Tuesday, July 12, 2016

Algebra: First Semester Lesson Plans 16-17

I stopped blogging here since it wasn't generating much interest or feedback. If anyone happens to be following along here, I just posted my first semester Algebra plans on The Fischbowl.

Friday, June 10, 2016

Day 17

We continue our work with Systems of Linear Equations.

Our opener will be Basketball Shots 2 (the sequel to their homework assignment)

Our lesson will include working through Atomic Weights (probably together), then the Types of Solutions activity builder, and then solving a couple of systems by both substitution and elimination for practice.

For homework they will decide when it might be best to use substitution and when it might be best to use elimination.

Day 16

Today's opener will be a short review of solving a system of equations by substitution.

Then we'll use this Activity Builder to start talking about solving systems by elimination. I tried combining (and tweaking slightly) two activity builders that I thought went well together, but I'm a bit worried it might be too much for the roughly 50 minutes I'm hoping to give for it. Your thoughts are appreciated.

Their homework will be a solving systems by elimination problem involving atomic weights. This might be a stretch for them, especially if we they don't have any class time to start on it (and I hope they do). That's partially why I'm not making this one a screencast (the other part of that partial is just to give them a break from making screencasts.)

Update: Changed the homework to Basketball Shots and moved the atomic weights to part of the lesson the next day. Just felt like it was a bit too complicated to give them that quickly.

Tuesday, June 7, 2016

Day 15

We'll start with an opener that eases them into solving systems of equations by substitution.

We'll then complete the On The Road Again Activity Builder to learn more about systems.

Their assignment will be to record a screencast discussing solving a system by substitution.

Day 14

We'll start with a short assessment over function notation and application.

We'll then begin looking at Systems of Equations using the Racing Dots Activity Builder.

Their assignment will be to complete the Playing Catch Up Activity Builder.

Monday, June 6, 2016

Day 13

Today will continue to talk about best fit lines and learn the least squares regression equation.

The opener will again be practicing finding x and f(x), but in the context of a best fit line.

Our lesson will continue with the air travel situation but in a Part 2 of the Air Travel Activity Builder. We'll now focus on a "best" fit line over a "hey, it looks good" fit line, and talk about what the correlation coefficient means. I really think the idea behind this one is sound, but I think the execution of it still needs a lot of work. Suggestions appreciated.

For homework they will complete a linear regression application problem. I think this one is pretty good, but it may be a case of me really liking it and the students not so much. We'll see.

Sunday, June 5, 2016

Day 12

Today we'll start talking about informal lines of best fit (soon to lead to correlation regression, and causation).

We'll start with an opener that practices solving an equation using function notation.

We'll then work two through Activity Builders, Line of Best Fit and then Air Travel (based on Dan Meyer's post from what seems a long time ago).

For homework I'll have them complete a short reading assignment (as well as look at some spurious correlations), then write a short summary of a second article (their choice).

Day 11

Today is all about learning function notation as well the difference between continuous and discrete functions.

Our opener will review figuring out whether a relation is a function from a graph of the relation.

Then we'll complete Function Notation on Activity Builder. My goal is to expose them to function notation, including solving when given either the independent or dependent variable, talk about continuous vs. discrete, and then do a couple of application problems.

For homework they will complete a similar application problem and record a screencast explaining it. In addition, I'll ask them to do a small additional amount of homework by gathering some data that we'll use in class on Friday (for an activity based on Dan Meyer's Air Travel).

Friday, June 3, 2016

Day 10

Today's topic is relations and functions. In the past I haven't felt good about this one, as I have trouble coming up with any creative ways to teach it yet, on the other hand, it just seems so straightforward to me that I can't figure out why students struggle with it so much.

We'll start with an opener that will review writing equations in slope-intercept, point-slope, and standard form, mainly because I do worry that the lack of repetitive practice I give students (i.e., not a lot of homework problems) compared to other teachers may harm their retention. We'll see.

Today's slides are most of the lesson, with basically just a rewrite of what I used to do with this topic, just updated with examples from activities I will have done this year. After we go through the basic definition of a function and some examples, I'll have them complete the Function, or Not Activity Builder (slightly remixed from the original by Daniel Henrikson).

For homework tonight I won't ask them to do a screencast but, instead, will ask them to see if they can "figure out" the vertical line test for functions. I'm curious to see how they'll do with this.

Day 9

Today we'll work more with point-slope form. We'll start with an opener that practices writing an equation in point-slope form, then substituting in for x and finding y, substituting in for y and finding x, then writing the equation in slope-intercept form.

We'll then briefly share some of their Des-Person creations.

The lesson will work through the How Long Does It Take To Sober Up? Activity Builder. I'm a little worried about the time it might take to do this, so still thinking if there's a good way to shorten it without skipping something important.

For homework, they'll do a modified version of Mathalicious's Domino Effect.

Day 8

Today is a PLC day, so we'll only have a 39 minute class.

Instead of an opener, we'll start with our first assessment over Graphing Stories. I'm not sure I like what I've come up with here. As I mentioned in the Day 7 post, I wanted to keep this relatively short (10 minutes or less) and have them demonstrate their knowledge of various parts of graphing stories (verbal descriptions, tables of values, linear equations with domain restrictions).

Well, I think what I have right now is perhaps a bit too complicated and will take a bit too long. I'm guessing this is closer to 15 minutes instead of 10. And, while I like the problem situation, I'm worried it's too "busy" for students. It's hard to tell, because after a week plus of working with these stories, maybe it will be as straightforward for them as it was for me (in my head) when I was thinking about this. If it is, then it's not too busy and they'll cruise right through it. But if they aren't feeling good about graphing stories at this point, I can see them getting lost in all the details. Your thoughts on this assessment would be appreciated as I think about this more.

After the assessment we'll briefly work on point-slope and standard form. I've never been enamored of standard form, but it's an expectation, so we'll touch on it. Point-slope form is trickier, because it's confusing for a lot of students but, once they understand it, it's useful in a lot of situations. Here are my slides for this quick overview. I'm not happy with these either, but perhaps a boring, straightforward quick look is all they need here. (We'll continue working on point-slope the next few lessons.)

For homework they will continue working on the Des-Person assignment they received the previous day.

This is the first day I don't feel pretty good about. I have questions and concerns about the other days (most notably with timing), but overall feel pretty good about them. This day doesn't feel all that good, starting with the shorter class period, the assessment not being quite right, and the lesson being less than inspired. I'm telling myself that not every day can be fantastic, but I'll be thinking about this one a bit more.

Thursday, June 2, 2016

Day 7

Slightly shorter class period today (53 minutes) because it's an advisory day.

We'll start with an opener called Sloping Letters, which helps them review the idea of positive, negative, zero and undefined slope.

We will then go over a homework screencast and talk about their first assessment tomorrow. This assessment will be over Graphing Stories and will ask them to put together what they know about verbal descriptions, tables of values, linear equations with domain restrictions, and Desmos. I'll explain to them my assessment philosophy and how I will give them an adequate amount of time for the assessment, but not unlimited (therefore they should be prepared). The actual assessment will include a link to a Desmos graph (or possibly Activity Builder, haven't constructed it yet). Right now (may change after I construct it), they will complete the problem, then take a screenshot and upload that to formative. I anticipate giving them about 10 minutes for the problem, but we'll see.

Today's lesson will be a combination of Polygraph Lines and my version of Des-Person/Winking Man Part 1 (part 1 because I'm hoping to create a part 2 and maybe 3 after we do quadratics later in the year). I'm hoping this will be a fun way to reinforce what we've done, including having them focus on some vocabulary (slope, intercept, quadrants, etc.) as well as domain restrictions.

Their homework will be to prepare for the assessment tomorrow (so no screencast), as well as their own Des-Person assignment that will be due on Friday (if I'm on track, today is Tuesday, assessment will be tomorrow on Wednesday, we don't have class on Thursday).

Wednesday, June 1, 2016

Day 6

Today we revisit Graphing Stories and the MARS task Interpreting Distance-Time Graphs, but this time we will write linear equations for all the stories that have all linear components - even if they are piecewise.

The opener will review how to find the y-intercept when you aren't given it but, instead, are given the slope and a point, or more often two points and you have to calculate the slope first.

We will then discuss one of the student's homework screencasts from the previous class.

Today's lesson will work through the Activity Builder Graphing Stories Part 2. This will solidify our ability to connect descriptions, tables of values and graphs, and then to be able to write equations for those graphs (including domain restrictions for piecewise functions). As part of this we will need to utilize solving for the y-intercept since we won't always have that for the different pieces of our graph.

For homework they will complete one more graphing story and record a screencast with their thinking. The hope is that by the end of this lesson they are feeling very comfortable with everything related to graphing stories, including writing equations for linear data.

Day 5

Today I hope to to cement the connection between a situation, a table of values, the graph, and the equation. The will also begin to connect slope more explicitly with the idea of rate of change and specifically with speed for distance-time graphs.

We'll begin with an opener that reviews slope and connects it to rate of change and speed (screenshots below).

We'll then complete an activity that requires gathering some data on three people walking, entering it into an Activity Builder, then using the data to try to come up with equations to describe their motion. The first walker will start at 0 and walk at an even pace for 10 seconds. The second walker will start at 3 feet (for example) and walk at a steady pace (hopefully slightly different pace than the first walker, we'll see). The third walker will walk a piecewise graph. Starting at 2 feet (for example), walking at a steady rate for 4 seconds, standing still for 3, then walking at a steady rate back toward the starting point for 3 seconds.

The hope is that they will not only connect the actual walk to the data tables and the graph, but they'll get a better idea of how speed relates to the graph and the idea of a domain restriction and piecewise equations. In our next class we will then revisit Graphing Stories and the MARS activity, coming up with equations for any of the linear graphs (including the piecewise ones).

For homework students will take a piecewise table of values, graph it on Desmos and come up with equations, domain restrictions, and a verbal description of what may have happened, then record a short screencast of their thinking.

Monday, May 30, 2016

Day 4

Today we'll finish the MARS activity we started yesterday, looking at the connection between the tables of values, the graphs, and the verbal descriptions.

I'll use today's opener to again review slope-intercept form, see the screenshots below.

We'll then discuss one of the student's screencasts of last night's homework problem.

The lesson will continue with the MARS activity, matching the various tables of values to the graphs and verbal descriptions (slides, see the MARS activity for the tables of values we're using).

Today's homework will be to tie together the verbal description, the graph and the table of values, and again use a screencast to share their thinking about the problem.

My hope is that after today they are feeling fairly confident connecting descriptions to graphs to tables of values, and perhaps seeing the connection to rate of change and slope (although we'll make that more explicit in our next class, which is two days away because we don't meet on Thursdays).

Day 3

Today I want to continue exploring the relationship between two related variables, and how to sketch a graph given a verbal description. Today we'll focus on distance/time graphs by using this MARS activity.

I'm going to start with an opener that will hopefully remind them of what they already know about slope-intercept form of a linear equation. Again, in Formative, so I'll give you screenshots.

After discussing the opener, we will then view and discuss one of the screencasts they did for homework last night (the assumption being that at least a few of them were successful). We'll talk about the math in the problem, of course, but we'll also talk about problems anyone had with the screencast process and possible solutions.

We will then move on to the MARS task (outlined in the slides). The entire task is going to take one and a half to two class periods, so I'm anticipating getting through the "sharing posters" phase (bottom of page T-6 in the MARS pdf), then adding in the data tables tomorrow.

Their homework will be to complete the Journey to the Bus Stop activity, including recording and submitting a short screencast to describe their thinking. I again hope they will have the opportunity to start the homework in class and perhaps only have to do the screencast portion outside of class.

Day 2

Since my first day with my Algebra students is a Friday (their second day of school, but Algebra doesn't meet on Thursdays), I sort of feel like Day 2 is my "real" first day with students. My first unit is "Everything Linear", and I want to really hit hard the ideas of relation (and eventually function) and rate of change, while liberally sprinkling in modeling. While it's hard to tell exactly what my students will have had mathematically before me, most of them theoretically will already know how to solve equations, have learned about slope/rate of change, and already done quite a bit of graphing using slope-intercept. (I meet with that incoming 9th grader this Wednesday, so I may have to revisit this statement later this week.)

This day's opener is based on Dan Meyer's 3-Act Sugar Packets. Right now I'm experimenting with Formative and, since I'll be assigning it to my class, I can't link to it so that you can see it. Hopefully these screen shots will give you an idea.

I thought this was an interesting way to start and hopefully immediately engaging. In the past, I've used this as a lesson activity, so I do have some concern that it might be "too much" for an opener. (I also wish Formative allowed a "page break" so that students could enter their estimates, click next, then see the information necessary to solve it exactly; worried they'll scroll down before making estimates.)

Then I decided a great lesson to start with was a Desmos Activity Builder remix of Dan Meyer's Graphing Stories. (FYI - you will be seeing a lot of Desmos and Dan Meyer in subsequent posts.)

I really like how this gets students to think about the relation between two variables in an informal way, yet one that leads to more formal mathematics pretty nicely. Because Desmos recently added the ability to sketch, it fits nicely into Activity Builder. (They are apparently working on the ability to embed videos, right now I just link to them.) I'm reasonably happy with the way this worked out, but am still debating if including all 10 of them is too much. I scaffold the first two, asking them to stop after their sketches so that we can compare everyone's sketches, then turn them loose after that. I think that they'll be able to run with it, but not sure.

Their homework (which hopefully they will get to start on in class - I think I will cut the lesson short if I have to to make sure that happens), is to complete one more graphing story, then record a short screencast describing how they went about coming up with their solution. This will be their first attempt at a "production" screencast (if all goes well they will have practiced on Friday), and I'll make sure to let them know that if they have trouble at first, we'll work through it and that I expect by the end of the week everyone will be able to smoothly make screencasts. (Having the ability to come in on an unscheduled hour will be really helpful here for any students who are really struggling with the screencasts at first.)

This sounds like a great day in my head, but what are your thoughts? Would love to hear feedback, suggested tweaks, or alternatives. (Day 2 Slides)

Sunday, May 29, 2016

Day 1

Our first day of school this year is Thursday, August 18th. My Algebra class doesn't meet on Thursdays, so my first day with them will be Friday, August 19th.

The class starts with announcements over the PA (we meet third period, which is when announcements are scheduled). As they enter the room (I'll greet them at the door) they'll see these slides displayed on the projector. They'll find their seats, listen to the announcements, and hopefully navigate to our class website just fine.

I won't go over Course Expectations (because most of them will hopefully have already read through them), but I will ask if there are any questions. I will then spend just a minute or two on "Fisch Philosophy" in terms of what I want them to get out of the course.

We will then sample all the tech, working through many of the things on the Setup page that they've hopefully already setup, with a big emphasis on helping each other, and generally just getting used to some of the tools we'll be using. While we're doing that, we'll experience a little math along the way, too. (I don't have the sample openers created yet in Kahoot and Formative, nor have I created the sample Activity Builder activity in Desmos, but all of those will be Algebra-related while learning the basics of how the tool works.) We will then create a sample screencast (not Algebra-related, but showing them how to get an image onto their screen that they will need to know for their homework problem each night). If we manage to successfully get through all of this, it will be amazing, but we'll give it a shot.

At the end of class there is a link to "Assignment 0" which is all of the things I suggested they do before school starts, but that is due in a week if they haven't finished some or all of it. Since our first day is a Friday, they'll have a weekend before I'll see them again, and then Monday will be a more "typical" day.

While I wish there was a bit more mathematics on this first day, I'm worried that the tech could be overwhelming so I want to expose them to as much of it as possible right off the bat, have them help each other out, then of course they will see each piece over and over again as we work through lessons each day. Right now, however, with our first class day being on a Friday, this is my best guess of what I'd like to do with this day. I'm still debating whether this is a good idea, or whether I want to introduce one thing at a time over the course of a week or so, so feedback is appreciated.

Day 0

Last time I was teaching Algebra, as well as for my Computer Science classes this past year, I sent an email to the students that were in my classes (and their parents) before the school year even started. I'm going to do that again with Algebra this coming year. (First day of school is August 18th, I'll probably send the email around July 31st.)

The email is an introduction to me and to the class, as well as asks for some information from them. While they can wait until the school year starts to provide me the information, I encourage them to do it ahead of time both to get it done when they have lots of time and so that I can read through the information before school starts. The email links them to the course expectations page on the class website, which will then have a link to a google form for them to "sign off" that they've read it. This allows them to get an idea of my philosophy and how the class is going to work.

I also have them read my About Me, and then write their own and submit it via a Google Form. This gives them a chance to learn a bit about me personally, and for me to learn at list a bit about them personally. I offer them an opportunity (optional) to join our class Remind group (parents can join, too). And then I suggest they go through some setup on their devices (although I will help them with this if they need it once school starts).

I then ask the parents to give me contact info via a Google Form as well as give them a chance to tell me anything they'd like me to know about their student. And then I give both parents and students a recommended, but completely optional, Mindset assignment. My school did a staff read, and then a community read, of Mindset a year ago, but even before that I thought this was a great way - particularly for incoming freshmen - to begin the year. There's no requirement, but I hope most of them at least try session 1 and that some of them go through all the sessions. We'll see.

This accomplishes (hopefully) several things. It allows them to start getting a handle on how my class is going to be, as well as allows me to start getting to know them. It also allows me not to use the first day of class going over rules and procedures, which they get more than enough of. I assure them that, if they don't want to start before school starts, this will be their first assignment and it will be due at the end of the first full week.

Feedback is appreciated.

Thursday, May 26, 2016

Organization, Structure and a Crisis of Confidence

One of the things I struggle with (as most teachers do) is the balance between covering the material I'm supposed to cover and taking the time to make sure students understand the material we are covering at the moment. I have no magic answers for this dilemma, but I try to at least ameliorate it by having a year-long plan and being very organized.

For me, I have to be organized. I'm not good at "winging it", and I need the structure (control?) that comes with having everything very well thought out ahead of time. There are (hopefully) obvious upsides to this, but there are some downsides, too. My personality outside of the classroom tends toward efficiency and getting things done, and I'm constantly fighting that tendency inside the classroom. Not that I don't want to be efficient and get things done inside the classroom as well, but I fear that too often that leads to me "telling" the students what to do instead of them figuring it out. The same with my need for structure and organization. While I think that overall that's very helpful to a good classroom experience, I have to be constantly aware that learning is messy and that I can't let my need for structure and organization override the needs of the actual students in the classroom.

When I'm honest with myself (and I try to be most of the time), this is probably my greatest failing as a teacher. The combination of wanting to be "efficient" and "cover" what I feel to be the most important topics in Algebra 1, along with the need for organization, "routine", and not "winging it", constantly puts me at risk of bulldozing through my lesson no matter what is happening on the student side. I'm also not particularly good at "thinking on my feet", at least in the sense of asking the right question at the right time and subtly guiding students. In my quest to "Be Less Helpful", this is a major sticking point.

This point was reinforced to me a day or two ago when I looked through my Algebra 1 lesson plans from the 2013-14 school year (first semester, second semester). (Quick side note for full context: second semester in 2013-14 had some complicating factors). My first response was, "Hey, these were pretty good." Still lots of room for improvement, and I'm willing to push the envelope a bit more now which will change some things but, overall, I liked a lot of the lessons/activities I used back then. And then I remembered how successful they were (or perhaps more accurately, weren't). Don't get me wrong, I think I did okay, and I don't think the students in my Algebra 1 class learned less than the students in the other Algebra 1 classes in my building, but I also don't think they learned anything close to what I thought they should have.

As I was discussing this with my wife, I eventually articulated what I thought the problem was. "I think the problem is me." I don't say that in a "self-deprecating, please compliment me" fashion, but with honest concern. This is not a new feeling for me, but one I had put aside the last few years as I was out of the classroom completely for a year and then teaching only computer science this year (which was sufficiently new enough for me that I don't have calibrated expectations for myself yet). I know that I want to teach like Dan Meyer, Fawn Nguyen, Robert Kaplinsky, Kate Nowak, Jo Boaler, <fill in your favorite math blogger here>, and I will greedily borrow and modify every good idea they talk about, but my problem isn't necessarily coming up with the ideas anymore, it's the implementation. Many (maybe most) of my lessons are great in the planning stage, but only adequate (or worse) when I implement them. Again, I think this is partly because of my desire for efficiency that leads me to short-circuit student thinking, but also my inclination to be a bit more "laid-back" (for lack of a better term) and let students get whatever they are going to get without pushing it.

This is a real dilemma for me, because I desperately want them to get the insights and understanding that I think these lessons should help them get, yet I apparently lack the ability (conviction?) to push hard enough to make that happen. I write that knowing full well how that's going to come across (not well) but, in the interest of being honest with both myself and anyone reading, I think it's important. I've said this before in various blog comments or Twitter replies, but I think often the problem is not that many math teachers don't see the wisdom in a lot of the ideas voiced by folks like those mentioned above, it's just that we aren't good enough to carry them out. (And, yes, it's very possible I"m just projecting here, but it's my blog so I'll project if I want to.)

Okay, so for whatever it's worth, that's a very long run-up to the ostensible purpose of this post, to describe my initial thoughts around the structure and organization of my Algebra 1 class. Let me briefly lay out what a typical day looks like so that, the above angst notwithstanding, you can give me suggestions for improvement if you'd like.

I like to start class with openers. (Many folks call these warm-ups. This may just be semantics – but I don’t really like the connotation of that. That somehow we’re “warming up” for the real work that’s to come, and that this isn’t that important. I like “opener” better because it feels like it begins the learning for the day, not just prepares you to begin. I’m probably over-thinking that.). Because my Algebra class will be 3rd period this year, class will start with announcements read over the PA system. This is both good and bad. It's bad because while we try to keep announcements short (2-3 minutes), you never know how long they are going to be, so you never know exactly how long class is going to be. It's good, however, because it (theoretically) allows the students to be ready to go (laptops on, logged in, opened to whatever link I've given them for the opener) the instant announcements are over. My current thinking is to use a combination of Kahoots and Desmos Activity Builders.

There's nothing magical about Kahoot (there are others you could choose), it's just an easy way to provide a few multiple-choice type openers in a format that's accessible to students and that they like. I used it with my computer science classes this year and it seemed to accomplish what I wanted with the opener, as well as be a little bit "fun" for students. Some enjoy the mock-competition, and I usually try to throw in at least one humorous or offbeat one, so it starts class off well.

Some days I anticipate wanting an opener that is perhaps a bit more in-depth than Kahoot lends itself to, so my plan at the moment is to build some of my openers as activities within Desmos. I haven't yet created an Activity in Desmos (that will happen as soon as I actually start the specific plans, hopefully within the next week) but, from what I've seen browsing through Activities that others have created, I see a lot of potential in this. This kind of opener would take a bit longer than a Kahoot opener and might blur the line a bit between what an "opener" is and just regular instruction, but we'll see.

After the opener (or conceivably before if it's a longer, Activity Builder one), I'm anticipating "going over" the previous night's homework. As I mentioned briefly, my plan is to usually just assign one homework problem each night, but that the emphasis will be on students not just completing the problem, but explaining it. My idea right now is to have them do a (very short, hopefully 1-3 minutes, max) screencast explaining their thinking as they worked through the problem. Some students will have access to a tablet where they could actually do that in real-time (screencast as they work the problem), but I anticipate most of them will work out the problem on paper, take a picture of it, upload it to Google Drive (docs, or drawings if they want to annotate a bit), then use something like Screencastify to record a quick screencast. (The screencast will be in their Google Drive, in a folder that is automatically shared with me, and I'll have them submit the sharing link to the screencast via a Google Form.)

My thinking is that this really gets them to think much more deeply about the problem, and their own thinking, than simply completing a bunch of problems. I will then pick one to share at the beginning of class the next day to address any questions or misconceptions. I'm still trying to decide between picking one screencast randomly versus previewing and trying to pick one that I find particularly interesting for some reason. I'm leaning toward random for two reasons. First, I'm not sure I'll have the time to preview them to pick the "most interesting" one to share. Second, it provides a little bit of "accountability" (as much as I dislike that word) for students if they know I'll just be randomly picking one. (I only plan to "grade" them - for "sincere completion" -  and enter into the grade book once a week, and I'll pick which of the four days at random.)

After the opener and going over the homework screencast, we will then proceed with the lesson/activity for the day. At the end of the lesson/activity, my hope is that they will actually have class time to start (and perhaps complete) the written portion of the homework problem, just leaving them to do the actual screencast outside of class when there's no background noise (so a relatively short amount of time required to do that).

My concern with this plan, in addition to the ones expressed in the beginning of this post, is if this is too "routine" and could get boring for students. While I think routine is often good for students (they already have 8 or 9 different teachers in a semester at my school, so that's 8-9 different sets of rules and procedures they have to learn), I know that sometimes routine can get too routine. My hope is that the lessons/activities themselves are varied enough, and engaging enough, that any sense of "too much routine" is mitigated.

The one variation to this plan would be on assessment days. As I mentioned previously, my goal is to give relatively frequent, short assessments (think 5-15 minutes, not full class period). What I've done in the past is on days that we are going to have assessments, the assessment takes the place of the opener (and perhaps the going over the homework screencast, depending on timing). My goal is to get good feedback on student progress using the least amount of class time to do it. (As mentioned previously, if students do poorly they will be able to re-assess outside of class as many times as they wish.)

So, that's my initial plan for the organization and structure of my class (with a large helping of angst on the side). I'd love to hear your comments and suggestions.

Wednesday, May 25, 2016

Content and Goals

Everyone plans differently, and I don't think there's one right way to do it. Over the years I've developed a process that seems to work well for me, so I thought I'd share the process I've gone through so far (and will continue to go through as I flesh out the specific lesson plans).

For me, I have to start with the big and then work my way to the small. By that I mean I need to have an overall plan for the entire year first before I start breaking down individual units, then individual topics within those units, and then individual lessons within those topics. I know this is very different from how some folks do this, but I find that I have to do it this way if I want to make sure my students learn the most essential concepts (as I determine them). If I don't look at the entire year first, I'll end up not getting to some concepts I feel are crucial in Algebra 1. (As always, this is a fine line between spending enough time on each topic that they understand it, but not spending too much time so that I don't get to topics that future math classes will assume they've had.)

As I mentioned in a previous post, our district's Algebra 1 course is aligned with the Colorado State Math Standards which, in turn, are aligned with the Common Core State Standards for Math. As I also mentioned in that post, our district has chosen Agile Mind as our online "textbook" resource for Algebra 1 (also for Geometry and Algebra 2). Agile Mind has a nice document (pdf) that maps their scope and sequence to the CCSS-M, and also some instructional notes for teachers that I went through and pulled out the goals and objectives for each unit.

At the top of that document you'll notice a note that says, "Topic order in 15-16: 1-7, 9, 11, 12, 14, 16-20, 8, 10, 13, 15". As mentioned in that previous post, with our Algebra classes only meeting four days a week, we can't possibly "cover" all the topics. So the Algebra folks went through and identified the order they would attempt the topics and see how far they could get. Their goal was at least to get to topic 20 (quadratic formula) and hopefully also come back to 8 (descriptive statistics). I think they had mixed success at achieving that, but that's sort of the "starting place" for my thinking.

I then went through all 20 of the topics (and associated standards) and tried to identify what I thought were the most important concepts in Algebra 1. (Obviously, this is very subjective, so I'd love any feedback you have on my choices.) Looking at my list, and comparing it to the order that the other Algebra teachers followed, my goal is to get at least through Polynomial Operations on my list. If I can touch on Rational Expressions and Special Functions, that will be a bonus.

So that gives me the basic outline for my year. I'm still waiting on some feedback I've asked for from an incoming freshmen about the topics they covered in 8th grade math this year. As I mentioned in that previous post, we have two main feeder middle schools in my district, but perhaps only 70% of my students will come from them because of open enrollment, with the other 30% coming from as many as 25-30 other middle schools (school-wide, obviously not that many just in my one class). But I figure if I can get some good feedback from this incoming student from one of our middle schools, I will at least have a better understanding of what students actually understand coming in (as opposed to what they theoretically have had based on the district curriculum).

My next step (in terms of content) will be to start planning those units, in order, and see where my semester break falls and try to make that a reasonably good breaking point. This can be complicated by the possibility of a common final exam but, in the past, we've had common parts of the final exam but then have been able to tailor it somewhat based on what we've covered, so I'm counting on that.

While students mastering the content is obviously a big part of Algebra 1, content is not my only goal. I also have other goals that, in my opinion, are even more important than the content (I know not everyone will agree). I'm still working on the specifics of this for this year, but I'll start with what I used in Algebra the last time I taught it (2013-14):
Course Goals:
  • Content Goal: Learn the Algebra skills.
  • Habits of Mind Goal: Become better problem solvers by getting better at asking good questions, thinking mathematically and reasoning mathematically.
  • Collaborative Goal: Become better at working together to achieve a common objective.
  • Metacognitive Goal: Learn more about yourself as a learner and use that to become a better learner.
One thing I know I'm going to add in (which I also had in 2013-14, but separate from the goals) is a Mindset goal. Here's the still-very-much-in-progress website for this coming year in Algebra. You'll notice a tab labeled Mindset which has a series of 3 sessions (plus a bonus session) that parents and students can choose to complete if they wish. This is something I will send to them before school starts and recommend that they take the time to complete. Especially for the incoming freshmen (the vast majority of my class), I think this is a great way to set the tone not only for my Algebra class, but also hopefully for their high school career. When I did this back in 2013-14, about 25% of the parents and students self-reported that they completed at least some of the sessions (and really liked them), which I figure is not bad (although I hope perhaps to improve on that this year given my school's emphasis on Mindset this past year). While the sessions will still be optional, I will create a Mindset goal to add to the course goals.

I've also toyed with delineating the 8 Standards for Mathematical Practice as course goals, but I feel that just becomes overwhelming. As you probably saw, I have a tab on the website devoted to those, and I will have posters in the rooms to refer to frequently, so I'm hoping that will allow me to make those an essential part of the course without making my "goals" list too long. Would love feedback on this as well.

I know there are many other goals I could include, but I think this gets to the heart of what I want my students to experience in my Algebra class. I'm still thinking about them, and I will probably at least tweak them (or perhaps even add or substitute) as I work through the more detailed planning this summer, but I think it's a good set of goals to have in mind as I start the planning process.

As always, I would appreciate your feedback to help me make this better.

Tuesday, May 24, 2016

Beliefs, Biases and Compromises

Forgive me for the multiple posts about things other than just lesson planning for Algebra, but I think it's important to lay the groundwork first. In my last post I talked about some of the specifics of my situation, because every school and every classroom is different, and those differences are very important in the planning process. In this post I'm going to talk about what some of my core beliefs are about teaching Algebra (or perhaps some of my biases if you prefer), and then some of the compromises I will inevitably have to make between my beliefs and the reality of my classroom.

If you've read The Fischbowl much over the years, you pretty much know what a lot of my beliefs (and biases) are, but let me summarize some of the most important ones as they relate to planning for Algebra 1 for next year.


  1. I believe that a lot of the courses we currently require - including Algebra - should not be required for every student.
  2. I believe that the specific skills we teach in Algebra are not important for every student to learn, and that standardization is not optimal for learning.
  3. I believe that the justification that it's okay if high school mathematics is sometimes useless and needlessly abstract because kids learn how to "problem solve" in math classes is well-intentioned, but wrong. (If our goal is to teach problem solving, I would suggest that there are more meaningful ways to have kids solve problems than abstract Algebra.)
  4. I believe that much of what we assign for homework is benign at best, and downright harmful at worst. I also believe that if homework is given, it is for exploring and for practice, and therefore is always formative.
  5. I believe that students actively construct their own understanding.
  6. I believe that all assessment should be formative assessment, and that students should be given as many opportunities as possible to demonstrate their learning.
  7. I believe that students should be able to use all of the tools and resources that are available to them, both in the learning process and in the assessing process.
  8. I really like it when my students do things on time, and I think it helps their learning, but I also believe they shouldn't be penalized for "late" work.


  1. Algebra is currently required for all students, and we do have a defined curriculum. Students who leave my Algebra 1 class will go on to someone else's Geometry, Algebra 2, etc. class, and I would be doing them a disservice if I set them up for failure later. Not really any compromise here, just capitulation, as I don't have any control over this.
  2. See #1, students have to take Algebra and I have to teach it. Future teachers are going to expect that I have "covered" certain topics and that students know certain skills. My compromise here will be to emphasize the parts of Algebra 1 that I feel are most important and most useful for kids, and simple expose (or occasionally even skip) those that I don't. This is a tricky line, but one I will try to straddle. Part of what gives me comfort is that most students are not really learning many of these less important (in my opinion, of course) topics even if I spent as much time on them as other teachers might, so it's a false comparison to suggest I would be depriving them. My belief (hope?) is that if I provide them truly meaningful learning experiences, that will serve them better in the long run.
  3. Again, kids have to take and I have to teach Algebra. I do value problem-solving, and certainly having students become better problem-solvers is something I would like to see happen. So while I don't think it's necessary to have kids take math to learn problem solving, since they are taking math, I will try to structure my lessons in such a way that they actually get to problem solve. This is tricky, since it's relatively easy to structure Algebra 1 where kids "solve problems" but don't actually "problem solve."
  4. The reality is I only have them for four days a week, and roughly 130 class periods (some of them shortened) a year, yet I'm supposed to "cover" all of the standards in Algebra 1. That's impossible to do without having them do some work outside of class. (In fact, even with them doing work outside of class, it's impossible to do.) There is also the reality of expectations - from other teachers/administrators, from parents, and even from the students themselves - homework is an expectation for many (all?) of those folks. My compromise is that I will assign one problem for homework each night, it will (hopefully) be more interesting and more in-depth than perhaps a "typical" homework problem in Algebra 1, and I will ask them to explain their thinking thoroughly (more on this in a future post). Homework will be graded on "sincere completion", not correctness.
  5. If students actively construct their own understanding, then I have to structure my class so that they are doing more of the thinking. This is hard for me because, like many teachers, I enjoy explaining, and kids enjoy being explained to too. It's often hard to structure lessons that let students actively construct their understanding that are also successful at the students achieving that understanding. But I'm going to try. My goal is a combination of Gary Stager's "Less us, more them" and Dan Meyer's "Be Less Helpful."
  6. With the exception of the final exam each semester, students will be allowed to re-assess as many times as they want (need) to in order to demonstrate their understanding. There is no "penalty" to their grade for re-assessing. If they ultimately demonstrate that they know the standard, their grade should reflect that. The majority of their grade will be determined by these on-going, formative assessments.
  7. With the possible exception of any "common assessments" I might be required to give, all assessments will be "open Internet". This is going to require me to come up with some really good assessments, so I'm going to need your help. At this point in time, my compromise is going to be that while I want them to be able to use all the resources they would be able to use in a non-school-test setting, and I'm going to allow all technological resources, I will still require them to complete their work individually. In other words, despite my beliefs, I'm not going to allow them to use each other on assessments. (That's my thinking right now, I'd love to be convinced otherwise, but just haven't figured out an effective way to do this.) As a side note, I also want to minimize the time taken for assessments in my class, in order to maximize the time spent learning. So think shorter (5-15 minutes) assessments, not longer (full class period). Conceivably some assessments might take place outside of class time (although I hesitate to ask of more time from my students).
  8. The expectation is that students will do things on time, because that's what's best for their learning. But to the extent that "homework" contributes to their grade (which will be a small percentage), students will not be penalized for "late" work. My compromise here is that when the work becomes "very late", I will perhaps penalize them slightly.
All of this is just "general" philosophical thinking to set the stage for the actual lesson plans to come. It will undoubtedly change as I enter the actual lesson planning process, and likely change again when I'm actually interacting with students, but it at least gives you an idea of where I'm coming from when we start discussing actual lessons.

As always, questions and feedback are welcome (that's the whole point of this blog, remember?).

Monday, May 23, 2016

Constraints and Opportunities

Every school is unique, and every classroom is different, so I wanted to take this post just to lay out some of the "constraints" and "opportunities" of my specific situation for you to keep in mind as we begin this journey together. (See how positive I'm being? I'm assuming you're along for the journey. So unlike me.)

My high school has about 2150 students, with about 90% of those white and generally middle class (although it's important to remember that not all of our students are well-off financially, and our school is slowly, but surely, becoming more diverse). Our schedule is a bit different than many high schools, as we run a variable schedule. It's loosely based on a college schedule, with classes that can meet anywhere from 2 days a week to 5 days a week. We have 6 periods in a day and each period is about 59 minutes long on a regular day. Like most schools, we have a variety of days that are not "regular" in terms of the schedule, including 10 PLC days (2 hour late start), 3-5 assembly days (shortened classes), 12 advisory days (shortened classes), and a variety of testing days (vastly shortened classes or split differently across days). In addition, I will miss at least five days of Algebra myself because I serve on the Board of Trustees for our retirement plan.

Algebra meets four days a week (MTWF for my class) and I expect to have approximately 63 days with them first semester and about 68 second semester. Of course, as mentioned above, not all of those will be full 59-minute class periods, and I'll miss 2-3 each semester due to my PERA commitments. This is somewhat problematic because we are still supposed to cover the same amount of "Algebra" as other schools who typically meet their classes 5 days a week (and, in some schools, for as much as 85 to 90 minutes each day). Time is one of my biggest constraints. While this is true for any teacher, I think it's even more true for my situation.

This also presents an opportunity, however, as freshmen can have up to four "unscheduled" hours each week (out of the 30 possible hours they could be scheduled). Both the median and mode for most freshmen is two unscheduled hours and, because I'm in the classroom only part time, there's a good chance that most of them have at least one unscheduled hour a week that I do. That means they can come in for help, or to re-assess, without having to stay after school or coming in during their lunch (although both of those are options). Even if they don't have an unscheduled hour in common with me, at least one (and usually more than one) math teacher will be available during their unscheduled hours and will help them if they ask (every math teacher but me is located in a math department office, so students can just walk in and ask for help).

My class will likely be 30-35 students. All students at my school have a laptop, either one they bring themselves (a little over 70%) or a chromebook that we provide them, and we have a pretty robust wireless network that supports that (and almost every student has high-speed Internet access at home). My classroom has a mounted LCD projector and a smart board. Most of my students will be freshmen (14 years old here in the U.S.), although it's typical to have 3-5 sophomores who are either taking Algebra again because they weren't successful as freshmen or are perhaps coming from a Learning Support Services Fundamentals of Algebra class. We have a fairly large number of freshmen who are in either Honors Geometry or "regular" Geometry because they took Algebra in 8th grade (and a few in Algebra II and even Trig); my (freshmen) students were in a "regular" 8th grade math class.

Two of the four middle schools in my district are our primary feeders, but about 30% of our students are open-enrolled, which means our students typically come from between 25-30 different middle schools (the two others in our district, from several adjacent districts, and from private schools). In many ways that's nice, but it does make it tough because you can't assume they've all had the same curriculum. The students from our two feeders are aligned with our curriculum, so theoretically are on track in terms of preparation for a common core Algebra class; the other students vary widely. This is another constraint.

Our curriculum is aligned with the Colorado State Standards, which means it is essentially aligned with the Common Core Math Standards. We have an online "textbook" to use as a resource (at least that's how I'll be using it). I have a lot of latitude in terms of how I teach in my classroom, but the expectation is that I'll "cover" essentially the same material as the other Algebra teachers (more on this in my next post). We have a final exam (85 minutes) each semester and, at times in the past, that has been a common (or mostly common) final exam for all Algebra classes. I don't know if that (the common part) will be the case next year or not. My ninth graders will take the PARCC test in the spring, any tenth graders I have will take the PSAT, and if I have any 11th graders they will take the SAT. My students will also take the MAP test once in the fall and once in the spring (two more days of instruction lost). I see this as both a constraint (standardized) and an opportunity (lots of freedom within my classroom to teach how I want).

Students at my school generally want to do well at school and have parents who value education. Having said that, they're still 14-year-olds who may not always think Algebra is the greatest thing ever.

So, that gives you enough background to play along if you'd like to in subsequent posts. I hope you do.

Sunday, May 22, 2016

I'm Going to Have to MTBoS the Sh*t Out of This

Cross-posted from The Fischbowl.

This year I got the opportunity to start a Computer Science program at my school, which ended up meaning I got to teach two semester-long sections of Intro to Computer Science in both the fall and spring semesters (and teaching myself Python last summer). The plan was that we were going to try to hire a real computer science teacher for 2016-17 but, since that didn't happen, I'll be teaching the Intro class again next year, along with an Advanced Python class and a Javascript class (and a colleague will thankfully be teaching a Java class) as we try to grow the program.

None of that preceding paragraph is really relevant to this post, other than to give some context as to why I'm asking for your help. Not that it needs context, because asking for your help is a good thing in and of itself, but I'm hoping to make you feel a little bit sorry for me and guilt you into helping. (Hey, it's worth a shot.) Because in addition to learning some more Python, and teaching myself Javascript, I'll also get the opportunity to teach a section of Algebra 1 again next year.

Now, the good news is, I don't have to teach myself Algebra 1, I sorta, kinda already know Algebra 1. Long-time readers of this blog may remember about 6 years ago when I got the opportunity to teach Algebra 1 after many years of being completely out of the classroom in my role as technology coordinator for my building. At that time I tried to blog my planning and did great for a couple of weeks and then petered out. This time I hope to do better, and to hopefully do a better job of tapping into the online community of teachers to get your help.

Six years ago I experimented with what's now almost universally called the "flipped classroom" (at the time there was still some debate about what to call it). While there are strong opinions on both sides of the flipped debate, I still feel like it was a worthwhile approach for me at the time because it allowed me to free up class time to do better things than I would be able to do otherwise if I had to "cover" the material in class. I was trying to bridge the gap between the expectations of my school and the rest of the math department and where I was hoping to take my Algebra class, and flipping allowed me to do that to some extent.

Well, now it's six years later, and I haven't taught Algebra the last two, and some things have changed. My district has transitioned completely to a common-core based Algebra course, using Agile Mind as the "textbook." But, more importantly, I'm more willing to go even further away from the mainstream (at least what the mainstream is in my building), and the resources available to me are even better, including even more teachers blogging about math, Desmos has gotten even better, and technology in general has gotten easier for students to use in the classroom. I think I can do better than flipping and, while at least some of the lessons/activities I used in class before are still great, I think they can be improved on.

So I'm sitting here planning my summer (last official day of work is this Tuesday) and trying to figure out how best to structure learning a bit more about Python (I have a rough outline for my new advanced course, just need to make sure I know it well enough to teach it), teaching myself Javascript and planning that course, and planning my new-and-improved Algebra class. I'm worried because the easiest thing for me to do is to focus on the computer science stuff that is new to me, and to slack off on the Algebra planning, because I know I can just rely on what I've done before and do an okay job.

But I don't want to do an "okay" job, I want to do a really good job, and take advantage of all these great resources (and my additional willingness to diverge from the traditional in my building). As I was thinking about how to do this, a line from the movie The Martian kept going through my head:
I'm going to have to science the sh*t out of this.
So the way I'm framing planning for Algebra is,
I'm going to have to MTBoS the sh*t out of this.
For the uninitiated, MTBoS stands for the MathTwitterBlogosphere, which is the self-given name of all the math folks who are sharing their thinking, asking questions, challenging each other, and generally discussing ways to improve their math teaching. My hope is twofold: first, I'm going to tap into (borrow/steal) all the wonderful resources the MTBoS has collectively created and, second, that by publicly blogging my planning I will not only encourage feedback from the MTBoS, but guilt myself into not slacking off on the Algebra planning part of my summer.

We'll see how that goes. If you're interested in helping, I would appreciate it if you would follow along with the blog I set up for this (right now the only post is a cross-posting of this one, but beginning on Wednesday I will start in earnest - RSS, Email). Fair warning that there is at least a 50% chance that this will flame out but, if everything goes swimmingly, perhaps this will not only help me tremendously, but serve as a resource for other Algebra 1 teachers.