Different approach to solve math problem

[Anonymous]

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

As a third grade teacher in public school, I just want to say, thank you! Thank you for understanding and working in partnership with us. All of what you said is correct.

[Anonymous]

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

+1000
I Stopped reading the responses with this one. I think number 2 is the primary reason. Math is like building blocks and future success at math builds on a good foundation.

I have a degree in math and My husband is better at doingplain math, but I am better at calculus. His way is most useful day to day. Mine was more useful getting a masters degree.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

If the kid already knows the math, then using the time to develop their weakness (writing) seems like a win/win. Hyperfocusing on the grade, which doesn't matter a whit in elementary school, rather than on learning is ridiculous.

I realize that it's gauche to suggest in this modern age, but the time could be spent working on more math. There's plenty to learn.

Like writing proofs?

Not writing the same proof 50 times with different numbers.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:the answer is all that matters.

Anybody who tells you differently is selling you something.

Not true in STEM, but maybe that's not where you're aiming?

In stem why does it matter how I get my roots? Or how I multiply? I know that 9 x 5 is 45 and where the curve crosses the axis and that's what matters.

People and teachers get caught up on memorizing things and concepts not what matters. It's like these new math things that were supposed to revolutionize math but just left us all confused.

It matters that people can communicate their process, and prove their work is correct. Practicing it early, even though they aren't yet in situations where they need to use that skill makes sense because it's a difficult skill to master.

I don’t know how anyone with common sense can argue against this. Showing your work as a student has been standard practice since forever.

[Anonymous]

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

If the kid already knows the math, then using the time to develop their weakness (writing) seems like a win/win. Hyperfocusing on the grade, which doesn't matter a whit in elementary school, rather than on learning is ridiculous.

I realize that it's gauche to suggest in this modern age, but the time could be spent working on more math. There's plenty to learn.

The fact is the kid could spend his time that way. The parent won’t let him, because the parent is absolutely stuck on whether the teacher gives him a gold star on a second grade worksheet that doesn’t count for anything.

How?
"You see Ms. X, despite what you might think, showing my work has limited pedagogical value relative to the time cost it incurs, therefore I will not do it. I will also magically force you to give me extra challenging work once I finish early and magically prevent you from labeling me as insubordinate or immature, even in your own head, thus ensuring an excellent GBRS score"

I don't think that's reasonable to expect from a 2nd grader.

As I implied above - the gold star does count for something - it reinforces the teacher's belief in the obed- erc, intelligence of the child, which makes a big different for 3rd grade AAP placement given how important GBRS is.

I have no idea what “GBRS” or “AAP” are, but goodness, what a difficult position to put a child in.

PP here. I'm glad we agree it's not right to expect a child to do all that, and therefore a child can't be expected to choose to do something instead of what their teacher commands.

[Anonymous]

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered.

You didn’t ace the tests if you didn’t show your work. I can’t get over how many people can’t comprehend how important it is to show your work.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered.

You didn’t ace the tests if you didn’t show your work.

Why don't you re-read the part where PP said they aced the test?

[Anonymous]

Many times. in life we just need to jump through certain hoops and pick certain battles and not others.

[Anonymous]

And they probably shouldn’t say “show your work” so much as “show/express one way someone could solve the problem.” That way, writing out an expression becomes part of the problem as opposed to the nit-pickyish “show your work.”

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered.

You didn’t ace the tests if you didn’t show your work.

Why don't you re-read the part where PP said they aced the test?

I believe that they did. There are very few tests where teachers have the capacity to hand grade and check that work/approach was shown. Certainly not any tests administered online or by scantron or equivalent means. This is, btw, not totally unreasonable when problems are posed in a way that guessing is not possible and cheating is ruled out. In this case, finding the correct answer is sufficient proof of mastery.

In general, though, the details are what matters. There is probably a tendency by some teachers to ask for work to be shown that's actually not necessary when a subject matter experts evaluates it. An example would be to show your work when multiplying 7 and 9. In general, it's highly context dependent as math builds on previously covered topics and techniques. A solution to a problem in a prealgebra textbook must prove facts that later are perhaps mentioned as steps, and even later simply omitted and left to the reader. Or take the simplification of expressions. This can be spelled out in 10, 5, 2, or 1 steps, and how many are reasonably needed depends on context.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:If the kid really understands the math they should be able to do it both ways no problem.

The problem is when kid is good at math but slow terrible at writing, should they get bad math grades / lose all that time to writing?

They don't get extra points in English class for their math prowess.

If the kid already knows the math, then using the time to develop their weakness (writing) seems like a win/win. Hyperfocusing on the grade, which doesn't matter a whit in elementary school, rather than on learning is ridiculous.

Writing out a math problem won't improve a student's composition skill. Punishing students who are good at math by preventing them from doing math is not a good solution.

Should kids who finish their essays early start doing math worksheets?

This. Writing out arithmetic steps in words is not quality writing practice. If kids can solve the school arithmetic problems in their heads, give them more challenging math. If the kid needs more writing practice, give them quality composition exercises, like analyzing a passage of grade appropriate literature.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The way I explained it to my kid was that
(1) the teacher didn't actually need to know the answer to the problem. They need to know whether the kid understands the math. If you do it in your head and make a mistake, the teacher doesn't know whether you understand or whether you just made a careless mistake. They can't see where you went wrong.
(2) At some point, you won't be able to do the math in your head. The numbers will be too big or there will be too many steps. Best to get in the habit of showing your work.
(3) You can get partial credit if you show your work.

This is the most important response. The problem is that with homework, teachers want showing work to include steps and no shortcuts on like 100 problems in hand writing and that's just for one class on one assignment. It's tedious. Especially for somebody who's not making those mistakes.

I remember when we first learned system of equations and would get 20 problems a night and I wouldn't do them and I'd get in trouble. I knew the material and Aced the tests. That's all that mattered.

You didn’t ace the tests if you didn’t show your work.

Why don't you re-read the part where PP said they aced the test?

I believe that they did. There are very few tests where teachers have the capacity to hand grade and check that work/approach was shown. Certainly not any tests administered online or by scantron or equivalent means. This is, btw, not totally unreasonable when problems are posed in a way that guessing is not possible and cheating is ruled out. In this case, finding the correct answer is sufficient proof of mastery.

In general, though, the details are what matters. There is probably a tendency by some teachers to ask for work to be shown that's actually not necessary when a subject matter experts evaluates it. An example would be to show your work when multiplying 7 and 9. In general, it's highly context dependent as math builds on previously covered topics and techniques. A solution to a problem in a prealgebra textbook must prove facts that later are perhaps mentioned as steps, and even later simply omitted and left to the reader. Or take the simplification of expressions. This can be spelled out in 10, 5, 2, or 1 steps, and how many are reasonably needed depends on context.

We're differentiating between homework and tests. On the syllabus/syllabi I've seen homework vary from 2% to 10% of the total grade. Tests on the other hand were going to take 10 - 25%, sometimes more for classes I didn't take but heard about from classmates and teachers I didn't take. So I just didn't care about putting that much effort into a problem that is going to take the same amount of time on a homework assignment but only be worth a small fraction of the test question grades while being exponentially more in quantity, it was almost no question that I would do things in my way. Especailly when I was in seventh grade and my first punishment was only -10, so for the year, I was able to simply turn in the answers (show no work) and only lose .10 points off my final grade max. It was a no brainer. Other classes treated homework differently, but no teachers wanted to punish the smarter students too harshly, so I would get stern lectures about the need for work and I'd let them know about how I have no time because I'm playing basketball and lacrosse and debating and running track and keeping a 3.5. Time isn't free.

Then on the tests I would always show my work. For the system of equations stuff for example, I'd use substitution or addition method or something like that to show them I know what I'm doing. But on a test there are whAat 5-10 problems in 60 minutes, thats a lot easier to do and manage. So I would always ace my tests. I hated this type of math though. Proofs are a lot more fun and should be taught in more High Schools.