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square_25

Misuse of the equals sign.

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I've also had some kids use words rather than symbols for a period of time until they really get it.  So write: 5+3 equals 2*4.  And if they are doing some mental calculation then: 5+3 leads to 8+2 leads to 10+5 which equals 15. Or some such. I hit this a lot in probability, because the notation can be quite odd and out of the realm of common experience, so we just use tidy/crisp wording of my choosing (not just any words), which can later be converted to symbols once the thinking process has been tidied up. 

So P(no heart attack given a patient taking aspirin)  later becomes P(H'|A)  because I've made the words directly line up with the symbols so they can move to the notation when their brain is ready, and just convert, and not have to completely reorganize the thought.

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1 hour ago, lewelma said:

I've also had some kids use words rather than symbols for a period of time until they really get it.  So write: 5+3 equals 2*4.  And if they are doing some mental calculation then: 5+3 leads to 8+2 leads to 10+5 which equals 15. Or some such. I hit this a lot in probability, because the notation can be quite odd and out of the realm of common experience, so we just use tidy/crisp wording of my choosing (not just any words), which can later be converted to symbols once the thinking process has been tidied up. 

So P(no heart attack given a patient taking aspirin)  later becomes P(H'|A)  because I've made the words directly line up with the symbols so they can move to the notation when their brain is ready, and just convert, and not have to completely reorganize the thought.

Oh, I did the very same thing when teaching probability to my sister! Then she moved to shortening it herself, but I think having HER decide when that was OK was a big deal.

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I wonder how much of this comes from calculators.  I use the equals sign on my calculator that way all the time, when I am working within a budget. 

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24 minutes ago, CuriousMomof3 said:

I wonder how much of this comes from calculators.  I use the equals sign on my calculator that way all the time, when I am working within a budget. 

I’d guess it’s worksheets more than calculators at this age. But I’m sure calculators don’t help!!

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51 minutes ago, square_25 said:

I’d guess it’s worksheets more than calculators at this age. But I’m sure calculators don’t help!!

 

Yes, but my guess is that the calculator usage might impact the way that people talk through math problems with kids.  

 

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7 hours ago, CuriousMomof3 said:

 

Yes, but my guess is that the calculator usage might impact the way that people talk through math problems with kids.  

 

You're probably right. Although I hope people try to stifle that impulse, given how confusing algebra is if you don't know what an equation is... 

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Loving this thread!

I just wanted to add that Miquon addresses this really well. They very often mix up the order (so just as many 5=2+3 as 3+2=5) and they have whole pages called 'other names for x' where x is a number, so x might be 10 and the student is encouraged to find answers like 5+5, 5×2, 2+2+2+2+2, 11-1, 100÷10, 1+9. I use that language a bit when talking about sides of the equals sign.

Another way I like to explain is with a scale, each side must balance. I actually have one of these https://www.amazon.com/Educational-Insights-1070-Number-Balance/dp/B000QDZYCK 

And always cuisenaire rods are great for this, to show how the lengths are equal. We spend a lot of time in early elementary making equal trains lol, finding all the different combinations to make 10 etc.

The elementary beast academy books are quite good on this too.

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1 hour ago, square_25 said:

You're probably right. Although I hope people try to stifle that impulse, given how confusing algebra is if you don't know what an equation is... 


In my experience, many people who work with small children, including parents helping with homework, don't have a strong enough memory of algebra to let it inform the way they talk to kids about math.  

A couple years ago, my kid's fifth grade math teacher decided to have us all do some basic math problems as a way to understand the procedures our kids were doing.  Now, my kids go to a private school, in one of the most educated counties in the country.  I seriously doubt there was a parent in that room who didn't study algebra.  There might have been a handful who didn't have a college degree, but there were more lawyers, and research scientists, and social workers, and other people with advanced degrees.  

I could do the problems easily, because I taught math.  But everyone else, had forgotten the algebra notation, couldn't remember order of operations, etc . . .  I had to help a PhD microbiologist!  And those are the people who are talking kids through their homework problems.  

So, I wouldn't assume that a parent sitting down to do second grade math homework is thinking of how their choice of words or notation will help or hinder algebra.  Given that, I don't think it occurs to them that these are impulses that need stifling.  
 

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7 minutes ago, CuriousMomof3 said:


In my experience, many people who work with small children, including parents helping with homework, don't have a strong enough memory of algebra to let it inform the way they talk to kids about math.  

A couple years ago, my kid's fifth grade math teacher decided to have us all do some basic math problems as a way to understand the procedures our kids were doing.  Now, my kids go to a private school, in one of the most educated counties in the country.  I seriously doubt there was a parent in that room who didn't study algebra.  There might have been a handful who didn't have a college degree, but there were more lawyers, and research scientists, and social workers, and other people with advanced degrees.  

I could do the problems easily, because I taught math.  But everyone else, had forgotten the algebra notation, couldn't remember order of operations, etc . . .  I had to help a PhD microbiologist!  And those are the people who are talking kids through their homework problems.  

So, I wouldn't assume that a parent sitting down to do second grade math homework is thinking of how their choice of words or notation will help or hinder algebra.  Given that, I don't think it occurs to them that these are impulses that need stifling.  
 

Yeah, I’m absolutely sure you’re right :-/. It’s just too bad.

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