First admit the basic wrongs
JE Trickey seeks to refute this claim by referring to HMI reports from the 1970s. He is correct in suggesting that some of these earlier reports were indeed gems. But it is disingenuous of him to suggest that this refutes my claim, because there was such a dramatic change in HMI reports in the early 1980s.
Jim Mayhew seeks to refute my claim by digging deep to find a suitable statement from the wide-ranging 1985 HMI publication Mathematics from 5 to 16. This booklet certainly belonged to the later genre! And no one at the time would have imagined for one moment that it might one day be interpreted as encouraging clearly focused teaching of basic arithmetic. Instead it was a mish-mash - advocating everything and nothing.
Your readers deserve a more serious response than these. Until we are able to admit that we got things wrong at this rather basic level, we are unlikely to begin to sort out the more serious problems elsewhere.
Dr TONY GARDINER
School of Mathematics University of Birmingham