and the world of work, and the world in general has shifted, and so I need you to shift as well, and that’s what I’m trying to do in this class. I’m trying to get you to be actively involved in your own education, to be independent and curious learners in mathematics, even if Algebra is never going to be your favorite subject.

I believe you need the skills I’m trying to get you to learn for three main reasons. First, to be a successful citizen in the 21st century you have to be numerate. In order to deal with all the data that is going to get thrown at you, and to make good, responsible, effective decisions, you’re going to need a lot of the skills we’re learning in Algebra.

And frankly, that’s not necessarily true about all the math classes you’ll take. Honestly, if you take Trig and Pre-Calc, the skills you learn there are very important if you go into the math and sciences, but perhaps not so much day-to-day life for most of you (some folks will disagree with that). But the skills we learn in Algebra you’ll be using every day to make sense of all that data in the world, to be informed voters and decision makers.

The second reason to learn the skills is if you decide that you are passionate about math and science, you need these skills in order to progress to more complex topics and to go deeper.

The third reason – and it’s the one I think is least important but you may think is the most important – is that right now in the short term you have to learn these skills to get a good grade in this class, to do well in school, and to get into college if that’s what you choose. So while I prefer that you focus on the first two reasons, this one is still a valid one for many of you.

And this is why it’s critical you do the assignments I’m asking you to do, like watching the videos I’ve created for you. Those videos are designed to help you master the skills, and to become more independent learners. But they’re also designed to free up class time so that we can become more curious, active learners, in class, and so we can explore interesting (or not for some of you) applications of Algebra like the bike gear ratios or Tim Tebow’s speed at the NFL Combine or a variety of other activities we’ll be doing this year. In order to apply the skills in class, I need you to do the necessary work outside of class.

But in order for that to happen, in order for us to use our class time to be the kind of learners I think you need to be to be successful in this century, your century, I need you to step up and take care of business. I need you to watch the videos, and use them as they’re intended, and do the other things I ask you to do outside of class. And I really, really need you to participate in class, to be active learners. To ask questions, and be involved, and talk to each other, and help each other, and be willing to take risks in order to learn more, even if that makes you a little nervous or uncomfortable. I need you to do more of the talking in class, and me to do less. I need you to do more of the thinking, and the questioning, and the figuring out.

So I’m asking you to please, please consider what kind of future you want, not just for yourself, but for those around you, and make an effort to be as independent, as curious, as responsible, as passionate of a learner that you can be. And I promise that I’ll bring the passion every day and do the very best I can to help you become that learner.

Day 9

Perhaps the most frustrating day yet, although it wasn't necessarily due to the lesson. The openers (pdf) - which I thought they should be able to do fairly quickly and easily - stumped them. Completely. Even #1, which they seemed to think was simple on Friday, was a problem for many of them.

Opener #2, which I thought was an "easy" dimensional analysis problem (because I realized that they were getting lost in the really long ones I had been giving them), wasn't. It appears as though speed (miles per hour, kilometers per hour) is not as straightforward for them as I thought it was (they don't get that distance should go in the numerator, time in the denominator). I need to do a better job of checking my assumptions at the door.

Then opener #3, which were the same problems they were supposed to do for homework over the weekend, except I specifically asked them to find k today, were a mystery to many of them as well. I think that after going over all the openers, as well as today's lesson, they understand them much better, but today felt like I was starting over at square one.

Then the lesson (pdf) was looking at direct and indirect variation via the gear ratios on a bike. Following Friday's lead (which I'm still not sure I want to do), I structured it out the wazoo. (Interesting - Firefox recognizes "wazoo" as spelled correctly, but not "pdf.") I brought in my bike, borrowed a stand from another teacher at school, and stepped them through how far the wheel turned for one turn of the pedals when in different gears. I pre-counted the teeth on the gears I was going to use and pre-filled in that part of the table, so the students could just concentrate on how far the wheel went each time. I had students volunteer to come up and turn the pedals, catch the tire, and write the number of wheel revolutions in the table, but other than that I led them through it. Again, I think there was value in doing this today, but I was still doing too much of the thinking.

For homework for Wednesday I gave them what I was anticipating would be a fun, but not too tough, problem involving Lance Armstrong and the Tour de France (although now I wonder), and had them finish the last two steps of the bike variation activity.

Day 8

Today went better, but I'm not sure I like why it went better. It went better because I did more. I structured it more, I scaffolded it more, I led them through it more. It seemed to go better, but at what cost? It's going against what I'm trying to get them to do, going against be less helpful.

So I'm torn. It's not that I mind structuring and scaffolding if I think it helps them become curious learners, helps them get to the place where they can inquire and explore more on their own. But I don't think that's what I accomplished today. I think I structured and scaffolded and therefore they didn't have to think much.

We explored inverse variation today by looking at distance, rate and time. The opener (pdf) was review, and I thought pretty basic, but they are still struggling mightily with dimensional analysis. Then we moved on to the lesson (pdf). We first looked at a digital picture of a falling tennis ball and then tried to figure out how fast it was going, how long it had been falling, and what height it had been dropped from. This was a hopefully fun way to look at inverse variation and solving one-step equations.We then used this video (downloaded and edited so they couldn't see the calculated mph) to look at d = rt again (thanks again Dan), and talk about inverse variation and solving one-step equations some more.

Overall, they seemed engaged, it seemed to go well, except I don't think it really did. Frustrated I am (in my best Yoda voice).

Day 7

I think I may actually be getting worse at this. While not horrible, today didn't go at all how I wanted it to. It started with us getting a late start primarily because they forget to reset the bells after Back to School Night last night (and partially because our Link Crew brought doughnuts for the freshmen and they met in the cafeteria, but mostly the bells). So we started a few minutes late and, well, you know how I'm doing on my timing, so that didn't help.

We started with an opener (pdf), as usual, and I really liked the problems on this one (my age in seconds, but without the units; converting Deepwater Horizon daily oil spill into number of 2 liter bottles per second). Unfortunately, they didn't really know how to approach problems 1 and 2, which are the ones I liked. That's partially because we ran out of time yesterday, but it's also partially because they seem hesitant to dive into anything they don't already know how to do. I wrote on the whiteboards next to the smart board where the problems were projected some hints to get them started, but they didn't even seem to be interested in writing that down. I think I'm not doing a very good job of communicating with them about how I want them to approach mathematics, or perhaps it's not so much communicating but I'm not convincing/encouraging/selling them.

We then moved on to the lesson (pdf), where I pulled data from The Biggest Loser to explore direct variation. The wheels really fell off here because it took them an inordinate amount of time to graph four points on graph paper. (Obviously, inordinate is in the eye of the beholder, in this case me.) Not only did it take a long time, but many of them didn't graph the points correctly. I had made the assumption, obviously a bad one, that graphing was something they had done enough of that asking them to graph four points, with a decent amount of scaffolding in terms of the how to construct and label the axes, would not be a difficult task. So, again, I'm left wondering if my expectations are too high, if my assumptions about their background knowledge are incorrect, or if I'm close to being right on and just haven't managed to get them to buy in. (And I think I showed some frustration for the first time today. I'm chalking that up at least partially to being tired from Back to School Night last night, but that's still not a very good excuse. I need to be more patient.)

I again had to cut my lesson short of where I had anticipated getting, but at least this time I cut it at the right point so that I didn't talk through the bell (perhaps 15 seconds to spare). So I asked them to finish parts a-f on the second page for homework (we did part a, and started on part b). In addition, their homework includes watching the video on solving one-step equations. This is the second instructional video I've asked them to watch, but I'm still unsure about how many of them are actually watching it. (As an aside, I've debated with myself about how much to "check up on them," and I'm still in the stage of letting them learn the ropes. I'm thinking we're at about the end of that stage, though.)

So, tomorrow is another day, but I'm pretty sure I have too much planned again. This weekend will give me a chance to redo my plans yet again, and perhaps I'll get closer to the sweet spot next week.

Day 6

Today was our first assessment (pdf) over something I've taught (the Math Skills Assessment was over stuff they've theoretically already learned) - Proportions and Percents. Overall, the students did very well, although I was still surprised by how long it took a few students to complete it.

We then talked about different measurements systems and the process of dimensional analysis (including calculating how much Steven Spielberg makes per second), but again it took much longer than I anticipated (lesson, pdf). We didn't get to the last set of examples, including figuring out today's price of gas in Australia - I still hope to share that sometime with them. (I did ask them to do the two problems above that for homework - we'll see how they do on that.)

For homework, they need to check to see how they did on the assessment and, if they need to re-assess, to start studying and then schedule an appointment to re-assess. On our online portal system they can see their grade on the assessment, and in the comments I included which problems they missed (if any) and sometimes some additional notes. With the key (pdf) posted as well, they should have a good start toward figuring out what they need to work on and then re-assessing.

They also have those two problems we didn't get to that I mentioned above, and a short survey on graphing calculators so that I can get a better feel for how many students have - or soon will have - those. I then reminded them that Back to School Night was tonight (I only had about 8 or 9 families show up out of 30 students) and they should invite their parents, and that they'll need graph paper tomorrow.

So, I'm still struggling with how long activities are going to take, but I'm pleased with the results of the assessment. Now if I could just get them to be a little more lively at 7:21 in the morning . . .

Day 5

Well, I did better on the timing today, but still not good enough. I had one extra example built-in that I had to skip, and I had wanted to give the students a few minutes to work on five quick review problems in class but we didn't get to those either. On the positive side, I think they were reasonably engaged in what we did do (although it's awfully hard to tell with teenagers in a first period Algebra class that starts at 7:21 am).

We started with an opener (pdf) like usual. I really liked the first problem and I shared my thinking with them when we went over it. I'm struggling a bit, though, with my expectations on the other ones. At this point my assumption is that they should be able to do the third and fourth one fairly quickly and easily, as we've spent several days on this. And some students are definitely there, but just not as many as I had hoped. That's at least partially because they are (so far) choosing not to do some of the things I've asked them to outside of class. We're still in the stage where I'm giving them some leeway to figure this all out, but pretty soon they are going to need to step up if they're going to be successful with the variable schedule that our high school runs. Is it unrealistic to expect high school Algebra students to do problems 3 and 4, with a calculator, fairly quickly after several days of practice?

We then went through several applications of proportion and percent (lesson, pdf). Borrowing from Dan Meyer (I'm going to be writing that a lot), I started with a clip from The Bone Collector. The character played by Angelina Jolie needs to take a picture of a footprint before it gets washed away by the rain, but places a dollar bill in the picture first. I showed the clip and asked, "Why did Angelina do that?" We then talked about needing a reference for scale and how to use proportions to figure out the length of the footprint (see the lesson for a still from the movie clip). Tip: It's always helpful to get a $20 bill out and put it on the document camera - gets their attention. We then figured out the length of the footprint, which I think is kind of cool. (Figuring out the length of a footprint created on a stage somewhere in California eleven years ago just from a still picture? Yeah, I think that's cool.)

We then looked at similar triangles and the fact that the lengths of corresponding sides are proportional (didn't derive that or anything, just asked what they noticed). We then used that to try to figure out the height of our gym from a picture I had taken a week ago. I think some of the students really got this, but some of them just thought it was more noise. Not sure what to do about that.

The third example was some basic sampling, following up on our capture-recapture work from Friday. We talked about whether our class was a good sample for the question (yes for lunch, no for driver's license), and then I actually went across the hall to Mr. Swomley's class to get the actual number for the dog question. (Aside: not sure if the student are appreciating my humor or quirkiness yet.)

Due to time, I skipped the fourth example about the chemical formula for TNT. I thought that was a nice, quick connection to Chemistry, but my inability to plan for time correctly is killing me.

We then finished with the stock market example. I really thought this was a good one when I was planning it, and I think it worked okay just in terms of practicing percents, but I think perhaps the stock market isn't quite something most of them relate to right now.

The last page of the lesson includes the problems I was hoping to get them started on, but instead suggested they work on as part of their review for the assessment on Wednesday. Visit the post on the class blog for the description I gave them of the day and their full homework (more on the upcoming Skype session in a future post).

Day 4

Yep, three for three. I over-planned again for Friday. I got closer to timing it right, but was still rushed at the end. I'm hoping that if my progress over the last three days is linear, then by about Thursday of next week I'll have nailed it.

We did an opener (pdf) and the students seem to be getting that down pretty well. For our lesson (pdf), we did a capture-recapture simulation. First I showed an edited version of a Discovery Education Streaming video (if you have Discovery, it's the one titled Estimating and Proportions: Counting Sheep). I edited it because I wanted to emphasize how they setup the proportions, and I wanted to step through how to solve them with the students, so I added a couple of still shots in the middle, and also cut out some for length.

The capture-recapture simulation was pretty standard. I gave them paper bags with an unknown quantity of red beans in them and a baggie of white beans. They then reached in and pulled out a handful of red beans, removed them, and replaced them with an equal number of white beans. We then took samples and tried to predict how many beans. It seemed to go okay, but their predictions were all over the place (despite having a similar number of beans in each bag) and it was hard to tell if they completely understood what we did. I'm not sure if I didn't explain things well enough/we didn't talk about it enough, or if it's just too early in the morning and they got it fine, they just don't express it at that time of day.

You can see their homework over on the blog (as well as a couple of photos). They have an online pre-assessment to begin preparing for an assessment over proportions and percents next Wednesday, they need to submit their expectations for the class via a Google Form, and they need to watch The Math of Rock Climbing video (more on why we're watching that next week).

On Saturday I also emailed each student (to their new Google Apps account, although they may not be checking it regularly yet) to see if they had any questions about the class, and also to encourage them to get caught up if they were missing any of the homework assignments. I also urged them to re-assess over the Math Skills Assessment if they needed to - that's proving to be a tough sell so far (not unexpected given that most of them are freshmen and still getting used to the idea that they're supposed to come in on their unscheduled hours, but still frustrating).

So, overall the week was okay, but not stellar. I'm hopeful that I'll improve my planning so that the timing works out better, and that the students and I will continue to get to know each other better which should help facilitate the learning. We'll see.

Day 3

Yep, over-planned today, too. After not having enough time yesterday, I removed one of the examples I had planned to use today, but still ran a little short of time. I guess that's progress, but I hope that either I get better at estimating how long things are going to take, or my students settle into the system a little bit and perhaps things will move a little more quickly (or, ideally, both of those things will happen).

Today we once again started with an opener (pdf). I was impressed that all the students were in their seats and had started the opener by the time the bell rang. When we did our first one yesterday, I said that was the expectation. If they want a little extra time, then they can start a couple of minutes early if they want (or even more than a couple of minutes since it's a first period class). If they don't want any extra time, then they just need to be ready and begin right when the bell rings. The students did a great job with it today.

I particularly liked opener #4 today, as it was a little non-standard. I knew it would throw some (most?) of the students a little bit, but Grant was willing to stick his neck out and try answering it. (I didn't make him write out his answer, so you can't see it on the linked pdf, but he explained it.) Interestingly, he solved it the way I would've solved it, which was estimating ceiling tile width, counting the tiles, and multiplying. He estimated 3 feet per tile instead of 4, but I still thought that was great thinking as well as a willingess to take a risk and share. I was disappointed, though, that when I asked for any other approached students took no one volunteered one, but I realize it's still the first week. Hopefully we'll get there.

We then talked about their Math Skills Assessment and how important it was for them to get help on any areas they weren't proficient in, then come in and re-assess. I can tell this is a tough sell for many of them, which is pretty typical since most of them are ninth graders, but I was still hoping more of them would jump on the chance to improve.

We then moved into our first real lesson, learning about ratios and proportions (lesson, pdf). I thought it went well except for running out of time and leaving one really nice example off (which I'm hoping to come back to next week). I definitely need to work on spacing of my Smart Notebook files so that I leave enough room to write. I think it's okay when I'm talking with them in the room, but if they go back to review the file online it can get confusing.

Today was also the first day they were in groups. When they walked in I already had the desks in groups. I had them work on their openers individually (and quietly) for about four minutes or so (many had more time, of course, since they started before the bell). Then they had a few minutes to discuss it with their group before we went over them as a class. Before they discussed as a group, I had each group do a quick whip-around, introducing themselves and telling what kind of pet they had (or, if they didn't have a pet, what kind of pet they'd like to have).

The lesson was also primarily group work, although I directed it a lot in the beginning and then tapered off some throughout the class. Again, because I misjudged on time, I think I ended up rushing them a little faster than I should've and didn't let the groups struggle for as long as I wanted them to. Again, I'll hopefully get better with this.

We then briefly talked about their homework, including a too-quick discussion of how they should use the video. I'm hopeful they read the blog post carefully to really understand the three main sections of the video and how to use them, but I suspect I'll have to revisit this several times over the next couple of weeks before it really makes sense to them.