I love Steve Leinwand. His video is amazing. His book is amazing. He has already influenced my teaching greatly and I can’t thank him enough. He’s got my vote!

Steve is an exemplar IGNITE speaker. If you don’t get fired up about teaching mathematics when watching or listening to him, you just might not have a soul. I’m on my third read through of Accessible Mathematics and I have this vision of Steve excitedly delivering it to me every time. Can we write Steve in for the November 6 Presidential election too?

“President” seems too formal of a title. Can we go with “Grand Poo-Bah”?

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.

The analogy I often use for the impact of technology on learning computation is that of transportation.

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.

Hi Dan, I don’t think that log tables and interpolation are necessary any longer – but the four basic operations on whole numbers, fractions and decimals are important to build number sense.

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!

Hi Christopher,

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.

@Eddie, I would say that paper and pencil arithmetic might be a little better than calculators for number sense, but mental arithmentic is really what is needed. I have often wondered if better number sense could be developed through the use of calculators that provide a visual image as numbers were entered and computed – some sort of visual to give a sense of scale.