What do you think of this idea?

[fraidycat]

I am getting SO frustrated with DD in math (and she with me!). I (and the curriculum) am trying to teach her concepts, while she is trying to do math.

 

So, I'm thinking about "rewriting" her math sheets - but REMOVING the numbers so she DOES THE WORK, not just "gets the answer".

 

IE: Today's lesson was on writing fact families and solving for x. The crux of the lesson was less about what X actually is, and more about how she got there. She wants to shortcut it all the time. She will NOT be impressed when she gets to algebra or geotrig if she can't/won't write down her steps!!!!!

 

My idea is to write myself a "code", using symbols (hearts, squares, diamonds, etc.) for the 10 digits and giving her the questions in code. So she can write out her steps.

 

What say the Hive?

[Mandylubug]

I would think it would get old to do coded problems daily but I can see it as a fun activity once a week or so. I am no math teaching expert and have kids struggling with math in this household, so please take my opinion as it is! :)

[fraidycat]

Oh, yeah, it definitely wouldn't be for everything, everyday. But for the questions where the actual learning is in the steps, and not getting the answer, I'd just take a couple of the questions in the book and have her do them coded first, before she works with the numbers. I think removing the numbers might actually make what she is being asked to do clearer because it won't just be "easy math". KWIM?

 

I think I'll give it a try. Tonight, I'll look at tomorrow's work and code a couple questions and have her do them first. Then she can do it with the numbers.

[SilverMoon]

Personally I'd warn the child that I wouldn't be accepting any further lessons without the work clearly shown unless it was clearly a mental math exercise, and I'd stick to my guns on it. If they were still in grammar stage I may warn them a week ahead of time to let them adjust. *shrug*

[Shmead]

You might try going ahead and putting the answer at the bottom, to make it more clear that the assignment is to record the steps, not get the answer. Right now she may be trying to impress you that she doesn't "need" the steps to get the answer. Also, if she is like most kids and likes to ask "why" about everything, you might turn it around with "Yes, it's three. But WHY?" You might even try scribing her verbal explanation and then showing her how the mathematical notation says the same thing.

[boscopup]

I'm with SilverMoon. If the child is old enough to require showing work (and I started that around the 4th grade math level here), don't accept a paper that hasn't had work shown. Just calmly hand it back and say, "I need you to show your work. I don't know how you arrived at this answer, and it's wrong until I can see how you got there."

 

I also explained to my son WHY it's important to show his work. I talked about how a rocket scientist may have a trajectory planned out, and then one little number will need to be changed - do you want to go through the entire equation again? Or just replace that one number in the big long series of equations you've just calculated on paper? ;)

 

In fact, that might be a good exercise... If she's old enough, give her some really long multi-step problem - as long as you can think up. Then say, "Oh, but what if this number changes? What is the answer then? <evil grin>"

 

Now if this is a child doing first or second grade math... meh... I'd just let it go for a bit, or have her tell you what to do on the white board. It's hard for young children to even figure out how they got an answer sometimes. I found that I had to talk about how *I* arrived at an answer with my son, to demonstrate how to do this. Talking about how he arrived at a mental math problem helped as well. He sometimes had some odd ways of getting the answer, but they were absolutely correct. :D Once he'd heard me talking about my own methods, he was gradually able to figure out how he did it.

 

It also helps to have problems hard enough that they do need work shown. If the problem is very clearly add two numbers together, I don't make him show his work. If the problem is add two numbers, then multiply by another, I do make him show his work, even though he had the answer right away.

[Down_the_Rabbit_Hole]

Using a code is just substituting symbols for the numbers. 5 is a symbol, to substitute it for a diamond is just extra work for you and her.

 

Showing work and even putting the problems to words would be more useful in my opinion then changing the number system to other symbols.

[silver]

It would depend on what sort of problems my child was working on. If it's something like "? + 4 = 9, find ?" (which you might see in K or 1st grade math), I wouldn't require showing steps. The idea here is to learn the math facts and to just know that 5+4=9, not to learn algebraic steps of "? + 4 = 9 --> ? = 9 - 4 --> ? = 5".

 

Now, if you're doing pre-algebra or upper elementary math, then yes, I would require her to show her steps. Maybe ask her to teach you how to do the problems to have her prove that she understands the steps.

[Walking-Iris]

Well with the fact family problem--how about just giving her three numbers, say 6 8 14 and asking her to make four problems with them. Then if she writes 6+8=14, 8+6=14, 14-8=6, 14-6=8 then she's showing understanding of that particular concept.

 

And if she understands that ?+4=9 means that she can do 9-4=5 then she's showing understanding. If she can do that quickly in her head, then I don't see a big deal?

 

I'm not sure what you're asking? If she understands fact families, why does she have to write her steps? What exactly is the "steps" to understanding them? I can think of a lot of things to challenge kids with in math, but fact families doesn't seem to be one of them.

 

 

[BugsMama]

What about a good proof based logic book? (at least I think that's what they would call it) I took a class in college (it was a logic class, but was a math credit) and we did things like this constantly (down to the hearts and diamonds.... and lots of steps and written out proofs)

[regentrude]

What level of math is she doing?

The problems need to be hard enough for the student to be able to "record steps". I am all for correctly documenting math, but if the problems are so easy that she "sees" the answer immediately, she may be confused as to what steps you are talking about.

So, it woudl help if you could give an example of the kind of problem she is doing and the sort of "steps" you would want her to show.

[BugsMama]

Some of this maybe? http://www.filozofia.uw.edu.pl/kpaprzycka/Publ/xLogicSelfTaught.html

[BugsMama]

Oh wait- I just realized we are talking about a child much younger than I had in my head- Sorry! :)

[fraidycat]

Personally I'd warn the child that I wouldn't be accepting any further lessons without the work clearly shown unless it was clearly a mental math exercise, and I'd stick to my guns on it. If they were still in grammar stage I may warn them a week ahead of time to let them adjust. *shrug*

 

This is where we are getting frustrated. I DO require shown work, so when I hand it back for her to re-do it, she gets a downright nasty attitude. It's a vicious cycle.

 

You might try going ahead and putting the answer at the bottom, to make it more clear that the assignment is to record the steps, not get the answer. Right now she may be trying to impress you that she doesn't "need" the steps to get the answer. Also, if she is like most kids and likes to ask "why" about everything, you might turn it around with "Yes, it's three. But WHY?" You might even try scribing her verbal explanation and then showing her how the mathematical notation says the same thing.

 

I like this idea. Thanks. I will give this one a try.

 

I'm with SilverMoon. If the child is old enough to require showing work (and I started that around the 4th grade math level here), don't accept a paper that hasn't had work shown. Just calmly hand it back and say, "I need you to show your work. I don't know how you arrived at this answer, and it's wrong until I can see how you got there." I also explained to my son WHY it's important to show his work. I talked about how a rocket scientist may have a trajectory planned out, and then one little number will need to be changed - do you want to go through the entire equation again? Or just replace that one number in the big long series of equations you've just calculated on paper? ;) In fact, that might be a good exercise... If she's old enough, give her some really long multi-step problem - as long as you can think up. Then say, "Oh, but what if this number changes? What is the answer then? " Now if this is a child doing first or second grade math... meh... I'd just let it go for a bit, or have her tell you what to do on the white board. It's hard for young children to even figure out how they got an answer sometimes. I found that I had to talk about how *I* arrived at an answer with my son, to demonstrate how to do this. Talking about how he arrived at a mental math problem helped as well. He sometimes had some odd ways of getting the answer, but they were absolutely correct. :D Once he'd heard me talking about my own methods, he was gradually able to figure out how he did it. It also helps to have problems hard enough that they do need work shown. If the problem is very clearly add two numbers together, I don't make him show his work. If the problem is add two numbers, then multiply by another, I do make him show his work, even though he had the answer right away.

 

She is doing fourth grade math. It is only going to get "harder" on her from here on out. Right now, I'm trying to build the habit so that it isn't harder than necessary. KWIM? She does not have the right kind of temperament to handle the setbacks she could experience - she will most likely shut right down and "hate" math. As for handing the paper back, see above. Handing it back is where most of our frustration is coming from!!!

 

I will try the long equation. As a matter of fact, I was planning to order some pre-algebra and algebra books for ME to brush up my math skills in the New Year, so I will be sure to let her see me work when I do that. This will be a concrete example for her, because she will eventually be working in those same books.

 

Using a code is just substituting symbols for the numbers. 5 is a symbol, to substitute it for a diamond is just extra work for you and her. Showing work and even putting the problems to words would be more useful in my opinion then changing the number system to other symbols.

 

Yes, but she has "cracked" the code with the symbols we use. All nice and good when that is what I want from her - a simple answer. She is very strong in mental math. She IS NOT strong in anything that requires steps, including word problems. She wants a shortcut all the time, then if her answer is wrong because she was thinking 26 instead of 16 or some easy little thing, she is instantly "stupid" in her words. If she had shown her work, she could see that "Oh yeah, I was thinking a, instead of b - Oops."

 

What level of math is she doing? The problems need to be hard enough for the student to be able to "record steps". I am all for correctly documenting math, but if the problems are so easy that she "sees" the answer immediately, she may be confused as to what steps you are talking about. So, it woudl help if you could give an example of the kind of problem she is doing and the sort of "steps" you would want her to show.

 

Fourth grade math. She doesn't necessarily see the answer immediately - she just tries to do it all in her head!

 

Here is one of her problems:

 

John's monthly phone service bill is $48. John said that with the money he earned on his summer job, he could pay his phone service for two months, spend $120 for a bike and still have half of his money left. How much did he earn?

 

** An example of her answer might be $422, because she simply forgot to carry the one at the end when doubling. But I wouldn't know that because she'd just write down 422.

 

 

 

I was using fact families as the first example because the question was at two part question:

 

a) Write a fact family using these three numbers: x, 59, 124.

 

b ) Solve for x.

 

Her answer to part b ) was correct. But she completely skipped part a) so I wasn't sure she even DID understand what a fact family was. She was in PS, using Everyday Math prior to pulling her last Christmas, so I'm still remediating gaps due to her "fuzzy math" experience. I still do not have a complete handle on what she knows vs. what she can accurately "guess" at, KWIM?

[Arcadia]

This is where we are getting frustrated. I DO require shown work, so when I hand it back for her to re-do it, she gets a downright nasty attitude. It's a vicious cycle

...

She is very strong in mental math. She IS NOT strong in anything that requires steps, including word problems. ...

Fourth grade math. She doesn't necessarily see the answer immediately - she just tries to do it all in her head!

 

I require shown work for word problems only. My older has a lot of written work for the other subjects and is honestly tired of writing. I am too lazy to write on his behalf. I do let him tell me the steps verbally for some questions if he has a heavy written workload day.

 

Maybe start from showing steps for all word problems and work up from there in the amount of questions she need to show working for.

 

My boys like cryptography for math enrichment though.

 

For fact family, just give her three numbers and ask her to write the four equations. My kids did that in public school for K and 1. Just for fun see if she can write the fact family using a,b,c or symbols.

[letsplaymath]

Remember, learning to show the steps of their work is *really hard* for students of any age. It feels like *torture* from her perspective, unless you happen to have a student with OCD. Of course your 4th-grader is going to balk at it! If this is a battle you are determined to win, then make it bearable by only requiring written steps on one or two problems each day.

 

On the other hand, talking about how they got an answer can be fun, and can help the math concepts settle deeper into the brain (like Charlotte Mason-style narration). So definitely ask "Why? How did you figure that out?" --- especially on the particularly challenging problems.

 

When my daughter was in 4th grade, we made such discussions the center of our math program by doing our workbook buddy-style. It really helped!

[fraidycat]

Buddy style. I like that. Sometimes I do scribe for her, so she MUST tell my step-by-step in those ones. I do only require her to show her work on one or two problems at a time. There are usually only that many on the page. I guess we'll just continue muddling through, and eventually she'll see WHY I've been harping on this.