How I Fail

I fail the potential of my assessments continuously.

I disaggregate them to such an extent that I can recall, even months down the line, that Alex confused adjacent with opposite in trigonometry, that Suzanne added before she multiplied in the order of operations, and that Derek thought 2x + 3 was 5x.

Several students came within an inch of mastering “sine/cosine/tangent” last week. I had a list. I knew how to remediate their weaknesses but I carried that list into class with me last week and I carried it out again having done nothing.

I don’t know how to make time for this, how to structure my class so that our momentum is forward-going, so that every student has something challenging on her desk, so that I can take some time to remediate the right skills with the right students.

I am a pretty-good marksman too hurried to load his rifle.

[BTW: I post the test questions on the next opener. Most kids run through the problem like it’s the first time they’ve seen ’em. I know which students to talk to and about which concepts. Halfway through I pass back their tests and they compare their work on the openers to the work on their tests. This will do for a start.]

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.


  1. Dan, have you experimented in collaborative pedagogical practices? Instead of you being the sole provider of knowledge, why not (since you know your students so well) group or pair up the students so that those who know something can teach it to those who don’t.

  2. I’ve become convinced that there are two mechanisms in play here.

    One is that your kids have too wide a skills distribution. In my district a seventh grade class can have kids with a 4 year spread in abilities. This means you’re laser beam lesson misses most kids. Result? Your life is remediation. This one’s out of your control as it is the product of antiquated and arbitrary placement policy.

    The other mechanism is that a standard classroom/curriculum/toolset is not equipped for heterogeneous groupings. Public education is all about teaching the median child (which doesn’t exist). Couple mechanism one with mechanism two and you have teacher as one armed paper hanger.

    In a nutshell, you are delivered kids in September with very wide standard deviation and tools with a very narrow one.

    My approach to dealing with this (cause I’m in the very same place) is to build a hybrid delivery, partly online, partly in the classroom. My hope is that the online piece widens my delivery distribution by allowing repeated exposure, hints, collaboration, with a reduced amount of 1:1 interaction.

  3. Actually, maybe this is another thread hijack, you could build the online piece once for a district, county, state, region, or country ( depending on your tolerance for group grope) and be done with it. Then the one armed paper hangers of the world could say “Go to link help_with_factors tonight and we’ll conference tomorrow”

    Put simply, we need to leverage technology to provide the tools to teachers that let them maximize quality interactions.

  4. This is one situation where to some extent I would just move on. Not to leave those who still can’t get the concept in the dust, but after the initial tries those who still have trouble with it as a separate entity are usually better served with it in context.

    As you go on, if some of them still need notes on prior concepts, wean them off slowly. The idea here is for them to realize on their own it would be a REALLY GOOD idea to have sine/cosine/tangent memorized.

    Then when they’re ready, toss the original assessment back at them and see how they do.

  5. TheInfamousJ

    June 11, 2008 - 6:53 am -

    I second collaborative pedagogical practices as a differentiation tool.

    I also second online activities to aid in remediation. I could point you to a bunch for Chemistry, but since you teach math I am a bit stumped except to say that the math teachers at my school (all two of them :)) use google >> “Geometry regents” to find whatever link it is that they are looking for at the time. And I do not teach in New York.

    For me, I use slideshare, create presentations and then narrate them, in much the way that you narrated a presentation for your sub the day you were absent. I further include instructions to my students to pause the show and attempt the problem and then work with me to check how they did. I don’t have much up yet (more of it is in google videos, but I’m migrating it to Slideshare) but here is an example of what I am talking about.

    I do not use powerpoints in the classroom, normally.

  6. @Tarmo, we’re talking about a dating algorithm for education, I guess. Something where the students who have achieved mastery help those who haven’t. Does anyone already have an effective algorithm for matching and then re-matching?

    Even as I gain time, I lose it, because those students won’t remediate anywhere near as quickly as I can. Which, I guess, sounds like more of the same “sage on the stage” self-absorption but it isn’t.

    The online component is tempting, if only because I have some passable a/v skills, and I build most of my lessons around a digital structure. But how well does that sort of thing scale? The time involved sounds prohibitive.

  7. TheInfamousJ

    June 11, 2008 - 4:59 pm -

    Does anyone already have an effective algorithm for matching and then re-matching?

    I have three practice problems that I have students do on their own. Not guided practice, which comes after modeling but truly independent practice. And I make them HARD.

    I set the students loose on them. And when someone thinks that they’ve got all three, they get to show me their answers. Right or wrong, we have a verbal conference about why they used the approach that they used. If it turns out to be an “oops” with regard to the way they punched numbers into the calculator, I point that out. If it is due to misunderstanding, I try to guide them in the right direction.

    If they get the right answer, I call out to the class as a whole, “Bernard had achieved expert level on the concept of Combinatorics! His brain is now yours to pick. Put it to work for you.” Hands start to raise all over the classroom for folks who wish to pick Bernard’s brain. Not only do they have the self-awareness that they could use extra help, but they are also aware enough to know that they need to hear another voice/perspective/take on the material or skill.

    Of course, all of this would be worthless without my first week of class where I review data with them that shows that peer teaching (aka collaborative pedagogical practices) is an efficient means of studying. I then do a lesson on efficiency (same output but less time, greater output if same time) to show them how this is ideal. Then I ask who wants to put in more hours for lesser learning. No hands, usually.

    Then we also have a heart-to-heart discussion about the benefits of learning from a variety of sources and how each other are a variety of sources.

    I know how to set up this classroom culture where students are their own advocates for these pairings, and the L3s (what my district calls those who learn most quickly) want to have their brains picked and take responsibility for helping their classmates understand the material. And this was my first year using it and it was a huge success. I just need to spend my summer reflecting on it to be able to identify the specific concrete steps involved.

    But I hope what I’ve given you is helpful. If it isn’t, feel free to pick my brain (I made a funny :) based on my previous typings) at the email address provided.

  8. @TheInfamousJ That sounds like an awesome setup in your classroom. How do you get the students to teach each other rather than tell one another the answer?

    @Dan One online option is to create screencasts using CamStudio (or similar) and some sort of tablet input. I’m lucky enough to have a school-provided tablet and I have created screencast movies that are available on our school portal. When students need to remediate a specific skill they watch the 3 minute clip, either at home or at school. The downside, up to this point, is that it is always the same problem. I’m hoping to create a larger library of movies from which to pick and choose.

    As for the scalability, I’ve found that all of my students (grades 8 – 11) are benefiting from the screencasts that I made specifically for my algebra unit in grade 8.

    The next stage (which connects the tech option to the collaborative pedagogy) is to have the students create screencasts for skills that they have mastered, or even as an assessment to show that they have mastered the skills.

  9. @Clint H – I do a very similar thing. From day one, I respond to kids questions/answers/statements with questions such as, “How do you know you’re right?” “What allows you to make that statement?” “Walk us through your thinking” (okay, that one isn’t a question.). The kids pick up on it. By the end of first quarter, my freshmen were getting pretty good at asking these questions of one another.

    By the end of the year, they rocked.

  10. TheInfamousJ has a pretty nice approach to connecting pupils for peer teaching.

    Other methods are the Jigsaw method (just google for it), which is an excellent group work method for dealing with freeloaders who usually don’t participate in the work very much.

    The Progressive Inquiry method is another method, which focuses on knowledge building in small groups. It’s especially suited for situations when the goal is to gain deep understanding of the subject area, and not so well for rote learning.

    There are some other methods as well listed in LeMill for collaboration:
    – feel free to add your own descriptions into LeMill, or improve the existing ones.

  11. Dan-
    While I do know your position on giving homework, couldn’t you schedule some flexible time at the end of a class where you focus on remediation of skills with a certain group while other students who don’t need the help work independently on new HW? Or perhaps it could just be a review guide of things that will be on an upcoming assessment.

    Maybe this could be a weekly or unit driven block of time, say every Wednesday, where 1 group works on a review sheet while others get your individual attention?

    Just a thought-

    Also, your blog is amazing. Have you read anything of late about “Disruptive innovation” in the classroom by Clayton Christensen? I’m about 60 pgs in in his new book. The reviews said his big prediction was that over half of classroom instruction in high schools will be done online within 15 years or so…..


  12. TheInfamousJ

    June 12, 2008 - 9:45 am -

    That sounds like an awesome setup in your classroom. How do you get the students to teach each other rather than tell one another the answer?

    It helps to watch them like a hawk in the beginning of the year. In general, it is the same students who are quick on the uptake of the material so once you get them on the right track, they’ll stay there. And those who become my peer teachers later on in the year (I’ve had a surprising handful of those in each class) will usually peer tutor as others had been doing.

    So I watch them, I go with them to their new groupings, I listen in. And when I hear them just giving away the answer I stop the session. I remind all at the table that the goal here is for everyone to have the “Feeling of Win” (I picked up a bit of their video game terminology but it seems to work) that comes with learning a concept and that being handed the answer actually results in a “Feeling of Lose”. And on top of that, I point out to my peer teachers that they, themselves, are being cheated. “Didn’t you struggle with this concept and have to think your way through it?” I’ll ask, “And then you are just going to give it away for free? Even I am not that generous.”

    On top of that, I model what I’d like them to do. I never answer questions directly. One of my biggest pet peeves when I taught at the university level was how often a student would cleverly reword, “Please give me the answer?” I learned that somewhat evasive helpful hints, would answer a concern without reinforcing the student’s ability to game the system.

    I usually answer questions with questions. Or I give “hints”. And if I’m asked a question from a struggling student my first question is, “Please take me through your thought process so that I can see where you are coming from.” “Why did you do [x]?” “Are you sure?” “Are you sure that you are using all the clues from the problem to craft your game plan, here?” “I’ll give you a hint, there is a very important word in the problem statement itself that you are ignoring.”

    My students seem to parrot that behavior. We teach as we are taught, no?

  13. Hey, look, last day of school, my mind’s just not in it right now, but I can still recognize one of the most valuable comment threads of this blog’s history. I’ll be checking back up in this one in the fall.

    Thanks, team.

  14. I agree with Jason. There are some people who are motivated to learn a concept when it becomes apparent to them that the norm in the group is that you know that concept. You are always open to helping them and in your case (and mine) assessing them again on the old more baseline topic. When they look around and see that everyone else is just using the new skill from the last unit, they start to use the skill. In fact often this learner in my classroom has been very resourceful about getting themselves the help they need to become proficient. In some sense you are providing motivation by moving on.

  15. Man, this blog is getting better by the moment. I just yesterday thought about changing my previous “every student does own work” into a more group-oriented style of working.

    My idea is basically to assign groups, and every week I’ll give the groups assignments to be handed in. Every member of a group is responsible for answering one of the excercises in the assignment, so they can’t freeload, and the group score on the assignment is given to every member of it. So, a “good” student would (in my mind) be willing to help “weaker” students in order to get as good a score as possible.

    The risk of the good student doing all the work is of course still present, but I would think that everyone in the group still benefits as opposed to a system where everyone does their own work. For some reason, my students have not been very group-minded previously. Something about the Finnish school system maybe, I couldn’ t say.