I have been interested in assessment ever since I stepped foot into education. I have always grabbed onto the constructivist framework of education - specifically the inquiry-based approaches that has been promoted by people like Darling-Hammond, Boaler, and more recently from the blogosphere, people like Meyer (both of them [@doingmath]), Doran @nik_d_maths , Nguyen @fawnpnguyen, .... and so many more. The question for me has always been - how do we appropriately assess these approaches? (this was in fact the question that I asked @ddmeyer when I met him a year ago)
Mathematics Assessment is in fact the focus of my M.A. All the research I deal with are primarily built on the foundation of inquiry-based learning, and necessitates standards based grading. With the emergence and acceptance of inquiry-based approaches, the challenges of assessments has taken a drastic turn. How do we develop appropriate assessments for the way that we are facilitating discussions? An activity like this where students are engaged in the process of learning, and are effective in demonstrating their understanding of various concepts... how exactly would we assess this? (my concerns are currently the summative and evaluative functions... which I will explain later) In my mind, there is a huge disconnect between the way that we are facilitating learning, and the way that we are presenting our evaluative assessments. All this stuff is precisely what I am (have been, will be) working on. It sounds like I gave a lot of detail on what my thesis entails... but my topic is actually a lot more specific. I will probably write about it later.
Which is why the recent growing interest in assessment in the blogosphere is exciting news to me. Daniel @mathymcmatherso and Tina
In any case, I thought I might start off what will likely be a series of posts about assessments, beginning with my general understanding of assessments (I won't say it is THE way to think about it, for obvious reasons!).
Assessments are not just in written form. There, I said it.
It seems like a silly distinction to make, but it's actually a very useful one. It's difficult to narrow down a one-liner definition for assessment, but we can begin to unpack this big idea by looking at the associated functions of assessment: formative, summative, and evaluative.
These three functions are huge ideas, but I will talk about them generally and separately. I will just tackle the formative function first.
The formative function of assessment is a huge piece of student learning. It's not just a buzz word that's being thrown around in interviews or teachers college. Dylan Wiliam, in my mind, brought this idea of formative function out to the forefront back 2 decades ago. The main concepts behind formative assessments have not changed. However, the details have been altered throughout the years. The most recent one that I am aware of states: "An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have taken in the absence of that evidence."
Heavy sentence, I know. Wiliam unpacks some features of this definition:
- it is based on the function served by the information yielded by the assessment, rather than a property of the assessment itself.
- the assessment can be carried out by the teacher, the learner, or her peers.
- the focus of the definition is on decisions regarding next steps in instruction, rather than intentions or outcomes.
- the definition is probabilistic
- the assessment need not change the direction of instruction (it might merely confirm that the planned subsequent actions were appropriate).
Now, you may be wondering why I wrote "formative function" instead of "formative assessment." Isn't that easier to write? Well, that's actually exactly what I've been trying to avoid. I don't believe that assessments should solely be formative -- and since "formative assessment" implies that it has a singular purpose, that phrase is not as useful to me. What do I mean? Well an assessment is what it is. It's an assessment. It is what we do with it that determines the function. Let's say it's an assessment in written form. If you decide to have them write it, give it back, then have the kids discuss and generate answers together -- then that's formative, and probably summative as well. I think a lot of teachers jump straight to the evaluative function of assessment, and they develop separate special "formative assessments."
Everything we do as teachers is for the sake of facilitating effective student learning. Assessment is a huge part of this. In a way, teachers are like researchers. We are gathering information about our subjects so we can accurately construct a picture of their learning. Any puzzle pieces that we obtain -- are assessments.
I plan on writing more on assessments and what I have learned about assessments in the future. I will likely explore more of the conceptual structure of assessment. If you are more interested in the pedagogical concerns, let me know. I can share how standard-based grading functions in my classroom, or how I deal with open-questions and why my tests have never had marks on them?...etc.
See, this is another reason why I didn't get to this blog post... It's such a giant topic for me. I have way too many things that I want to talk about that it's hard to break it down to manageable pieces. Oh well, one step at a time :)
Hopefully this roused some interests and questions for you to explore too!
*Click here to continue to read about my assessment practices
*Click here to continue to read about my assessment practices
I *think* I followed some of what you're saying (it's late and English wasn't my major for a reason :) ), but let me take a stab at it.
ReplyDelete"I don't believe that assessments should solely be formative -- and since "formative assessment" implies that it has a singular purpose, that phrase is not as useful to me."
Maybe this is why I never liked using the words "formative" or "summative" assessments (and not my lack of understanding of what they are...). Except for end-of-year exams, hopefully all assessments are both.
Is that sort of what you're getting at?
Oh, and because of blogs, I've rewritten every single quiz in all three of my classes this entire year to match this "Tiered Assessment" format that I found out from Steve Grossberg--you should check it out if you're into assessments. I've blogged a few times about it, but it's changed the way I've approached those kinds of assessments. One of those "I'll never go back to the old way again" changes.
"Maybe this is why I never liked using the words "formative" or "summative" assessments (and not my lack of understanding of what they are...). Except for end-of-year exams, hopefully all assessments are both.
ReplyDeleteIs that sort of what you're getting at?"
That was definitely part of what I was trying to get at. Narrowing what we can use from the results of assessments is very dangerous.
Tiered instruction + assessment is a very interesting concept. It does have a few challenges though, and I've heard a lot of arguments against it (good ones... I ignored baseless arguments). I have tried something similar in the past, I might share that at some point in the future? I will check out Steve Grossberg to see specifically what examples you are thinking of... unless you can throw a link my way? I am assuming you are not talking about this guy: http://en.wikipedia.org/wiki/Stephen_Grossberg
Haha, no, that is NOT the Steve Grossberg that I was referring to :)
DeleteHere's his blog on it:
http://itsallmath.wordpress.com/2012/08/23/tiered-assessment-for-geometry/comment-page-1/
I hadn't heard of "Tiered instructions + assessment" until you mentioned -- all of my knowledge of this "Tiered assessment" comes from that post. Here are other posts of mine on that kind of "Tiered assessment":
http://hilbertshotel.wordpress.com/tag/tiered-assessment/
I'm curious: what are some of the arguments against it? I much prefer it because it gives weaker students a way to say "hey, I can learn this much material and pass" yet gives stronger students a challenge to receive a 100.
Maybe I went over that response with too much of a broad stroke... I definitely liked the tiered assessments when I first used it. I saw a lot of pros with the method, but alas I had to divorce it.
ReplyDeleteOur school board had a push towards tiered assessment a few years ago, and then they left it once they encountered some convincing problems - along with some supporting research.
Our example was implemented was through levels instead of ABCD that Steve and your example seem to have. It's pretty much the same idea, though, except it's Levels 1234.
One of the problem was student choice - as it impacted self-efficacy, and motivation. Students were starting to peg themselves as a certain level. This then had a spiraling effect on what they think they can attempt, which affected what they actually attempt...etc. (this was actually the main selling point for me. I tried a lot of different things to mediate this effect)
Another problem was restrictions on the questions. Instead of thinking of questions as opportunities to demonstrate a certain level of understanding, the questions were becoming the dominant part - the deciding factor of student achievement. So the focus shifted away from evidence collecting and became too narrow. This may be fine for closed "level 1 and 2" questions like find the derivative of f(x)=sin(x), since there aren't many extended opportunities for students to show much more than the basics... but "level 3 and 4" questions became inaccessible to students, and sometimes they are still closed questions depending on the teacher. They are just harder.
Our current focus is establishing open questions that have multiple entry points and allow for opportunities to demonstrate a range of understanding. I am not sure if this was a helpful or clear explanation... let me know.
Wow, never thought of those points before!
DeleteYeah, I struggle with not just making them "harder versions of the same thing"--often my quizzes are just that and sometimes I think that's okay. But yeah, for me, it encourages me to continue trying to find those open-ended questions which allow students to show more than the basics.
About the "students pegging themselves in", now that you mention it, I can see that as a possibility, but I really wonder how many students would try all the problems if there weren't numbers next to them? I do want students to stretch outside of their "comfort zone", but we also have to be realistic. I wonder if there is a way to test this hypothesis. I mean, we an envision a student trying an 80-point problem, and that being a stretch for them conceptually, versus another student who is not challenged by a 100 point problem. But other than asking them (which would be subjective), how could we test that? (I may do just that--ask them then blog about it!)
In my classes, there are so few students that don't at least attempt the harder problems that I don't think it discourages them. Much more often, they're facing time constraints, and this allows them to see "hey, if I can understand this small part, then I can pass". I guess it's my job to make that small part hard enough that they really learn something when getting just a passing grade.
One more thing I did recently was make the first few questions still in "failing" range: so a 70 is passing in my class, and the first question only gets them up to a 60. The students now know the quizzes as 60-70-80-90-100 quizzes, like them.
It is interesting because I'm teaching 2 sections of Precalculus: one full of juniors and the other only seniors, and of course the juniors are ahead of their peers (other juniors who are in Alg II or Geo) because they were selected for their math ability. And I give the same quizzes to both groups, and I honestly don't mind the Seniors to not always attempt all the problems. There are a few who do really well, but I believe most recognize their "limit" and simply do the best they can.(Is it dangerous for a teacher to think of students having limits? Whole 'nother topic.)
On the flip side of the coin, I've definitely had students not try sections of problems on my tests (which are not tiered). So are we just getting students to try all the problems by keeping back information about which problems are harder and which are easier?
Yeah, lastly, my *hope* is that my Participation Points scheme is getting students to broaden their horizons (read: answering open questions), even if my quizzes do not always (or ever) help them do that.
Okay, I'm starting to ramble, but I definitely now want to blog about these thoughts--thanks!!