End of Year Student Evaluations of Me

Previously I posted the mid-year student and parent evaluations of me. At the end of the year I gave a slightly different (and shorter) survey to my students. This was given to them after they completed the final exam, was optional, and it was during finals week, so I only got 20 responses (out of 27 in the class, not too bad). (I didn't give a formal parent survey at the end of the year - not sure why, just didn't get to it, although some parents responded to my final email with some feedback.)

Here are the results from the 20 students who completed the survey (with their names removed).

Overall, I'm reasonably happy with these results. Several students mentioned they felt the pace was a bit too fast, and I would agree with that (the usual problem of too much required curriculum, not enough time - I tried to balance it well, but didn't always succeed).

I'd still like to find a way to get more detailed feedback from students at the end of the year, preferably with a face-to-face conversation as well as an online form. But there just isn't the class time to do that before the final exam, and then it's difficult to convince students to come in on their own time during finals week (or in the summer) and do that.

What are some ways you've tried to get better feedback?

Algorithms, Quadcopters, and the CCSS-M

So, as usual, the end of the school year (and then subsequent visit from my in-laws) ended up leaving not enough time to do my self-assigned homework around #algorithmchat in a timely manner. But, in keeping with my belief that it's more about the learning then the exact date of that learning, here's the results of my thinking.

First, I think my general thinking hasn't changed that much from the original post, where I stated:

algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning

I appreciated the detailed descriptions and explanations of the various algorithms in the Fuson and Beckmann article and they certainly got me thinking. The authors argue that the CCSS-M includes the meaning and sense-making as part of students' development and understanding of algorithms, which I agree with. They also state that in the past the algorithm was often taught without that meaning and sense-making portion, and I think most of us agree that is not a great approach.

The part I still disagree with the CCSS-M (and maybe Fuson and Beckmann as well, I'm not sure) on is the idea of the standard algorithm. I think the crux of this argument boils down to folks who argue for one specific standard algorithm because it is the most "efficient." I would argue that the most efficient way to do most of these calculations is with Siri or Google Glass or Wolfram Alpha. I'm more interested in students understanding the mathematical underpinnings of the algorithm(s) then in being able to quickly apply them. I want them to have number sense and mathematical understanding, but I don't think that necessarily means being able to "efficiently" compute a four digit by four digit multiplication problem by hand.

So, as long as I can change the standard algorithm to a standard algorithm that makes both mathematical sense and is most helpful to that particular student (which, I admit, doesn't flow quite as freely), then I'm good.

As a side note, this TED Talk happened to get posted just as I was trying to compose this blog post.


I think it's interesting in and of itself, but I also found it interesting how often he refers to "algorithms" and "mathematical modeling." I think this shows the power of algorithms, but also the need for our students to understand the algorithms, and also to understand that algorithms are first and foremost developed by humans and are not always set in stone, as when the algorithms appear to "adjust" or "learn" in the flipping sequence.

If our students can be begin to understand that algorithms don't supersede our understanding, but can help enhance it, then I think we're on the right track.

By The Numbers

It's both a fun time of year in high school and a time to reflect. I've had kind of an interesting juxtaposition of a couple of items. We have a couple of students that I know at my school who are graduating and think they want to become teachers (we have a great Teacher Cadet program where they get an opportunity to learn about teaching/learning as well as a mini-student-teaching opportunity).

In many ways I think this is great - we must be doing something right if we have bright, amazing students thinking they want to become educators. But the second item gives me pause, so I thought I'd take just a few minutes to share some numbers that I've come across recently.

From the Colorado School Finance Project:

1. Colorado’s teachers made $6,400 less per year than the national average.
   
   
2. When adjusted for inflation, Colorado’s teachers made $5,200 less than a Colorado teacher in 1992-93, a 9.6% decrease. During the same time period, the national average teacher salary increased by over 2%.
   
   
3. In 2010-11 Colorado’s teachers were paid at the national average level five years ago.
   
   
4. If Colorado put the same effort toward K-12 as it did in 1992, there would be $1.2 billion more dollars for K-12 per year.
   
   
5. If Colorado put the national average effort toward K-12, there would be $2.248 billion more dollars for K-12 per year.

Okay, so that's not terribly encouraging, but that's Colorado in general. What about my school district? Let's look at beginning teacher salaries.

1. Let's compare the beginning teacher salary in my district in 1991 with today. When adjusted for inflation (Bureau of Labor Statistics), beginning teacher salaries would have to increase by 9.5% just to break even with 1991.
   
   
2. When you take into consideration the increase in employee contributions for insurance premiums, that changes to an 11.3% increase just to stay even with 1991.

Okay, so that's not terribly encouraging either. But we have a fairly traditional salary schedule in my district (although a committee is about to meet to consider changes to that), so the beginning teacher salary doesn't reflect the built-in raises a teacher that's been in the district since 1991 has received. (By the way, I picked 1991 because that's when I entered the district.) When you look at my salary, I certainly have seen increases that put me comfortably ahead of inflation.

Well, until you look at the last five years, in which case I've lost 6.6%(and even more when you include increases in insurance premiums). This happened at the same time that I, and every other teacher I know, has had their responsibilities and expectations increase dramatically. My case is somewhat different because I wasn't - and am not - a full-time classroom teacher, but I still think it's instructive. Five years ago I was the full-time technology coordinator for my building. Today I am still the full-time technology coordinator for my building, but I also teach one section of Algebra. We have significantly more technology in the building than five years ago, plus that one section of Algebra added at least 15 hours to my work week. All while taking a pay cut.

Now, I want to be clear, this is not about my salary. I've even gone on record in my district with the somewhat blasphemous statement that I think I get paid enough, especially when compared with younger teachers. (Having said that, in case anyone from my district is reading this, that does not mean I would turn down a hefty raise :-). My district has a good relationship with its teachers and, while I don't always agree with the financial decisions they make, they have generally done a good job in a difficult time. What I think this is about reflects a larger issue in America today - the decline of the middle class.

I would say teachers are pretty representative of the middle class in the United States. What the above trends show is that, should those trends continue, teachers will no longer be able to achieve middle class status (unless they marry well). And I wonder what that says about what we value in this country?

Which brings me back to those two graduating seniors I know. They are both about to spend a fair amount of money on a college education. They are both very bright and very successful and could choose careers in a wide variety of areas. I really want them to choose to become teachers. My problem is I'm just not sure I should encourage them to do so.

And that makes me sad.

OK, Teacher

Jeff Utecht has a post worth reading on his Google I/O Reflection:

If you haven’t seen the demonstration of what is coming to the Chrome Browser than you need to watch this. How does this change the classroom?

The entire search presentation starts at 2:03:41 of this video, and it's worth 15 minutes of your time. If 15 minutes is too long, then just watch the 7 minutes of Johanna Wright's part at 2:11:29.

So, "OK, Google" is interesting and, combined with the other announcements by Google, may truly change "search as we know it" as they claim. But, as Jeff asked, I'm particularly interested in how it might change how we look at our classrooms. If our technology is becoming more and more responsive to our individual needs and requests, shouldn't our schools?

"OK, Teacher, I want to know more about . . ."

Ninth Grade CCSS Algebra 1 Scope and Sequence

I had some requests on Twitter to share this out, so here goes.

As many of you know, in addition to my tech duties I teach one section of ninth grade Algebra (occasionally some sophomores in there as well). Colorado has adopted the Common Core State Standards so our math curriculum - like most folks' - will be transitioning to match the new standards over the next couple of years.

If you've read this blog before you know I have concerns with the Common Core. Nevertheless, it's what we are tasked with so - while still advocating for something different - I'm attempting to get my head around the scope and sequence for Algebra 1 next year. As I looked into it I was surprised to not find very many examples that have already been created, so I decided to try to take our current scope and sequence and see how well I could "translate" it into CCSS.

Before I link to that document, I think it's important to remember that everyone's school and situation is different. There will be local variables and constraints that will make each school's implementation look different. For example, here is some information about my school that affects what I've done so far.

1. My algebra class meets for 59 minute periods four days a week (MTWF for me). When all is said and done, I see my students for approximately 126 class periods in a year, with about 110 of those the full 59 minutes and the rest anywhere from 20 to 40 minutes depending on the day (PLC days, assembly days, ACT testing days, state testing days, etc.). Because this is less time than in many Algebra classes, we do not typically cover quite as many of the "advanced" topics that some Algebra classes do. We have a six period day and freshmen (which is the vast majority of students in our Algebra classes) have between one and four unscheduled periods a week.
   
   
2. We are divided into semesters and, while most students have the same Algebra teacher first and second semester, not all do, so we attempt to have a clearly defined break at semester (winter break, we start in August and end in May) and all the Algebra teachers have "covered" the same material by then. So you'll see the year divided up into two 18-week semesters.
   
   
3. Our class sizes in Algebra are typically between 27 and 33. Not saying that's either good or bad, but it gives you information to compare to your classroom. We have 2150 students total in our school and the equivalent of 13 full-time math teachers (plus me teaching one section), and (this year at least) seven of those teachers that teach at least one section of Algebra (with 13 total sections). Whatever we develop has to meet the needs of the district, the school, those seven teachers, and the rest of the math department, and be both "backward" and "forward compatible." (And, oh yeah, it should meet the needs of the kids, but hopefully you get my point.)
   
   
4. We have four middle schools in our district, two of which are our primary feeder schools. They are also transitioning to the Common Core 6-8 Math standards, and should complete that transition next year. But we also have roughly 30% of our students open enrolled - from public schools in surrounding districts and from many private/religious schools (over thirty total feeder schools each year). So while we more-or-less know what the students from our middle schools have experienced in math class, we have about 30% of our students that come from widely varying backgrounds.
   
   
5. We currently use the 2007 edition of McDougal Littell's Algebra book. As we fully transition to the Common Core by fall of 2014, we may be able to purchase new materials (assuming they exist by then) but, until then (at least), we'll be using our existing book. (I'm campaigning not to purchase a new textbook, but that's a discussion for another blog post.)
   
   
6. We are a suburban school serving a primarily middle class clientele. The community values education and our school is generally considered a very good school.

Okay, that's probably more than you wanted, but hopefully it will address some questions that people might have.

So I took our existing scope and sequence, matched it with the ninth grade CCSS Math Standards, and came up with this still very much in draft Google Doc. Feel free to copy, edit, add comments, do whatever (appropriate) things you'd like to that document. It really is rough draft thinking to give us something to build on this summer as we try to translate that into actual lesson plans. I'd love to hear your thoughts (on the doc or in the comments to this post).

Chaos Theory, Twitter and the Common Core

Yeah, I'm pretty sure that's a blog post title that hasn't been used before. And won't ever be again.

I've read a little bit about chaos theory, although I don't pretend to really understand it. My very simplified understanding of it is that very small changes in initial conditions can result in very different outcomes of a dynamic system (often illustrated by "a butterfly flapping its wings in China can change the weather in Denver" - although I don't think that quite captures it). There are other conditions that have to be present (topological mixing - which I sort of get, and its periodic orbit must be dense - which I really don't), but it boils down to

When the present determines the future, but the approximate present does not approximately determine the future.

At some point today a fleeting thought crossed my brain and, as so often happens, I decided to record it here on the blog, even though I know it opens me up to ridicule do to my lack of real understanding of chaos theory. So be it. The thought was something along the lines of

What effect does something like Twitter have on complex, dynamic systems?

Note that it doesn't have to be Twitter, but any of the synchronous and asynchronous ways we have today of communicating, collaborating, and generally "topologically mixing." But Twitter is the one that came to mind, so I'm going with it. If dynamic systems with nearly identical initial conditions can result in very different outcomes, then can these various ways of "mixing" - how they are present and how they are applied - both constitute and amplify a change in initial conditions?

So what in the world does this have to do with Common Core? Probably nothing, but here is the premise of Common Core:

The Common Core State Standards Initiative is a state-led effort that established a single set of clear educational standards for kindergarten through 12th grade in English language arts and mathematics that states voluntarily adopt.

. . . High standards that are consistent across states provide teachers, parents, and students with a set of clear expectations that are aligned to the expectations in college and careers. The standards promote equity by ensuring all students, no matter where they live, are well prepared with the skills and knowledge necessary to collaborate and compete with their peers in the United States and abroad.

So the follow-up thought that came to my mind today was something like:

By trying to standardize on a common core curriculum to assure equality of preparation, aren't we ignoring what we know about dynamic systems?

Namely, that there's no possible way to standardize enough to prevent wildly different outcomes. We have so many variables in the inputs (background of the students, background of the teachers, the effectiveness of the HVAC system, . . .), and so many variables along the way, that we can't possibly use a controlled curriculum to pre-determine the outcomes.

So if the basic premise of Common Core ignores what we know about complex systems, where does that leave us? Perhaps jumping out of the Core (err, car). (Or maybe just talking to myself, both are possible.)

Algorithm Nation

As many of you are aware, I'm the "Director of Technology" (read, "building level technology coordinator) for my high school, but I also teach one section of Algebra. As a result I often find myself drawn into the math conversations happening on Twitter and on folks' blogs. This weekend I somehow ended up deciding to join a "reading group" around an article (pdf) titled "Standard Algorithms in the Common Core State Standards" from the Fall/Winter issue of the NCSM Journal.

Basically the conversation on Twitter began with some folks describing ways in which algorithms got in the way of learning and understanding mathematics. Then other folks pushed back a bit and asked if perhaps there was some value in algorithms. Christopher Danielson then pointed us toward the article in NCSM and suggested a "reading group" to discuss the issue. Feel free to "join" the group, which basically means you read the article and discuss it on Twitter or blogs using the hashtag #algorithmchat.

I thought I'd take a moment to put down my thoughts about algorithms in mathematics before I've read and begun discussing the article, just so I/we could see if my thoughts change after the discussion. While this is certainly a topic I have thought about, I also have not done a "deep dive" into the research or people's thoughts about algorithms. Right now I think I come down squarely in the middle (if that's possible). I agree that there are many times when algorithms have gotten in the way of learning and understanding mathematics. That we try to get our students to master the algorithms as quickly as possible so that they can be "efficient", even if it's at the expense of understanding. Then later we complain when they don't seem to have what we would consider basic number sense.

On the other hand, I don't see that as an inherent problem with algorithms, just the way that we sometimes deploy them. I do see algorithms as a valuable tool in working with mathematics (and other content and problems, for that matter). I think as long as we focus on understanding before (and while) we use algorithms, they can be very valuable in ways at making our thinking and processing "efficient" in order to then move on to thinking about more advanced mathematics, as well as to apply the mathematics.

So I guess my position right now, before this discussion, is that algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning. Feel free to join our reading group and contribute your own thoughts (on Twitter, on a blog, heck, even face-to-face if you have someone to talk to in your own building).

Running for PERA Board of Trustees

Forgive the brief departure from the regular content of this blog - this post is just for any Colorado teachers who might be reading this. If you are a current public school teacher who is an active member of the school division of PERA (our retirement plan), you should have received a ballot for the Board of Trustees Election (or should receive it shortly). You might recognize a name on there.

Ballots must be postmarked by May 31st. I'd appreciate your support.

Important Note: When the notice came from PERA about this election, I interpreted it as two open seats. It turns out there are two seats up for election, but both incumbents are running for reelection. I have nothing against those incumbents, so feel free to support them if you wish.

What I Learned in College (two days ago)

I was at the Colorado School of Mines on Saturday for a Science Olympiad competition my daughter was participating in. By all accounts Mines is a good school and we've had many graduates of the high school I teach at continue their education there and love it, and it's a beautiful campus.

In many ways, Science Olympiad is like a track or swim meet, a whole lot of waiting around until your event begins. In my daughter's case, she was in two events, right in the middle of the day, only one of which I was allowed to watch. So I had a spare eight hours or so to fill. Naturally I brought some books to read and a laptop, figuring I could hop on their wifi and get some work done. Conveniently School of Mines does have a guest network setup where they give you a guest login credential for temporary access. The only problem - they wouldn't give us the login credentials.

According to the person we talked to, it would be a "security risk" and a "liability issue" if they allowed us to use their network. Now, I don't know the details of their network, but I was a bit surprised by this, given that my public, K-12 school district has a guest wireless network available to anyone with no login credentials needed. Here they are hosting thirty teams from around the state, grades 6-12, and their parents, and the way you say "welcome" to these prospective students (this was Science Olympiad, after all, at a math/science/engineering college) is "we don't trust you to use our network?" (And, of course, the students were pretty busy, it would've been mostly parents and the teacher-sponsors using the network.)

But, I was polite, and returned to the classroom that was our home base . . . where I noticed that the teacher computer was turned on and logged into the network. Not only was it logged into the network, but it was also logged into the professor's home directory on the server and his Mines email account. So I proceeded to periodically use that machine throughout the day to check email and do a little bit of work.

What I briefly considered, but then refrained from doing, was emailing the CIO of the university (and copying the President) - from the professor's email account, of course - and pointing out that perhaps giving guest wireless access to prospective students and their parents was not the security or liability issue they should be most worried about. (And, no, I did not read any of the professor's email - although I did notice he had over 4000 unread messages . . .)

The second thing I learned at college on Saturday is in a slightly different vein. When I launched the browser on that teacher machine the professor apparently has it set to automatically open the tabs that were previously open. Here are screenshots of the three tabs that opened:

One was in the professor's Google Drive account, open to a PDF of a research article. The second was open to Wolfram Alpha, with a graph of an interesting square root function. And the third was open to a Wikipedia article about the Munsell Color System.

I don't want to read too much into which tabs were open, because I lack the context of knowing what the professor was doing with the information. But I think asking some questions about these open tabs would make for an interesting discussion in your school, and particularly in your high school math department.

For example, one might ask, "What implications might there be for your high school math curriculum (and classes) when a math professor at a high-end science and engineering school like the Colorado School of Mines has Google Drive, Wolfram Alpha, and Wikipedia open in his web browser?"

Or maybe you'd phrase it slightly differently, something along the lines of, "For the very small portion of your high school students who are going on to major in math/science/engineering in college, what should you be doing in your classes to prepare them for college math classes that utilize Google Drive, Wolfram Alpha, and Wikipedia?"

I imagine you can think of a few more questions as well, but I think it just might be a discussion worth having. As is a discussion surrounding, "If you have wireless, but you don't let anyone use it, is it really there?"

Are You Ready For Glass-nost?

Every once in a while when I'm presenting I say something interesting. (Hard to believe, I know, but it happens.) I was recently presenting and said something I hadn't planned on saying, but after saying it, I think it might be worth thinking about a bit more.

I was talking about the changes in how we access information, from books to text-based search to voice recognition search to image/location based search to Wolfram Alpha search, etc. And then I said something along the lines of:

Are you ready for all your students to enter your classroom wearing Google Glass?

There are lots of layers to that question, most of which I wasn't thinking of when I said it, but I think it's worth asking yourself - and your colleagues - some variation of that question. Are you ready for Google Glass-nost, the increased openness and transparency of a connected world? When you are endlessly debating CCSS, or your curriculum, or whether to go with a paper-based planner for your students, are you really thinking about a Glass-enabled world? Are you ready for your students to have a heads-up display with instant access to all the world's knowledge - and the ability to instantly connect with most of the world's people?

And, yes, I'm aware that not everyone is excited about the ramifications of Google Glass, and I think there are legitimate concerns. But that doesn't change the fact that we're basically on the verge of having the Star Trek Communicator, yet our schools are laser-focused on achieving a relatively fixed set of knowledge.

So, try this thought experiment. Pretend that next fall all of your students show up the first day of school with Google Glass. Are you ready?