I'm going to start with the Binder, et al paper: "Fluency: Achieving True Mastery in the Learning Process." (pdf file)
Here are teach effectively's posts on precision teaching. (Teach effectively says sentient beings should give The Cambridge Center for Behavioral Studies money!)
And here, courtesy of teach effectively, is I Speak of Dreams who posts this passage:
Precision teaching is not so much a method of instruction as it is a precise and systematic method of evaluating instructional tactics and curricula.Assuming the method is easily adaptible to one's home, this is something afterschoolers desperately need. The time I have to keep C. on task is extremely limited; every minute has to count.
And yet I have no real means of figuring out whether what I'm doing is worth the time or not.
For instance, after reading about contingency adduction yesterday, I started wondering whether I should have C. working on something simpler than what he's working on now.
Contingency adduction, as I understand it, is the sudden appearance of new learning without further instruction.
Here's the discussion of contingency adduction that gave me pause:
Contingency adduction occurs when multiple repertoires or components combine with little, if any, instruction.... Johnson & Layng (1994) described how fraction word problems were consistently a problem for their students, some scoring as low as 3 correct in a minute (with up to 11 errors). Probes of the component skills revealed that none of these students were fluent with simple addition math facts. An instruction sequence was put into place that taught addition math facts to rates that predicted fluency (component). Following this, and with no extra instruction, a probe of fraction word problems revealed that all learners had jumped to 13 to 14 corrects per minute (composite). This example is consistent with most reports of adductions, with the common feature being that they often occur without any formal instruction (Binder, 1996).
source:
Introduction
Behavioural fluency for young children with autism
David John Bonser
and here's Binder, 1996:
Solsten & McManus, 1979) demonstrated that frequency building of components not only allows more rapid acquisition of composites but sometimes seems to produce composites with virtually no formal instruction — an effect that Johnson and Layng (1992) have called response adduction (Andronis, 1983; Epstein, 1985).
source:
Behavioral Fluency: Evolution of a new paradigm
The Behavior Analyst 1996, 19, 163-197 No. 2 (Fall)
Saxon Math and contingency adduction
This is another synchronicity event. Just this morning I was emailing Barry G. saying that Saxon Algebra 2 had suddenly become much easier.
The reason it's suddenly much easier is that the lessons I'm doing now all involve combining components into composites. Since I've worked my way through 91 lessons, I'm fluent in the components. There are times when I turn to a new lesson and simply skim it, because I "already know" how to do whatever the lesson is teaching me to do.
Mind you, most of these lessons are on procedures and word problems I've never done before - procedures and word problems I've never even seen before.
I suspect there's no counterpart to contingency adduction for "top down teaching."
fluency and autism
Now that I've (finally) stumbled across precision teaching, I remember our ABA teachers starting to talk about it and work with it for autistic kids. The concept made perfect sense to me, because often an autistic child can do a particular skill - or come up with the proper word - if he works fast. (In fact, the three dissertations on fluency training I've tracked down thus far are on fluency teaching for autistic children.)
Fluency training struck me as a great idea then - and now, too.
fluency and KUMON
KUMON is all about fluency.
Speed and accuracy: the KUMON mantra.
KUMON is not about precision teaching, however. KUMON is almost the opposite of precision teaching. With KUMON everyone does all the worksheets, period.
There's no data.
There's no skipping ahead if you can already do the worksheets you've got super-fast.
There is patience and persistence. (you may need to refresh your browser a couple of times to access the page)
wholes, not parts: Martin Brooks and The Constructivist Classroom
whole math
10 comments:
I'm running out of patience with Kumon. They keep making my daughter repeat the same workbooks. She already knows the stuff, she's not moving forward and it's not helping her. There's an opportunity cost to making her do all these Kumon books when she should be forging through Saxon Math.
On the other hand, if I let her drop Kumon, will she ever master long division?
I'm running out of patience with Kumon. They keep making my daughter repeat the same workbooks. She already knows the stuff, she's not moving forward and it's not helping her. There's an opportunity cost to making her do all these Kumon books when she should be forging through Saxon Math.
That happened to a friend of mine!
Her daughter got STUCK!
She's been stuck in the same set of worksheets forever, apparently.
I'm guessing the precision teaching people wouldn't do things this way.
I IMAGINE (this is a guess!) they'd analyze the situation and move her back to practicing the component skills that go into division (which are....ummmm....estimation & multiplication???)
This is my question with C.: should I drop him back to the easy stuff.
KUMON, btw, always places kids according to this principle; KUMON starts you back on material that's easy.
But after that it's lockstep.
Everyone follows the same sequence, at least in my experience.
Great comments and posting about Precision Teaching. I would point out one key component of PT that Kumon and some many others lack, namely, fluency aims. How fast is fast enough? A fluency aim tells you. Is your daughter wasting her time practicing old materials? A fluency aim, with the content, will tell you.
A fluency aim is a frequency range that specifies how fast someone must go to be fluent. For example, if I asked you how fast is fluent typing you would tell me 60-90 words per minute. This clearly established fluency aim can be tested across ANYONE.
There is so much Precision Teaching has to offer - no catchy cliches (all children can learn) just good old fashioned practice, monitored humanely and effectively, and a graphical display of the behavior to tell you if what you are doing is working or if you need to make a change.
Good luck with your search/discussion of Precision Teaching, you have unearthed a very powerful technology.
I thought Kumon did have a "fluency aim", although I don't think they call it that. They call it target time which is a range of minutes per page. The objective is to attain accuracy within the target time. How is that different from the "fluency aim"?
Well, I just saw the celeration chart used in prevision teaching and boy is it detailed. They don't keep records like this in Kumon (only speed and accuracy).
Also came across a great source for precision teaching resources (even for writing!) go to the "Practice Sheets" section.
http://www.precisionteachingresource.net/
It's interesting that "endurance" is an important component
Endurance describes the ability to perform a behavior over significant periods in the face
of environmental distraction without performance decrement (Binder, 1996).
Precision Teaching is amazing. How had I never heard of it before?
Good question/observation.
"target time which is a range of minutes per page. The objective is to attain accuracy within the target time. How is that different from the "fluency aim"?
It could differ in a number of ways. A fluency aim would be a rang of behaviors to perform in a given period of time. For example, 60 words typed per minute (# of behaviors in time). In the Kumon example you cited above it becomes less clear as to the aim. Lets say I have a sheet of 30 problems and I have to do that in 2 minutes and be 100% accurate. Then I would have to translate this 15 problems answered correct per minute. So if the # of problems of the sheets change but the accuracy criterion stays the same you have a shifting criterion.
Think of a heart rate. All humans have a beat per minute range which indicates a healthy rate (generally speaking for people 14 years and older 60-100).
Fluency aims should be viewed similarly that you have an agreed upon aim.
Hope this makes sense!
Thank you... I definitely see how the fluency aim is much more specific than Kumon's set goal of pages per minute. I do think the Kumon instructors follow a guide that gives them a range for the different pages as they differ in difficulty and number of questions. They usually write the target range at the top of the homework pages so the child can set the goal of answering all the assigned questions accurately and within the target time (ex. 3-5 minutes per page) so in a sense it is "agreed upon" beforehand. The time per assignment is recorded and monitored carefully to consider the need to repeat an assignment to improve accuracy or speed. But the target time may vary based on the topic and as such the criterion does shift. Additionally, based on the details of the celeration chart I can see that precision teacing is much more, well, "precise".
One last thing, I believe there are many other differences between a PT fluency aim and what Kumon does. Namely, fluency aims (at least most of them) in PT are derived from research or, at the minimum, field tested. I would question how Kumon comes up with their aims. Have they shown that when students hit their target aims something good happens? Also, who did they base their sample on for the goals?
In PT, when students hit the fluency aim the research shows that three critical outcomes also occur - long term retention, endurance, as you have indicated previously, and something called application.
I don't want you to think my post is trashing Kumon, however, just pointing out the difference between a PT fluency aim and what Kumon does. And what they do, Kumon, is certainly better than 98% of the public schools who either do NO practice or practice very inefficiently.
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