Medium Term plans in Primary Mathematics

How does your school organise their mathematics curriculum? There are broadly two ways of doing this. You could, in a three term year, divide the content equally between each term and teach a third in the Autumn term, a third in the Spring term and the final third in the Summer term. Or you could teach each domain of maths in more depth, sequentially going through them during the year and not revisiting them.

Here are three different models that all have their strengths and weaknesses.

1. The Scattergun Coverage Model by Hamilton Trust.

I’m not entirely sure how this model was planned, except that it seems to have covered all the objectives throughout the year.

Hamilton Trust cover objectives in a seeming scattergun approach
Hamilton Trust cover objectives in a seeming scattergun approach

This little extract informs teachers in which weeks they will be visiting different objectives. In my school, with the amount of work required to adopt the new curriculum, we thought this would do us fine, but actually what happened (as I’ve written) was that teachers did not take ownership of their planning and instead merely delivered the lessons they found in the order they were given. The outcome was that, whilst individual lessons were often good, the units (a week or fortnight of lessons) were often aimless with no sense of the children being on a learning journey. Maths only happened in the maths lesson and was very much isolated from the rest of the curriculum.

Much of this was my fault. As the maths leader I hadn’t taken responsibility for the planning that teachers had adopted. I’m sure many schools can make the Hamilton Trust plans work for them, but for us it had led to failure and so we needed a change.

2. The year-long blocked approach by White Rose Maths Hub

It’s too late to adopt this now, but you could plan to take it on for September.

The Overview for the medium term plans created by the White Rose Maths Hub
The Overview for the medium term plans created by the White Rose Maths Hub

As you’ll see from the picture, all the number and calculation objectives are taught by the end of Week 9 Spring term, and in much longer blocks than we have used in the past, enabling children to learn concepts with a much greater depth. I think this model will work brilliantly, and I’m currently discussing with the staff whether to adopt it for the next academic year. This maths hub have created tests for their medium term plans so you can assess how well the children are getting on. You can sign up for their free resources here.

3. The Term-by-Term approach (by me)

This approach was recommended to me by a headteacher who was part of the first peer review we had after our not-brilliant Ofsted. She said that I should base my plans on the 1999 schemes of work. So I went back to them and found them still hosted on a website in Dudley. Then I used a document that I only have a paper copy of called the ‘Steps Up’. I believe this was created by a group of Birmingham mathematics SLEs and provides some useful guidance as to what are the steps up to achieving the age-related expectations in each year group.

The model I went for was for the teachers to visit each domain during a term. They would cover all the content by the end of the Spring term (half in the Autumn term, the other half in the Spring term) and then use the Summer term to consolidate the age-related expectations.

My medium term plans are here:

Medium Term Plans

You’ll see that they are not quite finished yet. I haven’t written the Summer Term, nor have I completed the mental maths part of the plans – what you see in the mental maths part are still the old expectations from 1999.

Finally, I made some tests for the plans. These tests are half termly and I used Testbase to make them – a paid for service that hosts all the test questions asked of children in the England’s testing system for the past 20 years. You can find the tests here in their own folder.

You may consider it quite an effort to write a whole load of medium term plans. But it’s given me a much better insight into the new curriculum and a much greater sense of ownership over what we are teaching at my school. The problem with using other people’s plans, is that you end up believing the lie that you shouldn’t have to reinvent the wheel, when actually the process of reinvention is healthy all by itself.

Three ways to Improve Planning in Primary Mathematics

Since June (and the bad Ofsted and bad SATs results) I have been working on improving planning in maths and it’s really worked. Here’s how.

1. Impose a planning format

If you know anything about union and indeed Ofsted guidance you’ll know that is the *wrong* thing to do. But it’s exactly what I did at my school. I imposed a planning format that everyone had to use.

But planning is for the teacher, not the senior leader, I hear many cry.

No. I disagree.

Planning is for the child.

For too long we had written plans that support what the teacher might say in front of the children, how they might model or an activity or what learning resources they should prepare before the lesson. What we had not done is really think about what the child needs to do during a sequence of lessons to achieve the goals set out in the unit of work.

So in fact, while it was an official planning proforma that I imposed, it was actually the principle behind it that was important. And the principle was this: start the unit plan by writing the final lesson’s learning objective. Then work backwards through the learning objectives that build up to the final one to create a learning journey for the children. It’s a bit like that picture I shared 2 days ago. Then, for each day, plan what children who were likely to exceed the set learning objective might accomplish, and do the same for children who would struggle each lesson.

When this was done, each lesson would have 3 learning objectives around a similar aim, and each lesson would also built towards the next lesson.

What was great was that the teachers who got this, swiftly diverged from the planning proforma I had set up. They got the principle, so who cares if the format looks different? So much for the planning format imposition! What I found is that the teachers who needed most support where those who thought they were doing it right by merely filling in the boxes of the planning proforma without really thinking about the principle. And for these the proforma was a great starting point for explaining the principle in greater depth, thereby developing their mathematics subject knowledge.

2. Supply some medium term plans

There’s a lot to think about in mathematics, especially when you’re a non-specialist dealing with a brand new curriculum that you’ve had little or no training for. While I’m a big fan of ‘ownership’, as I wrote about yesterday, there is a limit to how much new stuff any teacher can take on in one year.

So I gave everyone medium term plans. I had some help. Various folk from different parts of the country have made maths plans and overviews and the like, so I used a few different documents to create medium term plans for mathematics for Years 1-6. I’m going to save the post for the ideal mathematics medium term plan model for another day (probably tomorrow), but suffice it to say that the medium term plans I’ve written have been a useful framework for teachers creating their unit plans mentioned above.

3. Link the medium term plans with assessment

The big problem we have at the moment in Primary is assessment. Nobody is quite sure what the age-related expected standard will look like. To make that more confusing, if a child is ‘age-related’ by the end of the academic year in mathematics, what sort of maths should they be able to do by December? or Easter?.

I looked around for some tests, and found none that suited what I wanted, so I made my own. Well that’s not quite true. I am making my own. So far I’ve made tests for Autumn 1, Autumn 2 and Spring 1. Each of these tests is linked with the medium term plan that should have been taught during that half term.

Of course, I don’t actually agree with testing a curriculum that is not best-fit. I’ve already written about the problems of the previous level-based assessment system being best-fit and how it disadvantages children. And of course any test is a best-fit measure. It seems ludicrous to me to create an ‘expected standard’ curriculum and then use a ‘best-fit’ tool (like a test) to measure how well each child has done, but that, again, is another post, for another time.

The point is that by analysing the tests, each teacher has been able to find out which bits of that unit the child did less well on and use that knowledge to follow up and plan further interventions during the next half term.

In conclusion

I’m biased obviously, but I think mathematics is in a much stronger place at my school than it was six months ago. We’ve had more conversations around mathematics knowledge in the last few months than in the previous five years, and I can really see teachers taking ownership of their maths teaching, rather than relying on third party solutions and merely delivering lessons.

In my next post I’m going to attempt to compare some different models for mathematics medium term planning that I’ve seen.

The problem with a best-fit approach

Scattergraph
Here’s a handy graph, just ready for a best fit line to be drawn through it

It is not often that I read a 50-page government-commissioned document and get wildly excited. But that is what happened when I read the “Final Report on the Commission on Assessment without levels” (September 2015).

I found pages 12-18 particularly inspiring as the commission explains the rationale behind why levels are bad and ‘not-levels’ are good.

This statement was pertinent:

Levels also used a ‘best fit’ model, which meant that a pupil could have serious gaps in their knowledge and understanding, but still be placed within the level.

And this one:

Levels were used to measure both end of phase achievement and lesson-by-lesson formative progress, but they had not been designed to fulfil the latter purpose, with the result that formative assessment was often distorted.

Just as in yesterday’s post, when I tried to explain a character flaw that had held back my practice, here was a practical example of something I was doing day-to-day which was not actually any good.

As a key stage 2 teacher I had experienced this over many years. Children came up to my phase ostensibly as ‘a level 2 child’, but the best fit approach meant that while they could add a pair of 2-digit numbers with the support of a 1-100 number square, they had no idea of any other strategies for doing the same thing, nor really any sense of the the size of the numbers they were dealing with, nor the purpose of the equals sign.

And likewise I must have been doing the same to my secondary colleagues for years: children from key stage 2 going up to key stage 3 being able to scrape enough marks to get a level 4 in a SATs test, but not with the necessary number or problem solving skills to really go any further. In fact at my school, analysis of SATS shows me that number skills have always been high, but problem solving really low – the children have been able to scrape through with good routine number skills, but lack the fluency to really excel in maths.

What is even more insidious about the ‘best-fit’ approach is what it does to ability groups within a class, particularly low ability children. But that’s tomorrow’s topic.

Image courtesry of: https://upload.wikimedia.org/wikipedia/commons/a/a2/Scatterplot_r%3D.24.png

 

Remember that you are dust, and to dust you shall return.

The trouble with three

I noticed a really interesting thing when I was working with Ebony Rose in the Colouring In lesson.

She has a real problem with ‘three’.

As you’ll have worked out if you’ve read the post and considered the problem I set, the children have to colour in different amounts of squares. There are only two choices – when you come to a new colour you’ll either colour one of each square next to the old squares, or you’ll colour three squares. That’s the choice: one square, or three squares.

But Ebs has a real problem with three.

She could cope with all the ones. She could see that each old square would generate one new one, but every time we came to one that would make three squares she froze. If I wasn’t watching here, she would just blithely colour in a single square, even though three were required. And then when I was talking her through it, and getting her to talk it back to me it was like she didn’t want to even say the word three – whenever we came to it, it was like she was trying to out-wait me – to see who would crack first before saying the word three.

It became really hard work. The fact is that during the activity you have to colour in three squares lots of times – she wanted to progress and do well, but she didn’t want anything to do with the number three. I begun to believe that she had some kind of ‘three’ phobia – as if she thought it was cursed or out to get her or something.

Over the weeks since then I’ve begun to understand why: Ebony-Rose often confuses the ‘3’ digit with the ‘5’ digit. Show her ’50’ and she may say “thirty”. Show her ’13’ and she may say “fifteen”.

I remember last year when I was working with a child who, at the age of seven, couldn’t reliably count to ten (or for that matter in tens to 100). By ‘reliably’ I mean she could do it, but 4 out of 10 times, she would get it wrong. When I listened to her count I noticed that she didn’t like pronouncing the ‘f’ in five or fifty: she found it awkward to say. So instead of saying it she would just move swiftly on to six or sixty. We worked for  a few weeks on this reliability and (this academic year) her year 4 teacher tells me she is flying in maths.

Imagine being ten and trying to do maths when you can’t reliably differentiate between a ‘3’ and a ‘5’.

Now I know there may be lots of excuses I could throw at Ebony-Rose at this time  – dyslexia, dyscalculia and all of that stuff. But the excuses aren’t going to help me this week or next week. I need to teach her know how to diferentiate between those two digits. I need to get her confident at knowing ‘the threeness of three’ and give her practice at using threes.

Who knows, she may even master the 3 times table by half term…

The coming mathematics apocalypse

I am tremendously excited by the current maths curriculum in English primary schools. The expectations are higher by at least a year. It is a no-nonsense raising of standards.

I’m excited because if we can find a way of teaching the curriculum successfully, then our students will have levels of maths previously unheard of in this country. They will be on top of the mathematical world. The average will be above average. They will have the skills and knowledge to found an empire of learning.

Not only is the curriculum at a standard that is a year higher than the previous curriculum, but there is talk of the floor standards, already raised from 60% to 65%, to be raised further to 80%. This means that schools will have to find a way of getting more of their students to a far higher standard. What a fantastic aspiration.

But it’s the ‘if’ I see as being a problem. Let’s face it: we don’t currently have the maths specialists we need in Years 5 and 6 – the upper years of primary school. Secondary school maths departments complain of misteaching, cramming for the end-of-primary-school SATs and students without the knowledge they need. What will it be like with even higher standards, both on the level that children must attain, and also the number of children that must attain it?

I see three options:

  1. Success – we achieve the ambition. We find a way of teaching more of our children to a higher standards than previously attained. A golden age of knowledge is ushered in.
  2. Cheating – we pretend to achieve the ambition by blurring further the grey line between supporting students and telling them what to do in tests. The nation lurches towards a moral crisis.
  3. The Maths Apocalypse – We ramp up the stress. School leaders put the pressure on their teachers with the higher expectations. The teachers crack under the pressure and shout things at their students like: “why don’t you just get it!” A generation is turned off everything to do with mathematics. It’s a maths apocalypse.

The problem with raising standards for students is that we also need to raise standards of teaching. Many primary teachers have a ‘C’ grade GCSE in maths, yet the maths expectations now required would go a long way towards achieving one of those ‘C’ grades.

The clock is ticking. In 2016, the first cohort of students will be tested on the new curriculum. Only eighteen months away and staff rooms across the country should be buzzing with conversations around how we teach maths and the subject knowledge we need. Networks of maths co-ordinators will right now be exemplifying the standards – turning the words into maths that can be taught and practised. Experts from teacher training will be working closely with schools, finding ways of bringing their new trainee teachers up to the required standard and sharing some of their training expertise with teachers who are struggling with their own maths. Teaching schools will be focusing on developing their Specialist Leaders for Education in mathematics so that schools within their networks without maths specialists have a means of accessing their expertise.

We have time to prepare and to succeed. Doing nothing will only prepare us for the mathematics apocalypse.

What is Number Ninja?

The ultimate 'Number Ninja' badge. Nobody has achieved this level yet.
The ultimate ‘Number Ninja’ badge. Nobody has achieved this level yet.

Number Ninja is essentially an assessment system for maths that uses badges to reward children for making progress. It’s for children in the Primary age range from 5-11 years of age.

I had become frustrated with some of the maths assessment we were using at my school. I felt they were either too slow or too lenient and they didn’t reflect what I consider to be the golden triangle of maths achievement – understanding, pace and accuracy. For example we were using a ‘99 club’ – several iterations of this exist. It was a good system, demanding recall of multiplication facts and division facts. Each class would do the test once a term and the children would be rewarded with a certificate in an end-of-term assembly, with a class prize going to the class that had obtained the most certificates. However the one we were using allowed 10 minutes for each test, which was just too long for my liking.

We also use a system called Incerts which calculates a national curriculum level for each child based on the number of statements ticked. I find this system both convenient and accurate, but in my opinion the current National Curriculum under-rewards children for mental mathematics skills.

A second problem was inconsistency across the school. While we had two main whole school systems, teachers were using a range of assessment systems within their own classes that didn’t continue beyond that year group. For example some people were using the excellent mental maths assessment developed by Wigan LEA some years ago (get it while you can – this website is no longer supported). Other people used their own times table systems that they had borrowed from other places or created themselves.

What I wanted to do was create a wider system that demanded more from the children in terms of pace but still maintained a whole school rewards system in a big termly assembly – this is useful to keep a high profile for mathematics.

So I did 4 things:

  1. I kept Incerts and 99 Club – there’s no point throwing away good stuff if it’s already working.
  2. I developed a new mental maths assessment system called ‘Grid Club’. This is much more pacey than 99 Club.
  3. I introduced Khan Academy. While I’m not overly impressed with the instructional videos on Khan Academy, I do really like the assessment system that goes alongside it.
  4. I created a spreadsheet to collect all the scores from the different systems and calculate an overall Number Ninja score – this is what I use to award the badges.

Here’s an example of what the Number Ninja spreadsheet looks like. It’s from the Year 3 class. Teachers enter the numbers in the coloured columns and the number on the far right is what the spreadsheet generates. It is colour coded to tell you what ‘Number Ninja’ level the child is on.

Number Ninja spreadsheet
Here’s what the spreadsheet looks like

Any questions or suggestions about Number Ninja – I would be grateful to hear them!

A greater stretch in mathematics? If only.

I read the letter from Michael Gove to Tim Oates about how the new National Curriculum Review would affect the Programmes of Study within Primary Schools with a great deal of anticipation, and then a growing feeling of disappointment. There are various areas that disappoint me, but the area of maths teaching is perhaps the greatest. I read:

In mathematics there will be additional stretch, with much more challenging content than in the current National Curriculum. We will expect pupils to be more proficient on arithmetic, including knowing number bonds to 20 by Year 2 and times tables up to 12 x 12 by the end of Year 4. The development of written methods – including long multiplication and division – will be given greater emphasis, and pupils will be taught more challenging content using fractions, decimals and negative numbers so that they have a more secure foundation for secondary school.

Minor Disappointments

Let me break this down then. Here are some of the minor points that disappoint me:

  1. Knowing number bonds to 20 by Year 2 – this is already the case. How can it be more stretching to maintain an expectation – surely the bar should be raised somehow.
  2. Times tables up to 12×12 by the end of year – this is a slight rise in expectation as children are currently expected to know up to 10×10, but in my experience it is not the knowing of extra times tables facts that hold back children in the latter part of primary schools, it is the lack of knowledge of corresponding division facts (which happens to be part of the current national curriculum).
  3. Greater emphasis on written methods (like long multiplication and division) – this sounds good, but it’s already in the current programme of study. Just saying something more doesn’t make it more rigorous, nor does it necessarily raise expectations. In addition, I’m all for children learning skills in school such as the skill of performing long division, but I had been under the impression that the new curriculum would be more knowledge based.
  4. Pupils will be taught more challenging content using fractions, decimals and negative numbers. Again, these are all in the current programme of study for children from the age of about 7. Whether children are taught these are up to their teachers and their schools.

So when I read the phrase “much more challenging content“, and put it next to the above examples of challenging content, I’m struggling to see the giant leaps in standards that Michael Gove would be hoping for when his new National Curriculum is implemented.

A medium-sized disappointment

A greater disappointment is to see the phrase “more proficient in arithmetic” without any reference to algebra. As I have written before, children start learning about algebra from a very young age when they start investigating concepts such as larger and smaller. It is the concepts involved in algebra, often linked with precise language teaching, that I think are under-taught or mis-taught at primary level. Teachers shy away from this vocabulary-driven area because it doesn’t feel like maths to them – there aren’t numbers and operations written in children’s books – it doesn’t look as good as arithmetic. When children leave primary school I think they are often under-prepared for algebra – it is in this area that I was hoping for higher expectations within our new National Curriculum.

If you’re good at arithmetic you can go to the shops. Or maybe become an accountant. If you’re good at algebra you can become a rocket scientist. Not that education should just be about gaining a decent job – Gove himself says he wants “a love of education for its own sake” – but I have a feeling that for many algebra isn’t the elegant thing of beauty that I perceive it as, but is a rather lumpy, ugly thing, ringed with fire and tears.

A major disappointment

Aside from my algebra foibles, there is a further disappointment that I think will have a wider implication on maths teaching: teacher subject knowledge. No matter how detailed a Programme of Study or a National Curriculum might be, neither address this problem: we have many teachers within the primary sector who do not have sufficient subject knowledge to teach mathematics effectively. Many primary teachers only have a grade C at GCSE and have had to repeat their mathematics test required by teaching training in order to pass their course.

I have no problem with teachers teaching mathematics concepts that they’re not to sure about, so long as they know what to do when they’re stuck. There should be an expert teacher within each primary school – the maths co-ordinator or similar – who can share their knowledge and expertise when others don’t know the next steps. Too often less-skilled maths teachers don’t seek help from their more experienced colleagues, but struggle with the text of the National Curriculum and any scheme books that support it. Not knowing what to do, they either miss the tricky areas or teach it badly – characterised by repeating themselves more loudly and more slowly, a bit like the traditional Englishman abroad.

It is not a new Curriculum that is going to improve standards in mathematics. We will stretch primary mathematics only by increasing subject knowledge within our teachers.

 

Google Docs and the “Ofsted Outstanding” Lesson

It has taken 15 years and 8 Oftsed inspections, but I have finally achieved an Outstanding lesson at Ofsted.

For those people not from the UK, Oftsed is the national body that inspects state-funded education, and ‘Outstanding’ is the highest grade they give.

I’m aware that I could be answering the question “why has it taken you so long?” Or “what on earth have you be doing all this time?” But instead I’m going to tell the story of how I achieved outstanding.

It began the day before when the lead inspector briefed the staff. Gathered in the staff room, sweaty palms and hearts thumping, he introduced himself and went on to give us some friendly advice.

“Just be yourself,” he assured, in his soft Welsh tones. “Perhaps now is not the time to try that experimental drama lesson you’ve been wondering about, but if you were going to take a risk, then take it. Just be yourself.”

At this point the teaching assistant I was working with looked nervously across it me. Not only does my teaching demonstrate a tremendous lack of risk-aversion at times, but I had already planned some experimental drama that week. And the teaching assistant was leading it. And it was in a maths lesson.

The second piece of advice the lead inspector gave us (and I would recommend this to anyone about to undergo an inspection) was to do a ‘mini-plenary’ as the inspectors walk into the room. Inspectors used to watch whole lessons, but these days their time is so tight, they can generally only see half-an-hour chunks. A mini-plenary is where you would stop the activity or whatever was going on, check on how much the children have learned, remind them what they were aiming to show they had learned by the end of the lesson before proceeding with the rest of the session. The idea is to show the inspectors that progress has been made (even though the inspectors might not have seen it) and more progress is still expected. Inspectors get very excited when they see progress.

Of course I didn’t follow this advice either. Experimental drama and no mini-plenary? And I have the cheek to call myself a teacher.

Maths apparatus the inspector saw: cups on a stringMore of what the inspector saw: cards on the wall

Admittedly, the lead inspector was a little bemused when he walked into my room. Or so he told me afterwards.

It was 9:30am on the second day of the inspection. The lesson was half an hour old and the inspector could see:

  • one student playing shops with the teaching assistant;
  • another student playing dominoes with myself;
  • assorted apparatus scattered on the floor;
  • fraction cards stuck to the wall;
  • the rest of the students intently staring at the screens of their Chromebooks.

Half an hour later, when he walked out he said one word to me. “Stunning.”

So what had turned a potential mess of different activities into a ‘stunning’ outstanding lesson?

Answer: Google Docs

You see, Google Docs had enabled me to have high quality interactions with three different groups of learners, using only two adults. Here’s how.

Group 1: The experimental drama

I have some children within the class who, despite being eleven years old and nearly at secondary school, have great difficulty remembering maths facts and them applying them to real life situations. They just don’t get the link. Hence the maths role play area.

The week before we had set up a ‘stationery shop’ in the classroom – everything was priced from pencils to sparkly sharpeners. With the teaching assistant as the shopkeeper their task was to choose items for less than a set amount, say £10 – then work out how much they would have to pay and how much change they would get. The teaching assistant is particularly good at teaching the children how to add up quantities with differing amounts of digits, like £3, £1.15 and 45p – something that often causes confusion.

By the time these sort of children get to eleven years of age, they have often labelled themselves as maths failures. For them, maths become a grey despair. The drama adds a light-hearted element to their maths learning. Enjoyment brings engagement, engagement leads to motivation and motivation accelerates learning. The inspector was impressed by the motivation of these lower-attaining children and recognised that it was accelerating their progress.

Group 2: The dominoes game

Some of my children don’t know any games. Draughts, Monopoly, chess – they’re all a mystery. We have some marvellous versions of dominoes that are brilliant at showing the equivalence between fractions, decimals and percentages. However for many of the children I can’t use the game because the very act of playing dominoes is too much of a barrier.

In this lesson I was able to use dominoes 1:1 because the Google Docs (which I’m coming too) enabled me to. The advantage of playing dominoes with a child 1:1 not only could I support them with the game, but when they were stuck finding an equivalent for the dominoes in their hand, I could unpick their misconceptions and teach them the concepts. For me, a 1:1 interaction with a student provides the best moments of teaching and hence the most powerful learning. The inspector was impressed that I’d planned time for these 1:1 interactions to take place.

Group 3: The Google Docs

Different children represent two fifths on a Google Doc

Often, whilst a teacher works with a small group or an individual, the rest of the class complete tedious worksheets or engage in something known as ‘group work’. Not with Google Docs.

Each child worked individually on a small part of a Google Drawing to represent what different fractions would look like. This particular group of children need lots of concrete examples to help them understand the abstractness of fractions. Showing a child the digits ¾ is often not enough – children need to represent it with apparatus and images. In this case the children demonstrated to the inspector when he spoke to them that they were really understanding fractions in a way they hadn’t previously.

The five sixths drawings prompted most discussion in the plenary
The three eighths representations

Moreover, when the students were stuck, they contacted me via chat. So instead of shouting out (and disrupting their peers), or bringing their work over to me as the teacher (and thereby disrupting the domino game), they were able to silently ask questions of me.

I had opened  4 Chromebooks on the table next to me, each displaying one of the fractions Google Docs that different children were using. Two fifths had the most activity, but other children attempted five sixths and three eighths.

The inspector was particular impressed that the children supposedly on an ‘independent activity’ still had the means to seek adult support, and therefore be taught, rather than spending the whole lesson being stuck. And the Google Docs chat feature minimised the disruption to other learners.

The Google Docs them prompted some excellent discussion at the end of the lesson, particularly the five sixths pictures, which two students had drawn incorrectly. Each had drawn five sevenths instead of five sixths. The discussion in the plenary draw out their misconceptions and we were able to correct them collaboratively on the Chromebooks.

Google Docs had enabled both myself and my teaching assistant to work more effectively as teachers – to spend more of our time actually teaching. As a consequence the children were motivated and enjoyed their learning and so the inspector could only see outstanding progress being made during the lesson.


Good teaching decreases mathematics anxiety

This weekend, I found myself doing something I’ve not done before – disagreeing with Professer Derek Haylock. Giving his second lecture to Edge Hill MaST cohort 1, the man who’s seminal work “Mathematics Explained for Primary Teachers” has pride of place on my shelf, said some things that didn’t quite hang together for me.

 

His lecture was on the subject of mathematics anxiety – something that most adults have either experienced or can empathise with. His main point was this: if you teach mathematics well, you don’t get students who are anxious about maths. As someone tweeted on the day “My God I never thought of that. I hope the person giving this advice is paid a fortune.” Given that the audience was a room full of primary maths specialists, or ‘maths champions’, the advice is more purposeful if given a more negative slant: don’t allow bad maths teaching in primary – you’ll just get adults who are anxious about maths.

 

Briefly I will sum up what I thought were his main points and then I’ll say where and how I disagreed with him.

 

  • Many adults experience anxiety in maths when they are afraid to make mistakes in public, or given a mathematical challenge they cannot think clearly to carry it out.
  • These adults can trace their feelings of anxiety back to a single experience usually between the ages of 9-11 at primary school.
  • This experience is always a negative interaction with a teacher – Prof. Haylock quoted adults saying that their teacher had shouted things like “why can’t you just get it right?” There was a real emphasis on the negative experience being when maths is thought of as either right or wrong.
  • Many of these adults reported they could only learn maths by learning a rule by rote and couldn’t master any conceptual learning.
  • Some of these adults become primary teachers.
  • Teaching styles are to blame for mathematical anxiety – ‘traditional methods’ create more anxiety; a ‘problem-solving / relational approach’ creates less anxiety. Quoting from Newsted, he described a traditional approach as one of direct instruction, followed by practice and application, whereas in the ‘problem-solving approach’ the teacher acted as a facilitator, with the children suggesting their own methods and strategies for solving problems.
Aside from the dangers of telling rooms full of teachers that ‘rote learning is always bad’ and ‘this is the only way to do it’, my main disagreement was the way he linked the single negative experience with a given teacher to the traditional teaching method. It doesn’t take the room being in rows or table groups for you to have a bad experience with a teacher. Neither does it mean that you if are using a ‘problem-solving approach’ then teachers can’t lose their tempers and make everyone frightened of maths.

 

In my own experience I’ve tried both traditional and ‘problem solving approaches’.

 

I would call them using a rigid scaffold and using a negotiated scaffold. In the former, the teacher plots the course through the learning (the scaffold) and takes the students through that course through direct instruction, practice and intervention; in the latter the student and teacher negotiate the path through the learning.

 

Both approaches work.

 

In fact this time last year I did an experiment where I did 6 weeks of negotiated scaffolding in maths, then 6 weeks of rigid scaffolding in maths. The children made progress in both periods.

 

Delving a bit deeper into the Newstead report I see that the traditional approach includes: “The teacher decides what is right or wrong and intervenes in the case of mistakes. Later word sums may be used as application of methods. Social norms are more static and involve more discipline, rewards and teacher authority.” Now to me that’s not traditional teaching. Traditional teaching is where direct instruction is followed by practice, yes, but then appropriate intervention from the teacher. And so now it leaves me thinking that Haylock, quoting Newstead isn’t comparing ‘Problem Solving’ with ‘Traditional’, but is comparing ‘Problem Solving’ with ‘Bad Teaching’.

 

I’ll go on to say that Haylock is right by saying that for a student to have one-to-one negative interactions with an authority figure such as a teacher will cause anxiety, in any subject. The teacher that chooses ‘traditional teaching methods’ but can avoid the negative interactions can still teach a class without causing anxiety amongst the students. And a teacher that attempts to be a ‘facilitator’ but then loses their temper when the students don’t choose a method they were anticipating will also cause anxiety. It’s not about the style, or dare I even say it the teaching, it’s about the teacher themselves.

 

Good teachers reduce anxiety.

 

The book all primary / elementary teachers should read. #mathchat

I was just engaged in a conversation on #mathchat about skill levels in primary teachers, when I realised that the book all teachers of young children should read was sitting right next to me: ‘Mathematics Explained for Primary Teachers’ by Derek Haylock.

Photo