Category Archives: Uncategorized

Computer Science Week 1

This is the first year I have ever taught computer science!  I took my fair share of computer science classes in college but that was a long time ago!  My school sent me to an AP Institute this summer which was great and really helped me start to conceptualize how I wanted my course to go, but I foresee some false starts and chaos this year!

Our text is Java Software Solution by Lewis, Loftus, and Cocking, but I’m not sure how much I am going to use it.  We haven’t really gotten to that point of the course, yet (see below) and I’m considering using something like Blue Pelican Java or one of the other free textbooks available online.  At the moment I’m a little overwhelmed by choice.

In the spirit of my philosophy of working on big ideas before getting into the inevitable minutia that comes with starting a class, we have spent time this week working on less textbook dependent things.  This has been tricky because our school computer lab isn’t set up yet, so I have had to burn more time than I would like downloading JDK’s, IDE’s, and importing JARs.  But by today we were finally able to run some code!

The first day of class students spent playing with lightbot.  I was introduced to lightbot at my AP institute and it seemed like a friendly way to get students exposed to some of the thought processes and concepts of object oriented programming.  I tried to explicitly connect some of the ideas in lightbot to object oriented methods, but I was a lot clumsier about it than I would have liked.

Otherwise this week we have been working with Karel J. Robot.  I wish I had been able to spend the first few days in the computer lab, because we spent a fair amount of time trying to get things up and running and that’s time I think could have been better spent, but when we were finally able to get things really going today I felt like there was a good pay off.  I like that students are exposed to real code that’s more complex than something like “Hello World”, have to focus in on the relevant parts, and make changes.  I also like that they can immediately run their code and get visual feedback (we don’t do a whole lot with GUI otherwise in the course).  I also like that they have to interact with a class (UrRobot, etc) without actually seeing the code for it, just knowing what methods it has and what they do.  Already they are itching to write new methods to help the robot learn to do things it can’t already!  Also they love getting to rename their robot.

We will spend at least one more day with Karel next week.  At some point I will have to pull the chute and start with a more traditional course sequence.  Many of my students bring their laptops with them to class but some will only have the school chrombooks in class, so I plan to use tools like and codingbat as our primarily in class tools, and students will have to work on more complex projects outside of class (and we will reserve the computer lab as necessary).  I hope this is a workable model!  I also have a few students who aren’t interested in AP credit who would rather learn a language like Python than Java, and I’m trying to work with these students in getting something they find worthwhile out of the class.

We shall see what this year holds!  I expect a lot of challenges, frustrations, and set backs but also a lot of growth, and that’s very important to me.

AP Stat Week 1

I love teaching AP Statistics.  I love the content, but it’s also the course I’ve taught the longest.  I feel like it’s the class I teach the best.  In AP Statistics I often impress myself, in other classes that is less often the case :).

This year in AP Statistics I’m trying to move towards using simulation more throughout the course to support the concepts of inference, rather than just tacking it on as it’s own section during probability.  The simulation section has always felt like a weird not connected topic to me, which I don’t like, and it has so much potential I’m not making use of right now.  I think this will be a positive change.

We have had three different bell schedules at school this week.  Tuesday and Wednesday students were dismissed early after we ran each class for 30 minutes with no lunch.  Even with two planning periods these days were hectic!  I always try to start my courses off by spending the first few days doing what I feel like is the major work of the course, rather than going over the syllabus or reviewing material from previous classes.  I like the tone this sets and the message it sends about what is important in this class.  Then after a week or so we back up and kind of start from the beginning.

In statistics this year (and last year) I started off gathering some basic data on heights and looking at distributions.  I originally got this activity from a PDF on engaging activities for AP Statistics.  It does a great job of getting students engaged immediately, there’s a little bit of a mystery to it, and it gathers data that students are interested in (because it’s about them!) without it being too cumbersome or time consuming to collect the data.  After they make their post its I ask them to make some predictions about what set of guesses they think will be “best,” which usually leads to a good discussion about what best means in this context.  Usually someone says best is closest to the true average height (so already we’re getting that idea of a fixed but unknown true value), but then we discuss how that makes sense for a single observation but not a group of observations.

Then we make “dot plots” out of them on the board.  I have them do this themselves and it gets them interacting with each other.  They almost always run into some problems (how to scale it, what to do about the person who wrote an average height of 580″, how to deal with decimal guesses, etc) that we can discuss as a class.  Then I lead a discussion using the dot plots on things like distributions, shape, center, spread, precision vs. accuracy, bias, etc.

Usually the data is very cooperative about becoming more precise (less variable) as the guesses go on, and generally the guesses after the first group are fairly accurate.

Last we put their actual heights into the lists on the calculator and I show them how to do 1-var stats and discuss what the different values it produces mean, which ones we care about, etc.

This year this took the two 30 minute periods.

On the third day we moved into the Westvaco case study.  This is originally from Statistics in Action but I got it from Statsmonkey.  This activity does several things I really like.  It has some controversy that students get to have an opinion about (there either was or was not age discrimination) with no clear cut answer.  It has a largish but not too large data set for them to work with, and then it follows up by using some simulation to introduce some of the logic of inference.

The first day I gave them the case study and let them go to town.  They were making a lot of dot plots and finding various ways to process/color code the data.  The second day I gave them the data in a google sheet and showed them how to do some basic sorting and calculating in spreadsheets.  I have found my students generally have no idea how to use a spreadsheet so I try to introduce the basics early and often.  I also showed them how to use statkey to make dot plots.

Eventually I will have them take the work they’ve done on this case study, pick a side on the age discrimination issue, and make a statistical argument (1-2 pages) to support their argument, and I want them to use graphs and other appropriate tools to support their argument.  With statkey and google sheets they can hopefully just copy and paste these graphs in.  I will mainly be looking for them to have an argument that uses statistical evidence and clear writing when I grade their assignments, since they are still novices even at basic statistical methods.

Next week we will spend a day or two doing the simulation with Westvaco.  We will use index cards and keep our simulations physical, for now.  I find this helps slow things down and lets them focus on the main idea (the simulation) vs getting bogged down and distracted by simulating with technology.  Later in the course we will do simulations with google sheets and XLMiner.

After that comes Stats Modeling the World chapters 1-3!

A new year!

We are wrapping up our first week of school today.  I want to take some time and reflect on how it’s gone and remind future me why I did things the way I did.

I got some new tables this year.  They’re round.  They’re great.  When the math teacher gets round tables everyone talks about it so that’s been fun.  I think they fit in my room a lot better than the rectangular tables I had last year.  Those tables each sat two people so I needed 10 of them in my room.  They also weren’t very flexible both because of crowding and because they were really too narrow to sit people on both sides or on the ends.  Late in the year I stuck them together and made groups of four, but that always meant someone’s back was to the board when I was using the projector.

The round tables are much more flexible.  They can easily seat 4-6 students, and four students can sit there and all be clustered on one side to face the projector, if necessary.  Students have space when they’re just sitting and then more students can easily come join a table for group work, or I can pull up a chair and sit with them.IMG_1211.JPG

I also got rid of my big corner desk this year and now I have to standing desks (one in the front and one in the back).  I did this partially for my health (I was having some repetitive stress and nerve pain issues) but also because I didn’t like the way having my desk drew my to go sit down at it during class.  I felt like I was giving my students work and then going to my fort.  If they came up to me for help there was this big awkward barrier.  Now I’m on my feet more, which encourages me to move around the room more, and if I want to sit down I just sit at one of the tables with them.  I try to foster a “we’re all in this together” mentality, and I think these structural changes to the classroom support that.

Side note, if you want to use a standing desk you must must get an anti-fatigue mat.  They’re not very expensive (mine was about $40 on amazon) and they make a world of difference.  Right now I only have one but I want a second one for the other desk!

Also check out all the great cubbies and stuff on this podium/standing desk.IMG_1210.JPG

I want to blog some more about some changes I made to assessment and the lessons I chose for the first days of class, so that is to come!




Welcome!  It has been a long time since I blogged.  A very long time!  I had kids, and then I left the classroom for a few years, and then when I came back it took me practically a whole year to get back to where I was.  Now that I’m starting my second year back in the classroom I am starting to feel like I know what I’m doing, again.  I have gotten back on twitter and man has the twitter community blown up while I was gone.  There’s so much great stuff happening there.  Sometimes I find myself frustrated by the 140 character limit, though, and sometimes I want to be able to get my own thoughts out there as more of a monologue than a dialogue.  I also want to invest more in reflecting on my lessons and choices in the classroom, as well as recording more systematically what I did and how it went for future use.

So that’s what brings me back to blogging 🙂  My goal is to blog about once a week, but I’m sure it will sometimes be more and sometimes be less.  A week, to me, is a good length of time to both have seen how things develop and sink in with students, without having so much to say that I forget things or feel overwhelmed.

I’m teaching Computer Science and Statistics this year, so that will be a lot of what I blog about.  I’m also presenting some workshops in October about math in the media and visual mathematics in the high school classroom, so I expect those topics will also come up!  Probably a fair amount of general education interest will work it’s way in, too.

Academic "Hot Spots"

Lately, in the spirit of the new year, I have been trying to get my life in order. I like to think I have good ideas, but I have terrible follow through, partially because I am *so* profoundly disorganized. I’m one of those folks who has stacks of papers all over their classroom, often loses things, and leaves their clean laundry in the basket for weeks and weeks (usually until I’ve used enough of it that the basket is empty again.) I don’t like living this way, and I think it sets a terrible example for my students, so I’ve really been working on it. One website I ran across is It’s a little hokey, but some of the ideas have been really helpful, and I think I’m driving my husband and my custodians less crazy.

This is not just a confessional, though, I think two of the ideas from FlyLady are definitely applicable to my classroom. While they aren’t exactly revolutionary, they are new to me, and I would, of course, love to hear some feedback from anyone who has any!

The first is “you can do anything for 15 minutes.” This has really been helping out a lot at home and at school. At the very beginning of my planning period and as soon as I get home I set a timer for 15 minutes and do something I usually procrastinate about. Usually this means grading papers or putting away laundry. I want to use my experience as an example and encourage my students that they, too, can do anything for 15 minutes. I bought some timers for my classroom (I especially like this super-cool one which turns green, then yellow, then red as time runs out. Note that it is NOT the learning resources one, which I have found to be an overpriced piece of junk.) Especially with my freshman geometry class, I want to use this both as an individual intervention and a class wide attitude towards practice and cumulative review. I can picture students bringing in their own timers to use (and maybe having a competition for the silliest one) and using them to motivate themselves for practice. Like anything else, I can’t over use it, but I’m hoping it will be effective for at least some of the students and give them a tool that I desperately could’ve used in high school and college.

In conjunction with the 15 minute strategy I want to adopt a kind of centers approach with something called academic hot spots. FlyLady talks about hot spots in your classroom or house, places where junk gathers or you tend to collect mess and clutter, and setting aside time or taking advantage of extra time to address these areas. Academic hot spots would be areas, either prerequisite or current content, where I know students struggle. Of the of my head, that would mean rational expressions, radical expressions, solving for an unknown, solving absolute value equations and inequalities, piece wise defined functions, etc. Ironically, that list would remain virtually the same regardless of whether we’re talking about my geometry class or calculus class!

Below is an example of something I might use as a “solving equations” hot spot activity. It’s kind of a combination of notes and practice (I am recycling something I used as guided notes in the past, so it’s not perfect.)
Solving Equations

What I’m thinking write now is that these “centers” would be set up around the room all of the time, and whenever we had a little extra time, needed a break from what we were currently working on, etc, we would take time to “put out our fires,” or address academic hot spots. Students could choose (with guidance if necessary) what hot spots they wanted to work on. I also want to give students a chance to suggest topics for hot spots, and the hot spots could change throughout the semester (good opportunity for review and remediation.)

Like I said, these are not exactly new ideas, but I’ve never used them before. Anyone have any experience with anything like these they’d like to share, or any ideas I can add to the mix above?

Differentiated Testing

This idea was presented at the last NCCTM conference. I didn’t go to the session, but one of my colleagues did. He has agreed to collude with me on my idea for interactive notebooks next semester if I will collude with him on this project. I actually really like the idea, and I’m thinking about implementing it in all three of my preps next semester (not just the geometry class we agreed to cooperate on.) The idea is just a rough sketch at the moment, I would appreciate any feedback you had to offer!

So it works like this. Each test is divided into three parts, roughly equivalent to developing, proficient, and advanced. Students know it is divided into three parts and the three parts are clearly labeled (although maybe using less confrontational terms than what I used above, I don’t know.)

The idea is that a student can select to answer only the “easier” questions and know they got an 80, but might feel bolder to try some of the more difficult questions if they knew they had that 80 in their pocket. A more advanced student could skip the easier questions and do only the more advanced sections to demonstrate their knowledge.

See sample below.
DIff Test Example

This is very much just an early attempt at this. I took most of the problems pretty directly out of Prentice Hall’s Geometry book (the one with the creepy bee on it) and I”m not totally convinced I’ve broken them down correctly into the sections. I need to spend more time with my state standards and unpacking them into what is absolutely essential (that would all go in section I) what is important for students who I expect to be successful in a course like precalculus (that would all go in section II) and some tasks that are really going to be a stretch (section III.) I would expect the sections to typically get shorter as they go along.

One thing I want to avoid is varying the difficulty level by just ratcheting up the algebra. That is harder, and it has it’s place, but I would like the differentiation to happen, primarily, on a more conceptual level. Of course, those tasks are much more difficult to write!

Problems I think of immediately:

1. Difficult to design.
2. What if there’s a disconnect between the sections, i.e. a student solves advanced problems well but can’t solve the easier problems (I suspect I can avoid this if the test is designed properly, but still.)
3. Does solving a more advanced task like an application really demonstrate the ability to answer straightforward knowledge questions?

There are also lots of other problems I haven’t thought of, and I’m hoping you will, but I’m intrigued enough by the idea to try it.

What do you think? Please feel free to leave any feedback or ideas below, or tweet me @seetur.

First Day of School!

Today was my first day of school! It went pretty well. I tried something new, this year, and rather than diving right into the specific course curriculum, I taught a general course on Polya’s problem solving methods. I pulled some problems from “What’s Math Got to do With It” and gave my students a handout on Polya’s problem solving method from from Math Hombre.

I don’t think I explained Polya’s method very well, I just kind of went through the steps and I think my kids probably thought it was pretty lame, but I’m hoping that if I keep hitting it all year it will start to sink in. These kinds of things always seem so profound when I read about them, and then so lame when I go to say them in front of the class! Oi! 🙂

In my discrete class (our first unit is statistics and where data comes from) I finished up by having them read an article about texting while driving, and had them use an AVID strategy called “marking the text.” They are supposed to wrap that up for HW if they didn’t in class and we’ll discuss it tomorrow. I have several other texting news articles for them to read, too (all courtesy of chance news) and we’ll talk about what the data is, where it comes from, and compare and contrast the data in the various articles.

Discrete Math . . .

Drives me crazy. The math is not the issue. I like the math, and, frankly, it’s not that hard. What drives me crazy is how few coping skills the students in that class really have. That became starkly apparent when I assigned this project. They have been working on it in class the last few days. You would think after spending a full six weeks talking about graphical and numerical summaries of data they would at least know what data was, but you would be wrong.

This project required students to find three sets of data: a numerical set, categorical set, and a set they thought was normally distributed. Once they found them, they had to do a series of things like make a graphical display, calculate a numerical summary, etc. The hard part has been finding the actual data. They try to google stuff like “categorical data set” to find it. I encouraged them to pick a topic they thought was interesting, think of an example in that topic that would give them the right kind of data, and then google that instead. that helped some. Some of them are still floundering trying to find data, and the project is due tomorrow! Some of them don’t even understand that their numerical data set should basically be a list of numbers. They are downloading all kinds of tables and then wondering how to make a histogram. It has left me shaking my head wondering where I went wrong.

This project seems simple, but it has revealed a lot of misunderstandings my students have. It has me seriously rethinking how I will teach this unit if I teach the course again next year (God help me.)

Discrete Math First Six Weeks Project

Exploring Function

after spending six weeks pulling teeth with my precalculus students trying to get them to actually think about functions, rather than just parotting phrases like “domain is input, range is output,” we top everything off with this project. The whole idea of this project is to get students to analyze the graphs of functions, discussing their domain and range, intervals where they are positive and negative, where their combinations are positive and negative, etc. Students are encouraged to work from the graph of the function rather than the equation, and to that end I try to use screwy equations they aren’t very comfortable with. They can use whatever method they want to come up with the initial answers, they may graph the composition on their calculator to answer questions about it’s domain and range, for example, but then they have to justify that answer based on the two original functions.

We spend a lot of time analyzing graphs of functions in this chapter, we cover most of the aspects of functions from their graphs, only (my kids are already pretty good at most of the plug and chug algebra answers) to try to break them of this idea that graphs are somehow subordinate to equations. Every year, though, the answers to this project are absolutely abhorrent. I try to remind myself that it is more about the process than the final project. One of these years I’ll get around to assigning something similar towards the end of the semester to see if they do any better.

First Six Weeks Project


It always amazes me how my students get all the way to precalculus with such an underdeveloped sense of function. I often hear teacher’s complain about how their students can’t deal with fractions, or solve equations, but I find it much more alarming that they don’t have a basic understanding of domain, range, and function.

Sure, they can rattle off some basic facts about domain being x’s and range being y’s, but how much do they really understand about the role they play? Do you want to find out? Are you sure? If you do, try this:

Hand your students two graphs on the same coordinate plane, one f and one g. They can be pretty basic. It is best if they have some easily identifiable domain and range.

As them to identify the domain and range of both graphs (this is pretty easy.) Now, ask them to evaluate something like f(2) using the graph. Many of them wont’ know what that means. They will ask for the equation. It get’s better. Ask them where f(x) > 0. Ask them where f(x)=0 and what f(0) are. Ask them what (f + g)(2) is. Ask them what the domain of (f+g)(x) is.

For the clincher, ask them what the domain of f(g(x)) is. Don’t give them the equations. Make them figure it out from the graph. Start talking to them about getting the range of the inner function to fit in the domain of the outer function, and watch their eyes glaze over.

Last of all, when you really want to stump even your best kids, ask them where f(g(x))=0. Whoa.

These kidns of basic questions, which involve no algebra at all, will get your kids (and you) thinking more than you ever have about domain, range, and function.