**I. The first problem set involving multiplication and arrays in the 4th grade TERC/Investigations Math Student Activity Booklet** [click to enlarge]:

**II. The first problem set involving multiplication and arrays in the 4th grade Singapore Math**[click to enlarge]:

*Primary Mathematics 4A Workbook*
## 1 comment:

Arrays in connection with multiplication is taught a lot earlier in Singapore, introduced first grade, used for multiplication and division in second and third. In 4th they are not being used for multiplication, but rather to concrete/pictorially introduce the idea of factors. Briefly. And the concept is how many different arrays you can make with a number, not really using it to understand multiplication. Not a fixed array. And if arrays you see in the environment are discussed, it would be a brief discussion, not belabored upon in homework. It seems that in the US they try to emulate the idea of concrete to pictorial to abstract (sometimes leaving out the pictorial) but to the point that they hang on to the concrete or pictorial way too long. It is as if in the US they see something work well in certain situations, and the, wham, it must be good for everything, all the time, at all levels. Whether it is or not. They do it the other way too. Sometimes even something that is good for older students all of a sudden then must be good for younger students. Except that it is not, so then it becomes a step-by-step procedure that takes forever to teach, since it is no appropriate.

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