I do agree with your general point, but the numbers about what people remember seem to be similar to what's often associated with Dale's Cone of Experience. The research for that is not exactly solid, although similar numbers are repeated all over.

Where did you get your set of numbers for remembering 5%, 10%, etc.? Is there research that we can see to look at that?

Will Thalmeier has written about this extensively previously.

One aspect of assessment that continues to be controversial is the idea of assessing effort. You say a grade is a reflection of time, energy and effort. Many would argue that's not really a great way to assess. Assessment should consider achievement regardless of effort. What this needs is a pre-assessment to measure understanding at the beginning of a course. If at mid-term, a student has achieved learning, it may not have included traditional types of "effort".

There are 2 big gaps or variables here that continue to plague my thinking. First is the quality of the assessments themselves. Traditional paper and pencil testing likely still has a major place in the Mathematics world but in general is overused and still isn't providing us with accurate pictures of learning as your describing. In our efforts to be more accountable, I fear us stooping to the lowest common denominator in order to crank out data. Second, our perceptions of what is required to learn is also fairly narrow. We place high emphasis on attendance for example. That may or may not be a factor given the opportunity students have to learn outside the classroom.

These are simply some topics that for me, continue to cloud the ideas of assessment.

This is exactly why math teachers seem to know so much. They teach the same content year after year (hopefully improving they way they present) while the students try small sets of problems. After correcting work for a while, you get to know where things are going to go awry. You can't help get better at the subject.

I'm still working on changing the way I enable the students to create with mathematical content. The blog my sixth graders started with me this year is a step in that direction.

I'm not at all surprised at the huge swing in grades from 30 - 80 on the same test. For such a precise subject, grading from teacher to teacher is very subjective. Thanks for linking to NCTM's materials.

Darren,
What you have done with students creating content is inspiring. I think that this is harder to do in Math than in other subjects and a post like this reaches far beyond the scope of mathematics.

Dean, when Darren said,
"I don't believe a student's grade in any course is a measure of their intelligence. I do believe it is a measure of the time, energy, and effort invested in the class."

I don't think he was suggesting marking effort, simply stating that the mark often reflects the student's effort. As a math teacher I've seen 'B' students cram and memorize enough before a test to pull off an 'A'. Is there understanding at an 'A' level? I would argue 'no' for some of them. Likewise I've seen students fully capable, but without the effort their marks slide. So I concur that often a student's grades are NOT a measure of intelligence.
The idea that, "we're not going to throw out hundreds of years of tradition" is obtuse. Perhaps for the sake of tradition we should continue bloodletting for fevers or, for a more specific educational example, maintain corporal punishment in schools and bring back the strap!

Like the workshop you once attended, I ran a similar activity at my school, with my staff, where a test was marked with results ranging from 40-90% depending on the teacher (these were not all Math teachers).
http://eduspaces.net/dtruss/weblog/160945.html
Dean's two concerns are where I also struggle,
What are we assessing? Is our assessment measuring what we say it is? Are we assessing the right things?
As well there is one more thing I struggle with in teaching Math, which is finding the balance between rote memorization and concept comprehension. Both are needed (as I mention in the post linked to above) but finding the right balance in Math is tough.

One final thought...
Have you ever heard a teacher say, "I can tell you my students' final grades after the second test"?
Well to me, the dirty little secret is that if that is the case, have we truly taught them anything at the end of the term?

Darren,
You said, "I don't believe a student's grade in any course is a measure of their intelligence. I do believe it is a measure of the time, energy, and effort invested in the class."

Where is the teacher's role in this? How do we factor in the teacher's willingness to differentiate their instruction to accommodate for their students' struggles with the material? How flexible is the teacher? Can they adapt their material even if only one student doesn't "get it?" Isn't it our responsibility as educators to help our students master or understand the material to then use it in meaningful ways?
I work with too many students who invest time, energy and effort and still struggle with understanding and mastery. Whose fault is it if they are failing the tests?
Or how about the math teachers who don't give partial credit when the student demonstrates understanding of the concept but makes a "careless" error? Do punitive grading methods have any place in our classrooms?

Is the issue tweaking grades or scrapping them entirely? (my preference)

I concur with Seymour Papert who gave two grades at MIT - A & Incomplete

While I agree that teachers are part of the problem with the methodology they choose, at least at the K-6 level parents are also determiners of how math is taught as well. My district has several schools in the top 10 for the state of California in regards to standardized testing. Last year nearly 80% of my students showed an advanced level for math. As a consequence because I knew the math book would not be a challenge to most of my students I attempted to incorporate an NXT Lego robotics program in my 5th grade class last year to teach more advanced math concepts and shared with parents the NCTM 6-8th gr. math standards that were being met as well as the information and examples on the lessons designed at Carnegie Mellon. The attempt was soundly shot down by parents who preferred more text book and less robotics to teach and learn math. I now have 15 robotics sets sitting on a shelf gathering dust.

@christytucker Thanks for the link! I have also received an email from Christopher Harris who has also blogged about this hoax. (I love librarians! ;-))

So, the numbers are not based on any research at all. (I will edit this post to reflect that.) Nonetheless, as a teacher I know having to "teach" mathematics required a much deeper understanding of the content I had learned previously. As a general pedagogical principle, based on my experience and the experience I've had with students in the classroom, I stand by the idea of having students create content that educates as a powerful learning practice. Hmmm, maybe this is what I'll research when I get around to doing my Masters degree. ;-)

@Dean: The second point first. I do place high value on attendance. While students can learn the content outside of class, on their own, and well enough to do very well on standards tests, their learning is stunted (compared to their classmates) when they miss out on the conversations we have in class. Those conversations are how they acquire a deeper understanding of the content as they wrestle with the thinking of their classmates and we debate issues such as "good form" (how work should be clearly represented), special cases that arise in different mathematical contexts, the extreme limits of a problem (considering macro and micro perspectives), and common errors and misunderstandings.

It is only by "being there" that "teachers can engage students preconceptions." (see How Students Learn, finding #1)

The nature of assessment is also an important consideration. Research shows (Keeping Learning on Track: Formative assessment and the regulation of learning, Williams (2007))that students assessed using comments pointing to the steps required for improvement can result in improved standards test results of up to 30%. Students assessed using traditional grades see no such improvement, and perhaps, a decline in their learning.

Tough nut to crack, this. We still have to come up with "a mark." I'm still thinking about how I'm going to put these results into practice next semester.

@njtechteacher: While I agree with your general point, curriculum isn't really static. It's constantly changing. We're about to go thorough some sweeping changes in the math curriculum, K-12, here in Manitoba and across Western Canada.

With that said, I know I do try to change things up a bit every time a teach a course. Like you, I'm still working on how I can help my students amplify what they are learning. I guess the advantage we have teaching the same course multiple times is that we understand the content better each time. Deepening our own understanding allows us to also deepen our teaching. I think most teachers try to do this.

The huge swing in grades also came up last month when I did this exercise with the teachers in my Dept. We are spending the next few months reevaluating how we mark our unit tests and trying to develop some common practices vis a vis how we mark tests.

@datruss: Thanks David. ;-) You're right. I wasn't suggesting that we mark effort. I have a lot of very smart students that don't get good grades. My principal likes to observe how many of our "A" student graduates end up working for our "C" students. There's definitely a disconnect between student's scholastic achievement and success beyond the walls of the classroom.

I'm of two minds about your comment re: teachers who can predict their student's final grades at midterm:

(1) Bang on! This is one reason I'm continuing to have them create their Developing Expert Voices projects. So they can dig deep into what they have been learning and show it off to a wide audience beyond myself.

(2) I can also predict some students final grades at midterm. Like I said, I think grades are more a reflection of time, energy and effort expended by the student. If the student refuses to learn or make an effort to engage with the material we are learning then their midterm grades are often very close to their final grades.

@karenjan: No. Punitive grading doesn't belong in the classroom. Formative and summative grading does and I think there should be more formative than summative grading. I'm still trying to find the right balance. I'm not sure their is an optimal balance which is why assessment is such a thorny issue.

I certainly agree with you that differentiating instruction for struggling learners is an important part of all this. The interplay between instruction and assessment is such a messy game. I suspect this is why we've been having this conversation in education for decades; it may be one of the "unsolvable problems" of education.

Math has it's set of unsolvable problems. Fermat's Last Theorem used to be one of them. Maybe an Andrew Wiles will turn up in the field of education too. ;-)

@gary: I like that! A & Incomplete. I wonder how my principal/students (or their parents) will feel when I start grading like that? ;-)

@derrall: Oy!

Darren,

But won't achievement suffer because they've missed out on those conversations? It seems that you're punishing them twice. Once for not attending, and once for not achieving.

On the other had if they attend and do well, they're rewarded twice. If they attend and don't achieve, perhaps the conversations and value of attendance was not reflected in the assesment so it was flawed to begin with. If they don't attend but do well...then again, the learning through conversations and attendance likely wasn't included in the assessment.

If on the other, attendance is important and valued because of ideas of social learning and contributing to the learning of others, then I can see its importance regardless of a direct link to achievement. That's what I'm trying to foster in my undergrad classes. You aren't only responsible for your own learning but others as well and they will be assessed specifically on the level of their contribution to others. Sometimes this occurs synchronously and other times and more likely it occurs asynchronously or at least away from large class gatherings.

Another of academe's dirty little secrets: grades don't really reflect the quantity or quality of what students have learned.

In one of my classes today one of my most mathematically wounded students started participating in class. Standing next to her, at the back of the room while another student was sharing their work on the SMARTboard, she quietly started talking to me; sharing her understanding of what was being written on the board and correcting the work of the student at the front of the class in a way only I could hear. I can't tell you what a quantum leap this is in her learning, yet, it will never be reflected in any grades she receives and she'll most likely fail the course.

It sounds like you feel students are "unfairly" penalized when they do not attend class. Attending class results in all sorts of learning; some deep, some incidental. Students have a choice and there are consequences for the choices they make. I don't think that's unfair. I think that's reasonable, and fair. Students are free to choose not to learn. Any penalties they incur are a direct result of the choices they make. Aren't there consequences for you if you don't show up to work?

You said: "the learning through conversations and attendance likely wasn't included in the assessment."

Sure it is. All the common errors that were pointed out in class that the absent student didn't know about effects their test scores. How to deal with an ambiguous question (which often comes up in probability and combinatorics) we discuss in class. The absent student will do the best they can and gamble that they address the question in a way that maximizes the way they are assessed.

Attendance is important. As you say in your last paragraph, esp. as they come to rely on each other for their learning. I've seen that more and more as a direct result of class discussions that flow from each night's scribe post. The sense of ownership they have about their learning and their sense of responsibility towards helping each other learn are things I've only seen in my class since I established a blog for every class. Before the blog, this sort of thing just didn't happen. I suspect you found (and will find) the same with your classes at U. of Regina.

My point is simply not that attendance isn't important but it shouldn't be separated as a component of the assessment process.

The student you mentioned that demonstrated her learning shouldn't be given credit because she showed up but maybe because she gained understanding and/or insight.

To me it's almost akin to giving kids credit for having a tidy desk or binder. Yes, those habits may assist in learning but that's not the issue.

Even in the work place, the bottom line is "did you do your job?"If I can do my job, however that's defined, in whatever way or space I choose, that should be good enough. If I'm not doing my job, perhaps attendance or other habits may be the issue and they should be addressed.

Unless attendance is spelled out as integral i.e. if you work in at McDonald's you have to there, it's simply a habit that may or may not benefit your achievement.

In the case of school, again, it might be important, in your case i can see why but I wouldn't assess it since their level of achievement will be reflected in other areas. There's no need to isolate it.

Attendance is my class won't be graded separately but their contributions will. That does mean that they will need to attend for the most part but I'm also going to ask them to assess their social learning experiences that occur asynchronously as well. My course has no final exam so that may make it different but their work and learning should reflect conversations, readings and viewings that occur in all kinds of ways. Attendance isn't the issue, social learning is.

I agree. Students shouldn't get marks for attending class; they don't in mine, nor, it seems, do they in yours.

You said: "Attendance is my class won't be graded separately but their contributions will."

Grading their contributions in a fair and meaningful way is the difficult part. Imagine two different students who fufill the requirements of "making a contribution". One by following the guidelines you give them precisely the other by genuinely engaging with the material produces work that is qualitatively superior because it goes beyond the guidelines you've given them. To be fair, how can you give them the same mark? How can you not?

The nature of the course you are teaching is very different from what I teach so it's natural that the nature of the assessment should be different. The hard part, IMHO, in a course like yours, is that even if you articulate the assessment criteria in a way that everyone understands what is required to get an "A" all the "A" students will not be equal and it's very hard to reflect this in a single grade.