In short, three thoughts:
1) I am all for expertise and even believe in deliberate practice, but =
the 10,000 hour stuff is simplistic and easily challenged.
2) More importantly, you are applying a highly theoretical and =
optimistic paradigm to a quite predictable and pedestrian classroom =
concern - "The Kids Might Not Know Their Math Facts." The typical and =
wrong prescription for that misdiagnosis is to force kids to solve =
hundreds of identical decontextualized 'math' problems on worksheets and =
memorize facts from Flashcards. This is based on inadequate teacher =
preparation, the public's misguided notions of what 'math' is and =
teacher insecurity.
3) One does great violence to learners when the "practice" engaged in by =
expert musicians or chess players is allowed to be confused with what =
"practice" means in school.
I highly recommend two books:=20
David Perkins' Making Learning Whole: How Seven Principles of Teaching =
Can Transform Education - http://amzn.to/anC9oh
Jo Boaler's What's Math Got to Do with It?: How Parents and Teachers Can =
Help Children Learn to Love Their Least Favorite Subject - =
http://amzn.to/bnskps
On May 26, 2010, at 7:04 AM, Bigenho, Chris wrote:
> While I am not a fan of speed drills for "math facts", there is a =
place for core knowledge that all students must master to be able to =
develop expertise as a mathematician. I personally find that most =
drilling routines and targets for math facts miss the point of =
developing appropriate context in which to ply these skills. However, =
they do help to create proficiencies that allow students to reallocate =
limited cognitive resources to other areas of problem solving. Drawing =
from the work of Chase, Charness, Posner, Ericsson and Anderson in the =
arena of developing expertise, several things come to mind:
>=20
> 1. The development of expertise requires the development of basic =
skills over time. There is no substitute for this core knowledge. =
However, this skill acquisition must be context based.
> 2. Development over time- a lot of time. They have found that the =
development of expertise takes over 10,000 hours of work/practice. =
However, they add a qualifier here- Deliberate Practice. This is then =
defined as systematically evaluating weaknesses, working with a coach to =
develop plans to reduce these weaknesses then systematically practicing =
so that stronger cognitive connections are formed.
> 3. The difference between an expert and a novice or intermediate =
abilities in a domain is the expert's ability to immediately recognize =
patterns. This does not come from simple drills that are out of context. =
Rather this is developed through deliberate practice in "game", problem =
solving situations. However, the drills may allow for more cognitive =
resources to be applied to the more abstract areas of problem solving as =
students have largely automated their "math fact" processes.
>=20
> Much of this work was done with grand master chess players. In these =
studies, they found that the GM players had a library of board positions =
that they could immediately draw from when they looked at the board. =
However, when the board was arranged with pieces located randomly, their =
library of positions and plays was of little use and the performed only =
slightly better than their weaker opponents. This provides powerful =
evidence that context is a key component to skill acquisition leading =
toward the development of expertise. These studies have now been =
replicated in multiple domains with similar results. When I think of =
most math fact speed drills, I think of a page with 100 =
de-contextualized problems placed on the page with a simple goal of =
speed and accuracy. This will obviously help students develop their =
abilities to do these problems with minimal cognitive effort leaving =
resources available for other functions. However, I suspect that =
students would not perform nearly as well if these same "math facts" =
were embedded in contextualized problems requiring them to solve real =
world, relevant problems. It is in this context that meaningful =
relationships and connections can be created through the process of =
deliberate practice that can lead to the acquisition of skills and =
developing expertise. Therefore, while there may be room for both =
approaches, the development of expertise is largely based in =
contextualized practice where meaningful patterns can be studied and =
stored for later use.
>=20
> For more in this area, I would look at the work of Chase, WG., =
Anderson, JR. Ericsson, KA. and Posner, MI.
>=20
> Chris Bigenho
> Director of Educational Technology
> Greenhill School
> 4141 Spring Valley Road
> Addison, TX 75001
> Ph. 972-628-5479
> Fx. 972-628-5279
> bigenhoc@greenhill.org
> www.greenhill.org
> =20
> Blog: http://bigenhoc.wordpress.com/
> Twitter: bigenhoc
> AIM: chris bigenho
> Yahoo: chris_bigenho
> Skype: chris_bigenho
> Tapped In: ChrisWB
> Delicious: http://delicious.com/bigenhoc
> Diigo:bigenhoc
>=20
>>>=20
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>=20
> [ For info on ISED-L see =
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