Yes, that is the paper I’m referring too. I didn’t mean to imply that it was peer reviewed research – just that it is the opinion of several math PhDs backed up by what I find to be persuasive argument in favor of long division.

By the way I’m not married to any particular algorithm. As Hung-Hsi Wu points out – given a divisor and dividend a and b respectively what is important is finding q and r so that b=a*q+r in an efficient manner whatever that might be.

I sometimes speak to my students about “obstacle course” problems. These are not skills problems – these are decision making problems in which several different skills are necessary at different points throughout the problem. Long division is one of the first places I think that students encounter this as it generally requires their estimation, multiplication and subtraction skills to complete.

Regarding long division in particular, I would direct you to James Milgram’s paper on the importance of long division.

Just to be clear, we are discussing the unpublished one with zero research references?

The logarithms would be like riding a horse or sailing – something once very useful but no longer needed. But like walking and running – computation is the basis for everything else (and keeps us healthy!).

I believe that students build their number sense from doing calculation themselves. I’m not an absolutist but I think that the students should be given sufficient time to engage with the algorithms and achieve some level of proficiency before they shift to technology.

Thanks for taking the time to respond respectfully to a minority opinion!

Knowing what the “black box” is doing requires a certain amount of training – otherwise I believe that the students will only be able to follow in others footsteps rather than blazing their own trail.

I see this with technology – people are dazzled and say “How can I use these great (pre-set) features?” rather than thinking “How can I get this gadget to do what I want it to?”

In some ways technology is limiting, but don’t get me wrong, it’s also very enriching!

None of this is to say that students shouldn’t know that 843 divided by 293 is closer to 3 than 2. I don’t disagree with you on number sense. That’s quite a bit different than the long division algorithm for multi-digit numbers, though.

Simply because we have cars, planes, bicycles, segues and the like doesn’t mean that we don’t learn to walk. Do you see many people using motorized transport to get from room to room in their home?

Not developing the number sense that you and Leinwand seem to denigrate will put students at a significant disadvantage. I personally don’t believe that learning computation through technology generates the degree of number sense that pencil and paper does – in the same way that driving your car everywhere doesn’t help you be a better athlete.

Regarding long division in particular, I would direct you to James Milgram’s paper on the importance of long division.

Honestly, it would be great to have leadership that can not only inspire teachers to strive for better instruction, but could also serve as a face for national math education. Math suffers from a big P.R. problem, as math is still often seen as a rigid, bland colossus by both our teaching peers, and by the public. Who better than Steve to emphasize the excitement and beauty of math.