Robert Hansen (RH) believes that it is necessary (perhaps even essential) to PUSH children to learn math. There have recently been a fair number of exchanges between RH and myself that involved our different understandings of the verbs "TO PUSH" and "TO ENCOURAGE" and their relative utility in human affairs.
I believe, on the other hand, that (in nominally democratic regimes at least) it is quite inappropriate to PUSH children to learn math (or, indeed, to learn anything or to do anything at all). The 'right' approach (in nominally democratic regimes) is to ENCOURAGE children to learn math (or, indeed, to learn anything or to do anything at all).
It is true that, in our existing societal, educational and 'home' systems, there is much more PUSH (and, indeed, SHOVE and even BEAT) than ENCOURAGEMENT in a great many of our (adult) interactions with children. Likewise in our interactions, with other adults as well!
I claim that this sad truth is, in fact, evidence that we adults have failed to understand 'democracy' and, for that matter, that we've failed to understand just how we should learn to live in society with each other.
In particular, the children suffer the most because of this grievious 'societal failure' of us adults - they have to be (and are) PUSHED to do things and to learn the things that we adults want them to do. To a great extent, we adults may believe we 'succeed' in teaching them appropriate behaviour and disciplines - but, in fact, practically all our interactions (with each other and with children) in modern society are testaments to our utter failure as thinking human beings.
I claimed above that "the children suffer the most": the statement requires some qualification: I have not seen and have rather rarely heard of mothers PUSHING (or otherwise FORCING) their infant children to do most of the things those infants need to do to grow up from infancy into childhood. Rather, they mainly depend on the huge power of ENCOURAGEMENT of their infants to do (and otherwise learn) the things they must.
Quite soon, however (within just a year or so as a matter of fact), the rest of society including the fathers intrude - and the PUSHING (and the SHOVING and the FORCING) starts. Even the mothers (who initially had entirely ENCOURAGED their infant children to do and to learn) now start PUSHING and SHOVING and FORCING!!! Slowly but insidiously, the PUSHING takes over - until practically all of our social interactions are based on the power of PUSHING (and SHOVING).
It is my claim that - for the most effective learning (whether of math or of anything else), we need to re-learn the power of ENCOURAGEMENT (as opposed to PUSHING). There is a wholesale re-education required in society for this to happen: it may take a couple of generations to bring such a happy situation about. Our re-education must start somewhere - and it might as well be with us adults learning that infants and children can, in fact, learn practically everything they need in life most effectively through the power of ENCOURAGEMENT rather than through the power of PUSHING.
Most of my postings at Math-teach are, in fact, based on the clear understanding I have that ENCOURAGEMENT (of infants, children and adults as well) is significantly more effective in most circumstances than PUSHING and FORCING. I have often written of the utility of the relationship "CONTRIBUTES TO" to help us understand the complex systems within which we live and work. The importance of "CONTRIBUTES TO" in systems is in fact derived from the power of ENCOURAGING human beings to do things rather than PUSHING, SHOVING or otherwise FORCING them to do things. The attachments to my post heading the thread "Democracy: how to achieve it" (see http://mathforum.org/kb/thread.jspa?threadID=2419536) provide brief descriptions of tools that can help apply the transitive relationship "CONTRIBUTES TO" to help us model (and adequately understand) real-life issues in complex systems.
(With due apologies to Kirby Urner for the number of words capitalised in the above - I'm afraid that Math-teach provides us no other less intrusive way of emphasising important words and ideas).