Does anyone have a succint way to explain the difference between Teaching to Mastery and Spiraling? I am eagerly searching for clarity/brevity of speech.
(I find myself giving too much information and sounding kindof like a conspiracy theorist when I talk to people about math education these days.)
update from Catherine
I would start with this "fact sheet" I put together for a PTSA Forum a couple of years back (scroll down).
The salient passages are these:
You know, talk about curriculum, if I put in front of you a fifth, sixth, seventh, and eighth grade textbook in math and opened up to page 200 and I jumbled them up, and said, “order them from fifth through eighth grade in order,” you'd have a very tough time because they all look the same. That's because, unfortunately, we have this national strategy of “we're not really going to teach to master, we're going to teach to exposure and over lots and lots of years of kids seeing page 200 in the math book, eventually somehow they're going to learn it. We're going to teach them how to reduce fractions in fifth grade, in sixth grade, in seventh grade, in eighth grade, in ninth grade and continue until finally somehow magically they're going to get it.” Instead of thinking, “let's teach the kids how to reduce fractions at a mastery level in fifth grade, maybe spend a little time reviewing it in sixth grade but let's move on to pre-algebra and let's move on to algebra then.” And that's been our take and so it's not that we have a different math curriculum as much as we have a different math strategy and a different math philosophy.
Interview with Mike Feinberg, Co-Founder Knowledge is Power Program
(oops - just found this sitting open on my desktop - more in a bit)
Mr. Person responded to this some months ago when I asked a similar question. I think he said that spiral is defined as revisiting the topic several times within the same year Incremental is what Saxon does...a little bit each day. And Singapore is an example of mastery in which all the objectives for that topic are achieved and tested when the topic is presented. It doesn't mean that the topic isn't revisted the next year though. If the topic is taught the next year there would be a brief review followed by te teaching of new information and skills.
ReplyDeleteSingapore provides "distributed practice" of prior topics by requiring those skills to be used in the problem sets of new topics as well as periodic reviews.
As I understand it the problem with revisiting the topic over again the next year, as it's done in junk math, is that the kids are never accountable for knowing what to do. "Don't worry about not getting it, he'll get it again next year." Or if they are held responsible, through testing, then it's the parent that ends up doing all the teaching.
oh gosh, we must have zillions of succinct statements lying around
ReplyDeletegood grief
suddenly I'm feeling myself gripped by an impulse TO GO TRACK THEM DOWN
HMMM...
I'm thinking the first thing to look at is the hand-out I did for the PTSA Forum a couple of years ago.
back in a sec
don't worry about sounding
ReplyDeletelike a conspiracy theorist;
there *is* a conspiracy
and it ought to be opposed.
welcome to the desert of the real.
VME
Spiraling seems to have different definitions according to who is using the term.
ReplyDeleteWhen it's used in conjunction with math reform curriculums, it means going over a subject in which some kids show "understanding" while others do not. But not to worry because those who don't will be going over it next year. Of course, at that point it will be like starting over again for many kids.
That was not exactly succinct.
Some spirals work for mastery. Other spirals work for exposure. Mastery is secondary with these spirals. It is supposed to just happen from the,uh, spiral.
Is your head spiraling yet?
I'm going to put link inside the post, so if you're interested, look at the post again!
ReplyDelete"(I find myself giving too much information and sounding kindof like a conspiracy theorist when I talk to people about math education these days.)"
ReplyDeleteI think we have all experienced that reaction. Too much, too fast.
If they're talking about Everyday Math, call it "circling" or "repeated partial learning". I find that sound bites work well. They encourage questions, and it works better than attempting a brain dump.
Spiraling doesn't guarantee mastery. In fact, reform math uses spiraling to avoid mastery. Mastery is a goal and spiraling is a technique. Mastery doesn't just happen no matter how many times you circle the wagons.
Proper spiraling requires mastery of new material and skills each time through the loop. The next time through the loop, you use previously mastered skills to master new material. You get to review the material and then use it on more advanced topics. Everyone is on the same page. Spiraling and mastery don't have to be incompatible, but mastery of individual skills cannot be spiraled.
The key questions are:
1. When do they require mastery of each specific skill?
2. What is the required level of mastery?
3. How do they make sure that this level is achieved?
I just pulled this out of the National Mathematics Advisory Panel’s Conceptual Knowledge and Skills Task Group Progress Report. Wonderful stuff! Read the whole thing.
ReplyDeleteTeaching to mastery can be described as a coherent progression, with emphasis on mastery of key topics.
The reform math method of spiraling continually revisits topics year after year without closure.
After reading Steve’s comments, I would modify my sound bite to include “repeated partial learning”.
ReplyDeleteTeaching to mastery can be described as a coherent progression, with emphasis on mastery of key topics.
The reform math method of spiraling continually revisits topics year after year for repeated partial learning and no closure.
I still kinda like “closure”. It sounds like something Oprah would say
wonderful!
ReplyDeleteThank you!
Mastery is a goal and spiraling is a technique.
ReplyDeleteI knew Steve would save the day.
OK- I often term it as Spiraling vs. Mastery.
ReplyDeleteThat seems to be incorrect, (Thanks Steve)
Would it be accurate to term it as a difference in goals, Direct Instruction vs. Discovery.
The different approaches to achieving the goals is mastery vs. partial learning?
Agh- I've already lost the average parent by this point. They are looking at me like just told them I was an alien abductee.
"Agh- I've already lost the average parent by this point."
ReplyDeleteI can't say that I've ever convinced any parent. Some are already convinced, some are not sure, and some parrot back something about understanding and no drill and kill. Even today, one parent told me that she can understand my position because my son memorizes so easily ... as if I'm only concerned about the needs of my son.
It's not an easy thing to get parents to accept that schools are doing something fundamentally wrong. We're talking about a curriculum, not just one assignment. When some kids do well, the job is much tougher.
I think that's why some focus on the "special needs" of TAG or GATE kids. It's an easier sell, but it doesn't help the kids who need it the most.
I can't say that I've ever convinced any parent.
ReplyDeleteI've had some success, but very little.
The only time I get anywhere is when there is a problem and it was a surprise to the parent.
I had one friend whose gifted kid's scores dropped dramatically between 5th and 6th grade. I told her it was probably fractions, but she didn't believe me. I gave her the Saxon placement test to give to her son. She actually called me a few days later and said that, yes, it was fractions.
Sometimes being math phobic helps me to talk to certain parents. There are soooo many math phobes out there. They can get very confused.8-}
"It's not an easy thing to get parents to accept that schools are doing something fundamentally wrong."
ReplyDeleteThat is why I come to KTM. We all pretty much agree that there is something seriously wrong with the way our schools are teaching various subjects.
What James Audubon said about his experiences in Florida in 1831 could serve as a metaphor for educationist-created education:
ReplyDelete“The general wildness, the eternal labyrinths of waters and marshes, interlocked and apparently never-ending, surrounded by interminable swamps...” --James Audubon 1831
welcome to the desert of the real
ReplyDeletebrilliant!
of course, I, for one, am living in the soupy fog of the real
which is probably less fun
You know --- I never have trouble talking about spiraling curricula with parents here. People get it immediately.
ReplyDeleteThe middle school model is tougher to deal with, because it's so nebulous. otoh, parents here all find elements in the MSM to dislike with no prompting from Ed or me.
hmmm...
There is very, very little interest amongst parents in anything remotely like constructivism around these parts.
Which makes it ironic that our Strategic Plan lays out a path to the implementation of sweeping constructivist reform, of course.
I find that most parents assume the kids are being taught to mastery, but their particular kid is having problems.
ReplyDeleteI remember being stunned when I found out about spiraling curricula.
I can't say that I've ever convinced any parent. Some are already convinced, some are not sure, and some parrot back something about understanding and no drill and kill.
ReplyDeleteThis is fascinating!
Boy, this is completely not the case here. I can't say I've met a parent who, once he or she was aware of the nature of spiraling versus teaching to mastery, thought spiraling sounded like a good idea.
It's absolutely the case that most parents don't want to knock heads with their school district, but that's another story.
There is tremendous dissatisfaction with the quality of the schools here.
There is also tremendous dissatisfaction with recent reforms and innovations, etc.
If you took the "The country is moving in the right direction/wrong direction" poll around these parts, I think you'd get a pretty high "wrong direction" response.
Sometimes I feel like once there's a momentum about academics: parents are asking questions, weighing evidence, being more skeptical, something non-academic blows in like a tornado and turns things upsidedown. In the case of Irvington, it's the health fair. In the case of my district, it's an overcrowding issue. Is it the fates or some masterful plan?
ReplyDeleteIf you took the "The country is moving in the right direction/wrong direction" poll around these parts, I think you'd get a pretty high "wrong direction" response.
ReplyDeleteAround here, I think people are still too scared to think about it. It's much easier not to. Generalizing, it seems those with experience in other states or countries(we have a high population of translplants here) see it clear as day. Those who have called this home for any length of time are much harder to convince and become offended at the mere thought that are schools are moving in the wrong direction.
... our schools.
ReplyDeleteMy semi-informed guess is that NCLB is having an effect in terms of the climate in which public schools operate.
ReplyDeletePublic schools, through ed schools and probably more importantly through teachers' unions, have controlled the narrative.
This isn't a criticism of teachers' unions, btw; controlling the narrative is the union's job. That's why I feel no compunctions about giving constructivists equal time at ktm-2; equal time isn't the point of ktm-2.
Anyway, back on topic.
I've seen, around here, that once you have vocal critics of a school's policies and practices, the policies and practices don't change, but the climate does change. Administrators and teachers using ineffective curricula and pedagogy lose legitimacy, and, in time, the loss of legitimacy leads to loss of power and influence.
Witness the fields vote here.
In the past, the administration did what it did; the board did what the administration did.
Taxpayers and parents could go take a flying leap, and that's what we did.
Things are very different here now.
Although it is still an uphill battle, and will be for years I imagine.
"Those who have called this home for any length of time are much harder to convince and become offended at the mere thought that are schools are moving in the wrong direction."
ReplyDeleteOh, yes, I sense this is true of my area as well. I sense that the powers that be are not accustomed to being asked questions and they do not like it when you pry.
I say "pry" because I actually had a teacher ask me was I prying when I went to look at the science textbooks up for review at my sons' elementary school a couple of weeks ago.
Funny, you are asked for your opinion about the textbooks your county is planning on adopting, and you are told you are prying when you go to check them out.
Interesting about newcomers being more skeptical.
ReplyDeleteMakes perfect sense.
One of the factors here is parents who have one child in private school, another child in IUFSD.
That combination can be deadly, even though the private schools have their problems, too.
It's all about expectations and points of reference. For some people it's just much more challenging to conceive that anything could be possibly better. Especially when everyone keeps telling you how wonderful your schools are and you have good scores. It's hard to disassemble that imagery when it's so embedded.
ReplyDeleteMiddle school is the radicalizing experience for a lot of parents, I think.
ReplyDeleteCertainly true here, but I believe it's true elsewhere, too.
I'm a big fan of mastery, but I'm not an anti-constructivist. I think mastery has more to do with how you assess and what you teach than how you teach. I think every grade should have 2-3 core topics/skills that are taught to mastery--if most students don't get it, revisit it soon; if a few kids don't get it, arrange for extra tutoring within the school day. Even from a constructivist perspective, if you take the math serously you need this or there is no knowledge to construct the next layer on.
ReplyDeleteHey!
ReplyDeletelsquared!
Are you the guy from the great homework thread on unfogged??