Jump to content

Menu

I love Saxon but my child says she hates math....


Recommended Posts

9 hours ago, Not_a_Number said:

Sure. Say that a kid is dividing 402 by 3. They split up the hundreds between the 3 people and they have 102 left. Now we just have one hundred and 2 ones. How do we keep going? They don’t know.

You said knowing has different levels — for these kids would you say there is a level at which they in fact do know how to keep going? Do you think they are missing a piece of the puzzle or that they just need practice?

When my smoke detector chirps, there is a very acute level at which I know that I need to buy more 9-volt batteries. But I don't remember this at the store when I can do something about it, so perhaps that is a level at which I don't know it. Is this an apt analogy or still missing the point?

Link to comment
Share on other sites

6 hours ago, UHP said:

You said knowing has different levels — for these kids would you say there is a level at which they in fact do know how to keep going? Do you think they are missing a piece of the puzzle or that they just need practice?

I just don’t think in those terms. They aren’t fully comfortable with the model and its consequences. They have a certain level of comfort which makes it easy for them to do some things.

I don’t know what it would mean to say that there’s a level at which they can keep going if they consistently can’t keep going. 
 

6 hours ago, UHP said:

When my smoke detector chirps, there is a very acute level at which I know that I need to buy more 9-volt batteries. But I don't remember this at the store when I can do something about it, so perhaps that is a level at which I don't know it. Is this an apt analogy or still missing the point?

Hmmmm, I suppose that’s a bit similar? But I find that math mental models come up all over the place and the uses are often much more common and often can get much deeper.

Link to comment
Share on other sites

14 hours ago, UHP said:

Sure. Say that a kid is dividing 402 by 3. They split up the hundreds between the 3 people and they have 102 left. Now we just have one hundred and 2 ones. How do we keep going? They don’t know.

You said knowing has different levels — for these kids would you say there is a level at which they in fact do know how to keep going? Do you think they are missing a piece of the puzzle or that they just need practice?

 

This is the problem with the algorithm. If you had them do it as mental math, most kids could find a way to divide up 102 into 3 parts. I've seen some count up by 3s (this works but is not very efficient!), others will use 90 and 12, etc. But if you make them do it by the algorithm, most kids will have just memorized the steps and then be unable to remember what to do next because they have not connected the algoithm with any number sense -- so it is just manipulation of numbers without any thinking.

IMHO, if you have limited time, it is better to teach the number sense with mental maths, and use a calculator for very large numbers. I only teach the algorithm when the number sense is secure, which with the kids I work with is typically never. 

  • Like 1
Link to comment
Share on other sites

Just now, lewelma said:

This is the problem with the algorithm. If you had them do it as mental math, most kids could find a way to divide up 102 into 3 parts. I've seen some count up by 3s (this works but is not very efficient!), others will use 90 and 12, etc. But if you make them do it by the algorithm, most kids will have just memorized the steps and then be unable to remember what to do next because they have not connected the algoithm with any number sense -- so it is just manipulation of numbers without any thinking.

IMHO, if you have limited time, it is better to teach the number sense with mental maths, and use a calculator for very large numbers. I only teach the algorithm when the number sense is secure, which with the kids I work with is typically never. 

I actually think it's totally non-algorithmic to trade the 100 and keep splitting. I mean, what else would you do?? The only reason you wouldn't do that is if you weren't fully comfortable with trading up and down whenever you need to. But if you were splitting up a pile of things and some of them came in a box instead of as singles, you wouldn't just STARE at the box and say "I can't split this." You'd open the box and keep going. 

  • Like 1
Link to comment
Share on other sites

Just now, Not_a_Number said:

I actually think it's totally non-algorithmic to trade the 100 and keep splitting. 

I'm not actually sure what you mean here, but for my students who are very good at mental maths, they would be looking for a 'familiar number'. For a number like 282 divided by 3, they would quickly see the 270, and choose that, rather than dealing with the 100s first which would create a mess.

But because it is 402, they don't have their times tables up to the 13s, so they would not see the 390 so would start with the 300. 

NZ does not teach the algorithm at all. The only students who I have ever seen know it have used either a US based program (MUS), or Japanese based program (Kumon), or are gifted students and a parent taught them.  Even when I was actually teaching in a classroom in 1998, there was not a single student out of 150 who knew it, and they came from at least 10 different primary schools. 

Link to comment
Share on other sites

Just now, lewelma said:

I'm not actually sure what you mean here, but for my students who are very good at mental maths, they would be looking for a 'familiar number'. For a number like 282 divided by 3, they would quickly see the 270, and choose that, rather than dealing with the 100s first which would create a mess.

Right. That's fine. That also works. 

What I mean by "it's not algorithmic" is that if you're splitting 402, and you've distributed three of the hundreds already, and you have 102 left... I mean, if you're stuck at this point, you may as well split up the hundred into 10s, no? Otherwise, you simply don't have enough items to split up. 

I think one ought to have methods one uses that don't require spotting a "familiar number." That's a good method, but it's not always reliable. The idea that "you keep splitting until you split everything up, trading as you need" is not "algorithmic" in a rote way. It's simply how people split things between 3 people naturally. 

 

Just now, lewelma said:

But because it is 402, they don't have their times tables up to the 13s, so they would not see the 390 so would start with the 300. 

Yes, that's a fine way to do it, too. 

 

Just now, lewelma said:

NZ does not teach the algorithm at all. The only students who I have ever seen know it have used either a US based program (MUS), or Japanese based program (Kumon), or are gifted students and a parent taught them.  Even when I was actually teaching in a classroom in 1998, there was not a single student out of 150 who knew it, and they came from at least 10 different primary schools. 

That's kind of strange. It's a good algorithm if you can use it well. 

Link to comment
Share on other sites

25 minutes ago, Not_a_Number said:

That's kind of strange. It's a good algorithm if you can use it well. 

I don't think it is strange. If you have the number sense to do the smallish numbers in your head and a calculator to do the big numbers, why bother to teach the entire class an algorithm that only about 25% of the students will ever master. You have wasted the time of the other students. You are also teaching them that math is something to memorize and manipulate, and that feeling runs deep in society, so I'd rather not encourage it. 

Here they teach about 5 different mental maths techniques so kids choose between them. I don't teach this level of math, so couldn't tell you all of them, but have seen them listed on posters in primary school class rooms. 

 

Link to comment
Share on other sites

1 hour ago, lewelma said:

I don't think it is strange. If you have the number sense to do the smallish numbers in your head and a calculator to do the big numbers, why bother to teach the entire class an algorithm that only about 25% of the students will ever master. You have wasted the time of the other students. You are also teaching them that math is something to memorize and manipulate, and that feeling runs deep in society, so I'd rather not encourage it. 

It's a nice fast algorithm that reinforces place value. It really has never occurred to me not to teach it once kids are ready. It's actually a very straightforward way to divide with manipulatives. 

I tend to like things that are intuitive, use the definition, and have a clear path forward. When converted to manipulatives, long division is very much all of those. It's in written form that it becomes purely mechanical. 

 

1 hour ago, lewelma said:

Here they teach about 5 different mental maths techniques so kids choose between them. I don't teach this level of math, so couldn't tell you all of them, but have seen them listed on posters in primary school class rooms. 

Yeah, I don't love teaching 5 different techniques, to be honest. What I like to do is to teach the definition and then have kids use their sense to apply the definition. That winds up with 5 techniques, anyway, but they don't feel disjoint. The danger of teaching lots of techniques is that they wind up all feeling disconnected. 

I'm sure it can be done well, but it's a complain I hear about Common Core all the time, and I saw the issue with this myself with DD8. So I don't do it. 

  • Like 1
Link to comment
Share on other sites

The mental math conversation is interesting. Is this being taught at all in schools anywhere?  I being scolded in elementary for using some of these mental models. My teachers considered them to be "tricks" or short cuts, which was like cheating. 

It was easier to break down a big, ugly number into so many 100s and so many 10s, rather than fight my way through the standard algorithm. 

Link to comment
Share on other sites

Just now, MissLemon said:

The mental math conversation is interesting. Is this being taught at all in schools anywhere?  I being scolded in elementary for using some of these mental models. My teachers considered them to be "tricks" or short cuts, which was like cheating. 

I think Common Core tries to fix that? Lewelma is from New Zealand, though. 

 

Just now, MissLemon said:

It was easier to break down a big, ugly number into so many 100s and so many 10s, rather than fight my way through the standard algorithm. 

I very rarely use long division on paper, although what I do in my head isn't terribly different from it, unless I go up first. 

Link to comment
Share on other sites

11 minutes ago, NorthernBeth said:

So interesting.. I have never seen anyone teach long division without the algorithm.   I am curious as to what the 5 different ways might be.   Most kids just despise the algorithm due to the number of steps.  

You can do lots of things, really. It's not really "long" division, it's just division with bigger numbers. 

So you can do it as the opposite of multiplication, or you can cancel out common factors, or you can go up or down to easier numbers... lots of choices. 

Link to comment
Share on other sites

48 minutes ago, MissLemon said:

The mental math conversation is interesting. Is this being taught at all in schools anywhere? 

Yes. In NZ in all schools both public and private. It is in the national curriculum for primary school.

Link to comment
Share on other sites

Could you walk me through how exactly that would work?  I mean, I know multiplication is the opposite of division, but I wouldn't know how to use that fact ( separate from the algorithm) to help me figure out  a division problem with larger numbers.  I have no idea at all of what you mean by cancelling factors.  I can picture using base 10 blocks?

Link to comment
Share on other sites

27 minutes ago, NorthernBeth said:

Could you walk me through how exactly that would work?  I mean, I know multiplication is the opposite of division, but I wouldn't know how to use that fact ( separate from the algorithm) to help me figure out  a division problem with larger numbers.  I have no idea at all of what you mean by cancelling factors.  I can picture using base 10 blocks?

Sure! 

If you're fluent with multiplication, you might do 363/3 by, say, noticing that 3*121 = 363, and therefore that 363/3 = 121. 

In terms of cancelling factors, that'd be doing division like a fraction. So, 

330/15 = 33*10/15 = 3*11*2*5/3*5 = 11*2 = 22, 

canceling out the 3 and the 5. 

Personally, what I prefer doing is working on intuitions. I define "dividing by" as "splitting into that many groups" at first. So, for example, we'd do 363/3 by distributing 363 things (you could use base 10 blocks for that!) to 3 people so that each person gets the same amount. This one is very easy to distribute -- each person would get a hundred, 2 tens, and a one. 

But then you can get fancier 🙂 . If you're distributing between 4 people, you could split into 2 equal piles, then split each pile into 2 more piles. 

Or you could noticing that if you split a number into 5 piles, then you could check whether your answer is right by multiplying by 5 (if you have 5 equal piles, you should be able to add them all up that way by the definition of multiplication.) 

These are all things lots of kids can figure out themselves with just a bit of prompting and some manipulatives 🙂 . 

Edited by Not_a_Number
  • Like 2
Link to comment
Share on other sites

If the algorithm isn't taught at all, doesn't that have consequences when it comes to polynomial division later? Place value and mental math won't be helpful there. Maybe I'm overlooking something...

I found the algorithm teaching very robust and can still do it automatically even though I rarely had occasion to use it in the last forty years. I see value in an automated procedure and don't want to reason my way through grouping when the numbers aren't suggestive of an easy mental solution. ( I am capable, of course, but the algorithm is way faster)

Edited by regentrude
  • Like 4
  • Thanks 1
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...