teachers - how much maths should a child be getting right?

[inthesark]

In the way that in reading, two or three difficult words a page is supposed to be the right level of challenge, how would you judge this in maths?

Obviously if they're mostly getting them wrong that's a problem, but also if they're getting them all right, that's also too easy. But what's the 'right' level?

I'm partly asking because I've heard two different figures, and I'm really interested to see what the consensus is.

Can't speak for the teachers but this is how it strikes me:

If the child knows how to do the sums and is capable of doing them then surely she should be getting them all right, shouldn't she? Are the questions all of the same type? I suppose it depends on what the child is being asked to do and how she's being asked to do it. I remember maths homework as being one or two pages of the same types of calculations. Reading is different in the sense that words of varying difficulty can appear on the same page. Work of varying difficulty tends to appear in exams. But typically children don't get given exams for homework.

If the child is doing the work in school and getting it wrong then she hasn't been shown how to do it properly or she has been shown but doesn't understand it or she does understand it but it contains some elements which are too difficult for her to do. If the last one of these is true then she needs to practice the elements that she is struggling with first and then come back to the sums.

It's an interesting question, in that there are different schools of thought.

Some argue that children should be getting all calculations right.

Personally, I would worry that a child who ALWAYS gets all the questions right is not being challenged.

Personally, many of my lessons have a kind of 'base / core / extend' type structure:

1. Check that all children are happy at the base level (this is often a quick look-see on the carpet with whiteboards, no formal written questions at all - just check that everyone has the fundamentals in place. All children should get this right - I identify any who need to backtrack or will need support at this point)
2. Work on the 'core' level for most of the lesson (depending on the class, that might be a 5-way differentiated 'core for each group' arrangement, but definitely work that children should be getting right if they have understood the lesson)
3. Look at an extension. I would not expect all children to get the extension right - if some do, then I will often probe with 'extended extensions' to see what the limit of their understanding is, to decide where the 'new core' for that children should be for the following day IYSWIM?

Hmm interesting question.
As a teacher, my aim is for ALL children to be able to do something they couldn't confidently do at the start of the lesson. That's the short answer as my tea is getting cold! :-)

To clarify (I think I deleted a chunk from my post), I agree with stuffez - base work is stuff that they should be able to do confidently (but sometimes a few children may need it reinforcing / revisiting), the 'core' work is that 'next step up' which they can't do confidently at the start but should be able to at the end, and the 'extension' is 'can you take it further?' stuff.

Different patterns of 'wrong answers' crop up for different children, all of which can be useful in defining 'next steps' for the next lesson:

e.g. Mistakes in 'base' work - often followed by few mistakes, if any, in books for base / core work for the remainder of the lessson, as those will be children who are a specific focus for support by whatever adults are in the lesson

• Mistakes in early 'core' work, followed by an increasingly confident mastery of the area / approach.

• Similar patterns of mistakes throughout e.g. a common one is a problem when vertical addition leads to an answer of 10 in one column ... for some reason, children who cope fine when the column adds to 13 go to pieces with what to do with that 0! They are usefully diagnostic, and are often specifically picked up on at some point in the lsson or the beginning of the next one.

• No mistakes up to the extension task, and then some mistakes in this as the limits of what they can do are explored.

[Some children are just somewhat slapdash, with random errors throughout....]

That's really interesting, thank you.

This has come up because DD's school argue that children should be getting at least 90% of their maths work right, as this gives them confidence. We think that she is rather coasting along in maths lessons and could do more (in fact she is getting more than 90% right in the books we've seen).

Elsewhere I've been told something like 75-80%, which sounds more like what you are saying, teacherwith2kids, with "some mistakes in this as the limits of what they can do are explored." I think that's the bit that is missing from what her school do. But the 90% absolutely fits for the school's attitude, as they seem to think that it's a choice between happy and educated, and tend to come down on the side of happy.

inthesark,

I have in the past worked with someone who said that every child should get 100% right in every lesson, and if they didn't then the lesson should be repeated until they did, because they didn't understand well enough yet...and did only whole class teaching, no challenge tasks for specific groups etc...

So you should perhaps rejoice that the 90% isn't higher!

I would say 75-80% is not acceptable if most of the mistakes occur in 'base / core' work (or rather, that would indicate that the work is a little too hard). If the final 25% of the work is on 'extend' work, then 80% might be OK

ha ha ha. Yes, I will be thankful for small mercies.

I completely get what you are saying about the 80%, that makes sense. I think that's the chunk of her lesson that's missing at the moment (I didn't want this to be a classic MN stealth boast, but she's not getting very many wrong at the moment, which is why I am trying to find out what's a good level to aim for).

I find that sometimes it can be misleading looking at just right or wrong answers when judging the level of difficulty. I can find that I can teach a lesson, whereby if I had given the children the questions to do before I had taught them the concept they would get none right, but once they do the questions they get them all right, doesn't mean that the questions were too easy, just that the child has successfully learnt the concept/routine/method and applied it.

Also many children are reluctant to put pen to paper in maths until they know they are correct, so just looking in the book and seeing correct answers doesn't tell the story of how they got to the right answer. Some children hate teachers writing in their books and prefer me to do things with them on a whiteboard or post it note before they then do it in their book, so it looks like they are getting them correct with no help, but that may not be the case!

d'ya know, it's funny you ask this as my 7 yo dc had a bit of a wobbler yesterday as out of 15 questions, she only got 10 right...

i don't think it's doing her any harm, because she is normally 100%, top table, right first time etc...

so, not sure what that adds to the debate?

What types of mistakes did she make in the five that she got wrong?

learnandsay - I have an example of why they shouldn't be getting them all right.

My secondary DD1 is fragile on her maths. If she has done the type of question a few times before, she is generally OK, but if you change it slightly it can throw her.
e.g. last night she could do 3/18 + 1/3 no problem.
but couldn't do 3/18 - 1/3 (that would be less than zero! - but she knows numbers can be negative, but hadn't thought about fractions being negative, or at least had forgotten as we've had this problem before)
also couldn't do 1/2 + 1/3 + 1/4 (because her method for getting them over a common denominator doesn't work with 3 fractions, and she forgot she could do 2 then 1 more).

SO, a child might understand a basic method, but be confused on more advanced variations.

I suppose so, if that's how they're taught. But if my daughter was being taught like that I'd be horrified. I'd expect her to be shown not only the basic method of manipulating fractions but if she was going to be asked to manipulate more complex fractions I'd expect her to be shown precisely how to do this and then to practice it until she was comfortable with the method before being given a number of complex fractions to manipulate. What you're suggesting is a bit like teaching someone to drive a car, then shoving the vehicle off a cliff and saying to the pupil, well, off you go and save it then.

The trouble with a child getting them right all the time, every time is that it hits them hard when they finally do get to 'their level' and start to make mistakes/not understand new concepts immediately. That in turn can completely knock their confidence.

I think they should be working at a level where they DO make mistakes but not a high %, getting 100% right all the time isn't a good thing and means they aren't being challenged (in my opinion)

They are very different things and I dont think can be seen in the same way.

When a child stumbles on a word when reading and has to decode, this is seen as a mistake, even if the child decodes it correctly. This is because reading is also about comprehension and a child that decodes every words cannot possibly take in the content without having to go back and reread.

When a child approaches a maths question they will rarely know the answer straight away and will have to work it out. However if they ultimately get it right then it is a right answer, no matter how long it took. A child getting 100% could easily be taking their time, making errors as they go and correcting them, developing their understanding and skills and ultimately getting the right answer.

90% to me (depending on the number of questions, 1 wrong out of 10 wouldnt worry me) might still suggest this child is not fully secure. In independent maths work a child is consolodating and developing skills - they aren't coming across something new. (This would be an additional challenge). This is not so in reading - there will always be new words, the difference is the method is always the same.

Whether your child is being challenged cant be judged simply on amount right I dont think and I see where the school is coming from with 90%

L&S,

Maths is interesting because a really secure basic understanding of 'how it works' (whether 'it' is place value or fractions or symmetry or addition or algebra) can mean that it isn't always necessary to specifically teach evry single variation before a child with a secure basic understanding can apply it to relatively unfamiliar situations.

So, in the example of fractions, someone with a really secure grasp and fundamental understanding of fractions CAN apply a knowledge of equivalent fractions to add and subtract more than 2 of them, and can be quite happy adding in their knowledge of negative numbers to the mix to work out when the answer is one.

However, someone who 'knows how to follow a procedure to obtain the right answer', but WITHOUT that fundamental grasp, will need specific teaching for each new variation, because they need to be specifically taught the new procedure.

My 'extend' sessions (often the plenary bit at the end of the lesson), is often designed to differentiate between those with an emerging secure understanding from those who were 'fiollowing the steps' but without really knowing what was going on IYSWIM. Those who were following the steps may need to be give slightly adjusted steps for a new situation in the next lesson, those who have a secure basic understanding need to be given more and more unlimited examples to apply it to.

Your view assumes that every child needs to be specifically taken through all the steps. In fact, where the time is sometimes best used is in really developing basic understanding (place value e.g. decimals, very large numbers, is a classic one), after which all the different areas in which that can be applied are quite quick.

not sure learnandsay what they were.i did ask dc but you know how nonsensical they can be sometimes....

For some children they just tend not to make mistakes because they work carefully and don't lose concentration and make slips. So a child might be shown how to do something they've never done before and then do a page of examples with no errors. They still needed to do that page to reinforce what they've learned, so it's not that they are not being stretched, it's just that they are good at working accurately and learning quickly. Conversely if they are given a sheet that really is too easy for them, they may not give it their full attention (as it seems dull) and so be more likely to make slips.

Counting the percentage of mistakes is not a good way to determine if work is at the right level, certainly not for all children.

I think they do need to learn to get things wrong. My dd1 (8) went through infant school pretty much never getting anything wrong. She has now gone into the juniors where the work is much more challenging and differentiated and she gets herself in a bit of a state when she makes mistakes, as she's just not used to it. For her, getting a question wrong is a big knock to her confidence, but if she had been more challenged earlier then maybe she would have got more used to it....or been more stressed at a younger age.... Thinking about it not sure which is best actually.

Yes, that's one of my big issues with this whole thing. Learning reslience, someone called it, and I think that's really important. Because if you don't get things wrong, how do you learn to step back, work out what mistake you meant, and then do it again.

DS generally gets 100% in maths which I only realised when his books came home at the end of year 3 and I saw the pages and pages of immaculate and correct work.

I did worry a bit at the time that he might not be stretched and now in year 4 he seems to get 100% in tests and gets all his classwork and extension work correct but to be honest he is happy and enjoys his lessons so I am relaxed about it.

Unusually (or maybe not?) he is finding maths much more intersting and easier as he moves up the school. The way I look at is that he is fortunate to find it this easy - I don't see the need for him work any further ahead. I like the fact that he must have a really secure understanding of the topics and can obviously apply his knowledge when required.
I guess I would have a different view if he was unhappy or it was causing problems.

Very interesting question, and helpful thread!

I went to a "Raising Boy's Achievement" conference at the beginning of the year and the speaker said (and I happen to agree with him) that if you have taught your pupils well they should be getting their work 100% correct. If after I've taught my class and they are still making lots of mistakes then my teaching isn't effective.
It isn't the same as the work being too easy for the child. Obviously if the child can do the work error free before the teacher input then it is a waste of both the teacher's and child's time.

I also disagree with the idea that reading 2 or 3 words per page indicates the right level but that's another thread.

2 or 3 words per page incorrectly