The Comprehensive Math Assessment Resource
August 31st, 2007 by Dan Meyer
Due to time constraints in my corner of the world (school started a week ago) I'm gonna have to shelve my typically softspoken online persona and get straight to it. If you'd like to see assessment amount to more than a meaningless exercise in classroom control, if you'd like to see cheating drop and confidence rise, if you'd like to see a higher correlation between the grade you feel a student deserves and the grade on that student's transcript …
… take something from this page.
How Things Used To Be
- Textbook manufacturers directed assessment, issuing lengthy tests at the end of their chapters, tests long enough to both intimidate students and make their percent grade totally indescriptive of what they know and don't know. (i.e. two months down the line, what does a 67% on "Chapter 6 Test" really mean?)
- Assessment was the same for every student with every student receiving the same test no matter how many times they'd demonstrated competence on an assessment.
- Students hated tests. They complained about them. They scheduled absences around them. They cheated on them. And who could blame them? The tests covered broad chunks of texts, with trick questions seeded every few pages. If you did poorly on a test there was little ability or incentive to improve. The class moved on.
How Things Are In My Classes
- Learning directs assessment. Learning breaks across skills not chapter units. Instead of assessing at the end of chapters, we assess at the completion of a significant skill. Instead of lumping all the skills together under one grade (making that grade useless beyond a "did good" or "did bad" level) we track each skill separately in our grade book.
- Assessment is different for each student. Once a student demonstrates competence in a skill, once on a basic problem and then on a hard problem, she achieves "mastery" and can skip that skill on every test thereon.
- Students like assessment. Most do, anyway, and I'm not even playing with you here. Students like the process. They know which skills they need to improve (because we track them separately — me and them, both), they know how they can improve them (by studying or coming in for tutoring), and they know they'll be rewarded for their efforts (I'll increase their skill grade in my gradebook if they demonstrate improvement).
The Timeline
- You teach.
- As you teach, you try to sense when you've hit the end of a self-terminating skill. This skill shouldn't be so small (e.g. "Adding Numbers") that you'll be tracking ten such concepts on a week but not so big (e.g. "Factoring") that you can't tell how to remediate a low grade. In Algebra 1, "Integer Operations" is my first self-terminating skill.
- You write a test (here's the template) of either three questions or six, depending on how much you want to grade that week. Handwrite them or pull the template into your editor of choice. You'll number the first test of the semester 1, 2, 3, 4, 5, 6, but you'll number the last test of the semester 19, 20, 21, 22, 23, 24, depending on how many skills you pull out of your semester. This is to say, the test numbering is continuous throughout the year. The test numbering is very significant.
- You grade the test on a four-point scale. 4 is perfect. 0 is blank. The rest is at your discretion.
- You enter the tests into your grading program. The possible points for every concept on this first test is 4.
- You pass the tests back.
- The students record the new concepts and their scores on their Concept Checklist. (Template here.) They have now started a self-monitoring process which will continue throughout the year. This is one of the most beautiful parts about this system, that every student knows exactly what she does and doesn't know.
- You teach some more.
- You give another test. Perhaps here it's concepts 2, 3, 4, 5, 6, 7. The pace is such a specific thing between you and your class. Any question they're seeing for a second time, though, give 'em a harder one. Add terms. Use negatives. Make the problem about trinomials rather than binomials.
- You grade but this time you add only one new entry to your gradebook. That's #7. You keep the rest. You keep the rest and you change their possible points to 5. Now, as you go through, you overwrite low scores with higher ones. Grades that drop (and there will be some — the problem was harder, after all) stay the same. If a student pulls a second 4, you enter in a 5.
- You pass the tests back. The students write down the name of #7 and start penciling in new scores next to old ones. If a student has a 5 on a concept, they call you over and you put a stamp or a signature next to that concept, telling them they're done.
- You keep going.
The Handouts
- Blank Test
- Blank Concept Checklist
- Algebra 1 Concept List (suggested)
- Algebra 1 Sample Tests
- Geometry Concept List (suggested)
- Geometry Sample Tests
- Precalculus Concept List (suggested)
- Precalculus Sample Tests
Frequently Asked Questions
- Don't students try to game the signature/stamp process?
Nothing that happens when I'm out stamping changes the grade in the district's computer. A kid could claim two 4′s and I could stamp her paper in error, and nothing would happen to her grade. The stamping process is entirely for the students, so they can take ownership in the process and have a document in their hands that describes their learning. (Still I ask to see both 4′s before I stamp.)
- How do your class grades break down?
70% – Tests (strictly limited to these concept quizzes — no other assessment)
10% – Final Exam (assigned exactly once per term)
20% – Classwork/Homework (everything else) - Once a kid has mastered a concept or skill, don't they just forget it?
Do kids forget? Yeah. But that’s the nature of the thing. Everyone forgets everything given enough time. But with a system of objectives this clearly defined, can I pull them back quickly? Absolutely.
- How do you break the curriculum down into concepts? There's gotta be hundreds.
I've found it to be the hardest part of this system. My list has flexed every year so far.
I could write a post describing the slashing & burning process but the hardest work is done internally. You’ve gotta convince yourself that you don’t need to test absolutely everything.
Some concepts are great for classwork, for exercises, good for in-class formative assessment, but don’t need to show up on a summative test.
You then merge topics where appropriate (being careful not to make ‘em too large, unmanageable, or ungradeable) and write the rest off.
- How often can a student re-take a concept/skill test?
As often as she wants. She can come in at lunch or before school or after school. I don't let her re-take the same concept twice in a day, though. Gotta draw a line somewhere on the issue of rote, temporary memorization.
Earlier Posts
- How Math Must Assess, the PDF treatise that got things going on my campus.
- How To Assess, the practical implementation.
- The Presentation, a talk I gave to the faculty about all this.
- Assessment Part Deux Redux, some notes on the risk-reward cycle.
This post makes it official – you are a teaching genius, not to be confused with a mensa genius.
This is brilliant – how do you find your students respond as this is so drastically different from anything they’ve ever seen? They understand what skills they need to concentrate on and you are truly building on foundational skills.
Students can’t fail (and why should they because to me a poor grade oftentimes reflects poor teaching).
I will pass this along to the math teachers in my district.
Impressive, most impressive (I’ve heard that somewhere, DeathStar or some place like it).
Thanks for sharing. In the true interest of sharing, I look forward to directing my math teachers (and really, my entire faculty) to this post.
I am always amazed that there are educators complaining about time: time to reflect, time to redesign lessons & curriculum, time to grade, etc… yada-yada, so on and so forth.
Then, they “marvel” with satirical contempt that I have time to not only read blogs, but also write one.
They should sit down and talk to you (if, perchance, they could find some time). You sure seem to model the qualities of a (pick one, or all):
1. quality educator
2. life-long learner
3. 21st Century educator (Is that similar to #1 or totally separate??? I am always confused about this.)
And I totally agree with you; just about everyone forgets everything if given enough time.
What was your post about again?
Forgetful me.
Dan,
And you let students retake the individual concept tests as often as they want, correct?
Mike
You are my hero, sir. Do you happen to have a graven image that I may worship?
Hello, Dan,
I discovered this blog shortly before school started, and I want to thank you for all these great ideas! The first day of school was last week (8/20), and I decided that I would try out this assessment method with my precalculus students. I’ve given them two quizzes already. The kids love the method so far. They’ve told me they appreciate that they can learn at their own pace. And I love knowing exactly how each student is doing just by glancing at my grade book!
Keep up the great work!
Tanya Mills
P.S. I modified your course policy sheet for my class, and it was the smoothest and easiest and least boring presentation of class rules ever.
The district I work in does standards based grading. We have a list of concepts, and we grade individually on our report cards by each concept. I’ll see if I have the sixth grade list of topics to share on here. I have the larger one with all the power concepts on it, but they gave us hard copies that are easier to list out. I’ll email about a digital copy that I can share.
Dan, thanks for the templates. Those will definitely come in useful. I should be keeping my gradebook a lot different than how I am now.
Thanks for posting the actual concept lists and sample tests, too! Gave my first quiz of this kind today. My list of concepts is already rather long for two weeks – will need to work on pruning the list.
My math department has a similar concept grading system. Four point scale, but if they go down we average the score. Student must keep the score above 2.8 to be considered “passing.” The idea being that you’re not allowed to just memorize “sum of cubes” for two weeks and then blow it off for the next two months of the semester. If a score goes up, they get the new higher score. Once students realize how much of an impact their essential skill scores have on their grade (40% skills, 20% raw test score), they are more motivated to go for 4s.
Enjoy the long weekend!!!
Thanks for this – especially all the links to previous posts and the templates and tests. You have given me a lot to think about as we head into this long weekend. I stopped giving tests (almost completely) a couple of years ago because I had many of the same concerns that you have noted about the textbook tests. I am seriously considering your system.
Thanks for this blog. Your posts either give me a lot to think about or make me smile (or both). Either way, it is always worth reading.
Thanks, anyone, for passing this along to the math teachers within your locus. Anyone feel like donating a link back to this, I’d be much obliged.
Mike, short answer: yes. I added a longer response to the FAQ portion of the show.
Tanya, real glad to hear that some of this stuff is making life easier for you. I added a list of precalculus concepts and their assessments, for whatever good that does you.
J.D., you get a chance to share that list, be sure to let me know. Real interested in how younger grades do this.
[...] [Do check out the comprehensive resource.] [...]
[...] [Update: check out the comprehensive resource.] [...]
[...] [Update: check out the comprehensive resource.] [...]
[...] [Update: check out the comprehensive resource.] [...]
Dan, not sure if I’m reading this right, but when you give an assessment the students also get all of the past assessments that they haven’t received a “5″ on yet?
Now to share.
First is my districts benchmark power concepts for 6th grade. (If anyone wants any other K-8 grade levels, email me: jwilliams {at} gesd40. org)
http://gesdmath.wikispaces.com/space/showimage/6th-grade-power-concepts.xls
The good thing about his one is that it’s broken down to the chapters in the curriculum we use.
Next my 6th grade strands and concepts broken down. This is the one that I would use to choose what I would assess. (Any of the misspellings are mine, I had to re-type out this because I only had a hard copy).
http://gesdmath.wikispaces.com/space/showimage/Standards-based-strands-6th.xls
I’m hoping those links will work from Wikispaces.
[...] materials they create on public blogsites? A good example of teacher-designed materials is “The Comprehensive Math Assessment Resource” by Dan Meyer who constantly publishes lesson ideas that he uses in his classes. This kind of [...]
dan – thinking out loud – do you think there is any reason that this sort of approach couldn’t be adapted for other subjects? do you know of anyone else doing something like this in other subjects?
i teach IB middle years humanities, and students are marked on their “knowledge, concepts, skills, and organization/presentation”. perhaps it would make for a nightmarishly long gradebook, but i wonder if each of those categories couldn’t be broken down into something like what you’ve done in maths…or perhaps develop a model which factors in essays / projects as a major source of the final mark?
thanks for sharing! again i find myself admiring/coveting your ability to write frequent clever / tongue in cheek posts that leave me thinking about how to improve my own practice.
cheers,
-jp
J.D., lemme see if I can clarify. Every student gets the same paper exam on her desk. It contains six problems, some of which Student X has passed. She crosses those off and completes the rest.
Thanks for posting those links, too. Worked fine on my end.
Jeffrey, it’s always been a thought. I think a science teacher is gonna make a run at it this year but when I gave my faculty presentation last year, the goal was total campus-wide domination. A four-point scale just doesn’t lend itself so hot to abstract test questions, though.
Most crucial to any grading system, in my opinion, is respect for the individuality of learning. A kid might learn how to diagram a sentence or she might learn how to pick apart the themes of The Crucible looonnng after the rest of the class passed by the test.
There has to be some system in place where she can come in, demonstrate that knowledge, and see her failing grade for “The Crucible Theme Test” disappear.
Dan – I like the system, plan to implement it into both my algebra classes this year (my first year as a teacher) and will pass it along to other forward thinking math teachers.
I wondered about using an error analysis routine as a way for students to reflect on their mistakes and improve the grade they received for a concept…Do you think there is room in this system for that, or would you recommend applying the error analysis points towards the homework/participation grade?
I’m with jeffreygene- how could I apply this to an English curriculum? I’m having trouble applying it to reading and writing skills, but it would probably work very well with grammar concepts. I’ll work on it and see what happens.
I just found your blog. I like it. Thanks for tip.
There has to be a way to make that failing grade disappear… within the same semester. My administration has just proclaimed that second semester performance may not impact first semester grades. So if a kid figures out that thing about The Crucible in June and we covered the text in November, tough luck. Also, there’s a finite number of themes in any text, so, in an English classroom, what’s to prevent a kid who didn’t pass the concept test from getting the answers from the kids who did pass?
Beyond the most basic ones, reading skills do not break down into discreet, measurable concepts. I don’t think writing skills break down like this, either. As skills become more complex and/or subjective, there are as many “correct” answers as there are prompts. There isn’t a series of steps that always leads to successful reading or writing that can be applied to any situation.
Still, maybe this grading is possible for certain areas of an English teacher’s curriculum and essays are something we still have to assess holistically, using a rubric, etc. Not saying I like it, approve, or think it’s a good idea, but does this suggest that all essays can be re-written at any time? Students should be allowed to demonstrate their knowledge even after the rest of the class has moved on, right?
Re. Todd’s reply to dan at 18: Probably the answer is to look for general skills, not skills applied to a specific book. You can only ask “what are the main themes of The Crucible?” once, but you can ask “what are the main themes of this book?” once for every book you read. So the student who can’t find themes in The Crucible to save her life can redeem herself when you give The Scarlet Letter Theme Test. It’s not the individual assignment that gets a grade, it’s the skill, whether the skill be “find the theme” or “write an essay explicating a poem” or “read 100 pages of a book over a weekend, with reasonable comprehension”. You needn’t re-give exactly the same assignment over again, I don’t think.
(Unless the skill you want your students to learn really *is* some factual-knowledge question like “know the themes of The Crucible”, in which case it doesn’t really matter if they learn the themes by rote memorization of other students’ quizzes, does it?)
I’m doing this (sort of) with all subjects in an elementary classroom. I’m attaching a link to a flickr snapshot of my gradebook, made using Numbers in iWork.
Some were asking about how to writing this way. The photo is snapshot of my writing gradebook for first quarter. The standards that you see in the snapshot may not be the ones I “use” this quarter. That will change as I see what the kids need, but it will give you an idea of how I set up standards based grading.
This has evolved from what I did last year, so this is my testing year for this exact method. If anyone sees any issues, let me know!! That way I can tweak before running into snags.
http://farm2.static.flickr.com/1265/1304962624_b9846b12af_o.jpg
The link above only links to the image. This link (I hope) links to the flickr page so that you can see the notes I made.
http://www.flickr.com/photos/28642183@N00/1304962624/
Jason, that’s exactly the trouble I was trying to point out in the second paragraph of my comment. I dare say that finding a theme in The Crucible is much easier than finding a theme in The Scarlet Letter, if for no other reason than because of the complexity of the syntax in the latter, never mind the complexity of the plot. Also, notice that it’s a theme, not the theme, which gets at the trouble of subjectivity here. Identifying a more sophisticated theme, one that’s hidden a bit further down and perhaps is found only through monumental reflection and consideration, is not the same as identifying something as surface level as “the struggle between good and evil.”
In English, basic skills might be broken down like this. I just have a hard time applying this to reading and writing, particularly with grade-level students. This is trouble I echo over and over: English is a subjective course, filled with shades of gray instead of right and wrong answers. There are no steps to follow that lead to the right answer every time. So demonstrating the ability to find theme in this story isn’t the same as being able to find it in this other story by virtue of the differences between the two texts.
I’ve been thinking this over for the past several months. Maybe students write in an effort to show mastery of certain skills and that’s all I look for in that read. But, what… once a student shows that she can “use language in natural, fresh, and vivid ways” (Writing standard 1.5), she doesn’t need to exhibit that skill again? Once a student can correctly “analyze an author’s implicit and explicit philosophical assumptions” (Reading standard 2.5), he doesn’t need to do so in the future? When I evaluate the last piece of writing, I’m evaluating many of the same skills I evaluated on the first piece of writing, plus several more. I need to repeatedly know that students can correctly make subjects and verbs agree in number. There’s never a time a mistake like that can pass by. So the number of skills I’m assessing in writing is always growing and I’m rarely “finished” assessing a certain skill. I dunno, maybe I should be at some time for some students.
Jason, Todd – don’t think I can reply to all of your excellent thoughts. Thanks for keeping this thread going! Here are some thoughts that you’ve triggered in my brain.
Just wanted to pick up on Todd’s comment – “rewrite essays at any time”. I did that last time I taught high school English. The rule was that you can keep on working on any essay you like at any time (up until until two weeks before the end of the term). Still not sure if I should have kept the best overall grade or done an averaging between the worst and best.
I liked this because it meant that sometimes I could simply hand a poorly written piece back to a student with “Incomplete” on it – forcing them to rewrite it until they showed they had met the basic requirements.
I think the key is to mimic the function not the form – students are in charge of their grade, they know exactly where they are, and exactly how to improve. Rewriting essays allows for that.
Thanks for sharing folks.
-j
Yeah, for several years I did essays that way. As long as students made a first attempt by a certain date, there was no such thing as a “late” essay. Show me a paper on the due date and tell me you don’t want to hand it in right now. I mark it down that an essay was present and you take your time with it. I had some students to whom I handed back essays repeatedly. And I also accepted papers up until 2 weeks before the end of the semester. I’d keep handing papers back for rewrites if they were below 70%. I didn’t accept anything that couldn’t demonstrate at least minimum competency. This might be the primary way to keep students in charge of their grade as far as writing is concerned.
Attempt the essay as many times as you want, but it stays at 50% in the gradebook until the rewrite hits at least 70%, when I update the score. Hmmm… there’s still time for me to do that this year. I haven’t assigned a piece of writing yet. I did something similar to this with in-class timed writing last year and I liked the result.
If this is the way you’re going to do it, you have to keep the best overall grade, not an average.
Reflexive Objective Mastery Assessment Practices in English/ Language Arts Classes
Yes. It works.
Grammar fits without any trouble at all. Break down the skills, track Mastery, provide opportunity for assessment. Take much of what Dan outlined and substitute complex sentences for evaluating single variable equations. I have template-based five-question quizzes, that proceed up Blooms from definition to application. I operate on a four-tiered system (1,2,3,4), where students are expected to score a 3 — Master level. Level 4 is reserved for authentic assessment of work product. I assess writing in double-secret ways for previous grammar skills. Dig it, I’m grading the essay on structure and content, and have chosen 1-2 grammar skills (past tense verbs, use of prepositions, etc.) If they use and apply, the get a 4 on those skills — PhD level.
I teach the component parts of an essay in the same way: Intro, thesis, reason/argument, explanation/elaboration, transitions, citations, etc. Kids chart out what they’ve already been successful in and where they need to focus. [And for those who struggle with that stilted prose in 10th grade, remember that bad high school writing is exactly the same as good middle school writing]
I teach ELLs who struggle with reading, so high emphasis is placed on the application of various meta-cognitive reading strategies (questioning, predicting, visualizing). Kids are assessed in three different ways, assigned points, and track progress toward Mastery on a big ol bar graph.
The higher level lit analysis stuff is more problematic, but the key here is multiple opportunities to gain mastery. This does not necessarily mean kids are trying to assess theme of The Scarlet Letter over and over again, but it measns they’re trying to assess the theme of SOMETHING, over and over, receiving feedback on how they’re doing, and eventually placing a certain skill or analytical tool into the lockdown box of I’ve-got-it. By the end of the year, kids tailor their own reading/ analysis program based on past performance. Everybody is reading the same thing, but Osvaldo’s making text-to-text connections and analyzing conflict, Lupe’s questioning, visualizing, and looking at theme, while Tania’s writing an essay comparing the treatment of women charaters across the last three novels. This level of differentiation is thus brought about not about feelings or murky inclinations, but rather the hard data of past performance and the clear necessity of what needs to come next.
Except too many E/LA standards are written with “feelings or murky inclinations.” Language Arts implies that a certain degree of subjectivity is inherent. We’re quite often assessing good writing and that’s different than correct writing. Again, there are no concrete steps to follow that will always result in better reading or writing. There are as many possible steps to follow as there are texts and as there are readers/writers.
Some of my students might need to predict when reading the current text. So am I to assign predicting to those 10 students who I think need it and the other 20 get something different? That’s a nice idea, but I cannot differentiate for 160 students. I’m human and I have limitations.
Maybe we start with a checklist and everyone has to predict, etc. until they show they can do it at the drop of a hat. Then they are done and they move to another reading strategy. Pop quizzes on the previously covered strategies are possible at any time. Are there forms students have to fill out to show mastery of different reading and writing strategies? Can these kinds of skills be captured in a universal form? Maybe it’s that the homework is to predict with the current text. Then, there’s a test in class using a different text and students show their predicting skills (that they’ve ideally practiced on the homework). Or write a thesis. Or use evidence to support an argument. Or revise to improve style. But do standardized objective test items actually encourage better writing? I haven’t seen anything to make me believe that.
[did this comment already go through?]
Hi Todd, don’t drive angry.
You wrote: “We’re quite often assessing good writing and that’s different than correct writing.”
Fantastic, assuming your students arrive with the ability to write correctly — I’m assuming you have no qualms about defining and conceptualizing correctly, right? My guess is, most teachers don’t have quite the luxury, which is why this approach tends to make more sense. Me, for example. Here’s a random response to literature diagnostic, quoted completely:
“In the history there a girl and her Family. Then They see a hot-air baloons rides but the girl when she is in the hotel she thinking and the baloons then she feels panic, and she don’t wants togo in the an she go and she liked.”
Yar! I got some work to do there, because the state writing exam is in March, and homeboy’s gonna have to do a lot better. If you don’t have to teach kids like this, or really anyone like them, to write correctly, mazel tov, and maybe this approach isn’t right for you.
You wrote: “Again, there are no concrete steps to follow that will always result in better reading or writing.”
That word “always” is sticking out like one of those tiger-traps covered with leaves. If we change that “always” to “more often than not,” “most of the time,” or “almost always,” we can agree that you wrote something pretty silly, right?
As for your 3rd paragraph, I was digging it. Break those murky standards down into teachable/ learnable chunks. Teach, assess, monitor, remediate, differentiate. That’s some hard-hitting shit right there. But then you went off and started in on the standardized blah blah blah and everything went off the rails. No one’s talking about the Big Bad in May. Assess how you want, but do so on discrete units of instruction, communicate the importance of high-level Mastery, and provide opportunities for reteaching and relearning. While I understand that writing is an art-form, and all high school writing approaches this level of art, I assume you communicate some standards or means of differentiating the betterness you spoke of earlier. Assess on those measure of betterness and differentiate accordingly.
These are the things that facilitate the development of more compotent readers and writers.
Who’s angry? I’m enjoying this.
Silly? Nope. Tell me the steps that “more often than not” lead to better reading or writing in mainstream students. I don’t know what those steps are and they would certainly help me create those forms I questioned the existence of in that third paragraph of mine you enjoyed. I don’t mind if I’m silly because an answer to this one would be huge; if we have steps to produce better reading and writing, those are really steps to produce better thinking. Honestly, I don’t know of anything that I can hand to 9 students out of 10 and have them become better thinkers as a result. I’d even take 4 out of 10.
I am lucky in that I teach junior English (mostly). By the time kids have made it to me, they come with the ability to write correctly, though profundity and sophistication are quite often lacking. Students with lower writing skills usually are siphoned off to other levels of English (comp&lit, repeat classes, ELL, Read180, etc.).
And in that third paragraph I wrote earlier, I wasn’t talking about “the big bad in May,” either. I was talking about test items that are “aligned to standards.” I meant “standardized” more literally than is used in most teacher conversations. Sorry for the slip up. So you take something like “can write a thesis statement” and turn it into an objective test item. The ability to pick a strong thesis out of a line up does not mean the ability to create a strong thesis from scratch. Those are two different skills and I don’t think working on the one necessarily improves the other. Just like correcting grammar mistakes on a worksheet does not mean the student can correct those same mistakes in his own writing.
Do the students complain when they realize that their old score of a 3/4 = 75% will suddenly drop to a 3/5 = 60% if they don’t improve on the second assessment?
Yes, absolutely. Many do. So I make sure that first 3/4 (a near miss on a basic problem) is as close to my mental image of D-level performance as possible.
[...] dy/dan Blog Archive The Comprehensive Math Assessment Resource Dan’s posts about assessing math students is some of the most well thought-out [...]
I use a similar system. I have a big number of standard problem that all need to learn to pass my class. They can retake test on those untill they get it right. When they pass one concept I will not make them take a test on it again. I am thinking about a system when you need to pass it twice in a row since i see a problem with to many forgetting the skills.
To get a higher grade the students need to be able to combine the skills from two or more standard problem in a several step solution and for the highest grade they need to be able to use the skills on problemtypes I havent really showed. They have to show they understand the ideas enough to adapt to a new problem type.
On the problems that probe for higher grades I give myself permission to use any concept we have done so far in the course even if the recent onces are testet more.
I do not let students retake test for my higher grades. If I have problem deciding between two grades at the end of the course I normally let those students take one last exam to decide the grade.
/Per
I used a slightly similar approach in my math classes with a great deal of success. Thanks for sharing this with everyone. You’ve provided food for thought.
[...] Taking a page from Dan, the next time I assess ability to list evidence to defend an opinion, this grade will raise to and stay at 50 points. Students will have the chance to improve this score at any time during lunch based on a new topic I give them. [...]
Our school uses a similar system, but we have abandoned points and percentages all together. In listing out these concepts we decided that some of them were VITAL to a student being successful and moving forward. These are called “essential”. Students have to demonstrate proficiency on these skills to earn a passing grade. (We score on a Not Yet, Working Towards, Proficiency, Mastery scale).
The other skills are called “advanced” and the requirements for them vary depending on whether the student wants to earn an A, B, or C.
Part of my personal reason for going to this system is that I believe that percentages hide what students don’t know and allow them to move through the system with holes that are never filled. This way both the students and I are held accountable to fill the holes. (Maybe this is especially an issue in math?)
[...] congruent and comprehensive assessment, emphasizing a “menu” style assessment which sounded somewhat familiar. [...]
[...] congruent and comprehensive assessment, emphasizing a “menu” style assessment which sounded somewhat familiar. [...]
[...] Testen opstellen vind ik zowat het moeilijkste wat er is. Door de lerarenopleiding weet ik dat je moet proberen je doelstellingen en verder niets te testen. Ik probeer dit dan ook toe te passen. Als ik wil dat leerlingen primitieve functies kunnen bepalen van enkele basisvormen dan vraag ik dat. Maar wat als ik wil dat leerlingen “niveau” halen. Kan ik op een test een moelijker, open probleem vragen? Ik vind van niet en ben het daar dus eens met wiskundeblogger Dan Meyers. [...]
[...] What I really want to see is a concept list. Like this (thanks dan): [...]
dan…i reread this post this morning and for some reason my brain found a way to picture using this approach with grammar & vocabulary skills in my esl classes. i can’t give letter grades as final marks…using a rubric system, IBMYP…but i can see this working.
if the idea manages to stay bouncing around in my brain, maybe that’s a summer project to test out. would definitely share any results with you. faq #4 is hurting my head at the moment.
Dan,
My school uses PowerSchool for grading as well, and I just want to clarify one point:
If on the last day of school a student finally “gets” topic number 1, do you go all the way back to your very first gradebook entry and plop in a 5? In PowerSchool, will his final grade be affected by this change, even though the guidance office has already locked in the first quarter grade? Won’t there then be a disparity between your calculation of the final grade and the guidance office’s calculation of the final grade?
I know this picky stuff, but I’m definitely doing this thing next year and I want to have my bases covered. Any experience you could share would help.
(I think I’m also going to try this in my physics classes, so I’ll give you some feedback in the future.)
Jake, quarter grades at my school are nothing more than progress reports. We lock only at semester.
But playing this hypothetical game, last year, at semester’s end I told kids with F’s they could come in and remediate scores for first semester concepts. I’d just complete a grade-change form. However far you feel comfortable taking this thing.
Both Jeffrey and Jake: definitely drop back by with a note if this thing flies outside mathematics.
Inspired by this post last summer, I implemented it with my physics classes this year. I also made sure one of my APs was in on it and I had her full support.
I took each large unit and broke it into smaller pieces. For example, the unit on Dynamics (Newton’s Laws) became smaller topics: vectors, balanced forces, unbalanced forces, friction, and circular motion.
For each small topic, the kids were given a 10-point quiz. It could be one large problem, 5 muliple-choice questions, or a mixture of a small problem and some MC. Students received 3 of these topic quizzes every Friday. Each week, a new topic rotated in and an old one rotated out. Therefore, a student was quizzed on a topic 3 times in class. They could come after school to take additional quizzes if they wanted to, but only on Wednesday–science extra help day–and they had to tell me which topic they wished to retake, but no more than 3 at a time. I established those “silly” rules in January to keep me (and my family) sane. I counted only the highest 2 quizzes. Like Dan, kids can retake quizzes on 1st quarter topics in June. They keep track of their scores on a concept checklist (Dan’s) and store everything in their own quiz folders.
I like the idea of “mastery learning.” Physics requires a set of mental muscles kids aren’t used to flexing yet. A problem that gave them trouble in October is usually cake for them come June, because they now know “how to think.” And why should they be penalized for that?
Some things that have helped me institute this system: buy-in from the students, my old exams which have been sliced up into topic quizzes, and a test wizard program (eduware.com) for creating retake quizzes effortlessly. I’m in NY, and my kids take the Regents exam, so the test wizard is a must-have for my assessment system.
Now, has all this craziness made a difference? I can tell you this: the kids don’t feel defeated by physics as they did in years past. They can get a 2/10, realize that they didn’t know what they thought they knew, and come back to get a 9/10 and feel great. Plus, when it comes down to grades, there isn’t anything stopping them from getting a 100 each quarter. The ball in in THEIR court. How can a parent argue with a system like that?
In addition, I can immediately tell which topics need re-teaching by me and which the kids get right away.
We’ll see come June on the Regents exam if the actual year-end performance fairs better than last year.
I know my system isn’t perfect. If anyone has questions/comments/suggestions, I’d love to continue the conversation.
Frank,
Reading this gives me even more incentive to do this in my Alg 2 classes next year. If it can be done in physics (and I am certified for physics also) then it can be done in any math class or science class.
Thank you!
Frank –
As a former physics and math teacher, I love your ideas. Few classes I’ve seen beat kids down the way physics seems to. Had I used your strategy it would have been much more reachable.
In passing, I had to comment that I have a math teacher in my bldg who does something similar as far as mastery learning and I actually did have a parent call me to complain. After all, if her daughter is happy with a “C” in the class why should the teacher force her to continue to retake the quizzes until she gets an “A”? It’s her right to get a “C”.
*sigh*
I’m actually volunteering to teach a 12th grade math class in my bldg next year and will be structuring assessments according to this model. This will give me some additional “street cred” when I coach our new teachers along the path to understanding that just because that’s the way we’ve always assessed doesn’t mean it’s the best way.
Maybe I can share in the comments that here, at the end of the year, a line of kids stretching out the door before school, after school, lunchtime or any other time I’ll offer remediation and re-takes, I get really, really, weird.
Today there was ten minutes left in lunch. I hadn’t yet, y’know, eaten lunch. I had 34 tests to correct (quickly) and enter (quickly) before passing them back the next class. I had some slides to queue up. So I closed up shop early. Can’t take anymore, I said.
And I tell you the truth that if any kid so much as bats an eyelash at that directive, much less whines about it being “unfair” like two kids did today, I tend to go totally insane.
Y’know, it’s like, hey, I’ve tutored you and offered you re-assessment on Similar Triangles five times, which, if I’m not mistaken, is five times more than any of your last nine math classes would’ve. And you’re twisted up because I want to get some chicken in me before I have to teach you for two hours?
WHA?!?!?!
I can’t help it. I call ‘em out directly. I tell ‘em to come back next week after they’ve readjusted themselves.
This is more trouble than it’s worth sometimes. Get the math right the first time, kids.
Replying to Kate’s questions from another post:
I don’t think anyone consciously stops trying at 4/5. That first 4 is an easier problem, though, and some students never stretch past it. This will reflect in their final grade.
To the heart of your question, retention will always be a greater issue in this system than under traditional assessment. But it’s nowhere near unconquerable (with openers, review exercises, etc.) and the alternative (test every student on the same questions regardless of past performance) isn’t worth the consequences (students don’t feel ownership over their own assessment).
Please see the comment immediately preceding this one.
In a word, yes. But how awesome is it that when the kid comes in late semester with an F, I don’t have to say, sorry, man, I don’t think you can dig your way out of this one in time. Those kids, in a traditional setting, then check-out and become disciplinary migraines.
My proportions question is a two-parter, each worth 2 points for a total 4. The first part was an x-multiply, the second was a word problem. That’s worth a 4, or a B. With the second question, I’d turn the first half into an x-distribute. That’s worth the A-plus.
Basically, you’ve gotta integrate as many as you can under one heading without making it too large to direct remediation. This process does necessitate some cuts. I had to free myself of the mindset that, just because I taught it, I had to tentpole an assessment around it. But, I mean, they work through these concepts on classwork, homework, openers, and projects also.
Thank you for the response and your honesty (and sorry it took so long for me to say so, I didn’t see the redirect in the other post comments until now). If I ever have enough to say that I get a blog going, I’ll write about how this goes next year.
[...] 1) this summer, I tutor one or two students in high school math using nothing but pdfs, maybe scanned drawings, forum software with latex, … basically things that could be scaled to (3) below. I use in main part the assessment system described by Dan Meyer here and here. [...]
[...] A failing grade on this writing style still isn’t as specific as a failing grade would be in Dan’s gradebook. Did the student fail because of grammar issues, unfocused points, poor explanation, too little [...]
This sounds like a great system and I am very intrigued by it’s possibilities. However, what occurs to me is that this is fundamentally and singularly suited to skills assessment. As a result it works with Math and perhaps English. How can such a system translate for content assessment? In History assessment doesn’t measure skills. At least not how the standards are currently written. We cover content and students are tested on what they have internalized.
I have started using an assessment method that grades student responses to content based questions differentiated along Bloom’s Taxonomy, but if how do you retest the same question over and over again? In math you test the type of problem and change the numbers, but in History it’s not as simple.
I’d love to hear from anyone in social studies who is using Dan’s method. Meanwhile, I will mull this over some more and see what I can come up with.
From one Dan to another, I also like teaching. Great blog, I’m hooked. I’ll certainly be talking to our math department about this concept.
If they adopt I’ll let you know.
[...] Algebra 2, Dy/Dan, Geometry, Skill Based Assessments So I’m taking Dy/Dan’s lead and incorporate skill/concept based testing. I am excited about this because it gives me the opportunity to be more specific and [...]
Bringing you back to the discussion of these assessments. Are the sample tests here the easier or harder version of the questions you give?
Appears to be a little bit of both. Sorry. The hardest question should match the hardest variation you can find in any of your state’s frameworks. The others should simplify things by degrees.
Least helpful comment I have ever written.
Laughs, combined with my state’s framework, yup, pretty unhelpful. (I’ll use other state’s released questions.) But it is reassuring to know that it’s a mix–some questions seemed trickier than others.
[...] requirement of the writing, the Final score is the percentage earned on the assignment. In a nod to Dan’s method of assessment, I’ll be entering each score into the gradebook separately so that we can see development on [...]
[...] implementing Dan’s grading program, with some minor variations. I’m finding it to be almost all [...]
Great ideas! I can’t wait to try your system in my 6th grade math class. However, I am still having trouble understanding how you assign points to the problems. Is it four points per concept, or four points per test? What is the fifth point for? If there are six problems how do you translate that into four or five points? Could you clarify your grading process? Thanks!
I just watched your slide presentation and it all makes sense. Thanks and disregard my previous post!
[...] needs a more meaningful place in our grading schema than “token extra credit.” This is easy if you break your grades out by standard. Otherwise, [...]
[...] N., from the comments, co-opting this assessment strategy for physics. Now, has all this craziness made a difference? I [...]
Thank you so much for this! I have been sharing it with everyone in my department (and really, everyone I know as I am THAT excited about using something so awesome) and I’m greenlighted to test it out in two of my classes next semester and I cannot wait (or perhaps I can as the whole setting up the standards thing is pretty daunting
My question is if you have any advice for someone starting up the system? Beyond what you’ve written, is there anything in particular to look out for? Any particular way you explain to the kids how it works that help them comprehend it and appreciate it, or do they not really catch on until they’ve been doing it a while? I really want to do this right!
Can’t wait to start it up here in Washington and I’ll drop a line to let you know how it goes! Thanks again!
Ashlii, I hope the implementation of the thing meets your expectations for it it. My only words of caution and advice would be:
a) This system takes much more time than you anticipate now. The more opportunities you offer students to remediate their skillset, the more satisfying the process but the more time it consumes. My first year I let students retake as many concepts each day as I had time for. It felt like I never really left school some days. Now I let them make up one concept per day. And if they miss it, I send them home with a couple of problems of related homework they have to practice before they can retake it again.
b) As much as you can set-up your gradebook and templates and problem banks in advance the better in the long run, though that probably goes without saying.
[...] do we mean when we say “grades”? I don’t know what kind of results here would prompt me to pack up the shop and dole out monthly, summative unit exams (“Chapter 6 Test”) with the rest of my department. The [...]
Dan,
A colleague of mine turned me on to your blog six weeks ago and I love it. Great stuff. You are really helping to stretch my thinking about some things I’ve needed help with for a while.
I have a question, though. I love your assessment practices and look forward to applying this in my class. I notice that your questions are very procedural, California-STAR-test type questions. Do you give any assessments that require critical-thinking or problem-solving?
Thanks!
Hi Touzel – I can tell you what I do. After each assessment I hand out a small number (2-4) of more extended, problem solve-y problems and give the kids a week to complete and hand them in. These only count for 10% of their grade whereas the assessments count for 70%.
Yeah, what Kate said. Most important to me is that I prepare kids for continued math study so my assessments test procedure. I work critical thinking and problem solving into classwork and homework. They don’t weigh as heavily on the grade, but the only reason I want a kid to fail my class is if she lacks the requisite skills to move on to the next class.
Dan, I have a dilemma for you: if you had to choose between preparing kids for continued math study (in classrooms) and teaching them math that they’ll use in their lives outside of classrooms, which would you choose?
Kate, that sounds awesome. I’d love to see some examples of what this looks like. I am afraid of getting lost in procedures (which is very easy for me) and I struggle in developing problem solve-y problems on my own in a time-efficient manner.
I am getting better at writing them but I don’t think it comes easy to anyone at first. I would recommend getting some quality sources of good questions. I have some books called “cruising through the math a” and “cruising through the math b” which are supposedly regents exam review books but have some really nice questions in them, organized by topic. (Other state assessment review books are good too but those are my favorite.) If you have any older textbooks lying around they can be good – look at the “challenge problems” and easy them up a little if you have to. I also plunder the questions in the calendar in the NCTM publication “Mathematics Teacher” (it’s the centerfold of the magazine every month – which cracks me up). SAT and PSAT review books aren’t bad, either. I’d be happy to throw some of mine online for you but it will have to be when I get back to school next week.
Dan, I just learned of your site from my son. It is wonderfully challenging, fun, and real. As a teacher I have struggled with grading. The key question to considered in authentic grading is how to reward students. Do we reward them for effort? For demonstrating mastery of the correct procedures or prescribed content? Or, for creative problem solving of difficult/real problems? If the third option isn’t significantly rewarded, aren’t we sending a strong message to them that we, as professionals in our field, do not value critical thinking? I don’t suppose we have to give 30% of the grade to critical thinking, but 10% doesn’t seem to be enough to me.
[...] Meyer has a famously-interesting perspective on grading and homework. In a recent post, he offers a scenario of a student (Aaron) who has only attended 20% [...]
[...] struggling with 15.0, we need to be a bit more specific in order to fix the problem. I know that Dan has done a nice job of explaining the need to break the curriculum down into skills and he has a [...]
Ok I’m still a little confused on steps 10 and 11. Say Student A gets a 3/4 the first time on a certain concept. The next time she again gets a 3 out of 4. What is her grade now? A 3 out of 5? Does it stay that way until she gets two 4′s in a row?
If they get 4 out of 4 both times then that becomes a 5 out of 5, correct? Stamp and move on. So hey have to get two 4′s in a row before it turns into a 5?
Also, how do you grade homework? Is it also on a 4 point scale?
I grade homework for its attempt only. So long as a student gives me something we can talk about, it receives credit.
And your summary of steps 10 and 11 is correct.
Hi, Dan.
You and Spence Rogers have inspired me to transform my assessment process.
I read your assessment posts, the comments, and your responses to the comments.
I decided to try and tackle the “higher order level questions present?” issue.
Please take a look at the resultant ASSESSMENT FORMS and brief videos at http://teachinganyway.edublogs.org if you have the time.
I would LOVE to know what you think, as I have not yet tried standards-based assessment and you have. I’m sure you have perspective that I don’t.
Thanks so much! I’m enjoying the blog.
Sincerely,
Z
Zendre’, thanks for the heads-up on your site. Your settings require an edublogs account for comment-posting, so I’m posting mine here. I appreciate that you’re taking on the issue of higher-order thinking assessment. I haven’t done enough here. But I watched the video where you demonstrate a concept quiz and even though you’re asking some very difficult questions, you’re structuring them down the page and prompting students to the point that I’m not sure they’re really engaging in the higher-order thinking we’re after. You’re nudging them through the assessment. I’m trying to think of a modification that would leave the student with more of the process to complete on her own.
This is clearly a complicated issue. In case you find it thought provoking, here is Alison Blank attempting a solution to the same problem.
Hi, Dan.
Thanks for the feedback!
About the video: It was a snapshot of just ONE of the questions on a quiz with answers filled in. Perhaps that’s why it seemed to be too “nudging?” I filled out columns 1 and 2 for that particular question to let teachers see what STUDENT answers for these columns might look like. I would expect the VAST majority of the students to fill these columns out 100% themselves. Only students needing modification might need the teacher to fill in select blanks or the first column, for example.
You may not have time to actually look at the PDF of a BLANK quiz (Format A and Format B). I’ve been fiddling around with writing higher-order questions into the forms.
The point of that question shown on the video (1 of four) is to find SOME kind of way to make a question that asks students to iterate through an algorithmic procedure a task asking for higher-order skills. Right now I’m thinking that asking the students not just to calculate but to justify a calculation might be going in the right direction. The research I’m looking at right now says that American teachers especially take procedural competence as “understanding” when it’s possible to iterate through procedures with no understanding.
But . . . thank you so much for the feedback and the link to Alison’s post! I’ll show the forms to a couple of math ed professors I know and see how they can be improved to call for higher-order thinking.
Thanks!
I just mentioned Cornell’s Good Questions Project somewhere else, and I wonder if it would be helpful here, if we’re thinking about getting a deeper understanding.
How much and what kind of work do you do during class? I’ve been assigning between 2-4 problems of homework but I know they aren’t getting enough practice. I’m pretty sure you teach in a block schedule and I teach on a daily 52 minute schedule which I think makes a difference as well. My algebra concept list has 59 concepts on it and I don’t know if that’s too many or not. And I don’t see how you assess every concept twice but you assess weekly with only 3 or 6 problems. It seems like I will teach for 4 days, and assess those 4 days concepts on the 5th day. Then the next week I repeat, so do I now assess last weeks 4 concepts plus this weeks? I don’t know why I can’t understand this beast but I’m only halfway implementing this and I don’t know how to do the rest. And most importantly, how do I explain all this to the student so they understand how to improve and that their grades actually have meaning?
Fifty. Nine. Concepts.
That’s immense.
Do you have that concept checklist posted somewhere?
Yes, here: http://www.scribd.com/full/16986072?access_key=key-2ixkf96pv78rebieo0ao
It’s not really a concept list, it’s basically every section in the book I plan to cover.
Keep in mind that I am a first year teacher who only knows about traditional assessment and I basically have no idea what I’m doing.
I don’t know how to condense and get over the idea of assessing everything.
Go back to unit tests if you can’t. This will drive you nuts and that kind of nuts just isn’t worth the stress in your first year.
My encouragement would be to:
a) combine concepts as much as you can without invalidating the assessment. A good order of operations problem is good enough to assess adding, subtracting, multiplying, dividing real numbers and the number line. That’s five for one. But don’t throw a variable into that problem to make it six for one, right?
b) understand that a student’s grade is always an inference, a score determined by a model that’s flawed and subjective in its own way. I don’t assess “Graphing Circles In Standard Form,” but I assume that a student’s grade on “Graphing Ellipses In Standard Form” is a pretty good indicator for circles.
I think you’ve got to get comfortable with (a) and (b) or this thing is going to be more trouble than it’s worth.
I don’t know if I can leave it alone because I see so much value in it. It’s hard to knowingly go down the wrong path when you can see the right path and all the cool kids are on it.
I’m queen of categorizing so I suppose I’ve broken it down too far.
I need a concrete example. Could you give a summary of what a regular week looks like in your class? Day 1: Teach ____ and so on and then what that week’s assessment will look like?
Right now, taking notes and homework seem to have no meaning so I’m banking on assessments to take the cake.
[...] screencast and a checklist she uses to track and motivate students. Also consider exploring this blog post from a secondary math teacher explaining his assessment [...]
[...] specific skills. For the most part I am following Dan Meyer’s example, described briefly at http://blog.mrmeyer.com/?p=346, and working with a vague idea of what Hans, a logic teacher here, does. Instead of getting back [...]
[...] of my intended purpose. For example, reading Dan’s post on homework, I am lured into reading his supplementary documents and then the comments on them so that I take a huge amount of time getting the original article [...]
[...] dy/dan – A great argument for SBG in a math class with lots of practical information and examples. [...]
[...] SBG this year in Algebra, but really the people that have wrote nice stuff on the subject are: Dan Meyer, Shawn Cornally, and Kate [...]
[...] is a movement of sorts right now in mathematics education that some really excellent teachers have been implementing. Standards-based grading is a system of assessment that measures [...]
[...] was taught (one to teach, one for them to check and fix homework, then quiz) in the same fashion as dan. This way I’ll be forced to keep up on assessment, and the students will have a good [...]
[...] I read Dan Meyer’s manifesto “How Math Must Assess.” I simply broke up my major units into smaller skills. For example, my unit on [...]
[...] grading, teaching One of the first presentations on Standards-Based Grading that I read was Dan Meyer’s post, which seems to have started many others as well. I’ve also been reading Sean [...]