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thatThe tests that were being done by Shayer are things that according to
Piaget
were found to click in before age 10. Subsequent research revealed
these actually are understood at a variety of ages, and that someadults
never understand them. Conventional schooling does not seem to affectlearning
understanding of these tasks, but specialized teaching using the
cycle with hands on/minds on lessons does have an effect. Thecontinuous
drill which has been instituted in schools in place of educationcertainly
does not help students to understand these tasks. The waterdisplacement
task seems to be impossible for students before age 7, even when shownit
bydevelopment,
experiment. Understanding of these tasks requires both brain
and experience for students to construct this understanding. These areand
examples of conservation reasoning.
These tasks are considered markers of concrete operational thinking
arethey
necessary to be understood, before higher level tasks. Notice that
didas
not show research on the markers of formal operational thinking such
proportional reasoning. This latter maker of reasoning is onlyacquired
bysetting.
about 25% of graduating seniors in the US according to my admittedly
limited
survey. But this is confirmed by others.
As to recess, this is where students interact in an unstructured
This is absolutely necessary to normal development, and is where theyIt
acquire executive functioning according to the cognitive scientists.
islearning.
not acquired in formal classroom settings. Without good executive
functioning they can not control behavior adequately for good
There are some programs designed to promote executive functioning, but
theyused in
do not resemble conventional classroom lessons, and have only been
ado
small limited set of schools. The evidence is very positive that they
work. There was an article in the NY Times science section aboutthem.
learning.
As to the raising of the high stakes tests, there is no use beating
someone
for something that they have no control over. The teachers do not
understand or have the programs that are needed to promote good
When a student is at a low level of thinking, they can NOT learnthings
likesubtract
algebra. When they do not understand whether to add, multiply,
orreasoning,
divide, any advanced math is opaque. They lack proportional
andhave
the conventional teaching of ratios is not useful in teaching it.
The answer is that teachers need to be trained in pedagogical content
knowledge. The TIMMS report shows that European and Asian teachers
such knowledge and ask students better questions. And of course thestudents,
American texts are entirely too long and clotted with undigested,
confusing
material. But along with this districts need to allow different
approaches
rather than saddle teachers with one size fits all teaching. While
teaching
gobs of material may not be as damaging in schools with high SES
it is the kiss of death in lower level schools. Essentially itpromotes a
high dropout rate, which the school welcomes as a solution toachieving
goodof
test scores. And dropout rates are very high, but schools find ways
hiding it such as claiming the student transferred to another school,but
this is never verified.