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Post by Judy on Aug 17, 2020 8:19:50 GMT
Where do you stand on times tables? Do children need to learn them by rote? Why would that be important? Do you have any strategies/resources that have worked well? Do you have any examples of resources to be avoided at all costs? (see my link below) What message do you think we are giving to children by introducing a national times tables test? ( in the UK in year 4) Take a look at this resource www.multiplication.com/sites/default/files/files/ebooks/MeminMinStudentManual10-19-14.pdfScroll down to page 6....shoe x shoe = floor !!!! AAAAAAAAGGGH! |
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Becky
New Member
Posts: 23
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Post by Becky on Aug 17, 2020 10:37:56 GMT
I really dislike the times tables test and feel desperately sorry for those children who struggle to learn them or have memory issues. All it really tells us is how many children can remember them and how many do not. It does not offer any strategies for improvement. Another failure for those children with difficulties. Times tables influence every area of maths and so children do need them. The ones that struggle to retain them, end up spending so long working them out, the maths problem they are working on takes forever. This impacts them hugely in tests as well, especially the arithmetic paper in SATs. TTRockstars is a resource that many schools use but it is only really effective for children that have good memories, know the inverse and can process quickly. Anyone else will struggle. Speed tables is another resource that I see schools using. Again, the same issue with speed. I am looking into Perform with Times Tables with my son at the moment and so far so good (it is early days though).
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Post by Claire Martin on Aug 17, 2020 14:14:52 GMT
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Lina
New Member
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Post by Lina on Aug 18, 2020 9:44:09 GMT
I think that knowing your times tables is important as many calculations rely on them. Having said that, I often give the multiplication grid to a child who struggles with remembering x tables if the objective is to use multiplication as part of practising a different skill. As for the year 4 x tables test, it is set to put pressure on the teachers, like other tests, rather than anything to do with the children. The teachers know well where the children are at without it. It is a shame that the children have to feel that pressure, too.
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Post by suecarter on Aug 18, 2020 10:52:49 GMT
That book is awful!! The students would spend so long trying to remember the rhymes, they'd have forgotten what they were trying to calculate! As everyone else has said, times tables do need to be learnt as they are needed for so many other calculations as the students progress through school. However, I think the test is a waste of time and the timed element is too stressful. There is no substitute for practice, practice, practice, using as many different methods as possible until one that works is found. I find that many of the secondary pupils I work with on interventions do not have a sound knowledge of their times tables but think that's something you do in Primary and you don't need once you get to secondary. Many can say the answers by rote but have no idea when asked a fact out of sequence or a division fact. Many struggle to learn them, so I play lots of games with them (online and paper based) to try and reinforce the facts and use a variety of manipulatives, including dominoes, playing cards and flash cards. I encourage them to use their fingers, touching each finger in turn as they say their tables and this helps them with the division facts. If they struggle with a particular question, I will encourage them to turn it round the other way, 6 x 5 might be easier for them than 5 x 6 as they don't know their x6 table! For x8 facts they struggle with, they might know the x4 and be able to double it - this works for some. Most find x12 difficult so I show them how to partition the 12 and this is a bit of a light bulb moment for many. Like Lina, if the focus of the lesson is not specifically times tables, I will give them a multiplication grid to use.
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Jenny
Junior Member
Posts: 50
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Post by Jenny on Aug 19, 2020 11:26:38 GMT
I've always believed that children need to learn tables facts but was surprised to discover that my husband, who has a phd in physics, never learnt his. He just has reliable strategies for working them out. Thinking more deeply, I think I use derived facts, at least to double check my answers. For example for any 9x question under 10x9 I will always check that the tens are one less than the question number and the units form the number bond to 10.
A big problem with KS2 pupils who I come across is that their addition/subtraction number facts are not good enough to work out their tables facts or even to think whether their answer is sensible.
I've probably said this before but I think the times table test in Year 4 means that teachers stop focussing on addition and subtraction facts far too early.Children then can only learn their tables by rote as they don't have the mathematical understanding to try for example doubling.
The reading on the course strongly implies that time pressure can instigate maths anxiety which is very undesirable. We need to be helping children to find answers efficiently and confidently.
We also give times tables grids to students when they need these for a different focus although I'm aware that this reduces the opportunity to retrieve tables facts, and other research suggests that repeated retrieval is best for long term memory. Maybe we should be encouraging them to try to find the answer and just to use the tables grids for checking. I really like the L shape which Steve suggests for finding the correct number in the tables grid.
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Linda
New Member
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Post by Linda on Aug 19, 2020 11:51:50 GMT
Whilst knowing the times tables help learners to see number patterns, such as factors,etc., I think that learning by rote doesn't work for all learners. If a learner can learn through that sing-song method, then great. Saying that learning just the answers by rote (4 8 12 ...) has no purpose/ context. Jenny, your comment about learners struggling with addition and subtraction is interesting and I agree, there is often to much of a rush to move on to the next topic. Timed tests are horrendous and the learner is just thinking about their anxiety rather than the table. I have started to put some short videos on Fb for tables but agree a different method for each child may be needed. I enjoy the trick with the fingers for the 9 and 3 times tables (my girls used to do these with hands behind their backs so their teacher didn't realise  Doubles is a good method for the 2 (and therefore the 4 times tables) if the learner can manage doubles. One trick I used for my adult learners is to write down the multiples, say for 7 (they can quickly work these out using their fingers ) then the answers are there for both questions on multiplication and division. If the learner is good at halving and doubling, then the Russian method is handy. |
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Post by Judy on Aug 19, 2020 13:40:31 GMT
Thank you for all your comments so far. I think we all agree that automatic recall of times tables would be the goal and that it really helps to reduce cognitive load, but it is also clear that different children need different approaches and the more strategies they can be exposed to the more likely they are to find on that clicks with them. I would also give a multiplication table as a way of overcoming an otherwise insurmountable barrier. Earlier this year I was observing a lesson on equivalent fractions and to be honest it did not go too well. When I discussed it later with the teacher he was lamenting the fact that they couldn't do the equivalent fractions because they didn't know their tables. I suggested that he might have given them tables squares for that lesson as the objective was to understand equivalent fractions rather than recall of tables. He looked at me as though I was a genius for the suggestion, which I found rather sad as it was an easy obstacle to overcome and now the children were left frustrated with an area of fractions that they could have easily grasped.
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Post by bernadette on Aug 19, 2020 19:01:01 GMT
Times tables and the inability to learn them seems to be exactly the time when I get pupils. That, and when they can't do bonds of 10. Of course it always transpires that there is a lot more 'missing' further back than the TT or BOT! I do think there comes a point when they are pretty essential to making progress in maths, but that pupils can get by if their cannot rattle them off automatically.
I use a 'key's system for teaching them, focussing on 2x, 5x and 10x on the given table. (some use 1x2). I use laminated keys, real keys, drawings of keys as appropriate. At some point I give the child a laminated key shape with the times table on it. Whatever it takes to get them to remember to use the keys. My tables mat has key symbols on it and any time we write a 'list' of tables we draw a little key beside 2x,5x and 10x a number.So (oncethey can step count) if we know 2x 5 is 10, then we can work out or derive a correct answer to 3x that number by adding 5. If we know 5x5, then 6 times 5 is easier. For 9x5, we subtract 5 from 10x5 = 50. This reduces cognitive load generally, and helps dyscaclulic pupils and or those with weak memories, short term, working, to give them a place to go to that they 'know' and then use that known fact to get a correct answer. We also do this via spinner games, card games, chains, and little key cards. I like to keep repeating the keys to the various tables regularly. Quite often when practicing or learning a table, I will actually put the three keys on the top of the page, including the answers, as I know the child knows these quite well, and they can then glance at them and are prompted to use them to work out some others. In time most DO learn the tables, the hardest point for me is reminding them to 'use your keys' as part of the process of learning. The children actually like it though and games which is good. I watched the module on times tables here and love the idea of breaking down the tables, onto a chart,into what you know and what you don't, then with just a FEW(!!!) little rhymes or whatever, 8x8 etc. we can get more under our belt and make the whole task appear to be a bit less daunting to a child.
At other points I will move ahead anyway as I'm am happy to teach perimeter ,area for example but only use numbers/tables the child knows, or at least is comfortable with. If a child is in Year 3 I think I don't want them stuck in do not pass go times table hell! They feel bad enough sometimes about maths, and get delighted when they can do what they consider 'more advanced topics" and experience success. I had a child run through the house once delightedly shouting 'Daddy, I've cracked area' (she had) when he was probably thinking....I thought that woman could make her times tables fluent! Somehow the process of the other topics helps them see earlier why they do actually NEED to do the tables at least. Another point is, I think, that a lot of parents think the child will be taught and actually learn these tables in school, The days when we use to chant them are (probably thankfully) long gone, but a lot of parents don't really understand that the 'expectation is that they as parents will actually do most of the teaching and practicing at home. (schools just say practice but...) It does take a bit of work, no matter what the method though doesn't it! Unfortunately, they do need a degree of automaticity for fractions etc. Perhaps drawing the tables square might help if all else really does fail?
The times tables test is appalling. How awful too for children who process number slowly or generally need thinking time to produce their answers.
The book really really made me laugh Judy! I like the idea of the odd rhyme or trick, but hate these stories that supposedly help children remember tables. Seems to me like they just add to the list of things to learn generally and then you can't necessarily transfer that knowledge elsewhere!
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Post by Judy on Aug 20, 2020 11:15:58 GMT
Times tables and the inability to learn them seems to be exactly the time when I get pupils. That, and when they can't do bonds of 10. Of course it always transpires that there is a lot more 'missing' further back than the TT or BOT! I do think there comes a point when they are pretty essential to making progress in maths, but that pupils can get by if their cannot rattle them off automatically. I use a 'key's system for teaching them, focussing on 2x, 5x and 10x on the given table. (some use 1x2). I use laminated keys, real keys, drawings of keys as appropriate. At some point I give the child a laminated key shape with the times table on it. Whatever it takes to get them to remember to use the keys. My tables mat has key symbols on it and any time we write a 'list' of tables we draw a little key beside 2x,5x and 10x a number.So (oncethey can step count) if we know 2x 5 is 10, then we can work out or derive a correct answer to 3x that number by adding 5. If we know 5x5, then 6 times 5 is easier. For 9x5, we subtract 5 from 10x5 = 50. This reduces cognitive load generally, and helps dyscaclulic pupils and or those with weak memories, short term, working, to give them a place to go to that they 'know' and then use that known fact to get a correct answer. We also do this via spinner games, card games, chains, and little key cards. I like to keep repeating the keys to the various tables regularly. Quite often when practicing or learning a table, I will actually put the three keys on the top of the page, including the answers, as I know the child knows these quite well, and they can then glance at them and are prompted to use them to work out some others. In time most DO learn the tables, the hardest point for me is reminding them to 'use your keys' as part of the process of learning. The children actually like it though and games which is good. I watched the module on times tables here and love the idea of breaking down the tables, onto a chart,into what you know and what you don't, then with just a FEW(!!!) little rhymes or whatever, 8x8 etc. we can get more under our belt and make the whole task appear to be a bit less daunting to a child. At other points I will move ahead anyway as I'm am happy to teach perimeter ,area for example but only use numbers/tables the child knows, or at least is comfortable with. If a child is in Year 3 I think I don't want them stuck in do not pass go times table hell! They feel bad enough sometimes about maths, and get delighted when they can do what they consider 'more advanced topics" and experience success. I had a child run through the house once delightedly shouting 'Daddy, I've cracked area' (she had) when he was probably thinking....I thought that woman could make her times tables fluent! Somehow the process of the other topics helps them see earlier why they do actually NEED to do the tables at least. Another point is, I think, that a lot of parents think the child will be taught and actually learn these tables in school, The days when we use to chant them are (probably thankfully) long gone, but a lot of parents don't really understand that the 'expectation is that they as parents will actually do most of the teaching and practicing at home. (schools just say practice but...) It does take a bit of work, no matter what the method though doesn't it! Unfortunately, they do need a degree of automaticity for fractions etc. Perhaps drawing the tables square might help if all else really does fail? The times tables test is appalling. How awful too for children who process number slowly or generally need thinking time to produce their answers. The book really really made me laugh Judy! I like the idea of the odd rhyme or trick, but hate these stories that supposedly help children remember tables. Seems to me like they just add to the list of things to learn generally and then you can't necessarily transfer that knowledge elsewhere! Thanks Bernadette, I really like your idea of laminating pictures of keys as often the children forget the strategy- really good idea.I also agree that whilst the road to learning tables can be a long one we do need to veer down other more interesting paths that catch our attention along the way, as we all need to experience success in order to stay motivated. Very much like b/d reversals, we revisit it regularly but it can't be the focus of every lesson. |
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sami
New Member
Posts: 14
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Post by sami on Aug 23, 2020 12:05:09 GMT
Times tables are such a problem for so many and most of the schools I work with are grappling with how best to teach them. As with many of the comments above I agree that rapid recall of multiplication facts is a real asset to pupils who understand how to use the answer in problems as they come across them. I do think so many pupils judge themselves harshly according to the speed of their recall and for many this is where a feeling of failure in maths starts to take a grip. I try to support teacher in helping pupils to see how the tables build on each other and are interconnected and rather than recalling rules and tricks to use their understanding to help them. If a child understands, possibly having used a manipulative like Numicon to build the calculation, for example why all multiples of an even number will have an even product, they can carry this knowledge with them in all multiplication calculations. It is helpful for pupils to recognise which calculations they find tricky and practice these or have effective ways to reach the answer - if I know 5x4 then 5x6 is more manageable to find. Understanding the structure of multiplication and teaching it alongside division as the 'doing and undoing' as well as focusing on exploring the inverse nature of it supports pupils in the amount they have to remember. I think pupils should explore using concrete apparatus and pictorial representation why 3x5 will have the same solution as 5x3 but not arise from the same problem - I could earn £3 for 5 days or £5 for 3 days to bring in the same income.
I have produced a very simple PowerPoint (which I’m happy to share if helpful) to illustrate how the tables expectation build in the UK national curriculum and then how understanding the use of inverse reduces the number of facts to recall and teachers can the appreciate the need for pupils to develop their tables gradually rather than as a race as they reach the year four test. I use this in training, and it helps staff to appreciate the need to plan and build knowledge & understanding in order for recall then recall at speed. I find regular tables tests do very little to support improvement unless combined with opportunities to explore and practice, and where testing is used it should be focused on a pupil’s particular targets and success should be measured in terms of self-improvement.
I think the nature and structure of the national Multiplication Tables Check is entirely flawed. Having observed and then discussed the process with pupils during the pilot they found getting stuck on one question put them off for the rest of the test, decontextualised calculations to answer without any graphic or response as to whether they were correct was boring, only answering multiplication without division or empty box did not demonstrate their understanding and the process was not pupil friendly. We have already seen how the timed nature of a test will increase stress and impact negatively on working memory. In the real world our need for immediacy in calculation is rare and judgement of pupils by speed rather than mathematical agility is I believe, a waste of time and an unnecessary hoop for pupils to jump through.
My 12 year old dyslexic daughter is a great problem solver and a really strong mathematician as a result of it. She will often come up with approaches of her own, has a curiosity for pattern and makes creative connections between different aspects of maths learning. However, she will often use her fingers for single digit calculations and has to build her multiplication facts from what she can remember. It has taken her (and her school) a long time to appreciate that her recall of number bonds and multiplication facts are not an indicator of her capability, and her dyslexia makes the recall of facts and word problem aspects of maths that are difficult for her but if judged by these alone she would feel she was failing. She is now in the top set for maths and is clear that is a subject that she is excelling in.
Apologies for the rant…!
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Post by Steve on Aug 27, 2020 8:55:07 GMT
One of the 'great' topics in maths education. I published 'What to do when you can't learn the times tables ' in 1996. It appears to have had little impact on the 'thirsty-sixes' brigade and I do doubt that for any learner with co-morbid dyslexia difficulties may not benefit from so many words for so few symbols. Check out Pinterest for hundreds of ways to overwhelm kids.
Above all topics this one taught me that 'Nothing works for everyone' and 'Something will work for someone' and the topic acts as a good starting point for what we mean by educating children.
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Post by Judy on Aug 27, 2020 14:30:32 GMT
Times tables are such a problem for so many and most of the schools I work with are grappling with how best to teach them. As with many of the comments above I agree that rapid recall of multiplication facts is a real asset to pupils who understand how to use the answer in problems as they come across them. I do think so many pupils judge themselves harshly according to the speed of their recall and for many this is where a feeling of failure in maths starts to take a grip. I try to support teacher in helping pupils to see how the tables build on each other and are interconnected and rather than recalling rules and tricks to use their understanding to help them. If a child understands, possibly having used a manipulative like Numicon to build the calculation, for example why all multiples of an even number will have an even product, they can carry this knowledge with them in all multiplication calculations. It is helpful for pupils to recognise which calculations they find tricky and practice these or have effective ways to reach the answer - if I know 5x4 then 5x6 is more manageable to find. Understanding the structure of multiplication and teaching it alongside division as the 'doing and undoing' as well as focusing on exploring the inverse nature of it supports pupils in the amount they have to remember. I think pupils should explore using concrete apparatus and pictorial representation why 3x5 will have the same solution as 5x3 but not arise from the same problem - I could earn £3 for 5 days or £5 for 3 days to bring in the same income. I have produced a very simple PowerPoint (which I’m happy to share if helpful) to illustrate how the tables expectation build in the UK national curriculum and then how understanding the use of inverse reduces the number of facts to recall and teachers can the appreciate the need for pupils to develop their tables gradually rather than as a race as they reach the year four test. I use this in training, and it helps staff to appreciate the need to plan and build knowledge & understanding in order for recall then recall at speed. I find regular tables tests do very little to support improvement unless combined with opportunities to explore and practice, and where testing is used it should be focused on a pupil’s particular targets and success should be measured in terms of self-improvement. I think the nature and structure of the national Multiplication Tables Check is entirely flawed. Having observed and then discussed the process with pupils during the pilot they found getting stuck on one question put them off for the rest of the test, decontextualised calculations to answer without any graphic or response as to whether they were correct was boring, only answering multiplication without division or empty box did not demonstrate their understanding and the process was not pupil friendly. We have already seen how the timed nature of a test will increase stress and impact negatively on working memory. In the real world our need for immediacy in calculation is rare and judgement of pupils by speed rather than mathematical agility is I believe, a waste of time and an unnecessary hoop for pupils to jump through. My 12 year old dyslexic daughter is a great problem solver and a really strong mathematician as a result of it. She will often come up with approaches of her own, has a curiosity for pattern and makes creative connections between different aspects of maths learning. However, she will often use her fingers for single digit calculations and has to build her multiplication facts from what she can remember. It has taken her (and her school) a long time to appreciate that her recall of number bonds and multiplication facts are not an indicator of her capability, and her dyslexia makes the recall of facts and word problem aspects of maths that are difficult for her but if judged by these alone she would feel she was failing. She is now in the top set for maths and is clear that is a subject that she is excelling in. Apologies for the rant…! Hi Sami Thanks for your comments, I think we can all rant about times tables- it is such an emotive subject! Please can you share your powerpoint- that would be great. You can either send it to me or upload it to the padlet. many thanks Judy |
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Post by peterwhitehead on Aug 29, 2020 12:20:16 GMT
The book? Oh my goodness. Not sure there's anything I can add about its hideous examples ("dirty chicks" - seriously?): but we do not need to recognise that there are clearly two schools of thought in cognitive science about pictures and multiple representations?
It's self-evident to me that the way for me to remember railway ticket booking codes of random letters and numbers is to create a little story; far quicker and more reliable than just the letters and numbers themselves: but I only need to remember this for 10 minutes as I walk to the station so I don't need to get my phone out. I can't remember anything of Tuesday's code just a few days' later. Also, people who memorise the sequence of whole packs of cards do so by creating a story with each card representing an object or character.
On the other hand, we are also cautioned against the use of mnemonics because a student either 1) can't remember which mnemonic belongs with each concept, or 2) the mnemonic does not precisely describe the concept and is open to misinterpretation (eg "BIDMAS"). In my own experience, I was never taught any mnemonics in maths at any level. I used various mnemonics in preparation for professional actuarial exams years ago but now can't remember any of them as they really were just revision tools. The only mnemonic I use in day-to-day life is about the colours of the rainbow. More common mnemonics such as "SMART" are no use to me as they've been used in too many different contexts with too many different meanings.
I was aware anecdotally that there existed various pictorial systems for learning times tables but this is the first I have seen in all its horror. Judy, do you have an example which is better thought through with fewer inconsistencies and less contrived examples?
In my teaching context, I am dealing with number fact deficits in 16+ students and adults so the way we approach this has to be rather different from early years. They're not going to be exposed to the national testing but as Steve says "they've got to know something" on which to build.
Most of these older students already recognise that having more number facts to hand is going to help then in their day-to-day maths and in their maths classes. Since I invariably only see these students once a week, the responsibility for practice has to be passed to the student which makes progress slow and difficult as I am trying to change many years of hiding and being embarrassed by this deficit. The strategy that seems to be working is to really focus on Steve's core 1,2,5 and ensure that the number sense sessions we do focus on strategies using that core. Thus the TT practice has a direct benefit on the arithmetic practice and any money practice. As regards tools/apps for learning these, I just want something that represents the number fact in as many useful ways as possible (and both ways around): as an array; as a multiplication fact; as a division fact; as a rectangle area fact; as a missing rectangle side fact.
As a side note, it's worth remembering that the reasons why 2 and 5 are the easy times tables to learn is simply because they are factors of 10 in our decimal system. If we worked in a duodecimal (12) system then all the factors of 12 would likewise have easy TT patterns. Eg, the 3x,4x,6x tables are
3, 6, 9, 10, 13, 16, 19, 20, 23, 26, 29, 30...
4, 8, 10, 14, 18, 20, 24, 28, 30...
6, 10, 16, 20, 26, 30...
(I'm not one of these duodecimal enthusiasts, btw!)
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Post by Katherine Bishop on Dec 28, 2020 6:06:25 GMT
It is such a contentious issues among teachers and educators. I work with some wonderful teachers, but some of them are still hooked on the fact that students need to have number facts, including tables in a timely manner - as fast as possible. Students are put under such pressure that they are slower than they would otherwise be. The anxiety created is significant.
In looking at the link above that you shared in the opening discussion point Judy, it reminds me of one that is used by a few tutors I know. I had twins handed over to me to do some remedial tutoring work with them. They had been introduced to 'Times Tales' (https://www.timestales.com/) which seemed, on the surface, to be helping them remember some of the trickier tables answers eg 7 x 8 etc. It is what I consider to be an elaborate system of a story (first they watch a DVD to introduce them to the number characters) then each times table is connected to a rhyme.
I found it enormously confusing. The girls I was tutoring remembered a few of them as long as they were drilling the flashcards at home several times a week. If they were going to spend their time doing that and still having no understanding whatsoever of the number patterns that made up the answers their time was ill spent. I stopped that and we began to look at early number bonds, early addition and subtraction with manipulatives and patterns in the times tables when we coloured them in the 100s charts. They began to make progress and then their parents stopped their tutoring. Frustrating but an interesting learning experience for me as well.
The website even has a section talking about how it helps students with dyslexia and dyscalculia. I think it is very misleading to parents and homeschoolers also who are not sure what to do.
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Doubles is a good method for the 2 (and therefore the 4 times tables) if the learner can manage doubles. One trick I used for my adult learners is to write down the multiples, say for 7 (they can quickly work these out using their fingers 
