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It's not necessarily the algorithm that matters. There are a few different algorithms you can follow for division and a few ways you can accurately represent th

It's not necessarily the algorithm that matters. There are a few different algorithms you can follow for division and a few ways you can accurately represent the results. For example, kids these day commonly learn something called the "lattice method" for multiplication. It's a different algorithm from what I learned, but that doesn't necessarily matter. The point is not for students to learn how to follow an algorithm (or master doing it quickly), but that they learn why the algorithm works and how to interpret the result.

knaik94 4y ago
Honestly, I hadn't come across the lattice method until you mentioned it. I would strongly argue that it hinders learning because it's hard to draw an association between the numbers you are writing down and how the lattice method is set up. It is equivalent to long division after you recognize that the lattice method removes the shifting to the right as you multiply by the next digit. With the standard long multiplication method, you recognize that what you were really doing is splitting the multiplier by powers of 10 once you learn the distributive property. The lattice method is actually weirder because you don't move by increasing powers of 10, you go in the reverse direction. You still have to carry and you still add up numbers in column/power of 10 order, starting with the smallest power at the very end. If anything, the lattice method represents everything about the common core math approach that many parents and teachers dislike. The algorithm matters and I argue that once students can naturally derive the algorithm on their own, there's no place for human calculations. Computers and calculators should be used. We're no longer living in a society where students will have to worry about "what if you don't have a calculator on you". It seems as weird as memorizing unit conversions to me. What's interesting is that the purpose of implementing the common core standard was exactly what I am arguing for. A shift away from algorithmic memorization to a number sense way of doing math. The failure lies with the teachers not being able to teach well much more than students not learning.

knaik94 4y ago

Honestly, I hadn't come across the lattice method until you mentioned it. I would strongly argue that it hinders learning because it's hard to draw an association between the numbers you are writing down and how the lattice method is set up. It is equivalent to long division after you recognize that the lattice method removes the shifting to the right as you multiply by the next digit. With the standard long multiplication method, you recognize that what you were really doing is splitting the multiplier by powers of 10 once you learn the distributive property. The lattice method is actually weirder because you don't move by increasing powers of 10, you go in the reverse direction. You still have to carry and you still add up numbers in column/power of 10 order, starting with the smallest power at the very end. If anything, the lattice method represents everything about the common core math approach that many parents and teachers dislike. The algorithm matters and I argue that once students can naturally derive the algorithm on their own, there's no place for human calculations. Computers and calculators should be used. We're no longer living in a society where students will have to worry about "what if you don't have a calculator on you". It seems as weird as memorizing unit conversions to me. What's interesting is that the purpose of implementing the common core standard was exactly what I am arguing for. A shift away from algorithmic memorization to a number sense way of doing math. The failure lies with the teachers not being able to teach well much more than students not learning.