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Mental Maths - I need teachers (and advocates) to weigh in please


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#1 Sancti-claws

Posted 13 February 2018 - 08:38 PM

We had our Welcome to Grade Three classrooms talk with the teachers and got the "don't show them the old way to do maths as we have a new way" spiel.

Now, this isn't my first rodeo and my older child (after a similar directive in lower primary about the new way to do reading) suffered as a consequence of me doing as asked - so I am not so easy with being told what to do by them these days.

So - please sell it to me.  Why is the new way of doing maths better than the way that I learned?

My old school methods included carrying, borrowing and lining things up - apparently that is all out the window.

#2 SeaPrincess

Posted 13 February 2018 - 08:41 PM

If my children don’t understand how the teacher shows them to do something, I am definitely going to show them how I do it. But I’m not going to pre-empt it and teach them my way first.

#3 seayork2002

Posted 13 February 2018 - 08:51 PM

Unless we are shown the 'new' way how would we know how it is different to how we would do it?

I hear there is a 'new' way to do long division for example but unless the child (any of our kids) can show us parents how would we be able to help them?

I only know my way which is more modern than my mum taught ne but older than how they learn now.

How many ways can there be to learn the same thing?

Edited by seayork2002, 13 February 2018 - 08:52 PM.


#4 Princess Sparkles

Posted 13 February 2018 - 08:54 PM

Not knowing what your school does, the method used in our schools is grounded in understanding why something works not just  learning that it does. I am constantly amazed at how my kids work out complex problems mentally. I have to generally used pen and paper to get the answer as my learning is all formula abd algorithm based. On the odd occassion that I have showed them something they get it but then proceed to deconstruct it and tell me why it works.

So in my experience it is a far superior way of learning then how we were taught.

Edited by Princess Sparkles, 13 February 2018 - 08:55 PM.


#5 chickendrumstick

Posted 13 February 2018 - 08:55 PM

I still teach vertical algorithms for addition and subtraction, as well as other strategies just as number lines, split strategy...
Some of the changes in how algorithms are taught is in relation to the terminology - 'carrying' and 'trading' can be confusing terms for some kids. I usually refer to 'regrouping as ten/hundred' when teaching these algorithms but I'm sure other teachers have other ideas!

#6 Manicmum

Posted 13 February 2018 - 08:58 PM

They need both.

Schools teach multiple strategies, jump, split etc. good mental strategies, but I believe it’s impirtant to know both.


#7 Princess Sparkles

Posted 13 February 2018 - 09:01 PM

View Postseayork2002, on 13 February 2018 - 08:51 PM, said:


How many ways can there be to learn the same thing?

You'd be surprised. I went to a parent PD when our school swapped to the action maths program. The facilitator got us to do a simple problem, something like 83-34. Out of the 20 odd people in the room there were 4 or 5 different ways people mentally cane up with the answer. Ages of people ranged from their 20's to 50's. By trying to instill a deeper understanding of the manipulation of numbers, kids are taught, or come up with themselves, different stratagies to solve problems.

Edited by Princess Sparkles, 13 February 2018 - 09:02 PM.


#8 Coffeegirl

Posted 13 February 2018 - 09:04 PM

View PostManicmum, on 13 February 2018 - 08:58 PM, said:

They need both.

Schools teach multiple strategies, jump, split etc. good mental strategies, but I believe it’s impirtant to know both.

^^.  This.   My kids are in high school now, and although their teachers were all about the ‘new’ way in primary school, they also realised that not all children learn the same way.

So while the ‘new’ way was the preferred way, some of the children worked better using the ‘old’ way  

And honestly, I still don’t understand the new way.   As long as I get the same answer in the end, and understand the concept, does it really matter which ‘way’ I got the answer?

#9 seayork2002

Posted 13 February 2018 - 09:04 PM

View PostPrincess Sparkles, on 13 February 2018 - 09:01 PM, said:



You'd be surprised. I went to a parent PD when our school swapped to the action maths program. The facilitator got us to do a simple problem, something like 83-34. Out of the 20 odd people in the room there were 4 or 5 different ways people mentally cane up with the answer. Ages of people ranged from their 20's to 50's. By trying to instill a deeper understanding of the manipulation of numbers, kids are taught, or come up with themselves, different stratagies to solve problems.

Then i presume some of these ways were old and some new?

So kids can still be taught both?

#10 FeralRebelWClaws

Posted 13 February 2018 - 09:10 PM

This reminds me so much of this...

https://www.youtube....h?v=UIKGV2cTgqA

#11 FeralRebelWClaws

Posted 13 February 2018 - 09:14 PM

When DS gets into school I will teach him additional strategies. I want to make sure that he gets to the end of primary school with the skills that he needs moving forward.

Edited by FeralRebelWClaws, 13 February 2018 - 09:18 PM.


#12 seayork2002

Posted 13 February 2018 - 09:17 PM

View PostFeralRebelWClaws, on 13 February 2018 - 09:10 PM, said:

This reminds me so much of this...

https://www.youtube....h?v=UIKGV2cTgqA

Que?


#13 Neeps

Posted 13 February 2018 - 09:21 PM

As long as they are being given explicit instruction on the different ways and given opportunity to practice then I am 'old' v 'new' neutral.

DD sees a specialist primary school maths tutor and she teaches that children should know a number of different algorithms.  



#14 Kreme

Posted 13 February 2018 - 09:24 PM

In grade 3 at our school the kids are taught a whole range of different methods. They are tested on each method specifically to ensure they understand it, but by grade four they are mostly using the method they find most useful.

#15 Princess Sparkles

Posted 13 February 2018 - 09:27 PM

View Postseayork2002, on 13 February 2018 - 09:04 PM, said:



Then i presume some of these ways were old and some new?

So kids can still be taught both?

It was just mental maths...not sure what classifies as old or new. I know when I was at school, mental stratagies (besides times tables) were not learned or promoted. It was all about writing and completing algorithms.

#16 Expelliarmus

Posted 13 February 2018 - 09:59 PM

I find the term 'new maths' to be a misnomer. What I have discovered in my professional development in maths is that I did not learn enough mathematical thinking as a child.

I didn't do it all enough ways. I didn't learn enough 'things' to hang my mathematical hat on and I didn't know how to do enough in my head to make it efficient. Mental computation strategies are designed to give students the language and understanding to make maths efficient, make sense and correct through checking. If you can only do it one way - how can you check it?

A few years ago if you asked me to add any two digit numbers higher than 20,I probably would have had to get out either a calculator or a pen and paper to figure it out. It wasn't automatic for me to recognise 30 and 30 were 60 for example. I might not have to complete the whole algorithm but I I would probably ave to write it down before I saw that it was a double. I would then take a bit to search and find the double for three because these were not facts I carried in my head. I received a truncated and ineffective attempt to get multiplication facts in my head in the form of times tables - which was less than successful as I was being rote taught them instead of learning them in a meaningful sequence. So something like 87+52 was not something I could do in my head.

Maths was difficult. It was hard. I had to get out a pen and paper to do the smallest thing. So this 'new maths' is not actually new maths. It's an attempt at ensuring that children actually have all the things they need to become successful and efficient mathematicians.

Another aspect to it is correcting misconceptions. Developmentally children will have misconceptions about things that need to be 'undone' and the correct conception developed. Unless a child has the opportunity to explore and change their mind about the misconception it generally remains. I was told how to do a lot of things and can perform a lot of operations but I couldn't do it efficiently. Combine an inefficient way of doing mathematics with a lack of understanding (Why am I putting that number down there? It changes columns? But why? Okay then, I'll just move it ...) and sometimes it was just too much effort to figure something out.

Take 87+52 now - now I can do that in my head because I have been taught strategies. That's the so-called 'new maths'. They have always been there because they are naturally occurring but unless they are pointed out, many children do not see them. Unless they are given permission to practice them and use them children won't and they will limit their ability to perform at an efficient and higher level.

87+52
7 and 2 is 9, 80 and 50 is 130 and I know that because if I use 20 to get to 100, I have 30 left which is easy to add to 100, then add the 9 ones to get 139. The strategies I used there were counting on and bridging the ten. By naming the strategy it gives the child a metalanguage to discuss their thinking with others and enables them to use discourse in their learning. That's a whole lot of edu-speak for - learning is social, we learn through self-talk - all based in various educational psychological research.

When I was at school and I sat there quietly doing my page of sums I learnt how to borrow and carry and set out the algorithm - but did not actually learn how to do the maths and how it worked. I didn't get to use the best ways we have to learn - by talking and discovering and arguing and sharing.

87+52
If I make the 87 into 90 by using the 2 from the 50 and another 1, I can get 140 by adding the 50 that is left. I take off the 1 I added to get 139. The strategies there are compensation and bridging through ten. The aim of naming and practicing and using mental computation strategies is to give the students deep understanding of number.

If a child can demonstrate that - in more than one way, they have shown understanding and reasoning as well as fluency with the numbers - all of which are required to achieve A or B in mathematics along with problem solving. A page of nicely set out algorithms is not enough to earn an A or B because it cannot show understanding of number - only of algorithms.

That said "don't show them the old way we have a new one" is pretty poor communication ... ask if they will have a parent information night (so you can hear this sort of stuff from someone who explains it better than me.)

#17 22Fruitmincepies

Posted 13 February 2018 - 10:17 PM

That’s interesting expelli. I remember my mum trying to teach me similar techniques, and thinking it was a lot of faff for something so simple. But I’ve since realised a lot of people find those techniques really helpful. DD likes numbers, so it will be interesting to see which approach she likes best (years off though).

#18 Bereckii

Posted 13 February 2018 - 10:35 PM

View Post22Fruitmincepies, on 13 February 2018 - 10:17 PM, said:

That’s interesting expelli. I remember my mum trying to teach me similar techniques, and thinking it was a lot of faff for something so simple. But I’ve since realised a lot of people find those techniques really helpful. DD likes numbers, so it will be interesting to see which approach she likes best (years off though).

Same - my Dad used similiar techniques, but I just didn't "get" it.

DD is much more "fluent" with maths (due to all the techniques she has learnt at school) than I ever was. I am slightly shocked to say that I have enjoyed being brought along this part of her learning journey - maths has always been "hard" for me, but it makes so much sense and I have found the techniques she uses useful for me too!

#19 ~J_F~

Posted 13 February 2018 - 10:41 PM

If they want me to help my kids, I have to do it the way I understand or I am not going to be any help to them at all.

Also isnt the "old" showing kids another alternative, which cant be a bad thing, surely?

#20 PocketGingerJingle

Posted 13 February 2018 - 10:46 PM

View PostExpelliarmus, on 13 February 2018 - 09:59 PM, said:

I find the term 'new maths' to be a misnomer. What I have discovered in my professional development in maths is that I did not learn enough mathematical thinking as a child.

I didn't do it all enough ways. I didn't learn enough 'things' to hang my mathematical hat on and I didn't know how to do enough in my head to make it efficient. Mental computation strategies are designed to give students the language and understanding to make maths efficient, make sense and correct through checking. If you can only do it one way - how can you check it?

A few years ago if you asked me to add any two digit numbers higher than 20,I probably would have had to get out either a calculator or a pen and paper to figure it out. It wasn't automatic for me to recognise 30 and 30 were 60 for example. I might not have to complete the whole algorithm but I I would probably ave to write it down before I saw that it was a double. I would then take a bit to search and find the double for three because these were not facts I carried in my head. I received a truncated and ineffective attempt to get multiplication facts in my head in the form of times tables - which was less than successful as I was being rote taught them instead of learning them in a meaningful sequence. So something like 87+52 was not something I could do in my head.

Maths was difficult. It was hard. I had to get out a pen and paper to do the smallest thing. So this 'new maths' is not actually new maths. It's an attempt at ensuring that children actually have all the things they need to become successful and efficient mathematicians.

Another aspect to it is correcting misconceptions. Developmentally children will have misconceptions about things that need to be 'undone' and the correct conception developed. Unless a child has the opportunity to explore and change their mind about the misconception it generally remains. I was told how to do a lot of things and can perform a lot of operations but I couldn't do it efficiently. Combine an inefficient way of doing mathematics with a lack of understanding (Why am I putting that number down there? It changes columns? But why? Okay then, I'll just move it ...) and sometimes it was just too much effort to figure something out.

Take 87+52 now - now I can do that in my head because I have been taught strategies. That's the so-called 'new maths'. They have always been there because they are naturally occurring but unless they are pointed out, many children do not see them. Unless they are given permission to practice them and use them children won't and they will limit their ability to perform at an efficient and higher level.

87+52
7 and 2 is 9, 80 and 50 is 130 and I know that because if I use 20 to get to 100, I have 30 left which is easy to add to 100, then add the 9 ones to get 139. The strategies I used there were counting on and bridging the ten. By naming the strategy it gives the child a metalanguage to discuss their thinking with others and enables them to use discourse in their learning. That's a whole lot of edu-speak for - learning is social, we learn through self-talk - all based in various educational psychological research.

When I was at school and I sat there quietly doing my page of sums I learnt how to borrow and carry and set out the algorithm - but did not actually learn how to do the maths and how it worked. I didn't get to use the best ways we have to learn - by talking and discovering and arguing and sharing.

87+52
If I make the 87 into 90 by using the 2 from the 50 and another 1, I can get 140 by adding the 50 that is left. I take off the 1 I added to get 139. The strategies there are compensation and bridging through ten. The aim of naming and practicing and using mental computation strategies is to give the students deep understanding of number.

If a child can demonstrate that - in more than one way, they have shown understanding and reasoning as well as fluency with the numbers - all of which are required to achieve A or B in mathematics along with problem solving. A page of nicely set out algorithms is not enough to earn an A or B because it cannot show understanding of number - only of algorithms.

That said "don't show them the old way we have a new one" is pretty poor communication ... ask if they will have a parent information night (so you can hear this sort of stuff from someone who explains it better than me.)

I wish I'd learnt this way. Doing the same method with different numbers 24 times over put me off maths for life. Though I loved physics...

#21 Expelliarmus

Posted 13 February 2018 - 10:50 PM

View Post22Fruitmincepies, on 13 February 2018 - 10:17 PM, said:

That’s interesting expelli. I remember my mum trying to teach me similar techniques, and thinking it was a lot of faff for something so simple. But I’ve since realised a lot of people find those techniques really helpful. DD likes numbers, so it will be interesting to see which approach she likes best (years off though).
My mum used to add strings and strings of numbers and I could never figure out how she was doing it.

87
92
54
68
73
22
13
67

I'd have to grab 2 or three numbers at a time and add those, then get another 3, add those and so on.

87 7 and 7 is 14, cross out those two sevens ...
92 a 3 and a 3 and a 2 .... I can add those - 3, 4, 5, 6 - 7, 8
54 oh wait cross out the 3 and the 3 and the 2 ...
68 um, what's left - oh another 2 - I should have made a 4
73 okay so, I didn't ... add 8 4 and 2? Nah just 2 and 4 - 6
22 so now I add 14
13    8
67 8
6 ... have  I missed any? I didn't cross out the 2, 4 and 8 ... oh yeah they are there in the 6 and the 8.

I then had to add them again and I would go oh look - 16! And now I'd be adding 14
16
   6

And I have't even done the tens column yet!

It was exhausting.

Now I can mentally add:

87   alright ones - 7, 9, 13, 21, 24, 26, 36 ones
92   okay tens, I'll pick out near friendly numbers (numbers that end in  
54   0 - easy to add) 8 and 9 are 17 (near double) then 5+6=11 so 28,
68   7+2+1=10, 38 +6=44 = 440
73   440+40=480 .
22 subtract the 4 I used to compensate = 476
13
67

or ...

87 87 and 13 is 100
92 92 and 54 is 146 = 246
54 68 ad 22 is 90 = 336
68 73 and 67 is 140 because if you take the 3 and make 70, that's
73 2x7 so there are 4 hundreds and 4+3 is 7 so 476
22
13
67

What was I even doing before? I had no idea.

Edited by Expelliarmus, 13 February 2018 - 10:51 PM.


#22 Expelliarmus

Posted 13 February 2018 - 10:58 PM

View Post~J_F~, on 13 February 2018 - 10:41 PM, said:

If they want me to help my kids, I have to do it the way I understand or I am not going to be any help to them at all.

Also isnt the "old" showing kids another alternative, which cant be a bad thing, surely?
It's not bad - but not allowing them to practice their own invented ways or the strategies they have been working on collaboratively in class by saying "Well I don't understand that, here's how to do it." Will not give them the mastery they need.

The "old" ways are frequently abstract, formal concepts and skip the step of understanding. They remove the need for a child to change their mind by giving them a formula or process that may or may not apply to the next context they encounter.

It's okay for kids to struggle and do hard maths. It's okay not to help. The way they will grow new pathways in their brain - and grow it - is to do hard maths. To think their way through it. It doesn't matter if they didn't set their working out like an algorithm. Their working out in diagrams is useful. It gives understanding of where they are at, enables them to see patterns and refine their thinking. It will enable them to find the mistake and correct the error because the steps haven't been coalesced into a few numbers - but all their messy thinking is out there for them to sort through. Then they can find the bit they can shortcut next time, fix the error and develop their own thinking and working out.

#23 Sancti-claws

Posted 13 February 2018 - 11:02 PM

I don't have a problem with new ways to learn, per se - I have problems with being told that the way I learned is wrong and that the games that we play with our child (because we are nerds and I have always played maths games with my kids) are not to be encouraged.

I also used to play with words with my older daughter - and was soundly rebuked by her first grade teacher because... and so I backed off and so my older daughter struggled big time with reading and I had to bite my tongue and she is now a university student who struggles with such things - and I worry greatly that I should have said bugger you to the teacher.

And so yes, I am willing to learn new ways (were they to explain to us or have it explained well enough to my younger daughter for her to teach us) but I am no longer the compliant parent who takes what teacher says is the best way as gospel.

(and I know that my daughter may well have struggled anyway - not everyone GETS reading as easily as others - but it is still the stain on my parental soul)

I am very much enjoying this discussion though, so thank you.

(oh - and the you tube video - that is the nerdy maths that I know!!)

#24 Expelliarmus

Posted 13 February 2018 - 11:07 PM

View PostSancti-claws, on 13 February 2018 - 11:02 PM, said:

I don't have a problem with new ways to learn, per se - I have problems with being told that the way I learned is wrong and that the games that we play with our child (because we are nerds and I have always played maths games with my kids) are not to be encouraged.

I also used to play with words with my older daughter - and was soundly rebuked by her first grade teacher because... and so I backed off and so my older daughter struggled big time with reading and I had to bite my tongue and she is now a university student who struggles with such things - and I worry greatly that I should have said bugger you to the teacher.
All the maths advocates I know say that playing games is important. I would not take away from this parent night the message that you should not play maths games.

My mum had a similar experience re: teaching my brother to read - was told she should not be doing that and she has now ruined him for their teaching. So she didn't teach me.

My brother has dyslexia for crying out loud. It wasn't my mother attempting to teach him to read that 'ruined' him. *bigfateyeroll*

Meanwhile I learned to read (super early and faster than my mum) in spite of mum not teaching me to read - BUT as a result she never taught me her fancy maths ...

Edited by Expelliarmus, 13 February 2018 - 11:08 PM.


#25 Sancti-claws

Posted 13 February 2018 - 11:07 PM

Oh - and for the above math problem:

87
92
54
68
73
22
13
67

My workings from my childhood would have been:



Ones - adding 7 2 4 8 3 2 3 7 - so 9 13 21 24 26 29 36 - six and carry the 3


Tens - 3 8 9 5 6 7 2 1 6 - so 11 20 25 31 38 40 41 47 - answer 476.






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