I have read Mr Sauter's web page carefully as well as all the responses (quite carefully) to the original post from Mr Sauter.
(I should confess that I needed to refresh my own understanding of 'mean, median and mode' at 'Purple Math' and Wikipedia).
A: I largely agree with Donald Sauter that most of this is not useful to the beginning student - who really needs to get the underlying concepts of arithmetic (+,-, *, and /) firmly fixed and usable in his/her mind. The underlying issue for the beginning student is that he/she must do enough examples, instances and meaningful problems so that these pretty sophisticated concepts become *effectively* usable in real life. How is that to be done? -- THAT is the issue!
B: I strongly agree with Robert Hansen (RH) that there is nothing like the 'raw data';. It's the teacher's huge responsibility to get the concepts *effectively into the students' minds* so that they are able to put them to use in their daily lives. Some teachers do that very successfully; many teachers do not. Which indicates that there's a lot of 'rectification' to be done with the 'teacher education system'.
C: I also take mind of Richard Strausz's somewhat cryptic (but most meaningful) instance about the costs of houses on the block where his cousin lives (more or less alongside Mr & Mrs Bill Gates).
However: After ALL of that, what I do not yet perceive is a clear answer to these quesitons:
a) WHAT specifically is the arithmetic that a beginning student should get, at various levels, in order that he/she may 'cope *effectively* with life' after school?
b) HOW specifically should the various parts of arithmetic be 'taught' (followed by beginning algebra; slightly more advanced algebra; etc, etc)??
I'm ENTIRELY in agreement with Mr Sauter's several claims in his first pargraph.
So, now, what's to be done about this fairly sorry situation?
Keep in mind that *effective* education is critical to the future of the human race (if we have a future at all) AND that early math is a critical part of education.
I don't believe we here at Math-teach have adequate answers yet to these real issues. I don't believe the 'educational system' as a whole has adequate answers.
I suggest that some 'systems modeling' based on the late John N. Warfield's contributions to systems science would help very significantly. In fact, that's the 'whole ball game' if I have the 'US expression' right.
To provide some 'light refreshment' after all that heavy lifting, here are a couple of problems that someone recently challenged me to do:
1) What is the number (say 'N') that, when the 'units digit' is put as the 'inital digit' of the number (as we write it out) becomes = to 2*N?
2) Your doctor gives you a bottle of liquid medicine with the STRICT instruction that you must take EXACTLY half a drop of the medicine three times a day. How do you manage to do this?
(I succeeded in doing No. 1 [with some trouble]; didn't succeed with No. 2).
[I am not directly involved in teaching myself - though I do conduct workshops on 'systems' for teachers].