Teaching: My Retrospective

Okay, I’m rolling along on my task of drawing clear lines of demarcation between my particular brand of squish and traditional progressive education (heh–traditional progressive. Get it?). First up was my new no homework policy.

I then decided to take on sitting my kids in groups (as opposed to group work), which led me to look back at some old post, which forced me to look back at my practice over the years, and that’s been a trip. So much of a trip that I decided to do the retrospective first.

The introspection kicked off when I reread one of the first posts I ever wrote on this site, over 3 years ago, halfway through my third year of teaching. Some key observations:

  1. I focused almost entirely on classwork, even then. The essay doesn’t even mention homework which, at that time, I assigned in much the way I describe in my last essay.
  2. At that time, the school I worked at used a traditional schedule of 60 minute classes, so the 3 day span per lesson is about two days at my current school. Additional evidence I was focused primarily on what kids learned in class, although as I said, my original homework policy goes back even further than this post.
  3. Here’s a real change. Me on low ability students three years ago: lowabilstds3yrs
    I’m so cheered to realize how much I’ve improved. I had good student engagement back then, but in rereading this I can remember how many students I had to nudge endlessly, how I had to constantly pick up pencils and hand them to kids to get them to work. Recall I was teaching algebra and geometry, and had just begun what is now my bread and butter class of Algebra 2. So my experience at the time of writing those words was with a lower level of math class, which will always mean lower engagement. Nonetheless, that simple paragraphs reminds me of the struggles I had to get total engagement. I’ve come a long way. Yay, me.

  4. Interesting to see my off-hand mention of EDI. No one seeing my teaching would think of me as using the direct instruction mode, but in fact I always, at some point, give kids specific, explicit instructions on the concept at hand.
  5. While I talked about differentiation and my need to challenge top students, I have actually moved away from different assessments for different students. At that time, I was just three months of teaching out from year two, all-algebra I-all-the-time, and I basically taught 4 different classes. I’d tentatively planned on continuing this approach, but learned that year (and confirmed in later years) that this wouldn’t work for any class but algebra I.

I wrote this post on January 8, 2012, at almost exactly the same time I began an experiment that utterly transformed my teaching. I speak, of course, of Modeling Linear Equations, which I’m amazed to realize I wrote just one week after the “How I Teach” post. So shortly after I began this blog and described my teaching method, I started on a path that took my existing teaching approach–which was pretty good, I think–and gave it a form and shape that has allowed me to grow and progress even further.

I haven’t really read this post in over two years—I tend to link in Modeling Linear Equations, Part 3, written a year later (two years ago today!), when I’d realized how much my teaching had changed. So reading the original is instructive. I talk about the Christmas Mull, something that stands very large in my memory but don’t remember quite as described here:


The part that’s consistent with my memory: Christmas 2011, I was depressed by the dismal finals in my three algebra II classes. In the first semester, I had gone through all of linear and quadratic equations, including complex numbers, at a rate considerably slower than two colleagues also teaching the course. Yet the kids remembered next to nothing. Every single person failed the multiple choice test–the top students had around half right. I had experienced knowledge fall-offs in algebra and geometry, but nothing that had so sublimely illustrated how much time I’d wasted in three months. So I came out of the Christmas break determined to reteach linear and quadratic equations, because to continue on teaching more advanced topics with these numbers was purely insane. And I wasn’t just going to reteach, but come up with an entirely different, less structured approach that allowed my students to use their own understanding of real-life situations.

What I hadn’t remembered until reading this closely was my rationale for ignoring the regular curriculum requrements. At the time, Algebra 2 was considered a “terminal” class; students weren’t expected to take another course in the college-prep sequence. This has changed, of course–these days, algebra 2/trig is, if anything, experiencing a fall-off in favor of a full year of each course. But at the time, I justified my decision to go off-curriculum based on the student needs. These students’ primary concern, whether they knew it or not, was what happened to them in college. How much remediation were they going to need? Could the best of them escape any remedial work and go straight onto credit bearing courses? This, of course, still remains my priority–I’d just forgotten how linked it was to my initial decision to try something new.

Also interesting that I described this approach by the specific method I used for linear equations–using “inherent math ability”. That’s not how I describe my approach these days, but I can see the germination of the idea. At the time I wrote this, I had no idea I would go beyond linear equations and use this approach consistently throughout my instruction.

I think the best description I’ve come up with for my approach is modified instructivist, which comes in one of two forms: “highly structured instructivist discovery, and classroom discussions with lots of student involvement”.

As for the latter: I don’t lecture, with or without powerpoints. When I do explanations, they are classroom discussions, and you can see this demonstrated in all my pedagogy posts. However, I am constantly migrating my classroom discussions to structured discovery.

What’s structured discovery? Imagine a teacher and students on a cliff, with a beach below. There’s a path, but it’s not visible.

In a traditional lecture or classroom discussion, the teacher shows them the path and leads them down to the beach.

In a discovery class, the teacher doesn’t even tell them there’s a path or even a beach. In fact, to the discovery/reform teacher, it doesn’t matter whether there’s a path or not—the kids will all find their own way down. Or maybe they’ll just find some really cool flowers and stop to examine their biology. Or maybe they’ll just kick back and have a picnic. It’s all good, in reform math. (sez the skeptic)

In what I call structured discovery, the kids are given a series of tasks that use their existing knowledge base and find the path themselves. They may not yet know there’s a beach. They may not know what the path means. But they will find the path and recognize it as a consistent finding that makes them go “hmm”. In some cases, an interesting finding. In other cases, just something they can see and understand.

Sometimes the path they’ve found is the concept–for example, modeling linear equations or exponential functions, or finding gravity in projectile motion problems.

In other cases, the model just introduces an inevitable observation that leads to the new concept. For example, I teach my kids about function operations when we do linear equations–adding and subtracting are good models for simple profit and loss applications.

So I kick off quadratics by asking my students to multiply linear functions, which they can see clearly as an extension of adding and subtracting them. This is an activity they can start off cold, with no intro (I haven’t written it up yet). I designed this because parabolas just don’t have a natural “real life” model other than area, which gets kind of boring. Plus, I need to cover function operations anyway, so hey, synergy. In any event, the kids are seeing an extension of a concept they already know (function operations) and seeing a new graph form consistently emerge. Then we can talk about factors (the zeros) and realize that we are looking at products of two lines. Could a parabola exist without being a product of two lines? Well, this is algebra 2 so they are fully aware that parabolas don’t have to have zeros. But what does that mean in terms of multiplying lines being factors of parabolas? Well, they must not have factors. So are all parabolas the product of two lines? And we go from there.

Understand that my classes still have lots of practice time where kids just factor equations and graph parabolas, learn about the different forms, and so on. But rather than just saying “now we’ll do this new thing called a parabola”, I give them a task that builds on their existing work and leads them into the new equation type. I don’t define the path. But nor do I let them go off on their own. I give them something to do that looks kind of random, but is in fact a path.

And all of this came from the results of the Great Christmas Mull. The previous Christmas had been productive, too–it’s when I came up with differentiated instruction for my algebra class.

So what can I say about my teaching, 5.5 years in? What’s consistent, what’s changed?

  1. I never lectured. I always explained, with increasing emphasis on classroom discussion.

  2. I have always been focused on student work during class, emphasizing demonstrated test ability above everything, and minimizing (or now eliminating) homework.
  3. I have always tried to move the student needle at all ability levels, from the no-hopers to the strugglers to the average achievers to the top-tier thinkers. I’m not always successful, but that’s consistently my stated priority.
  4. I have always designed my own curriculum and assessments.

  5. My teaching was transformed Christmas of 2011, when I realized I could introduce and teach topics using existing knowledge, forcing students to engage immediately with the material and start “doing” right away, increasing engagement and understanding. I have evolved from a teacher who mostly explains first to a teacher who only occasionally explains first. And that is a huge change that takes a lot of work.
  6. The observer might think that this change makes my classes student-centered, but I disagree. My classes are definitely teacher-centered, and let’s be clear, I’m the star of my teaching movie.
  7. Thanks also to the Great Christmas Mull, I’ve become far less concerned about curriculum coverage than I was in my first two years of teaching.
  8. I have always been a teacher who values explanation. It’s the heart of my teaching. I’ll explain through discussion or demonstration, but I’m not a reformer letting kids “construct” the meaning of math. I’m there to tell them what it all means.

I have plenty of development areas ahead. I’m working on tossing in the occasional open-ended instruction, just to see if I can come up with ideas that don’t waste hours and have some interesting learning objectives. I still have many concepts waiting to be converted to a “path to the beach”. And I’m now teaching something other than math, which gives me new challenges and more opportunities to see how to construct those paths without running off the cliff.


About educationrealist

18 responses to “Teaching: My Retrospective

  • Jason

    Just stumbled onto your site… Redirected from a comment you posted on another site of a guy writing about the non-education jobs of those holding a major in education. Very well written response.

    Your site is great, well written, and interesting subjects. I’m looking forward to reading more of your posts.

    Elem teacher in CA – possibly switching to JH or HS soon

  • Phillipmarlowe2terry

    “The observer might think that this change makes my classes student-centered,”
    Hey, considering that’s the big thing for Charlotte Danielson and FFT (very, very big here in Maryland, especially Prince George’s County), so long as they think that, or atleast check it out like that, you are on the path to be rated “highly effective.”

  • Roger Sweeny

    What is EDI?

    • educationrealist

      Explicit Direct Instruction. It was making a comeback before Common Core, briefly.

      • Roger Sweeny

        Thanks. Is there any technical, or generally agreed on, distinction between Explicit Direct Instruction, and direct instruction, and Zig Englemann’s Direct Instruction?

      • educationrealist

        EDI is kind of a systematized version of steps. Englemann, as I understand it, takes all agency from the teacher, has scripted responses and everything. Direct Instruction is just the practice of telling a student exactly what to do, rather than let them figure it out. But that’s a bit misleading. Every teacher, at some point, tells their students the procedure, unless they are insanely hard-core reform.. So for example, I use direct instruction, but I do it after an illustrative discovery. Others would only use direct instruction.

  • Ben Heisler

    Absolutely intriguing, educationrealist. You must definitely be the star of your own teaching movie. It’s really unfortunate that you weren’t cast for the sequel of “Good Will Hunting” so that we could see you break down in front of a shrink and explain why you have so much deep-seated animosity for famous Korean math teachers who are the real deal while you’re still here pining away about why a bunch of duds in your remedial math class don’t understand basic Algebra.

  • Lagertha

    yeah, he is SO annoying…and like, whaaa?…bragging about banging someone’s wife/gf in a Mercedes? like, eeewwww…bringing up movie plots in some ersatz way to embarrass/stalk Ed? Is Ben Heisler trying to make all of us discussing education( kind a’ booooring, btw) in the USA on this blog to think he has something constructive to add to the discussion? Or, is he just into shocking people with vile stuff and freaking us out? If he has a vendetta with Ed, well, do it face to face…not involving thousands of people. By, the way, Heisler, for a supposed teacher/tutor you make a lot of grammatical and spelling errors.

    Dude, did you really have to put that image into my mind about banging someone’s woman in “your” Benz? or threatening to throw yourself off of a bridge because you drank too much booze? that is just stupid crazy, or you need help. You need to get a grip, or just STFU and go away.

    • educationrealist

      His next two comments were unprintable, so I unapproved them and spammed them. Unless there’s something wrong with WordPress’s mechanisms, he won’t be back.

      • Lagertha

        – good…extreme with this anger…a nutter. After you delete all his posts (good idea since his rants might bother newcomers for future discussions – it’s YOUR blog,) delete mine…disturbed people scare me.

      • educationrealist

        I think I removed all the ugly ones, didn’t I?

      • Lagertha

        well, I would still jettison the ones from “SAT is corrupt…” since that is when he begins to go off the rails – I just think it’s your blog and he is going postal on you about something else…and, pls, get rid of mine where I just let him have it. I’m usually never that mad…but he reminded me of X boyfriends that would drunk-dial me back in the 80’s. Plus, I try to avoid “crazy,” and prefer to delete all comments dealing with someone who sounds crazy/violent. Thanks.

  • Peter Lund

    Parabolas have a model as satellite dishes and other kinds of focusing mirrors, such as in head lights.

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