Breaking News – We all want high standards!

10 Oct

Sometimes it’s easy to feel that those in charge of education in our country believe that most teachers don’t actually want the very best for the children of our country. The rhetoric sets out a battleground where on one side there are those who want rigour and high expectations. On the other side are those who just want to give children warm fuzzy experiences and don’t care about high academic standards.

I believe that this view is, to put it politely, absolute balderdash. There is no question that most teachers want the very best for the children in their schools. In short we’re being led into believing that an argument exists where in actual fact almost all of us are in complete and utter agreement.

The debate that needs to be had is not about the outcomes we all desire, but rather about how we get there. Currently the prevailing argument seems to be that high academic outcomes go hand in hand with rigorous inspection regimes, frequent quantifiable tests, traditional chalk and talk teaching, rote learning, streaming of children into sets and teachers with high level degrees in their chosen fields.

However I would argue that high academic standards are reached through different means. Here are a few examples (the links below offer evidence to back up these arguments)

Supportive inspections that seek to offer advice, support and actively share good practice.

Constant formative assessment.

Mixed ability classes with an emphasis on responding to the needs of each child.

A focus on helping children construct concepts, beginning with real world models and images.

Teachers with a high level of pedagogical knowledge – (knowing how children learn the subject matter they are teaching)

I feel that is vitally important that the assumptions those in charge of education make about the sort of teaching that leads to high academic standards are strongly challenged. And if we are going to have a debate about how to raise educational standards in our country then we need to frame that debate properly. In my eyes it’s a debate about the best ways to help children learn. So let’s argue by all means, but first we have to be sure we’re asking the right questions.

Squeak to you soon

Monty Mouse

Core knowledge curriculum

5 Oct

You may or may not have heard of the core knowledge curriculum. Based on the ideas of E.D Hirsch, it’s followers advocate that there is a core of knowledge that children need to learn in order to achieve highly. These ideas have been heavily drawn upon in the recent creation of the new National Curriculum in the United Kingdom which is currently under review.

However all this rather misses the point. The content of a curriculum, especially a mathematics curriculum, is not really an area where I imagine there can be a lot of disagreement. Instant recall of number facts (including multiplication facts) – yes! Ability to add, subtract, divide and multiply – yes! Understanding of the number system – yep put that in too!

I don’t really therefore understand why there is such a focus on deciding what we want children to learn. However I do feel that the current emphasis on this aspect of education is based upon a rather worrying assumption. Namely that the simple fact of putting together a curriculum and stating that this is what children will learn by a certain stage will somehow improve standards.

Where is the logic in this? Are you really telling me that stating that children will know all multiplication facts by the age of nine, rather than eleven will somehow make it so? If that’s the case then why stop there? Why not say that all children will have this knowledge by seven or even five?

Children are not mindless robots who learn by command (thank goodness!). Age related expectations of children, however, carry with them an assumption that this is the case. Can we help children learn maths more effectively than they currently do? Without doubt this is indeed the case. However the way we will achieve this will not be by debating the mathematical knowledge children need to attain by a certain age, but by improving the way we teach children and understanding the ways they learn best.

In fact my real worry with age related expectations is that they will lead to a dumbing down of standards. When shown and taught in the right way for them children quickly progress in their understanding of mathematical concepts. However if we state that children should not learn certain mathematical concepts until they reach a certain age then there is danger that we hold children back from progressing in their mathematical understanding.

Of course the flip side of this is that by holding too firmly to these age related expectations we force children to encounter concepts that they may not be ready to understand. Therefore we may leave these children, at best, with a superficial understanding of maths, based on quick fix tricks (to multiply by ten just add a zero), and at worst with huge gaps in their mathematical knowledge, with misconceptions that are ignored as we seek to race them on to the next level.

There is clearly a debate to be had about the order in which children learn mathematical concepts. For example in my experience we can teach children to tell time best by introducing the concepts in a certain order: However there is an important distinction – stages not ages.

What is missing from the current focus on core knowledge is the debate about how children learn best. It is vital therefore that we move the focus off the distraction of the core knowledge curriculum and move onto the important question of how best to ensure children acquire the skills and knowledge they need to become confident and able mathematicians of the future.

Squeak to you soon,


Monty and the addition number sentence

30 Sep

Go bananas!

30 Sep


When children enter the mathematics classroom, they are confronted with two different worlds. There is the real world, which contains objects and then the maths world with all its symbols and abstractions. The goal of the maths teacher is often to bring these two worlds together.

Therefore it is vitally important that when introducing children to mathematical notation, we give them real practical experience of what these symbols and notations actually represent. For example, on a very basic level children need to learn that the symbol 7 represents seven objects.

As a society we are usually very proactive in giving children real, practical experience of small numbers. Fortunately it is rare that children learn to count to ten without counting actual objects in the real world. However we become much less proactive when it comes to giving children real life experience of other mathematical symbols and notation they come across in the future. Indeed we expect children to understand many mathematical symbols without giving them any practical real world experience – no wonder so many struggle!

Take number sentences of the type 3 + 4 = 7. For some children their experience of this type of number sentence can be limited to being asked to find the symbol 3 on a number line and count on four more and notice that they ‘land’ on the symbol 7. No wonder so many children become convinced that the equals sign means find the answer! No wonder so many later have difficulty understanding number sentences such as 3 + ? = 7 (they answer 10). Their entire experience of the mathematical notation is based on counting on from one number to find another.

Real life experiences of these notations changes all that. Show children 3 bananas and 4 bananas and they can quickly tell you there are seven altogether. There is no need for them to refer to the arbitrary symbols when they can simply count what they see in front of them.

Having given children a practical experience, we can then link the mathematical symbols to this. In so doing we are empowering children to really understand these number sentences. We are embodying them with real meaning. Indeed we can show them all the different examples of how we represent this real world example in the maths world:

4 + 3 = 7, 3 + 4 = 7, 7 = 4 + 3, 7 = 3 + 4
7 – 4 = 3, 7 – 3 = 4, 4 = 7 – 3, 3 = 7 – 4

Wow – who would have thought – maths really is bananas!


Maths vs Reading

26 Sep


I was always hopeless at maths!

When I hear these words I feel like running into an open mousetrap and ending it all. Yet this idea that it is somehow socially acceptable to be hopeless at maths and wear it as a badge of honour is one that permeates our society.

How many parents spend time reading with their children? Many parents do this every night. It is more often than not viewed as a pleasurable activity. Yet the idea of spending time working on maths puzzles and problems or playing maths games is somehow seen as boring or hard work.

Many people when asked what they like doing in their spare time will cite reading as one of their favourite activities. Yet the idea of doing mathematics for pleasure is so absurd that it more often than not leads to laughter.

I love reading and it is indeed one of my favourite activities. However, I also love maths. Spending time thinking about puzzles and problems is, if not relaxing, at least hugely stimulating and entertaining. I’m not talking about dry arithmetic but real maths such as the puzzles and problems featured on the wonderful NRich website.


To paraphrase a great man ‘I have a dream’. My dream is that one day mathematics will be elevated to the same level of reading. That we create a generation of children who pick up a maths puzzle in the same way that they would pick up a book. That up and down the country we could have maths clubs, just as we have book clubs, where groups of people get together to discuss mathematical puzzles without being viewed as weird. That maths moves from being viewed as a dry boring subject to the wonderful creative art form that it is.

Squeak to you soon



What’s in a name?

15 Sep



Many of the children I come across in my teaching career tend to have a somewhat limited understanding of the number system. In particular, I notice that many of the children who have difficulties in maths lack an understanding of the value of numbers they are dealing with.

Most children are taught the skill of dividing numbers up into their constituent parts of hundreds, tens and ones. For example, they have no trouble saying that the number 378 consists of 3 hundreds, 7 tens, and 8 ones. However, when asked to split this number in a different way they run into difficulties.

What they have been taught is to look at the numbers in an abstract way. Their knowledge of what hundreds, tens and ones are is simply based on the position of the digits. An actual understanding of the value of these numbers is missing.

A common way of teaching children is to use dienes blocks to give children a practical example of what a number looks like in the real world. For example, one may place in front of a child 3 hundreds blocks, 7 tens and 8 ones to illustrate the number 378. However, how often to we present this number in a different way? For example, the same number can be represented as 37 tens and 8 ones, or 378 ones, or 2 hundreds, 17 tens and 8 ones.

This experience of number is absolutely vital in order to give children a deep and concrete understanding of the number system. It also is essential if children are to become efficient and reliable at calculating.

Consider the child whose understanding of the number system is purely based on the limited understanding of the number system described above. When asked to perform the calculation 173 + 50, they are faced with the challenge of adding 7 tens to 5 tens and then remembering to add the extra hundred they have created to the hundred column. That’s complicated enough just to write down, let alone understand. It gets even worse when dealing with subtracting. However, consider the child who is confident at renaming numbers in a variety of ways. This child understands that 173 can be divided into 17 tens and 3 ones. Therefore it is an easier step for them to add on these 5 extra tens and realise that the new number will consist of 22 tens and 3 ones (223).

It is my belief that, in Britain at least, far too little attention and teaching time is given to helping children understand the different ways in which numbers can be represented and renamed. I would also contend that this skill is absolutely vital in helping children become confident and efficient when calculating.

Squeak to you soon,

Monty Mouse


Community classroom

1 Sep

A new term is about to begin and children up and down the country are ready to enter their new classrooms, but what type of classroom are they entering?

In many schools now there is a clear onus on teachers to take responsibility for all that goes on in their classrooms. Behaviour standards, standards of learning, children’s happiness, amongst many other areas, are the standards by which teachers are held accountable. But what type of environment does this lead to?

I would argue that the more responsibility that teachers put on their own shoulders (and the more this responsibility is put on their shoulders by others such as government, colleagues, OFSTED, and parents) the more they take this responsibility away from those who need it – their pupils.

Take this example, shared by headguruteacher from King Edward Grammar School for an example of the power of handing over responsibility to pupils:

A few weeks ago, looking for a colleague, I stumbled upon a room with 20 lower school students in it. They were in the middle of a debate: ‘This House Would Invade North Korea’. The Chair was a Year 9 student and the whole business was being conducted with total order and sincerity and the level of debate was superb. The teacher running the debating group had left them to it. I have been back since – this happens on a regular basis. Most recently, they were debating the value of Drama in the curriculum!

What a fantastic example! I read this and my first thought was how can we turn all schools into places like this?

So how, practically do we lift this onus of responsibility from teachers and onto the pupils so that they become independent thinkers and learners? And how do we avoid the whole system sliding into anarchy and a Lord of the Flies scenario?

As with all communities the key aspect is setting common goals. One of the best ways I have seen this applied is when a teacher asks their class at the start of the new academic year ‘how can we make our class the best possible class to be in?’

This goes beyond agreeing a set of class rules together, but is more about establishing key principles. For example some of these might be being kind to one another, listening and respecting one another, working hard, presenting ourselves well etc.

Another brilliant example of instilling a sense of community that I have seen work incredibly well with children of all ages is to disestablish the teacher as being the font of all knowledge. In these classrooms children know that they can help each other, rather than always turning to an often busy or occupied teacher.

A few key phrases are often very useful in achieving this and helping children blossom into independent, resilient learners. Phrases such as “what do you think you should do?”. “have you asked your friends for help?” and “can you think of a way to find that out?”

Let me stress this isn’t about being lazy. It’s about freeing up your time as a teacher to give support and extend where it is truly needed.

These are only a few examples, there are many more out there and do feel free to share your examples of how you move your classroom away from being one where the teacher holds all the responsibility to where this power and responsibility is shared between the whole class. Or if you disagree then let me know – I’m always happy to debate and learn.

Squeak to you soon