Further my post dt. Sep 4, 2013 8:20 AM - http://mathforum.org/kb/thread.jspa?messageID=9252704?, I need to make some important additions: > > What an excellent article, Professor Becker, and <snip> > > One implication is that the "constructivist approach" > is not necessarily the perfect and only way: it's > just an approach that has many sound concepts within > it - though some of 'constructivism' has been > discredited by the 'traditionalists'. The article > indicates (for instance in the matter of 'teaching' > multiplication): > <snip> And much of the 'traditionalist' approach has been thoroughly discredited by real life learning that children have shown us.
In particular there is the theory that "children need to be PUSHED to learn [math; or anything else]" - this is part of the rubbish that should be thrown out of education theory entirely.
Children will learn anything they find interesting.
In general, they place a lot of trust in the elders around them (unless those elders prove themselves untrustworthy). Children, will genuinely try to learn anything the trustworthy elders tell them is important. (Unless, of course, they definitely find it unimportant or boring).
In general, we adults have little understanding of what children find 'important' or 'interesting'. Too often, we tend to take our own ideas into consideration, not the child's. We need to learn to take the cues from the behaviour the children themselves display. Often, the child's instincts lead him/her to judge correctly what is important/ interesting. (In many cases, the adults around the child have managed to render the child's natural instincts invalid).
In the Montessori system of education, Maria Montessori tried to *enable* the child's own learning instincts and judgement by creating a whole lot of 'tools to enable learning', an *environment* to promote the child's learning. (Creating such an environment is not easy to do successfully, and many so-called 'Montessori schools' fail entirely to provide the needed *learning environment* notwithstanding all the expensive equipment they may have purchased - see below).
Because of my great interest in 'learning systems' (at all levels; from child-learning to adult-learning), I've visited quite a few Montessori schools: from whatever I've observed, only a few of the so-called 'Montessori schools' actually succeed in creating an adequate *learning environment*.
It does require a great deal of empathy with the child on the part of the director and the teachers of the school to bring about such a *learning environment*.
Often, the other societal systems around prevent even the person who is empathetic to the child from putting up an adequate *learning environment*. For example, in India we have generally very incompetent and quite corrupt 'education departments' and 'state boards of education' that impose a whole lot of bureaucracy on people who are genuinely trying to give their wards a real education. Mostly, all of that is designed only to extract some 'under-the-table' money from the promoters of the schools. Quite often, the promoters are forced to succumb to such pressures.
It's not only the expensive equipment the school puts up to impress the parents that matters. You need to check out the children in the school and how they are actually learning.
Learning is the most natural thing for a child to do: no PUSHING is required. The societal pressures exerted by the child's peers in the school are generally all that is required for any *normal* child to enter into the *learning mode* - PUSHING by elders is rarely (perhaps never) required, and it is definitely not recommended. If PUSHING is found necessary, that is an indication that an adequate *learning environment* has not been created.
(Words enclosed in *s [*----*] have some technical meaning beyond what is seen in any conventional dictionary).