Hi Dan,
Thanks for posting this. I’m in the process of beginning to teach, and I wish my alternative licensure program would have given us nuggets like this. It makes sense to me. I have a couple of logistics questions for you:
What type of rubric do you use for assigning a final grade?
Do you still administer traditional final exams?
Do you find students don’t have sufficient practice with longer tests? Could be a possible disadvantage that you might have to counterract, especially for AP classes…
How many questions per skill do you use on average for each assessment?
Many thanks for this, and for all of your posts so far (I’m reading as of 27Dec)!
You remind me of a former co-worker of mine. It may be that you are meant to do things other than teaching, but I bet there’s a lot more teaching in you yet. And once you leave, be aware, you will do nothing but teach. (Out in industry, I never realized how much of my job was teaching until I decided to go back to school so I could teach high school math.)
Grazie,
Kay

Dan,

I’ve been doing this type of assessment (different method, but same idea) this year as well.

And I have to agree with the statement you said about how this is your best year of professional development. And especially, this is the “year that assessment changed, and then changed everything for me.”

I spent four years teaching and not feeling comfortable with assessment (and especially with communicating to students and parents about those assessments and what they really meant). Then I became a gifted intervention specialist with a more time to explore what assessment really should be.

Now, I’m teaching fifth grade and have radically changed so many of my practices. However, like you, I’m still perfecting. But the message I want to share with everyone who reads this is, that for the first time, I feel like I’m actually doing things in a meaningful way and that, for the first time, I can fully explain the “why” of what I’m doing. And, in a strange way, I think assessment is easier now and less time consuming because I get the information I need, the students get the information they need, the parents get the information they need and it’s not this big “secret” about what we’re doing and why.

But, as one teacher trying to figure this out to another, I’m wondering how you handle report cards. For example, Johnny hasn’t yet figured out how to multiply fractions, but it’s the end of the quarter and grades must be assigned. He hasn’t yet mastered that skill, so perhaps he’s at a “B”. However, in the second quarter, he gets it. If we had a different reporting system, we could check him off on that skill on his “official report card”, but in my district we can’t go back and change grades. Do you have any thoughts on that?

I am familiar with Tomlinson. Do you have a title of the article? She and many other voices have swirled together in my mind to help me form my understandings about education.

Unfortunately, I have to agree with you. I won’t be able to do much about the time of mastery if it happens after grades have been cut off.

To work with the situation, I’ve tried something this year that seems to be going well.

I’m sending home, with each report card, another sheet of info. On this sheet, I list all of the standards we’ve been working on that quarter and highlight any that the student is still “squeaky” on. (We use the term squeaky in my room because a squeak can always be oiled. It doesn’t represent a permanent deficiency.) So the parents can very clearly see what their child is doing well and can see areas that need work.

There are two reasons I do this. One-I truly want the students and parents to know meaningful information about their education. An “A” or “B” on the report card doesn’t really say much. And it helps me to see it all laid out for each student.

And two-I want the parents to start saying, “Why don’t we get this type of information all the time?” I want them to start expecting it and to start to question the way things are done. I want them to see the value in knowing specifics about their child’s learning. I’ve found that when parents start demanding, school districts listen. If parents see the value and want this type of information, perhaps it might become reality.

I do know that my parent/teacher conferences this year have been WAY more meaningful and successful than any I’ve had in the past. And that was because I had meaningful things to say, rather than just something like, “He didn’t do well on the chapter test.” What does that mean anyway?

Mindy

ps-Dan, I’m so glad I’ve stumbled onto your website. I’ve been craving this type of dialogue with other teachers. As I said I have a few teachers in my school who aren’t afraid (is that the right word) to explore the fact that we might not be doing things in the most meaningful way. But we don’t have as much time as I’d like to discuss these important issues.

Anyone know of a dialogue like this going on about reading instruction? I have some questions, observations, and disagreements there also!! Reading is the area I could really use some help.

Mindy, email me at nbosch@aol.com and I’ll send you the name of the Tomlinson article or the article itself. It sounds like you do a wonderful job in your classroom. After 21 years of teaching gifted students, I could not fo what you do day in and day out. Kudos to classroom teachers, N

Reading your entry how math must assess reminded me of a program we have instituted at my school. It is called Accelerated Math. It is broken up into objectives instead of chapters you can get an example of how subjects are broken up at http://www.renlearn.com/mathrenaissance/ContentLibraries/

they also provide individual review cards for each objective so that a student can review an objective they did poorly on.

The main difference seems to be that accelerated math is all managed by the computer instead of a teacher.

My biggest warning is it uses a lot of paper. about 1000 pages per student per year, and that is with using the program only once a week with regular teaching the other 4 days.

If nothing else you might want to poke around there website for some ideas

Dan,
I have been developing an assessment system that is similar to yours in record keeping for my Algebra and 7th grade math classes. I’m interested in knowing a little more about how you design your assessments and grade them.
From the sample test on The Audit it looks like your assessments are not multiple choice. When you design assessments, are they ever multiple choice? Is your final exam multiple choice? I am wondering about the effects of this on their CST exams.
When grading assessments or assigning them, how does a student know if they’re after the first four/second four (5?)? Are there generally two questions (one “4” and one “5”) on each concept on a test?
I am in the process of refining my own system, and I really like many of your ideas!

Dan, I’d love to hear more of your thoughts on multiple choice. I do 0% multiple choice, other than when we’re doing our Stanford testing. Initially my students are less-than-thrilled when I tell them that I don’t “do” multiple choice, but I try to help them see that this way I’m actually looking at their work to see how they arrived at their conclusion/answer. I’m fairly strong on developing their process skills, so I fear that a focus only on the answer (i.e., via multiple choice-type testing) doesn’t encourage their process skills.

While a common argument against my format is that it’s “soft” on correct answers, I am extremely “hard” on correct answers (if hard = emphatic about). Ten years of engineering before my teaching career taught me well that accuracy in my math work is critical (I could tell you a story about an entire apartment site where the buildings are all about 6″ too low).

I’m keenly aware that my preference for non-multiple choice obviously leads to more grading work for me – I am writing this as I finish up the third batch of final exam papers!

Multiple choice tests are interesting. If stuck, the student can start from the given answers and work backwards. A handy probability trick is also to eliminate all answers you don’t think are correct and then make a higher probability guess. These are problem solving skills that multiple choice testing helps to encourage.

That said, I’ve known several students who’ve used multiple choice test tricks as a crutch for lack of understanding with much success. I applaud you, Dan, for requiring full work to justify an answer to a multiple choice test question, but otherwise I’m wary of the format. It’s best not to teach bad habits, because in engineering you don’t always have a finite set of possible answers to work back from.

I understand the desire to familiarize the students with multiple choice questions, but make sure the tricks aren’t tolerated!

I’m not coming down all that hard on multiple choice, and I have to acknowledge that for the foreseeable future, students’ test-taking skills must include the ability to succeed at multiple choice tests (our era of standardized testing seems to confirm that). So I’d agree with Steve’s point about narrowing down the pool of possible answers to the best/smallest set sure helps — and I do coach my students on exactly that when we do our annual Stanford test (since we’re private, we don’t do the FCAT, which is Florida’s equivalent to your CST).

Now since I’m here and on the topic of assessment, I’d love your thoughts on this: our school (remember, I’m at the middle school level) doesn’t require any cumulative testing during the year until we get to final exams in May (just did them late last week). Their primary rationale for doing them at all is to prepare our students for high school, when they will presumably take final exams twice a year in most every subject. However, up until late May there is no requirement imposed on any teacher to structure her/his testing other than just to do what’s deemed appropriate. But what I’m finding is that after such an extended period with no structured cumulative testing (yes, I know that in math much of what we do is by its very nature cumulative, and yes, I’m still expecting my students to remember what they learned all through their previous years of math in elementary school, but I’m talking about pulling out questions that we tested/quizzed on back last August, last September, last October and so on. So you could say an “explicitly” cumulative test, not implicitly cumulative.)

My students sort of get starry-eyed and tend to freeze up because they’re used to doing sprints for my class assessments, not marathons (a tangent – would some connectivists suggest that we should prepare them more for relays??). I’m thinking very strongly of adopting/adapting your proposed approach for weekly quizzes, based on a sliding set of questions, the four-point scale, etc. for next year. But what would you think if, once per quarter, I also threw in a cumulative test “experience” so that they could stay in shape for the longer haul too? That is, the first quarter’s test would cover what we learned in the first quarter, the second quarter’s test would cover the first and second quarters, and so on…. until we finally reached the final exam in May, and it didn’t seem so darned scary and huge!

I’m just wondering what you (and other readers) think of that….

Going back to the multiple choice tests, it seems to me that the best way for students to prepare for them is to actually write multiple choice questions of their own. They need to get into the habit of trying to anticipate how those three or four wrong answers are chosen. They aren’t just pulled out of thin air, but rather are results of common computation/logical errors. If the students have practice trying to trick themselves or each other with their own multiple choice questions, they will be better able to get inside the heads of the test designers.

Dan,

I’m quite intrigued with your assessment plan. A few questions:

1. Suppose the first assessment of the year tests skills A, B, and C. Do you write one problem for each? i.e., is it a 3-question test?

2. Suppose Suzie gets A and B correct, but gets C wrong. Suzie gets 4 points for A and 4 points for B. How many points does she get for C? Would it be 0 to 3, based on her work?

3. Now suppose Clarence gets C correct, but gets A and B wrong. So he gets a 4 for C and something less than 4 for A and B.

4. On the following week’s test, you have skills A, B, C, D, and E (i.e. you have a second crack at A, B, and C, and you introduce D and E for the first time). Are the questions for A, B, and C the easier types of questions, or the harder types? Clarence seems to need an easier question to answer for A and B but a harder one for C, while Suzie needs an easier question for C but harder ones for A and B. Of course, this easier vs. harder question issue resurfaces with each successive week. Do you provide an easier and a harder question for each skill tested on each test?

Thanks in advance for your time.

[Edited to close a couple html tags.]

Hey Dan,

I stumbled on your website while looking for assessment alternatives for math and I was thrilled to find something I can use this year! Just a question: I teach in Alberta, Canada, and our curriculum covers more than just concepts. We are also expected to assess other areas (communication, connections, problem-solving skills, reasoning). Some specific examples to be assessed are: use math in everyday life; recognize how different math concepts are connected; explain how manipulatives, pictures or diagrams were used to arrive at an answer. Do you have ideas on how to assess these in addition to the tests you give?

Thanks again for helping me out already!
Becky