math curriculum 2.0 -- explaining math strategies

[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.

If you cannot tell that this is in fact different then the 2*8=16 +1 =17 example, then you have a problem too.

[Anonymous]

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

Do you still draw circles whenever you need add 2 to 8 ? Or do you just know the answer because at some point you have memorized the answer?

Its useful to teach preschoolers or kindergartners the concept of quantity to understand a numerical symbol. Its also useful to teach then how to visually move these quantities back and forth for addition and subtraction. However, once they have this they will end up memorizing the math facts anyway.

There is little value in making a child who understands the concept of addition and subtraction and has already memorized the math facts keep drawing darn circles everywhere. This is boring and repetitive and not deeper. It also does nothing to strengthen the understanding of using that "strategy". The kid is smarter than you and knows its stupid but they have to do it. They are simply executing an assignment in instruction following.

[Anonymous]

What words should a 3rd grader use to explain that 3/4 = 6/8?

She has a rectangle with 8 compartments in it and was told to shade in 3/4 of the boxes. She correctly shaded in 3/4 on one side of the rectangle and another 3/4 on the other side.

Is the explanation, 3 out of 4 (equal parts) of one half of the rectangle and 3 out of 4 (equal parts) Of the other half of the rectangle = 6/8 of the whole rectangle?

Seems like a LOT to ask a 3rd grader to write.

[Anonymous]

Anonymous wrote:

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

Do you still draw circles whenever you need add 2 to 8 ? Or do you just know the answer because at some point you have memorized the answer?

Its useful to teach preschoolers or kindergartners the concept of quantity to understand a numerical symbol. Its also useful to teach then how to visually move these quantities back and forth for addition and subtraction. However, once they have this they will end up memorizing the math facts anyway.

There is little value in making a child who understands the concept of addition and subtraction and has already memorized the math facts keep drawing darn circles everywhere. This is boring and repetitive and not deeper. It also does nothing to strengthen the understanding of using that "strategy". The kid is smarter than you and knows its stupid but they have to do it. They are simply executing an assignment in instruction following.

IMO, MCPS is missing the "fluency" aspect that Common Core demands. You are correct that eventually one is supposed to "know" or "memorize" certain steps. Every time we do long division, we don't justify via place value concepts each move; we just use the algorithm without thinking about why it works.

As a parent, I am extremely concerned that MCPS is focusing on this "deeper understanding" in a way that denies the development of fluency. It would be OK if they emphasized both. That this is a problem will become more apparent when kids move on to higher math and take the SATs, etc. They will simply not be able to do the calculations quickly and easily, they will increasingly dislike math and have to spend much more time than is necessary to study/achieve in the upper level subjects.

[Anonymous]

In my opinion, everything MCPS requires of students will be driven by what is on the PARCC test for math.

If on the PARCC, when asked to explain their thinking, students are allowed to say "I memorized that fact" then school districts will follow suit.

So keep a close eye on what types of questions are being designed for use on the PARCC and provide feedback if you don't think they are mathematically necessary.

[Anonymous]

Anonymous wrote:What words should a 3rd grader use to explain that 3/4 = 6/8?

She has a rectangle with 8 compartments in it and was told to shade in 3/4 of the boxes. She correctly shaded in 3/4 on one side of the rectangle and another 3/4 on the other side.

Is the explanation, 3 out of 4 (equal parts) of one half of the rectangle and 3 out of 4 (equal parts) Of the other half of the rectangle = 6/8 of the whole rectangle?

Seems like a LOT to ask a 3rd grader to write.

I don't think that's a good explanation, because it sounds like 3/4 + 3/4 = 6/8, which of course it doesn't.

How about, "I drew a rectangle with 4 boxes, and I shaded in 3 of them. Then I divided each box in half to make two boxes. Then 6 out of 8 boxes were shaded."? Do you think that would be a lot for a third grader to write, and if so, why?

[Anonymous]

If the original question was that 3/4 was 6/8 then a good explanation would be a picture that showed that equal amounts were shaded.

I agree with PP that the original explanation was not good.

I don' t think that is too much for a 3rd grader to write.

I don't mind when my 3rd grader has to occasionally explain his reasoning. When they have to do it over and over and over for stuff they he understands it gets old.

[Anonymous]

Anonymous wrote:If the original question was that 3/4 was 6/8 then a good explanation would be a picture that showed that equal amounts were shaded.

I agree with PP that the original explanation was not good.

The problem I am having is that I got this question from a sample 3rd grade PARCC assessment question called "THe field"

http://www.parcconline.org/samples/mathematics/grade-3-mathematics-field

The FIRST part of the question has the child using a picture to demonstrate 3/4 of a field cut into 8ths.

The SECOND part of the question asks the child to write in numbers a fraction that is the same as 3/4.

The THIRD part of the question then asks the child to explain IN WORDS how she knows that 3/4 = 6/8 (or whatever equivalent fraction the child wrote for part 2).

So please tell me, using words, what a good answer to part three would be.

[Anonymous]

Anonymous wrote:

I don't think that's a good explanation, because it sounds like 3/4 + 3/4 = 6/8, which of course it doesn't.

Well, 3/4 (1/2) + 3/4 (1/2) = 6/8, though!

3/4 of half the rectangle plus 3/4 of the other half of the rectangle would be 6/8 of the entire rectangle, no?

[Anonymous]

Anonymous wrote:
How about, "I drew a rectangle with 4 boxes, and I shaded in 3 of them. Then I divided each box in half to make two boxes. Then 6 out of 8 boxes were shaded."? Do you think that would be a lot for a third grader to write, and if so, why?

I do think that is a lot for many 3rd graders to write, because in 3rd grade not all kids are writing fluently at grade level yet. My own daughter would be able to write that without much problem, but my son in 3rd grade would not have been. I dislike how math ability is being linked to writing ability now. Kids who can't write well tend to write shorter sentences and get less credit for having complex ideas. writing ability should not be linked to math assessment.

[Anonymous]

Most kids understand how they get the correct answer...few have the interest in writing three sentences about it. I wouldn't worry about it...especially if it's homework since homework isn't graded and doesn't factor into the ultimate "grade" (P).

[Anonymous]

But they are expected to write out their explanations on tests and often the explanation part counts for more than the answer part.

[Anonymous]

Tests? You mean assessments? Most kids pass regardless of what they write on assessments.

[Anonymous]

Anonymous wrote:

Anonymous wrote:If the original question was that 3/4 was 6/8 then a good explanation would be a picture that showed that equal amounts were shaded.

I agree with PP that the original explanation was not good.

The problem I am having is that I got this question from a sample 3rd grade PARCC assessment question called "THe field"

http://www.parcconline.org/samples/mathematics/grade-3-mathematics-field

The FIRST part of the question has the child using a picture to demonstrate 3/4 of a field cut into 8ths.

The SECOND part of the question asks the child to write in numbers a fraction that is the same as 3/4.

The THIRD part of the question then asks the child to explain IN WORDS how she knows that 3/4 = 6/8 (or whatever equivalent fraction the child wrote for part 2).

So please tell me, using words, what a good answer to part three would be.

Anyone? This is a genuine question -- I'd love to know how to answer the question.

[Anonymous]

Anonymous wrote:Suggestion from a Ph.D. who earns his living from math: Don't worry about it. Make sure she understands the concept, and is able to solve the problems. You should be able to say if she understood or not without forcing her to write 3 explanatory sentence why 10 x 10 = 100. Otherwise you will just make her hate math. MCPS math curriculum is ridiculously easy. And yet it insists students to write and write and write to "show their understanding" of primitive concepts.

Agree with most of what you said (not the part about ridiculously easy).
The kids who are good at math are having their space invaded by turning it into a verbal subject. That is a bit unfair.