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.

Dan,
And you let students retake the individual concept tests as often as they want, correct?
Mike

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.

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.

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.

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.

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.

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?)

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, 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

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.

[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.

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?

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

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?)

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.)

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 –

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.

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.

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!

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!

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!

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.

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?

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

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!

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?

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.

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.

I noticed that 20% of your grade consists of classwork/homework. How, exactly, do you assign point to these activities?

does it take AT LEAST 2 separate quizzes for a kid to master a LT? also, just to make certain I’m getting this, could a particular students test look like: 3, 8,9,10?

Learning Target (LT)

I clearly wasn’t thinking when I posted that comment….I was forgetting about reassessment! In BC Calculus, I’m having trouble limiting the number of concepts. Any suggestions?

An added side note–yesterday I purchased a subscription to ActiveGrade, so I do plan on using it, and then transferring those grades to IC.

[My testing gradebook looks like this: 3/5 2/5 5/5 3/4]

Dan,
Am I missing something? If a 4 is perfect, then why do you have 3/5, 2/5, 5/5, etc.?

I also counted my final for 10% this past year. It turned out that an annoying feature of this was that kids and their parents were upset when they did way better on their final after being less good on the topic tests. The way that I got around this is that when there were really significant improvements — like, 20 points or something — I counted the final for more.

Yes, can’t please everybody, and you have to do what’s right for the kiddies and provide them incentives to do what’s best for them (i.e. study assiduously durin the year, and not to cram for a one-shot final). Still, this was something that I had to deal with both semesters.

You’re tired of me….aren’t you:) It never takes you this long to give me your opinion!!

Thank you, Dan!
I guess I’m thinking that I have to be totally prepared for everything before Day 1.
When you first began this process, did you just create authentic assessments as you needed? Were you overwhelmed with school work initially? Did you try SBG in one class, and then add others as you felt comfortable? If you can believe it, I’ve been teaching over 15 years…..

On June 1st, at a PD day, our curriculum specialist showed our department a video on Formative and Summative Assessments. It didn’t go into great detail, but it seemed cool enough for me to investigate….which is what I’ve been doing since June 1st! I can’t wait to let you know how it is going after 9 weeks of this!

Nice Moodle page Anne!!! I bookmarked it. Here is one of mine although after August 2 we move them to another server so the address will change. But it gives you an idea of how I broke up my concepts. http://moodle.esu11.org/course/view.php?id=7. And you are right on. This assessment strategy frees you up to teach and I have way more students coming in to get help as they need it and instead of reviewing a dragon of a review that seems impossible to slay. I look at their sheet that marks how they have done on each concept and concentrate on what they are struggling with. It has been very liberating. All of my courses will use this method and I teach Geometry, Algebra II, Trig/pre-calc, and two other math courses that are tailored to our progression.

I think I downloaded your template–the one with 3 or 6 questions, right? Since we last “talked”, I have visited several helpful sites for assessment ideas. Our district has adopted the National Core Standards, AND we attempt to incorporate the standards put out by ACT. When searching both of those topics (ACT Standards and National Core Standards), there was a plethora of information. Thanks for helping me become a better teacher!

Dan,

I also have many of the same questions as Tina on how to implement the system on a daily basis. I am very inspired by the idea and am considering changing my assessment techniques as a result.

If a student gets a 2 on the first question and a 4 on the hard question, I believe their grade becomes a 4. How does this student make the grade a 5? Do you allow them to re-do the first question, or do they have the maintain a 4 on the next hard question or a retake hard question to acheive a 5?

Also, do you define your categories by key skills or essential understandings? What do you do if you feel you cannot assess a concept in one question? Do you split the concept into smaller more focused categories or give more questions per topic?

Do you ever weigh some concepts more than others in the grading system?

Thanks for the help… I may be the new Anne :)

I printed your thesis today and gave it to 3 administrators and one fellow math teachers. I am excited about the possibilities this has to offer.

Dan,

I know this assessment method has problems with synthesis, as has often been pointed out, but I just had a thought and was wondering what you thought about it, if it might work.

The details are shaky, but imagine your grading system went up to 6 instead of 5. You still have the normal 1-4 scale, and they get 5 for mastery when they have gotten two 4s.

But after they’ve gotten enough 4s and 5s, you can start giving them questions that synthesize a bit. If a student can solve a question that involves the Pythagorean Theorem and the Surface Area of Cones (as you mentioned once), and then on another problem they can solve a problem that involves that Pythagorean Theorem and Ratios, then they might know how to synthesize the Pythagorean Theorem into other problems, and so on the checklist they get a 6 for it.

That way you can still have the checklist for each concept, but include the synthesis and still see which concepts are giving problems. If a student has a 5 on both the Law of Sines and the Law of Cosines, but can’t get a 6, their problem might be knowing when to use which, and that’s what you can remediate.

Maybe you can even make the “unit test” that is full of synthesis, using the grid system I though about here: http://rootsoftheequation.wordpress.com/2011/06/26/facts-in-five/ So you can check synthesis on 10 topics at once by grading the rows and columns.

Great model of assessment. I am in the midst of changing to your model. I am wondering what you think of a student who loses a certain concept over time but performed well earlier.

For example, if a student scores a 4/4 on concept A. Then 5 weeks later scores a 2/4 on concept A. It is my inclination to make his current level < 4. How can we say that he is a 4 in this concept still? I understand students forget, but I still would like to keep these concept levels as accurate as possible while he/she is still in my class. Thoughts?

Does the example above happen a lot for you?
Why is it not worth doing?
Is it too overbearing to do this?

Sorry if you've already discussed this somewhere and I missed it.

I generally have four versions of each concept when I give one of these concept tests where I just slightly change the question. For instance if I ask for slope I will give different ordered pairs on each test . . . etc. Although this does not eliminate cheating. It at least makes it more sophisticated cheating when they do cheat :)

Dan,
You give a end of term test to check for retention, yes? How is this scored? I’m thinking that if I cover 12 concepts in one quarter, I will give them a 12 question test, and make it worth 48 points. Then I will score each question out of 4 points. What do you think?

That is how I’ve set it up, Dan…..all stolen from you, the Master of SBG!

Thanks!

ND, perhaps you could have the parents initial their student’s concept checklist every so often. That way you can be sure the parents are seeing the progression and exactly what is going into that report card grade.

I started this at the beginning of this school year and I have to say that this is the most profound change my classroom has ever undertaken and I am very impressed with how it is going. The concept checklist has been a very important tool in terms of communication between school and home. I made a big deal of it at back to school night and told the parents to check their students’ orange folders (that’s where I have them keep all their sbg stuff) often. The parents love it and I can tell they are keeping an eye on that folder from the types of emails I am getting. It is better information on their kids’ progress than they have ever gotten before.

Tina

Thanks Tina and Dan for your responses, I’m looking forward to trying this in my classroom starting with tomorrow’s quiz

Dan,

I really like this idea. The one thing that is bothering me (and it was mentioned in earlier comments) is that a 3/5 = 60% or a D. You said, “a three is perfect conceptual understanding with minor mechanical errors.” Do you agree that this kind of understanding warrants a D grade? Would a C be more appropriate? I think that a D is a very poor grade (barely passing) and a student who has a perfect conceptual understanding of a concept deserves a little better. Or maybe I just need you to clarify what you mean by “minor mechanical errors.”

So, the only solutions I could think of would be using 0.5 increments (like a 3.5/5 = 70% C) or using an 8-point scale. Two 8’s would become a 10. Perfect understanding but minor mechanical errors would be a 7 or 6, depending on how “minor” the error. At least this way you could differentiate between the D’s and the C’s.

What do you think?

Oh yeah, one more question. Do your students need to get two 4’s in a row or two 4’s in any particular order to get a 5?

Krystle,

I think Dan mentioned that he does not require the 4s to be consecutive in order to obtain a 5, though certainly you can choose to implement that restriction.

As far as the 3/5 issue goes – I think it is probably reasonable since the students can choose to reassess. If you think the points are two low for the situation (“a three is perfect conceptual understanding with minor mechanical errors”) then you could decide to give half points, i.e., make that score 3.5/5 on your own grading rubric. I think the 1-5 scale is excellent for this kind of application, but you could also change to x/10 or x/100 and work out a similar scale.

@Dan – I have been reading your blog for the last week or two. Thanks for all of the fantastic information. You’ve convinced me on the merits of SBG, now I just need to figure out how to get it to fit within the heavily structured grading outlines that I am given from on high.

NOW… I have a little problem. I’m trying to make my concept quizzes harder for Geometry. Take volume for instance. I tried a little something out today to see what would happen. The kids needed to know the height of a pyramid, but I gave them the slant height instead, hoping they would realize they need to calculate it with the pythagorean theorem first. I know they know the pythagorean theorem, but they just overlooked it.

I know that’s combining concepts, but I can’t figure out how to make volume, surface area, or any problems like that MORE difficult without adding in a previous concept.

This has to make sense to you… because I know you’ve had the same problem.

What did you do?

@Eric, I like your idea of combining more than one concept. You want students to view using more than one conept in a problem as routine. If you get too carried away with this, though, it just turns into an intelligence test.

I love your ideas and am thinking about implementing it this year, but I’ll use it for next year for sure in my Geometry courses.

I noticed on your comprehsive tests that there are multple parts a, b, c, etc for each question number.

http://www.mrmeyer.com/blog/wp-content/uploads/070830_5.pdf

On your weekly tests do you just put 1 part or are there multiple parts on each number? If there are multiple parts do you try to give a 1-4 score for each part or just an overall score for the whole question?

Also, at my school we use the following grading scale:

A = 93 – 100
B = 85 – 92
C = 77 – 84
D = 70 – 76
F = Below 70

Should I adjust the percentage scores I give for a 3/4. 3/4=75% which is a C for most schools but it would be a D in my county. If I use your system, it seems harsh that a student who just barely missed a question is “rewarded” with a D in my school disdtrict. I was thinking of scaling the percentages as follows:

4/4=100% A
3/4=80% mid C
2/4=60% hi F
1/4=30% F

5/5=100 A
4/5=85 low B
3/5=75 hi D
2/5=45 F
1/5=35 F

Am I crazy to try to adjust these percentages to my county’s grading scale? Maybe I should just not use a 1-4 grading rubric. What do you think?

@gasstation
Sometimes the school district MAKES you put in a grade. It doesn’t matter how WE feel about it. I have no “obsession” with assigning numbers to categories… but we have to. So sometimes we have to look for a work-around.

I think SBG is usefull in some instances, but it is sometimes difficult to tell how much students understand and how much is just pattern recognition for different types of problems.

Keith Devlin has an interesting post on his blog that references this apparently well known study from the 1970’s: http://www.wou.edu/~girodm/library/benny.pdf .

In it is described a student that demonstrated mastery by getting 80% or better on a series of assessments that test individual skills or concepts. The student was very good at finding ways to answer the questions correctly, but had some serious misunderstandings about the content. It is a quick read and both amusing and interesting.

I think the study is relevant to some of the dangers of relying too heavily on assessments that test skills individually — even if the assessments are more thoughtfully done than the very low quality assessments in a heavily used online program.

@Timon
Well said. I’ve been thinking the same thing…

@mr bombastic

Great examples, let’s take a look at volume/SA.

If assessing volume ask, “Find the volume of the cylinder.”
If assessing SA ask, “Find the Surface area of the cylinder.”
If assessing their ability to choose ask, “How much material is needed to make the following pop can?”

Or something along those lines. That was a quick lame example, but I feel illustrates the point. With the first two standards I can see whether or not they can do the procedure, which for many students is difficult enough. The third question gives the student a decision to make; does the surface area or the volume tell me how much material is needed for the pop can?

Hi Dan,

I think that tracking assessment of distinct concepts to show growth and highlight areas that need to ba addressed is a powerful use of assessment. Similarly, basing your final evaluation on the final level of achievement also makes clear sense.

I was wondering, however, why you focus so heavily on concept mastery, but do not assess students on the development of their ability to use the math processes? Your teaching ideas seem to rely heavily on problem solving, representing and modeling, reflection and selecting appropriate tools and strategies. Shouldn’t you include assessment and feedback to your students on these areas as well?

Dan,
I just realized that this is where I should have posted my question:
Type I items that address basic details and processes that are relatively easy for students
Teacher asks: about this measurement topic, what are the basic details and processes students should
understand or be able to do fairly easily if they were paying attention in class?

Type II items that address more complex ideas and processes and are more difficult for students
Teacher asks: about this measurement topic, what are the more complex ideas and processes students
should understand and be able to do if they were paying attention in class?

Type III items that require students to make inferences or applications that go beyond what was
taught in class
Teacher asks: about this measurement topic, what inferences and applications might students be able
to make even though they go beyond what was taught in class?

Dan,
Concerning the above information, on my summative assessments, should I include “three-part questions” for each of my concepts?
Completing my first year of implementing SBG, I am beginning to reflect on what I might need to do differently next year. I am afraid my assessment questions might not always be authentic.

Another question? Because standardized testing is such a big deal in the state of KY, particularly End-of-Course exams and the ACT, should I include any multiple choice questions on my summative assessments?

I’m trying SBG out for the first time with my summer school Geometry class. I figure they’re good guinea pigs. I’m struggling with workflow as it is and I want to make sure I’ve got things in place to successfully start with this next school year (and not over-burden myself in the process…I’m known for developing fabulous plans that end up being way too hard to implement and quickly abandoning them.)

I’m struggling to decide if, during the school year (at least the first year) I want to just give them level 1 assessments in this way or if I want to do the two-level version. I’m committed to giving (small m/c) department cumulative assessments about every other chapter and district multiple choice benchmarks at the quarter marks (quarter 2 and 4 usually serving as the final). I know that the district benchmarks are very CST like (CA’s standards assessment). They’re set for next year. I’m happy with them (at least in Geometry…I haven’t seen Alg 2). I’m thinking that given those commitments, that level 1 will be enough AFA my concept checklist driven tests go.

I am thinking that, while it won’t be a one-to-one mapping of what gets assessed at that higher level compared to the lower level on the concept checklist, it’ll be assessed. The question comes up as to how to allow students to improve their grades on those higher level concepts. Do I map the common assessment questions onto my lower level concepts on my checklist? Do I treat each as their own mini-concept checklist and let them remediate and re-test on those? (seems like too many balls in the air)

You refer to students testing on each concept twice: once easy, once harder. That’s what I meant. (ie: one test would have Question #5-harder, 6-harder, 7-easy and then the next test might be #7-harder, 8-easy, 9-easy)

I am considering having my own assessments just cover the easy level, knowing that the benchmarks and the department common assessments in between benchmarks will BE that harder level assessment and aren’t really optional.

In a chapter or unit (algebra, geometry, or ?), how do you integrate SBG with “big picture” problems (like in ‘Math needs a Makeover’)?

Dan, Thanks for your quick reply. Do you introduce a new concept (such as volume of prisms) with a problem like the water tank, then have instruction/activities on skills, then assess (SBG), then go back to the water tank problem? I guess what I am looking for is the sequence and/or structure of how you “pull it all together” for a skill or unit. -Jill

Hi Dan, I have a question about how the logistics of “second questions” on a topic work.

Any question they’re seeing for a second time, though, give ’em a harder one.

When making up the daily assessment for the group, even if it’s the group’s 2nd assessment on a given topic, many of the students will not have achieved a 4 the first time, and thus may not be ready for a harder problem. How do you handle the logistics of this?

Also how many times will you put a topic on the daily assessment for the group? Just 2, or until most people have achieved mastery (and those who have just skip it)?

I’m a volunteer at a small private school. In the past I’ve taught mathematical problem solving and “contest math” where the goal isn’t necessarily “mastery” of anything, but rather taking a student from where she is to somewhere further along. But this year I’m teaching a small group (7 middle schoolers) the equivalent of honors Algebra I and I do want to make sure they achieve mastery (and hopefully retention) of the key concept areas. So I’m planning to use some version of your method, which I’ve loved since I first read your blog many years ago.

Was looking at sample Algebra 1 test above, so use to grading using percentage scale. How would I grade that test using four point scale? Seems easy when you have 4 problems/questions for each topic/concept, but what if you have only 1 or 2 problems/questions. I know am probaly making it more complicated than it is, but I want to adapt this for my science class. Any help on how to actually grade the paper, using the 4 poingt scale would be helpful.

I’m a relative newcomer to this blog, making my way through the old postings and very happy to be finding so much buried treasure.

This one is a whole chest full of gold!

Hey Dan… I had a quick question I’ve been wrestling with. I teach Algebra and Geometry and to make my Evaluating Expressions Concept Quiz an A-level I threw in decimals and fractions to make it harder. Very few kids are getting their second 4’s (maybe 2 out of 90) and I’m kind of torn about it.

On one hand, this is an old skill and if they want an “A”… they should be able to do operations with decimals and fractions. This is what the hard-ass side of me says.

On the other hand, I’m not assessing operations with decimals and fractions. This is what the unicorn side of me says.

Something tells me I’m destined to struggle with this the rest of my career…

I like to give a synthesis learning target every 5 or so concepts. This way I can assess how students are applying the more granular concepts into a multistep, more complex math problem. Harder to diagnose/remediate these types of learning targets, but shows the students that all of the other targets don’t only exist in isolation.

I’d love to see an algebra II concept checklist and assessment.

I started it last year at the beginning of Quarter 2 because I have struggled with the equity of grades for years.

The kids and the parents LOVE it. I have never had one complaint and I implemented it exactly the way Dan does it. It took me a while to figure out all of the intricacies of it… but it has gone wonderfully.

The stress level in my classes dropped instantly. I was no longer stressed about how kids were going to do on a “test”. The kids have COMPLETE control over their grade. Parent-Teacher conferences have never been better. If a student isn’t happy with their grade… they know exactly what to do about it. I can point to what concept they need to work on. And I was shocked at how bad 8th graders will work for a stamp. :) I have kids come in after a quarter is done working on concepts from 6 months ago… not to bring up their grade, but just to get a stamp on their checklist! Craziness.

The stress of homework completion has dropped dramatically. Since homework and classwork is only 20% of their grade… kids focus more on learning a concept to bring their grade up as opposed to turning in missing assignments.

I have practice baskets for every concept on the wall, so that if they are struggling with a particular concept and they need extra practice… they can practice till their hand falls off. And the amazing thing is (and you just can’t explain this to people that don’t grade this way) they WANT to practice. Since Concept Quizzes are 80% of their grade… they realize the importance of learning the skill. I also probably give 5 re-takes a day during lunch or after school.

I will say this… it was a lot of work up front. And I get that comment from almost every teacher I’ve talked to about it. “Isn’t it so much work?” Well, yes, it’s more work initially. But it gets faster the longer you do it… and I truly believe it is what’s best for the students.

Hector, I am in my second year using this system. I had so much success with it last year that we have gone department wide with it this year. I have to say that I feel bad for giving unit tests to 13 years of students before switching to this system. I now realize what a complete waste of time unit tests were. They took a whole class period to review for, a whole class period to administer, and a whole lot of pro bono time for me to grade. And for all that, I got very little useful information from the results. I think it’s fair to say that no, I don’t miss having them at all. :)

Advice for starting off – do as much front loading as you can in terms of the quizzes. Last year I worked with a colleague over the summer and we set up a bank of 6 questions for each concept. I then drew from that bank to make the quizzes. We found that focusing on the types of questions we wanted to ask one question at a time allowed us to be very strategic in how we wanted to assess. I saved that bank and still refer to it when I want to see all the questions for a concept at a glance. It’s really about the same amount and type that would be asked on a unit test, just spread over time. Also, make sure your concept list is done in the order you will be teaching. Last year we had a couple mistakes in the order and the numbering on the quizzes got very confusing mid-year.

Good luck with your transition to this system. I think you are going to love it!