math curriculum 2.0 -- explaining math strategies

[Anonymous]

Anonymous wrote:

OK. At our MCPS school (in the US) in 2nd grade, the kids ARE given the option to use pictures, formulas, or diagrams. As the teacher who teaches at MCPS (in the US) says.

Do you disagree with the idea that if you can't explain the concept, you don't understand the concept?

In 1st and 2nd grade, kids were allowed to draw pictures, or diagrams but were discouraged from using formulas. In 3rd grade, they are specifically asked to write an explanation using language and sentences.

I do disagree with the statement that if you can't explain the concept, you don't understand the concept. This is plays out in many, many fields. A great violinist hears, feels, and understands fully the concepts of pitch, harmony, tones etc. This same violinist may not be able to write an essay explaining in sentences how they play so well. A english major or music history major may be able to write a wonderful essay comparing and contrasting or explaining this but can't play a simple tune. An artist may be able to construct beautiful compositions but again is far less successful in translating this into a writing skill to explain what they already know and have learned. There is no value in forcing everything to conform to a language assignment approach.

Equations, numerical values, and symbols are the "language" of math. Proofs and theorems, as well as simple equations, do explain math. There are many ways to go deeper in math at the elementary school level and to show how math is a serious of related interactions.

MCPS's interpretation that understanding problem solving means that you can write essays or explain in English sentences how math works is just plain wrong. You don't approach or teach math the same way you approach language arts. You don't teach math as if you are afraid of it and want to avoid numbers and equations.

This is so true. Thank you for explain it well. I don't like the way math is taught here. Elementary math is the foundation of more complex math, not just simple calculus. Math language should be emphasized more. It's a pain to see sticks, bundles and other objects to be used to teach kids math beyond number 20 and poor math expressions everywhere. I'm not kidding, a random sheet from kid's homework pile has 2*8 = 16 + 1 = 17 as an example to let them exercise addition and multiplication. Isn't it more of a problem to incorrectly use "equal" sign here than not to be able to explain in english why 2*8 = 16? Seriously!

[Anonymous]

Anonymous wrote:

This is so true. Thank you for explain it well. I don't like the way math is taught here. Elementary math is the foundation of more complex math, not just simple calculus. Math language should be emphasized more. It's a pain to see sticks, bundles and other objects to be used to teach kids math beyond number 20 and poor math expressions everywhere. I'm not kidding, a random sheet from kid's homework pile has 2*8 = 16 + 1 = 17 as an example to let them exercise addition and multiplication. Isn't it more of a problem to incorrectly use "equal" sign here than not to be able to explain in english why 2*8 = 16? Seriously!

I'm guessing that this was

2*8 = 16 [separating space here] + 1 = 17

Which, actually, is a good way to teach elementary math as a foundation of more complex math.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

This is so true. Thank you for explain it well. I don't like the way math is taught here. Elementary math is the foundation of more complex math, not just simple calculus. Math language should be emphasized more. It's a pain to see sticks, bundles and other objects to be used to teach kids math beyond number 20 and poor math expressions everywhere. I'm not kidding, a random sheet from kid's homework pile has 2*8 = 16 + 1 = 17 as an example to let them exercise addition and multiplication. Isn't it more of a problem to incorrectly use "equal" sign here than not to be able to explain in english why 2*8 = 16? Seriously!

I'm guessing that this was

2*8 = 16 [separating space here] + 1 = 17

Which, actually, is a good way to teach elementary math as a foundation of more complex math.

Math teacher here. No, I wouldn't express it like that at all. The number sense doesn't make sense, space or no space. YOu could do this:
2*8=16
16+1=17

[Anonymous]

You wouldn't say something like "Two times eight is sixteen, plus one is seventeen?" I would.

[Anonymous]

both ends of an equal sign have to be equal with or without space. Period.

I'm sorry to tell you that math expressions should be more rigorous and formal than what you say in everyday life.

[Anonymous]

Anonymous wrote:both ends of an equal sign have to be equal with or without space. Period.

I'm sorry to tell you that math expressions should be more rigorous and formal than what you say in everyday life.

And yet Singapore Math has expressions like 65 - 10 [fill-in-the-blank] - 2 [fill-in-the-blank] as a mental math strategy for 65-12.

[Anonymous]

Anonymous wrote:

Anonymous wrote:both ends of an equal sign have to be equal with or without space. Period.

I'm sorry to tell you that math expressions should be more rigorous and formal than what you say in everyday life.

And yet Singapore Math has expressions like 65 - 10 [fill-in-the-blank] - 2 [fill-in-the-blank] as a mental math strategy for 65-12.

depends what's in the blank

It's perfectly fine to have

65-12 = 65 - 10 - 2 = 55 - 2 = 53


big mess if

65 - 12 = 65 - 10 = 55 - 2 = 53

I won't use that book to teach math.

[Anonymous]

Anonymous wrote:You wouldn't say something like "Two times eight is sixteen, plus one is seventeen?" I would.

You could write:

(2*8) + 1 = 17

[Anonymous]

Anonymous wrote:Is anyone else's elementary student having trouble with the required narrative explanations in math homework -- e.g., explaining the "strategies" used to solve the problem? DC has no problem getting the right answer but is struggling to put the thinking/reasoning into words. I've suggested just writing it out as DC would explain it to me (which has mixed results) but it's an ongoing issue. Any advice? (Fwiw, DC is a good writer in other subjects.)

I would suggest contacting your child's school's math lead teacher, perhaps with some other parents in tow, or at a PTA meeting. Ask for concrete example from grades k-3, for example, of what types of narrative explanations are expected and accepted, and for a rationale of why these and not others.

"Please show us exemplars of how kids should express in written narratives the following computations:

2+8

(I said the bigger number, 8, then counted on a number line 2 more times)
(I made a 10, because 8 is 5 and 3, and 3+2 is another 5 , and 5+5 = 10)
or my personal favorite
(I know 2+8 is ten because IT IS A LAW OF ARITHMETIC that I memorized)

8*3

(I counted by 8 three times)
(I counted by 3 eight times)
(8 is 5 and 3; so I multiplies 5x3 and got 15 and 3x3 and got 9 and I know 15+9 is 24)
(8 and 8 is sixteen and then I added another 8)
(I know 8x3 is 24 because IT IS A LAW OF ARITHMETIC that I memorized)

20*15

(I multiplied 15x2 tens and got 30 tens which is 300)

425 + 375

(I added 400 and 300 to get 700. Then I added 25 and 75 to make another 100. That gave me 800 total)

500 - 98

(I subtracted 100 from 500 to make 400. Then I added back 2 (because 98 is 2 smaller than 100), and got 402.

700 - 23

(I subtracted 1 from both parts of this problem and turned it into 699 - 22. Then I mentally subtracted and got 677.)

[Anonymous]

Do they accept "I know that 8+2=10 because I have memorized my math facts"?

[Anonymous]

My son wrote something along those lines PP on a math test and second grade and had that explanation marked incorrect. Ridiculous! Eventually you want the students to get to thw point where they've memorized their math facts but apparently not in 2nd grade.

[Anonymous]

Anonymous wrote:

Another Ph.D. who earns her living from math here -- disregard this PP. If you can't explain the concept, that means you don't really understand the concept. And, as the MCPS-teacher PP says, you don't have to write "3 explanatory sentences". There are lots of different ways to explain it.

Sorry, we're a two Ph. D household and I agree with the earlier poster. This is bad and a perfect example of why the US ranks so low in math compared to other countries. If you have county level education majors who do not understand math writing the math curriculum, you end up with language curriculum not math. They really do not understand the subject and can only translate it in terms that they can comprehend. Its a mess.

At our school in the 3rd grade, the kids are not given the option to use pictures, formulas, or diagrams to explain the answer. The worksheets and assessments ask the student to explain it and gives them several lines (clearing indicating text and sentences). The kicker is that the teacher corrects the spelling, grammar, and punctuation!

I agree.I come from a country that is fairly poor but is constantly in top 10 in math, science and reading.Don't remember ever having to explain it (show step, yes), specially in earlier years.What a waste of time.

[Anonymous]

Anonymous wrote:Do they accept "I know that 8+2=10 because I have memorized my math facts"?

From what I have seen that is not OK. That doesn't demonstrate deeper understanding LOL

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:both ends of an equal sign have to be equal with or without space. Period.

I'm sorry to tell you that math expressions should be more rigorous and formal than what you say in everyday life.

And yet Singapore Math has expressions like 65 - 10 [fill-in-the-blank] - 2 [fill-in-the-blank] as a mental math strategy for 65-12.

depends what's in the blank

It's perfectly fine to have

65-12 = 65 - 10 - 2 = 55 - 2 = 53


big mess if

65 - 12 = 65 - 10 = 55 - 2 = 53

I won't use that book to teach math.

I laughed at this post. I think this is the problem. A lot of teachers are not comfortable with the language of the math. They are English majors at heart.

[Anonymous]

Anonymous wrote:Do they accept "I know that 8+2=10 because I have memorized my math facts"?

No, you have to draw a bunch of circles.