place value makes the "short list"

cross-posted to Beyond TERC:

terrific post on place value:

Place value is one of those things non-mathematically trained grownups tend to take for granted (at least, I did).

The Singapore Math series teaches place value year after year. Singapore Math has a "true" spiral curriculum in that kids learn to mastery in year one, then study the same topic in more depth in year two and master that material, too, then study the same topic in still greater depth in year three and, again, master the material. Place value is one of the spiraled topics.

I didn't quite understand this, even though Christopher's brilliant 5th grade teacher (I don't use the term "brilliant" lightly) told me how important the topic was. She said she'd asked her friend, who had a Ph.D. in math education, what were the most essential & fundamental topics for K-5 kids to master.

He said "place value."

I wish I could remember what Ed said about it the other day. We were talking about some "guess and check" problem-solving situation that was supposed to be a model of higher order thinking.

Ed said, "The way these kids are solving the problem shows they don't understand place value, and if they don't understand place value they don't have conceptual understanding."

One of the things that would be SOOOO helpful to parents like me (to most parents, that is) would be to have a list of the CORE topics you MUST make sure your child knows.

For instance, the other day Vicky said that decimals aren't as important as fractions.

I sort-of knew that already, but only because I've spent 2 1/2 years of my life immersed in K-12 math & math education. But, otoh, I didn't know it with conviction.

Most parents can't teach math on the side; even parents who have the capability to teach math on the side are going to find that their kids won't cooperate past the age of 10. (You can still teach a middle school child on the side - I've done it - but the amount of time you have to spend wrangling with them to get their attention steeply reduces the amount of time on task.)

What we need is a short list of THE essential skills our kids MUST have.

My list, so far, is:

• fractions

• place value

• long division
  

• measurement
  

from Lynn:

• automatic recall of basic facts

from independent george:

• order of operations
  

• properties of arithmetic

from instructivist:

• In addition to total mastery of math facts, I would put equivalent fractions on top of the list. Equivalent fractions directly leads to an understanding of proportions, percentages and all the other good stuff (scaling, unit rates...)

from Mr. Person:

I've had a list for a long time of core concepts/skills that are emphasized at each grade level.

1: Place Value
2: Addition/Subtraction Facts
3: Multiplication/Division Facts
4: All operations with whole numbers
5: All operations with fractions
6: Ratios and proportions

from Susan J:

Estimation.

Common sense. (Such as if you subtract a positive number the result should be smaller.)

[question: do the reform math programs do a decent job with estimation and common sense? do we know?]


update: it strikes me that the list already exists. It's the TOC for the Primary Mathematics series.

I'll pull it & post.