Every year I teach grade 12 students how to divide polynomials. I always start by reviewing long division with natural numbers. As I put an example on the board, I'm always met with groans and comments such as "I never learned this. I was taught it but I never learned it.". I always reassure students that it will be much easier now than when they were in grade 4. I'm blown away by how many students hate long division and these students are our best math students. If the majority of the best math students hate long division, what do the rest of the students think?
Every time I teach this lesson I can't help but think that students in grade 4 aren't really ready for long division. It's a long algorithm that likely makes little sense to them. Perhaps they aren't ready for it cognitively. I'd even go so far as to say that although many adults can perform the algorithm, how many of them can actually explain why they perform those steps?
I'd like to see long division scrapped from the elementary curriculum. Instead I'd like to see students focusing on understanding what division really means in a wide variety of contexts. Clearly it's a skill that my division-phobic students have not used since grade 4 so what's the point in teaching it then? Often when I mention this in conversations I get the reply "How will you teach them to divide polynomials if they can't do long division?". This argument seems incredibly weak to me. Does it make sense to teach students something in grade 4 and then ask them to recall it eight years later, without having used since grade 4? Why not just teach the algorithm in grade 12 when students have a better mathematical background and can understand what is being done rather than memorizing an algorithm that is likely to be forgotten?
As a side note, I really like James Tanton's representation of long division here. I think that conceptually it gives a better understanding of what is going on than the traditional algorithm.
What are your thoughts on long division?