https://time.com/7008332/math-kid-myth-essay/
I really find these kinds of articles tiresome, because the accusations or “myths” as expressed by Shalinee Sharma, are assumptions made by people who are generalizing about all math teaching in order to peddle their programs.
The first myth — “Math is only about speed” is such a simplistic point. No one that I know believes that math is only about speed. However, fluency with basic facts should include speed. By the time students are in algebra 1 and are trying to factor a trinomial such as x^2-2x-24, there is simply not enough time to draw pictures or arrays to figure out what are factors of 24. Students shouldn’t have to mentally apply the distributive property to figure out what 6 times 4 might be (e.g. (5+1)(4) would be 20+4, or 24.) In my mind, fluency would mean that a student could answer nearly immediately that 6 times 4 is 24. On the other hand, managing products of larger numbers might indeed include some properties, such as (13)(12), which could be thought of as 13×10 + 13×2.
Myth #2 says that “Math is a series of tricks.” It can certainly look that way if teachers do not carefully develop and derive algorithms. No doubt, many K-8 teachers do not understand math well enough to develop and provide clear explanations of standard algorithms and procedures. I am still puzzled by the almost criminal status the word “borrow” has in teaching and performing subtraction. The politically correct term is “rename,” which is certainly fine, except that “borrow” makes plenty of sense, too. The idea that one could borrow 10 ones from the 10s column while subtracting something like 32-19 is simple to explain: Instead of 30+2 minus 10+9, we have 20+12 minus 10+9, giving 10+3, or 13. (it looks better when presented vertically, which is also a convenient way to present subtraction of polynomials). I once asked my algebra 2 class why cross multiplication works and no one could answer me. I was asking in the context of solving rational equations. I showed them first something like x/2+1/3=3/4. We cleared the fractions by multiplying both sides of the equation by 12 — the least common denominator, producing the much simpler equation of 6x + 4 = 9. Then if we have 12/x =x/3, and multiply both sides by 3x — the least common denominator, we get the same result as cross multiplication — which is why it works! They seemed stunned that it was that simple. I have looked in middle school textbooks and pretty much, in presenting cross multiplication, it just says something like if you have a/b = c/d, then ad=bc, followed by some examples of how to use this technique — absolutely no development of why it works.
Myth #3 says that there is “only one way to do math.” All math teachers that I have ever met know that this is not true and in fact, the best attribute that a strong math student can have is flexibility. I once had a student who felt that he had to use the quadratic formula for all quadratic equations and he refused to use anything else. I asked him if he knew where the quadratic formula came from and he said he didn’t care — he only just wanted to use it. Of course, the quadratic formula is derived by completing the square, another technique used for solving quadratic equations. If one has to solve something like x^2=9, the quadratic formula is quite inefficient. If one is trying to find the x-intercepts of y=x^2-x-12, the quadratic formula is much less efficient than factoring. If one wants to put f(x)=x^2-x-12 into its vertex form, then completing the square is handy.
I don’t like the idea of using keywords to solve math problems, such as the problem about 6 bags of marbles costing $18 leading a student to use multiplication because of the word “of.” I think the keyword approach to solving problems is ineffective because it takes focus away from visualizing and making sense of a problem and tries to impose a “recipe” approach. Drawing pictures, acting out problems, and using physical objects can be helpful in getting young students to figure out how to solve their math problems.
The bottom line for me is that articles like this just promote the very myths that the author is trying to use to promote her “Zearn” program. That is, the accusation is made that kids struggle in math because teachers abide by the “myths,” and that online programs like “Zearn” are much better than teachers in a classroom. Sorry, but I don’t accept that. I tried to get some specific examples of this program but was always asked to “sign in.” I’m not sold that easily…
this was really good