You See The Problem, Right?

This is true:

It is May. Aaron has attended 20% of my classes this year. His grade is a C+.

This scenario is uncomplicated but it illustrates precisely the philosophical chasm between me and my colleagues (local, national, maybe international, too – who knows) and how we teach math.

[Update: I’m a little less coy in the comments.]

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


  1. Here, Aaron would generally be held back and held back, never getting access to math challenging enough to require his efforts.

    What a waste of everybody’s time. How detrimental to the formation of good study habits.

    And the chasm is NOT an international one, I think.

  2. (rats, the trademark didn’t come out the way that I wanted….) (I wasn’t trying to rename your blog)

  3. Your approach is so solid, I and gleaned a few Ideas about HW and i’m all over skills based assessment, but being a history teacher there are so many terms to master I foresee difficulty….any thoughts on how to make it work??

  4. What kills me is all the “standards-based” programming that I see and have been involved in that still has a major seat-time requirement. How much of seat-time, do you think, is an assumption about learning versus an internalization of the idea that, while parents are at work, kids need someone to look after them?

    And what, do you reckon, was Aaron up to when he wasn’t in class? I suspect something that he thought, rightly or wrongly, was more important that being in the room with you. (No offense.)

  5. I’ve come to believe that grade level groupings are disasterous.

    There should only be one thing that determines what lesson a student gets today and that is his/her readiness to receive it, i.e. does that student have enough mastered ‘dots’ to connect to this new material.

    If the answer is yes, deliver it irrespective of age, grade, ed plans, etc. I believe technology can enable this kind of delivery model and it is being stymied by a 19th century delivery model.

  6. Does your school come with an attendance policy?

    Any teachers w/ similar attendance but full pay every week?

  7. At my school, peer grouping is seen as a way to keep kids in school. I teach grade 8, in the middle school and kids can fail classes in 7th and pass through, and then the situation can repeat itself in 8th “they will be less likely to drop out later if they stay with their peers.”

    Does anyone else find this situation? Does research warrant this?

    It creates this huge glut of failures in grade 9, as 9th grade they won’t be pushed through w/o passing.

  8. I’ll admit to being old-school, but I have a difficult time with grading that allows for 20% attendance and a “C+” grade. Maybe it’s that Woody Allen saying: 90% of success is showing up. Many schools have no credit policies after 10 absences for whatever reason during a semester, which can be evaluated individually through an appeal process. There is something to this.

    On the notion of flunking kids, the data is pretty clear that repeating a grade more than once is negative on learning and increases drop-out chances significantly. I did quite a bit of research on this topic when I was a Jr. High principal. We used the Light’s Retention Scale at 7th grade.

    The problem is one that Dan’s assessment / grading strategy works to address — much of the standard grade is based upon compliance, not learning. On the other hand, I think it’s possible to go too far the other way. I think Ken’s comment on full pay for a teacher who doesn’t show up (but maybe gets good results on student assessment) is at least interesting.

  9. These are interesting interpretations. I left the end a bit open, but I hadn’t realized it was this open.

    Aaron’s situation is tragic and, indeed, for a lot of the reasons mentioned (somehow I’m drawing a paycheck even though I only teach him one day out of five; whatever my school’s attendance policy, it clearly doesn’t have teeth enough for Aaron; my teaching is pretty irrelevant to his success here; etc.) but one tragedy dwarfs the others:

    He is enrolled in my remedial math class.

    Obviously, I would claim this but I’m pretty much blameless here. Because here is the chasm.

    Most math teachers, incl. Aaron’s grade eight math teacher, weight some combination of a) homework, b) notetaking, c) attendance, d) behavior (thinly disguised as “participation”) into a student’s final grade

    Me, I chase one metric at the expense of all others: a) what the students knows.

    I’m not gonna claim I find it exactly. I am constantly tuning this system, asking better, harder, more focused questions, but after four years I’m confident I haven’t wrecked a kid like Aaron, a kid who knows so much but who didn’t play the game, nor have I passed along a kid who wasn’t ready but who knew how to float along with the tide.

    The party icebreaker question is this: what do you do with a student who can demonstrate mastery of every standard on the list but has a) completed no homework, b) completed no classwork, c) shown up only enough days to avoid expulsion.

    Four years into this job and the answer, to me, is obvious and exciting.

  10. If a student can show up one day a week and pull a C+, then obviously he is in the wrong class.

    If he is not working to master the content, and can then show mastery (on some level), then obviously he has already learned this and did a heckuva job playing ‘dumb’ for his previous teacher or he missed 4/5ths of his math assessments last year without making them up.

    One can assume from your comment, Dan, that you do not include homework, classwork, participation, or attendance when determining his grade is a C+? So, here’s my question: how do you go from 1 – 5 on concept quizzes to a grade of C+? Do you consider each concept/skill worth 5 points and take an average? Do you count the number of concepts mastered and have some handy conversion chart? Don’t get me wrong, I like this method of assessment (and use a bastardized version in my grade 8 class), but how do you go from metric to the other?

    And the answer to your icebreaker question: you get Aaron out of remedial math into something that will challenge and, hopefully, engage him.

  11. A Swedish highschool teacher speaking.

    In the Swedish school system the grade is supposed to be decided upon what knowledge the student have shown. How he came to that knowledge has nothing to do with the grade. If the student only shows up rarely but manages to show all the required knowledge at those few moment he/she could get the highest grade. If the student is disrespectful and cuss out his/her teacher shouldn’t effect the grade.

    In some subjects it is hard or even impossible to show mastery with poor attendance (like a foreign languages class or the lab part of chemistry ) but it is never the attendance in itself that decides the grade. Some teachers have hard to accept this but the law is very clear.


  12. It sounds like Aaron has figured out your system, unfortunately the rest of Aaron’s teachers probably don’t assess in that manner.

    The policy over here is that if a child shows “mastery” of the material, then that child will move on to the next grade level. But, what is “mastery?” Is it an A, C+, or just barely passing? Regardless, they move on anyway.

    Aaron might possibly move on with a D-, so my question is, why not miss more days and do the bare minimum?

    Final thought: What happens with the kids who miss 1 out of 5 days and aren’t even close to passing your subject (S.S.), but are passing what your district “really counts” (math and language arts)?

  13. The real kick in the teeth here is that this is a controversial subject after having “standards-based” reform shoved down our throats for almost 20 years. If you actually believe in “standards,” this is a no-brainer.

  14. Is this the same scenario as if someone went to 20% of SAT prep classes and got an 1100 or went to 20% of law school and passed the bar? No one would take those results away from the student.

    I guess the question is whether someone’s score should be based purely on a test or include other factors like attendance. I think there are other ways to communicate a student’s work habits or attendance patterns than muddling them in with specific subject grades. For example, I can’t imagine a great letter of recommendation being written for someone who misses 80% of class.

  15. My district has an attendance policy that would automatically fail this learner. Even if he could demonstrate mastery of the topic, he would earn an F because of credit.

    For my school, because we are on a block schedule, that means an F after 4 (on the 5th) unverified absence! Luckily I had none of these last semester (that 5 absence rule is per semester) but my wife has had learners fail because of that, even though they could demonstrate that they learned the material.

    It does rub me the wrong way that we are supposed to be teaching to mastery and the standards, and then we fail a learner simply because they skipped some classes.

    Disrespectful = maybe. But if the learner knows the material, they know the material. Like someone else said, it should be a no brainer.

  16. There are a couple ways of looking at this:

    First: “Aaron has earned a C+” — no problem — a student earned a C+

    Second: “Aaron attended 20% of my classes” — unless this attendance issue manifested itself with a spate of skipped classes starting in February, if an attendance issue is going to be “solved” the solution needs to start in October. Knowing what I know of you, Dan, I’m assuming that you are omitting details in your blog post intentionally, as a rhetorical device intended to highlight the different corners of this situation. However, if attendance and grades are related, then they need to be clearly related from the beginning of the course. But I know that’s not what you’re getting at.

    If the classroom is a place someone goes to learn (as opposed to do) something, then there really isn’t a problem here, at least in the context of your particular class.

    There is, of course, an enormous problem here, in that a student’s mis-placement by last years teacher did this student an enormous disservice. And this is the main problem here: a lack of flexibility in scheduling and curriculum.

    But, as Tom Hoffman said earlier, for people who actually believe in standards, this is a no-brainer.



  17. Maybe it’s that Woody Allen saying: 90 percent of success is showing up. Many schools have no credit policies after 10 absences for whatever reason during a semester, which can be evaluated individually through an appeal process. There is something to this.

    Agreed. School was never really intended to actually teach any content — we always knew that content will be forgotten. School was intended to prepare students for the workplace.

    Aaron, in the workplace, would be fired. Aaron, in school, should be flunked.

  18. Actually, grading based on attendance is against CA ed. code. Attendance cannot be a factor in reaching a student’s grade. Now, missing work due to poor attendance can, but attendance itself cannot. The grade received is to be based on the degree of mastery of content/standards/skills.

    Benjamin, where did you get the notion that “school was intended to prepare students for the workplace”? And that “school was never really intended to actually teach any content”? I’ve never read or heard that before and both claims sound at odds with the purpose of public education as I know it (though I don’t have a source for my ideas, either).

    I see “college prep” all over the place, though. And I aced some classes in college that I attended less frequently than Aaron.

  19. To Benjamin – may I ask for clarification of your last statement? That is, do you mean that if Aaron has a traditional 9-to-5 job, Monday-Friday, he would be fired?

    It sort of seems to me that the 21st century has more and more non-traditional sorts of careers where 9-to-5/M-F is not the norm. So if Aaron becomes a web designer and does his best work at 2:00 a.m. but rarely darkens the doorstep of a *regular* office, he can still be quite successful. If I hire a web designer, or architect, or just about any other creative sort of person, I don’t know that I care too much about what hours s/he keeps, do I? Sure, they need to show up for critical meetings (and apparently Aaron has shown up for enough of Dan’s quizzes to get a C+) but otherwise, I’m not really going to look over their shoulders each weekday to see what they’re doing.

  20. @Benjamin – If I can sell as many insurance policies in one day as you can in 5 days, why would I be fired? If I can paint the same house in one day that takes you 5 days, why would I be fired? If I can deliver the same number of papers in one hour that takes you 5 hours, why would I be fired?

    If you were the employer, wouldn’t you want to keep the person who was five times more efficient? The more important question, as an employer, would be: what can you do to entice him to work more so that he can be even more productive?

    Isn’t this the question that our schools need to ask about students like Aaron?

  21. My district has an attendance policy that would automatically fail this learner. Even if he could demonstrate mastery of the topic, he would earn an F because of credit.

    Could it be that schools perpetuate such anachronistic attendance policies because that is how they receive their funding, via the daily head count?

    I’m just sayin’…

  22. To me, it seems Aaron should not be in school. He would learn more outside than in it.

    My guess is he’s learned the material in previous years but won’t play the game and so he gets shuffled into remedial classes.

    There’s a book I read during my sophomore year in high school – The Teenage Liberation Handbook – How to Quit School and Get a Real Life and Education. It tells readers how to get out of school and get their GED. Sort of like homeschooling, but more focused on experiential learning – the student goes after what they think is important and learns it. I’m willing to guess I could have passed the GED around 9th or 10th grade, and I think a student like Aaron could too.

    Unfortunately for me, my parents didn’t buy it and I remained in Catholic high school for another three years.

    Aaron knows the math he needs to know. I don’t know what he spends his time outside of class doing right now. If he isn’t spending his time learning other things, that’s fine – he’s dealing with school and schooliness. But give him a few months of no classes and he’ll start to get thirsty for the real learning that for him might take place more outside of an institution and in the real world.

    Dan, like Clint I’m interested in how you add up your x/4s on your assessments. Is it just a straight average?

  23. How I longed for a day away from class while in college — I always had wistful thoughts about students in universities where attendance wasn’t notice. Attendance was strict at Alverno College: 1 abscence fine, 2 requires talking to teacher, 3 and you’re out of class w/o discussion. Can’t remember that actually happening to anyone, but it might have. I think the same went for tardiness.

  24. I suppose this is tending off the topic, but I do think that the purpose of education goes beyond just gaining knowledge — if you have not see the 5 minute university by SNL’s Father Guido Sarducci, check it out on this subject

    As to the purpose of public education, the authority would be state constitutions — law makers usually include good citizenship as part of the purpose. Here are two examples:
    SECTION 1. A general diffusion of knowledge and intelligence being essential to the preservation of the rights and liberties of the people, the Legislature shall encourage by all suitable means the promotion of intellectual, scientific, moral, and agricultural improvement.

    Washington State Constitution ARTICLE IX EDUCATION
    SECTION 1 PREAMBLE. It is the paramount duty of the state to make ample provision for the education of all children residing within its borders, without distinction or preference on account of race, color, caste, or sex.

    For some young people, attending high school doesn’t work — other alternative do work for some, but many times poor attendance links with problems, whether it’s depression, drug use, criminal activity, or other negatives. Graduating from high school, continuing education, and successful jobs all require showing up regularly. I’d agree that not showing up for work generally links highly with getting fired — a few alternate examples don’t prove the opposite.

    But back to the main focus, grading & attendance. Whether or not state laws allow it, attendance & behavior are simple to include in grades. Teachers have so much control of how grading works. For example, give regular in-class assignments that impact the grade. Limit and make difficult the opportunities to make-up the assignment. Another example, turning in daily homework — making compliance & attendance part of the grade — can be a key grade component. Add a no late work procedure — to teach responsibility — throw in “0” grades on a 100% scale using averaging, this can lead to a quickly discouraged learner.

    Responding by only considering what student know & can do has it’s own share of problems. I’d suggest a good balance.

  25. This is fantastic. It’s ridiculous how novel the idea of education-as-education is – as opposed to school being seen as a 6 hour block of time (7? 8? how long are students in class?) during which students and teachers need to occupy themselves. A little trust might (might) go a long way here. I.e. the students get learned in whatever amount of time they need and then go out and put that practice into play. Idealistic, obviously, but for many a good deal of time is much better spent outside the classroom than in, no?

  26. Sorry to write so much, but let me add a quick retort to Michael. Yes, I agree that opportunities outside the classroom for education are wonderful — challenging to organize, structure, and afford, but fantastic nevertheless.

    I wasn’t speaking so much of “education” as of “public school”, which I believe are not exactly the same thing with the same goals. Having a place for students to be during the day that’s structured, meaningful, and supports community goals is part of public education– learning outcomes are crucial, but not everything.

    Seat time has been abused perhaps, but it is part of the institution– its history and its values. I’m not thinking about trust so much, as structure and opportunity. Just opening the school house door doesn’t provide much opportunity for students– school is usually only 180 of 365 days as it is.

  27. Clint said: “Could it be that schools perpetuate such anachronistic attendance policies because that is how they receive their funding, via the daily head count?

    I’m just sayin’…”

    I would agree with you, if my state funded that way. My state funds through 1 count day in September. That’s it! One day in September decides all funding for the year. If 200 kids move into the district later in the year, too bad, funding has been set.

    My district set up this rule about three years ago after the local newspaper ran a series of articles about truancies and the fact that the district did not have an automatic failure policy due to attendance. The parents bombarded the school board repeatedly, and the board (elected parents) gave in.

    Sometimes politics (okay may times) wins over educational good sense.

  28. Michael K. homeschooled through high school, if that helps anyone.

    @Ben and Clint, it’s an average, which I then weight at 70% their final grade.

    @Joel and anyone else toeing the Aaron’d-be-fired-from-a-job line, I don’t disagree, but Aaron would be fired less for his employer’s high esteem for attendance than for simply not doing anything. In my class, Aaron doesn’t need to do anything. He learned this last year, so he doesn’t bother to wake up. I don’t worry even a little bit for his first post-grad job.

    I’m basically in line with Steven and the rest of these standards-based nutsos. Education is called to more than simple credentialing (eg. the College Board’s function with the SAT) but, when it comes to declaring a kid’s entire year a do-over, lack of comprehension is the only justification that’ll satisfy me – not class participation, not active citizenship, not good manners, not compliant behavior, or any of their friendlier, equivalent categorizations.

  29. Dan, I have a question about how you do your grading. I promise I’m not trying to be oppositional, I just want to understand better, and maybe I missed something when I read your post about it.

    It seems like you allow remediation at any time that might go something like this: you teach a little mini-lesson, they practice it a couple times, and then they complete an assessment of that problem on the spot. They earn credit for mastery of the concept, and get on with their lives.

    Is that accurate? And if so, do you assess to see if they can still do it a week later? Because…I am constantly amazed by kids who by all appearances have some concept on lockdown, and then bomb a quiz, like, the next day.

    How do you assess “mastery” vs “procedure stored in short term memory”?

    I’m not trying to say I’ve cracked the code, because it’s final exam time, and some days it seems like no one remembers anything, and if you or anyone else is doing it better, I want in.

  30. They don’t earn credit for mastery of the concept until they pass the concept twice, the second time on a harder problem, without the same coaching. I don’t let a student take the same concept twice in a day and, most times, I’ll ask the student informally for a summary of mistakes made on the last re-take.

    Do students slip through and game this thing? Absolutely. The execution needs work but none of its flaws is convincing enough to bring me back to the status quo.

  31. OK thanks for the clarification. I have a couple more questions I hope it’s ok. I’m hoping to pilot something similar with one class next year.

    Do you have kids who say 4/5 is good enough and don’t want to keep working to 5/5? What do you do about them?

    Do you have a problem with kids slacking because they know they can make up credit later? Is the last week of the marking period a nightmare for you? I’ve experimented with “retakes” and found that the kids didn’t do as well because knowing they could do retakes eliminated their sense of urgency, and it created much more work for me to boot. (I don’t have a problem with working more/harder if there’s a payoff, but there wasn’t.)

    Your list of concepts seems like it’s in pretty big chunks – is the suggested list you posted really what you use? I wrote out a list for Algebra 1 from the NY standards and it has 122 things on it. For example you have “Proportions”, I split that up into simple x-multiply, x-multiply with distribution, solving a word problem with a proportion, and sides of similar figures. Am I doing it wrong?

    Thank you, Sensei.

  32. Dan, when did you realize the student was underplaced? Could you have moved him up to an appropriate class earlier in the year?

  33. @JackieB, I promoted three or four obvious cases at the start of the year but mitigating factors with Aaron were a) he didn’t show up until maybe three weeks in, and b) our Algebra teachers stubbornly resist anything resembling differentiated instruction and stonewalled most of my transfers.

    There I said it.

    @Kate, did my best to answer your questions here.

  34. What I’m interested in is how all this (not just this particular example, but Dan’s whole approach to assessment) translates to courses in the humanities in general and the English discipline in particular.

    I don’t want to hijack this thread, but I also don’t want to clutter this mostly-math blog with humanities discussions. I thought I’d offer a post on my blog for that separate discussion if anyone wants to have it.

    [Dan: edit away if you’d rather that happen here.]

  35. Huh. Somehow I had created this vision of an entire department assessing students based upon mastery of mathematical concepts. In reality, you’re the maverick. I should have know this. :)

    There has to be a better was of doing this.

  36. Somehow I had created this vision of an entire department assessing students based upon mastery of mathematical concepts.

    Nope. That was the last school. This one has made some impressive strides in two years, though.

  37. Bah. School computer eats my comments but the when I try them at home WordPress won’t take the duplicate. Here’s my $0.02.

    I totally recognize the situation. My school recognized those with high attendance at our awards ceremony two days ago. Students were honored for 90% attendance. You miss one day every two weeks and we praise it? It makes me wonder how so many of our students do pass from one year to the next.

    Have to say I’m happy with my 60% mastery and 40% other work* breakdown this year. Since I’m not pure mastery, Aaron would probably be failing in my classroom. I’d give him the extra credit assignments** I have and he’d be set to pass. He still wouldn’t have the stellar grade, but it doesn’t sound like he’s got the material down cold yet either.

    *Warm-ups, cool-downs, homework if I give it…

    **Extra word problems a la warm-ups and concept posters. The posters are my new favorite thing. Give the students a method of studying. I leave them up so you can use them as memory prompts during quizzes. It goes back to the can you apply the information task instead of the can you just remember the information.

  38. I’m not exactly totally up-to-speed with the American education system. In fact, most of what I know is gleaned from throwaway comments on blogs and school scenes in films.

    Anyway… this type of teacher assessment seems crazy to me. Teachers obviously want to appear successful and therefore are likely to ‘upgrade’ marks and grades. At least over here it’s only coursework that’s affected. And even that’s changing next year!

    We still have problems in the UK, however. Mostly it’s the other way round – kids being ‘hothoused’ when they’re in primary schools which gives them artificially and almost impossible-to-attain targets for GCSE examinations.

    It’s a mad old world and schools don’t make it any less so… :-o

  39. I never buy the idea that school prepares kids for the workforce – worked with too many high school grads. That idea seems more a justification for certain schooly things, like attendence, then an honest explanation or sound reasoning.

    My guess is that Aaron doesn’t show up to school because it doesn’t have meaning for him. When he gets a job it likely will have meaningly, if only because of the need for a paycheck, and he’ll show up.

  40. @Dawn, absolutely correct.

    @Doug, generally speaking, teachers in the States aren’t rewarded for test scores, much less tests which aren’t normed against anything greater than one’s own class, which doesn’t give me a lot of incentive to inflate my students’ grades.

  41. Fair enough – as I said, I don’t fully understand the situation, so thanks for clarifying it. In the UK ‘performance-related pay’ has been mooted several times. It would mean even more teaching to the (far too numerous) tests would take place… :-(

  42. Rory = Aaron

    at least in High School

    Ask yourself this… if you suddenly found yourself back in middle school, would you attend everyday if you knew you could get away with not attending. Would you want to?

    My issue in school was always homework. I didn’t see the point in doing it if I knew the material. What is the goal of your class?

    A. master material

    B. master material, spend 4 hours a week doing math at home

    C. master material, spend 4 hours a week doing math, spend 5 hours a week sitting in chair

    Bottom line: give him the C+

  43. Yeah, it’s like that. Teachers oughtta ask and re-ask, what is the goal of my class, and are my grades an accurate reflection of that goal?

    Me? Perfect attendance, classwork completion, homework completion, these aren’t my goals.