Colin, some of the "reform math" programs in the United States from the 1990s to the early 2000s insisted that school pupils routinely learn to do their multiplication with a lattice, supposedly because that is easier to learn, with the result that I have had very smart pupils in my local supplemental program who couldn't do multiplication by any other method. Fortunately, these days the insistence on lattice multiplication as the best procedure for school mathematics is decried by many and is gradually falling by the wayside.
P.S. A good website for articles on education reform issues is Education Next,
http://educationnext.org/
which has much better articles than most articles that are submitted for discussion or comment on Hacker News about education reform and education policy.