Category Archives: Maths

Success criteria in maths

I vividly recall maths lessons as a child.  I was in the bottom set and I remember a general feeling of bafflement as it appeared to me that others seemed to know what to do while tasks remained a mystery to me.  I don’t remember anything being explained and years later as an NQT, reading the numeracy strategy unit plans, I had a moment of realisation that there were ways of calculating in your head.  In your head!  All I’d known was formal written methods. For everything! What I needed whilst at school was to be let in to the secret of how to do maths.

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Filed under Curriculum, Maths, Memory

Teaching Ratio

Novices and experts see problems differently.  Whereas a novice sees superficial features, an expert notices deeper underlying patterns, discarding the often irrelevant and distracting contextual information.  Here’s an example:
Nick-hart-blog-post-image-1.png

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Acronyms like RUCSAC prevent children from thinking mathematically – we need a different approach

I’ve got a thing about success criteria. Very often, the line between what we want children to learn to do and the task that we ask them to carry out is blurred. The gap is perhaps most stark when it comes to problem-solving in maths.

In many classrooms the “read, underline, calculate, solve, answer, check” (RUCSAC) acronym, or something similar, will be plastered on the wall and used as success criteria for problem-solving.

However, I’d argue that RUCSAC does not present a valid set of criteria for such an important part of maths; rather it prevents children from learning to think mathematically. Here’s why…

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Maths — the big ideas

The beauty of maths lies in the interconnectedness of ideas and concepts yet this concept of relationships is often lacking in children who struggle with maths.  Mike Askew, Professor of Education at Monash University, Melbourne, has written about what he calls the big ideas of maths. These help children to connect different areas of mathematical understanding, yet are small enough to understand in their own right.  

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Principles and practices of effective homework

Homework can have quite a negative reputation.  It is often the source of familial tension as parents make sure their little ones have done it, not to mention the effect on teacher workload.  Research organisations like the EEF have not found it to be too effective either.  That said, research can only judge the effectiveness of existing practices so the job of teachers and school leaders is to find better ways of doing it.  When it is done well, homework can undoubtedly have a positive effect on learning.  The EEF states that effective homework is associated with short, focused tasks which relate directly to what is being taught and is built upon in school.  It also recognises the importance of parental involvement.  With these conditions in mind, here is a set of principles and practices for making homework as effective as possible. 
Read the rest of the article on the Rising Stars website…

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SATs not as hard as it looks!

One of my favourite responses when working with with children on tricky problems is, ‘Oh is that it?  It looked much more difficult!’ As May draws closer, children in Year 2 and Year 6 up and down the country are preparing for end of key stage SATs. Tests often invoke strong opinions among teachers. As adults who have typically done well in the education system, tests may never have been a worry and we may see them as a chance to shine and something to look forward to. Others may hold the view that testing children is barbaric and sucks the life out of curricula as schools teach to the test. Either viewpoint, or any gradation in between, does not change the reality that schools are accountable for the success of children on tests. Perhaps more important than accountability though is ensuring that all children, particularly those who are disadvantaged, are able to graduate from an education system that provides qualifications through examinations and have access to wider opportunities in the future.

Every school will be familiarising children with the upcoming tests, most likely by using practice papers, with the aim of children knowing what to expect and in turn doing the best that they can when the time comes. In my experience, there are a number of strategies to do this well and there are also some strategies that could well do more damage than good.

SATs are the ultimate summative test for primary school children and it can be tempting to recreate these summative conditions when preparing children for them. Practice tests done in exam conditions where they receive an overall score at the end have some value but could well set children up for failure, creating anxiety as the high stakes take their toll. Removing the test conditions gives children a chance to learn how to take tests. If the stakes are made lower still, for example by removing the importance of the score achieved, then we can go some way to normalising test situations and therefore reducing the likelihood of anxiety.

It is very easy to get hold of past papers and although the examples here are maths questions, the principle applies to reading, spelling and grammar tests too. One important first step in teaching test technique is to model what a successful test taker does and verbalise their thoughts. Displaying certain types of question, saying what you’re thinking and showing what is appropriate to record is crucial to encouraging children to do the same. From this modelling and explanation, teachers can co-construct success criteria for how to go about the test. The criteria will be a selection of tools to choose from depending on the question being tackled. Sure, those who are successful in tests know subject content very well but by explicitly showing what it is that successful test takers do, we can unlock the mystery of how to be successful. Looking at the KS2 sample tests, the success criteria for answering those types of questions might be:

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Over time, advice like this can build up and if children can internalise it, they will be equipped to deal with tricky problems. Of course, strategies like this are no use without good content knowledge but when combined, set children up to succeed.

Once strategies have been modelled, children can be set off practising. Again, it’s tempting to give children their own paper and have them complete it as they would have to during the test. However, it becomes a much more valuable exercise if children talk about what they’re doing so getting pairs to complete papers collaboratively gives them an opportunity to talk and hear how someone else goes about tackling a test. A few guidelines help to keep them focused:

  • Both work on the same question.
  • Agree an answer before moving on.
  • If you disagree with your partner, explain why you think you’re right and listen to their explanation too.

One of the stressors of testing is the time constraint. When children are practising test techniques there is no need for such constraints. Over time, they’ll get quicker and the strategies they work on will become more autonomous. At that point, time restraints can be put in. For example, you might set the target of getting to question 6 in 10 minutes or halfway in 15 minutes.

We’ve all experienced that frustration of seeing children answering a question wrong in a test. This doesn’t have to be the case when they are practising and like in any great lesson, teachers react formatively to the information before them. If everyone is struggling with question 4 about fractions of numbers, then stop them and teach them how to do it, give them a few extra practice questions and make a note to return to it soon. If it is just one pair or a handful of children struggling, then a little scaffolding, followed by some more practice will help. The example below comes from the KS1 sample test:

KS1 Maths SATs.png

Having seen that this pair of children did not know how to approach the question, the teacher explained that division can be seen as sharing and that this is asking to share 35 into 5 groups. The teacher, in blue pen, drew five groups and began sharing one at a time before the pair completed the question. Now evidently that won’t be enough for that pair to have understood completely so it can then be followed up with sufficient practice to internalise the idea.

Once children have completed the practice tests, teachers will be keen to know the score they achieved as well as looking for specific detail about which questions and topics children struggled with. The well-worn phrase ‘Check your work’ will I’m sure be repeated countless more times with varying levels of patience but that means nothing unless children are explicitly taught how to do so effectively. The way that test are marked can encourage the habits of checking. The most structured way would be to mark each question with the number of marks awarded:

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When scripts are marked this way, children can see which questions they were successful in answering and which they got wrong. When the tests are returned, children can look for the questions they got wrong, and if it was a case of making a mistake, can discuss what happened with their partner and make the necessary corrections.

This may be a sensible place to start but of course it makes children reliant on the marking to see where mistakes have been made. A gradual removal of that scaffold could involve marking the score for each page rather than individual questions:

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In this example, out of the 3 marks available for the questions on this page, the pair of children scored 1. It is then down to the pair to re-read questions to first of all determine which are incorrect and secondly to work through it again to see what went wrong.

A third option, to remove the support a little further, would be to count up the total marks, only telling children something along the lines of ‘You scored 33 out of 40. Find and correct the mistakes.’ It goes without saying that these marking strategies push for corrections of mistakes and will do no good if the child never knew the content well enough in the first place.

Test papers are valuable resources to use in the classroom, not least because of the teaching opportunities for test technique that they allow. One subtle but significant benefit is the varied practice they provide too. During maths lessons, the focus may be narrowed to one objective or concept, and rightly so to provide focused support and practice. Tests’ varied questions though provide a great opportunity for revision, to interrupt forgetting and to provide teachers with a wealth of information with which to inform future lessons.

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A place for everything and everything in its place

Place value is very often one of the first units of work for maths in most year groups and is absolutely fundamental to a good understanding of number.  By getting this right and giving children the opportunity for deep conceptual understanding, we can lay solid foundations for the year.

For the purpose of this blog I’m going to assume that children can count reliably and read and write numbers without error. If these things are not yet developed to the appropriate standard then targeted intervention needs to happen without the child missing out on good modelling and explanations of place value.

Children need plenty of practice constructing and deconstructing numbers, first using concrete manipulatives like base ten blocks or Numicon.  This is to show that 10 ones is equivalent to 1 ten etc.  While they’re making these numbers they should be supported to talk articulately about what they are doing, perhaps with speaking frames: ‘This number is 45.  It has 4 tens and 5 ones.  45 is equal to 40 add 5.’

Read the rest of the article on the Rising Stars Blog.

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