Conception of the good

School visited: Uncommon Collegiate Charter High School

Class observed: AP Grade 11 Statistics (UK equivalent Year 13)

Theme of post: Pedagogy and Curriculum

This is the second blog of a series to complement a workshop I delivered at #Mathsconf6  on Mathematics Pedagogy at USA Charter Schools, following my visiting a selection of Uncommon and North Star academy schools in New York and New Jersey. During the workshop, I discussed how the common denominator in each maths lesson I observed was the level of academic rigour. I am still trying to find a way to define this term, because it is overused and poorly defined.

Nevertheless, I believe I can state that the teaching and learning delivered by such extraordinary teachers in the classrooms I observed displayed features of academic rigour. These features of academic rigour are evident in the structure of a teacher’s pedagogy and instruction:

In my workshop, I discussed the four main elements that all teachers up and down the country can implement into their teaching practice with minimal effort and maximum impact. I will discuss each of these four elements in turn, by way of one per blog post; today I will discuss the sequence of instruction.

I was observing a lesson, Grade 11 Statistics, and the teacher had organised the lesson so that he was trying to have pupils factorise cubic expressions where one of the expressions in the factorised form could be further factorised into two expressions because one group  was a difference of two squares. (Figure 1) The sequence of instruction to explain to pupils how they can factorise such cubic expressions is what made his lesson so powerful.

Figure 1 – Sequence of Instruction in terms of expressions used in teaching

Here, I entered the classroom, and the teacher had displayed the following algebraic expressions that he wanted pupils to factorise. (Figure 2) Before the pupils had even started to factorise he spent some time identifying the common features which determined this expression to be a difference of two squares. It is known as the difference of two squares because we have even powers, square numbers as coefficients and one positive term and one negative term.

Figure 2 – Difference of two squares expressions + common features of this type of expression

What I found really fascinating was the examples that he had initially chosen in order to begin teaching pupils how to factorise such expressions. Previously, whilst teaching, I would begin teaching the topic by using the following examples and non-examples to state what the common features of an expression known as a difference of two squares actually looked like, and therefore what it would not look like. Therefore, I utilised simply examples and non-examples. (Figure 3)

Figure 3 – Examples and Non examples used in the initial stages of teaching how to identify an expression known as a difference of two squares

The way the teacher started was better, because the expressions he had used made the common features more obvious to pupils. So the initial examples of a difference of two squares that I would have started to teach from are actually more nuanced and special; the coefficient of x² being 1 is hidden, and instead of having two terms where the variables both have even powers we have a constant which is a square number.

Second, he then introduced the consistent algorithm he wanted pupils to use to go from the expanded form to the factorised form of the expression. He was very systematic (Figure 4 – consistent algorithm):

Step 1: square root both terms;

Step 2: divide both exponents by 2 and

Step 3: Write your answer as such.

He did this with a selection of examples, as you can see below:

Figure 4 – Consistent algorithm to factorise an expression known as a difference of two squares

Following this, he then introduced the notion that the pupils would now learn how to factorise a cubic expression. At this point in the lesson, I wasn’t fully sure with where he was going (until we reached the end of the lesson). He stated that when we factorise a cubic expression as such we need to factorise the first two terms and the last two terms. He structured it for his pupils because he pre-empted a common mistake that pupils would have made unless he structured it for them. We are factorising the first two terms by dividing both terms by 1, whereas with the last two terms we are going to factorise by -1, because -1 is the greatest common factor of -8p and -24. (Figure 5)  Therefore, the first step of the algorithm is not line 2: it is line 3. This was so powerful because by pre-empting this misconception, and by being very explicit with this instruction and guidance, it made the lesson run more smoothly because pupils were more independent to get on with the practice set of questions – because they weren’t making this mistake.

Figure 5 – Structuring the first step of the algorithm

He then carried on to lay out the consistent algorithm between the expanded form and the factorised form.

Step 1: factorise the first two terms, and the last two terms. (be careful when factorising the last two terms)

Step 2: Now factorise the greatest common factor for both terms (ensure that you are factorising the GCF of the coefficients as well as the variables) However, he posed the question one more time: “What is the greatest common factor  of 16p^3 and 48p^2?” Students then noticed that we are no longer factorising by identifying the greatest common factor of the coefficients but also of the variables of each term. (Figure 6)

Figure 6 – Step 2 – Step 4 demonstrated

Step 3: factorise the greatest common binomial of the expression:

Again, the algorithm was consistent. Furthermore, he said factorise “the greatest common binomial”. This level of technical language being used in the classroom is fantastic, and is something I certainly intend to implement in my teaching practice.

Step 4: “Are we done with this problem?” he asked this question with the intent of having students identify that the first expression in parenthesis is not fully factorised – which pupils identified.

Here he paused and said to his pupils “Now you are thinking that we are finished because we have two groups that can then be expanded and simplified to form the expanded form which we start with, but we are not finished. What is the greatest common factor of the first group?” However, he posed the question one more time “What is the greatest common factor of 16p^2 and 8 ?”.Pupils then identified this to be 8. He then proceeded to do a selection of examples to complement the first example, and to also reiterate the consistent algorithm. Figure 7 

Figure 7 – Further examples of factorising cubic expressions presented in class using a consistent algorithm

Now, this was the pinnacle of the lesson. This was the point where the teacher introduced the next expression to factorise but in doing so he was combining the procedural knowledge of factorising a cubic expression where one of the groups could be factorised because it was a difference of two squares. The sequence of instruction was incredible. Let’s have a look.

Again, he used the consistent algorithm he showed in the previous examples:

Step 1: factorise the first two terms, and the last two terms. Pre-empt that we may be factorising the last two terms by 1 or -1.

Step 2: factorise the greatest common factor of both expressions:

Step 3: factorise the greatest common binomial of the expression.

He asked “can you factorise the greatest common factor of the second binomial? Hands up – what is the greatest common factor of the second binomial?” Pupils confidently answered – “1”. The teacher responded “Excellent, you can display it like this (teacher writes it on the board) and can you do the same on your mini-whiteboards please.” Again, he pre-empted another misconception that the pupils could have potentially made. (Figure 8)

Figure 8 – Structuring a key step in the algorithm where pupils are more likely to make avoidable mistakes though explicit instruction.

Figure 9 – Introducing an expression where one group is an expression known as a difference of two squares

Step 4: factorise the greatest common binomial, which he got above (Figure 9):

He asked pupils to pause. He then asked pupils to look at the problem on the board (the one above). “Can you raise your hand when you can identify what type of binomial expression we have for the first binomial .” Ten hands were raised within the 5 seconds. In total there were 22 hands raised 10 seconds later. Now, after 30 seconds in total following the initial posing of the question, the teacher had an overall 28 out of 32 of pupils’ hands raised. The teacher selects a pupil to state the answer: “Sir, the first binomial is an expression which is a difference of two squares.”

The sequence of instruction here is incredibly effective. What I saw in real time, and what I have outlined for you, is not necessarily profound or extraordinary – on the contrary, it is very simple. It can be performed by all teachers.

It was evident from this lesson that the teacher had put a significant amount of thought into the sequence of his instruction to his pupils. It was well-crafted and sequenced so that all pupils could see the re-iterated key points. What are the characteristics of a problem which is a difference of two squares? What are the characteristics of factorising a non-linear expression? What is the greatest common factor of this expression – ensuring the greatest common factor including coefficients and variables?

I am still working on trying to collate a few different examples in my teaching practice of minimally different examples, and how I have interleaved concepts via sequence of instruction. I shall get back to you on this. Watch this space. Any questions then please do not hesitate to contact me or DM on twitter.

School Visited: Uncommon Collegiate Charter High School

Class Observed: Algebra 1 Grade 9 Statistics (UK equivalent Year 10)

Theme of post: Pedagogy and Curriculum

This is the first blog post in a series complementing a workshop I delivered at Mathsconf6 entitled “Mathematics Pedagogy at USA Charter Schools”. Here I spoke of my experiences whilst visiting a selection of Uncommon and North Star academy schools in New York and New Jersey.

I discussed how the common denominator in each maths lesson I observed was the level of academic rigour in the teaching delivered to pupils. I am still trying to find a way to define this term, because it is overused and poorly defined. However, I do believe I may be able identify the evident features of academic rigour in the structure and delivery of each teacher’s pedagogy and instruction:

In my workshop, I discussed four examples of academic rigour that different teachers up and down the country can implement with minimal effort and maximum impact. Each blog post will discuss one example at a time. Today, this blog will address using minimally different examples during instruction.

Minimally different examples are examples to explain different concepts where the difference in the algorithm between one concept and the other can be distinguished as one additional step. This was one example I witnessed in one of the classrooms I was in.

The teacher presented the first expression to factorise, where the coefficient of a in the quadratic expression is 1. This was a recap exercise where she stated the values for the coefficients, and then she determined the two values of which the product gives us the value of c, and the sum gives us the value of b. She wrote the expression in its factorised form.

She then introduced the next expression to factorise. She stated that it looks visually very different to the first one, but that there is only one difference between the algorithm to factorise the first and second expression. She defined the minimal difference between the two as one additional step – which was at the start of the algorithm. She asked her pupils, “What is the greatest common factor (GCF) of all the terms in the expression?” Pupils spotted the GCF to be 3p, which she then factorised. She said “look, we now have an expression in the parenthesis which looks similar to the first expression we factorised.” The minimal difference between factorising the first and second expression was classified as one additional step. Traditionally, in my training, I would have seen the algorithms to factorise both the expressions as isolated and fragmented. Instead, they are connected; pupils were empowered to factorise more complex expressions from prior knowledge of the algorithm to factorise the first expression. Minimally different examples are a good strategy and example of academic rigour in the classroom because they help pupils to understand knowledge and concepts which are initially complex and ambiguous. Here, the difference between the two examples is classified and determined as one additional step in the algorithm. The possibilities are endless.

I plan to show different examples of how I have used the idea of minimally different examples in my teaching, sometime this week.

I always believed that I had high academic and behaviour expectations of my pupils whilst working at my placement school in South Manchester. I was known to be strict at times because of my high expectations. I would give sanctions out to pupils who would not be giving me their 100% attention. I would insist my pupils SLANT whilst I was teaching to avoid fiddling. I would teach from the board and go through worked examples. My pupils knew how I wanted them to behave in my classroom. My pupils knew how I would behave if they were compliant or defiant. However, when I arrived at Michaela, my expectations were seen as low, and they were, and here I explain why.

At Michaela, we have 14 teachers and 6 teaching fellows where 9 members of staff are founding staff. I was observing a founding member of staff guiding and monitoring pupils to ensure that they were transitioning around school corridors in silence. I saw founding members ensuring that all pupils during assembly and class were slanting, if they weren’t then a teacher would give non verbal cues where a teacher would slant themselves and pupils would follow. I saw members of staff giving pupils demerits for not tracking them whilst they were speaking. At the same time, I saw founding members hysterically laughing with pupils during break time and lunch time when staff made witty comments about Mr Smith having luscious long locks of hair sarcastically (…Mr Smith has some hair). Pupils would be playing basketball or ping pong with teachers during lunch time. I would have pupils talking to me in the morning to greet me “Good morning Miss Rizvi, how was your evening?”

Now I look at pupils around the school and think now I know why Michaela pupils were so kind and polite. Let’s remember pupils did not come to secondary school as polite, kind or obedient as they currently are now. Pupils were trained and moulded to embody Michaela values. During our initial behaviour bootcamp, teachers taught pupils how to sit up straight in class. We taught pupils how to address a teacher. We would over exaggerate our behaviour when pupils made mistakes. For example,

“Excuse me Mr Rubbie, how dare you walk past me and not respond ‘Good Morning’ when I have wished you a pleasant morning. I am always polite to you so I expect you to always be polite to me,”

and “Zakye I am incredibly disappointed in your disingenuous apology and in you rolling your eyes when I was speaking to you! I am utterly horrified over how disrespectful you are to your teacher who works so hard for you.”

We would overexaggerate when pupils demonstrated exemplary behaviour:

“I am so proud of you Yasmine for scoring 100% in your science quiz this week, I would like to give an appreciation to Yasmine for her excellent self quizzing which resulted in her scoring 100%. We all want to be as successful as Yasmine. 1, 2 *two claps*,”

Olivia Dyer, Head of Science and Founding member of staff, said to whilst giving me feedback that “we act the anger, and feel the warmth.” Being angry and negative is emotionally draining for a teacher so we act when we over exaggerate and over justify why talking in the corridors is unacceptable.  Furthermore, we are wholeheartedly loving when a child is successful and we celebrate it to make that child feel valued, and to have surrounding pupils identify the kind of behaviour they need to demonstrate to be identified as an exemplary Michaela pupil.

This gives pupils clarity on how to behave and how not to behave. We do not give leeway to different extents of behaviour. If a pupil is doing something that they are not supposed to do then we would pick them up on it, no matter how subtle. At my previous school, I would give demerits because pupils would not be tracking me whilst I was teaching. If a pupil was rude even in the most subtle way such as smirking or curling their hands I would go ballistic. Surrounding teachers thought I was crazy for it.

At Michaela, teachers have sky-high expectations of pupils and our behaviour management is consistent because we all use the same language for rewarding and sanctioning pupils.

At my previous school, there was minimal consistency in rewarding and sanctioning pupils. We did not all have the same dialogue for sanctioning or rewarding students. If I ever pulled a child aside in the corridor for being too loud or demonstrating inappropriate and unprofessional behaviour then I would hear the response “Well [insert a member of SLT’s name here] did not say anything down the corridor when I was behaving this way.” It was exhausting. I would be the teacher who was crazy or too strict because of the high expectations I did have of the children. I would be unapologetic for giving a child a detention for not having a pen with them. I had one pupil who always forgot to bring in their exam prep folder, so for two weeks I proceeded to call the pupil’s house every morning at 7:15am to ensure that their daughter would bring their folder to school so they could be more prepared for my lesson.

At Michaela, all teacher’s have unapologetic and uncompromising high expectations of each and every pupil. Even more so our expectations are even higher for the pupils with the most tragic circumstances. We cannot change a child’s tragic circumstances at home but we can control their learning circumstances at school. If anything, it is more important to have high expectations for pupils who have those tragic circumstances so they have all the potential to escape their situation using education as the engine for such mobility. I know that the sanction I give to a student for a particular issue in science would also be sanctioned three floors downstairs in MFL by another member of staff. We are incredibly consistent. And students know that too…isn’t that the dream in any school? Students do not push their limits with us.

For example, we expect all pupils to bring a pen to school, and if they do not have one then we provide them with the opportunity to rectify the issue in a way which does not impact others around them. We have a stationary shop open between 7:30 – 7:50 am just before schools starts. The onus is on the children to meet our high expectations and we are explicit with what our expectations are. We are all consistent with the dialogue we have around school when we interact with children which contributes to a consistent and strong school ethos. As teachers we have bought into what is considered as Michaela standards. We have children bought into Michaela standards too.

There are many reasons behind the success of Michaela Community School and one of them is the uncompromising high expectations that all teachers have of each and every pupil our school serves. Children respect our standards because they understand that we want the best for them. Furthermore, to be the best pupil then pupils need to meet those high standards. My standards were considered high at my placement school where teachers were inconsistent with the dialogue they used and the reasons for sanctioning pupils or rewarding pupils. At Michaela, I realised my standards were not high enough. I had to raise my expectations, and I still am, but now I could not imagine reducing them. I would be failing myself as a teacher and the pupils that I teach. High expectations are underprioritised at majority of schools where at Michaela Community School it is part of the golden triangle of success.

We know that what we are doing having our sky-high expectations is right when a pupil who I have given detention to, which I have accidently forgotten to log, goes to detention and informs Mr Miernik that he has detention and that he is here to serve it even though Mr Miernik has informed him that he hasn’t got one. Or when I get an appreciation during Family lunch “I would like to thank Ms Rizvi for coming into school today and teaching us even though she isn’t feeling 100%” or when I get a postcard from a pupil expressing their gratitude.

Our Michaela high expectations in sanctioning and rewarding pupils comes from a place where we want our pupils to be the best possible student and human being. If you want to see us Michaela teachers and pupils in action then do come and visit us during a school day. Our doors are open to all. Come and have lunch with us.

Today, I had a random flashback to a formal observation I had at my placement school. I remember having a discussion with the observer, a maths teacher, where we were debating over one particular point. I was teaching my second lesson on simplifying surds: from √a  to the form k√b  where k is an integer. Given that this was the first time my 9X2 set were learning surds, I went for a very explicit selection of worked examples, structuring one type of method to simplify a surd to k√b form. In my lesson I was structuring the teaching as below, where I wanted pupils to identify the highest common square number, which is also a factor of the ‘a’ in surd √a.

In the lesson preceding this lesson, and in the weeks throughout the year, I would have pupils complete a recall activity frequently in which they had to identify the square number of the first 15 integers, and also square root the first 15 square numbers. The point was to ensure that pupils could recall these facts from memory, and develop automaticity in doing so, to the extent that there wasn’t an act of mental processing.

Figure 1 – Worked Examples for simplifying surds effciently

I would ask pupils to select a factor which can divide 72 or 160 and which is also the biggest square number that can divide 72 or 60. They would then identify the square number and then write the root number of the square number below and continue on with the multiplication to simplify the surd to  k√b form. This was done because it is the most efficient and accurate method to simplify surds. If children are taught one accurate method to simplify surds at the start then they will get the correct solution and feel successful. If children are taught one method to get the solution and then you explore the different routes to get the same solution afterwards then you are building on their existing understanding of how to simplify surds.

The observer was suggesting that it would have been more beneficial for pupils to not have been taught one technique but to have explored instead a myriad of techniques. However, I think that what he was suggesting is only beneficial after they have first understood how to simplify surds in one accurate and efficient method. His suggested method could potentially cause several misconceptions insofar as you will have 30 pupils listing 6 possible attempts consisting of 12 different factors of 72. The lack of guidance and structure can lead to misinterpretations which leads to misconceptions.

In the early stages of learning such an abstract concept it is best to provide one accurate, structured and efficient worked example for students to replicate with different problems and in order for them to consolidate their understanding of how to simplify surds. This is, effectively, pattern spotting. Only then you can start to explore the different routes to the same solution without risking many misconceptions developing, as opposed to the converse.

Figure 2 + 3 – Comparing simplifying the square root of 72 using one algorithm, where we always select the highest common factor to be the highest square number that can divide 72, to the other multiplication sums when simplifying the square root of 72.

As a maths teacher, and even when I was as pupil myself, I knew the most efficient way to simplify a surd such as √60 was to have a multiplication sum with a factor, which was also the highest square number, because this would result in an integer multiplied by a surd. I knew this because my teacher explicitly told me. Later on we explored different routes to get to the same solution. Since I knew the answer for simplifying  √60 then when I got the same answer through different routes I felt successful and reassured. Why? Simply because I knew one concrete and accurate method to get the simplified solution for the problem. Teaching pupils one accurate method to solve a problem allows pupils to feel successful, and it further empowers them when exploring how to solve the same problem through different routes.

At Michaela, we spend a significant amount of time discussing our worked examples; whether Dani, Bodil or I have made the section of the textbook which is being taught that half-term, we discuss what is the best strategy to solve problems where pupils are adding and subtracting algebraic fractions and where the denominators are integers. What is the best worked example to solve problems where pupils are to substitute a positive integer into an algebraic term or expression? We outline it very clearly in our textbook, and we organise three or more worked examples where we interleave fractions, GEMS, decimals etc., but the cognitive process which pupils go through is similar in all three worked examples. This is because we want pupils to look at a problem and be able to identify each step between the problem and solution. How do we do this? We explicitly state it: step 1, identify the lowest common denominator; step 2, form the equivalent fraction by multiplying the numerators by the common factor; step 3, add the fractions with like denominators etc.

Figure 4 – Example of worked example made by Dani Quinn.

Our pupils are taught explicitly and we demonstrate clearly using our visualisers one concrete, accurate and efficient algorithm for the problem in order to get the solution. The different routes to the same solution of the same problem are explored later on once we know that all kids in the room are proficient at solving a selection of well-sequenced and crafted problem types with the one method we taught them initially. Our pupils are mathematically proficient; they love to learn and they feel this way because they feel successful knowing one accurate method between the problem and solution as to how to add and subtract fractions with integers as the denominator, or variables as the denominator, or expressions as the denominator. They then feel empowered when they can get the same answer through different methods.

And so, I respect that our opinions differed but I am sticking with the way I delivered the initial teaching of simplifying surds. It was the second lesson of this topic and despite not 100% of pupils were getting the right answer on their mini-whiteboards – where they were at the fourth lesson.

Why I believe Mary Bousted’s article’s concluding point is wrong; and, if you think she is right, then that is concerning?

Dr Mary Bousted, General Secretary of ATL, published an article on TES this week which, in my part, caused utter fury. I read it and immediately expressed my disagreement on twitter. I then emailed her article with all my comments to my Headmistress. I saw the article and thought that what she said reflected her poor understanding of how the New Blob has helped the poorest children in the country to get a better education in which they are able to use their education to escape their poverty-stricken circumstances.

I am writing as to why Mary’s article is written in a similar manner to how a politician would write a speech to gain the votes of the ill-informed, change-reluctant (status quo) masses. Her article reflects a lack of appreciation and understanding over what has been accomplished over the last 10 years in education. It also lacks discussion of how the work of the New Blob of educational commentators has effectively empowered many teachers across the country by openly speaking out about the impact teachers across the country can have for the poorest children in the country, going against the status quo.

Mary starts off by writing about “what a career as a teacher has become”. Teachers have an excessive workload which is leading to a high turnover of teachers within the profession. The marking load, excessive level of bureaucracy and ridiculous administrative tasks, seemingly only serving the purpose of pleasing Ofsted, are some of the countless reasons why teachers are overworked and leaving the profession. I agreed with the first few paragraphs because Mary was just stating the reality of teacher workload. This is nothing new, the awareness of teacher workload has increased through the work of the New Blob, which I shall go into later.

She wrote in a manner politically strategic as to getting readers to agree with her from the get go; as politicians begin their speeches, where they try to win over the audience, with agreeable premises in order to make the audience more likely to agree with their ridiculous conclusion.

She then takes a direct 90 degree turn toward the crux of her argument: that the New Blob of educational commentators are ignoring the reality of teacher workload and are expecting teachers to compensate more for the poorest children to have the better life chances.

She describes educational commentators who are in the ‘exclusive’ New Blob as “experts” with limited training or teaching experience, naïve, dogmatic, idealistic, accusatory and, most importantly, preachers from the “heights of their [own] ignorance about the complexities of classroom practice”. She then audaciously goes on to conclude on the following threatening note:

First, the article ignores that the New Blob of educational commentators consist of a group of people who have had the greatest impact on education in the last ten years. Teach First believes that we can tackle educational disadvantage in this country. Through their vision, it has encouraged young, intelligent and resilient graduates to join the teaching profession. I believe that it has raised the standards in what qualifications a young graduate needs to enter the profession in the first place. It has also made teaching become an even more important profession by speaking about the Teach First vision that teachers do have the capacity to change the life of the children they teach. I believe that I can change the life of some of the poorest children in this country by providing them with the best education I can possibly give. Now, I work proudly at a school where all teachers, teaching fellows and its Headmistress believe that this is possible.

I am going to start by pointing out a few of the amazing new free schools which have been set up as a result of the idealistic vision to provide the best academic education and opportunities for the poorest children in the country.

King Solomon Academy (KSA), a free school started in September 2007, based on the KIPP program in the US, is now the best non-selective secondary school in England according to the Department of Education GCSE League tables. It was started by Max Haimendorf and a selection of teachers who trained via the Teach First programme. It is a school which serves an area where 75% of their pupils are eligible for the pupil premium, and the school is situated in the ward with the highest deprivation affecting children in London. This school values academic excellence and has built a curriculum which resulted in their first cohort of pupils leaving school with 93% of pupils achieving 5 GCSE A* – C grades including English and Maths, and where 75% achieved the English Baccalaureate.

If it were not for the high aspirations and expectations of young people, KSA wouldn’t have had the impact it has had on some of the poorest children in the borough which it serves.

Education empowers people. It provides young people with the knowledge and skills to enter the working world as capable, independent and competent members of society. This is something that Mary would not disagree with. However, we would disagree with her thoughts that teachers cannot compensate for the lost life chances of the poorest children. We absolutely can and what King Solomon academy has done sets a precedent for existing upcoming free schools to achieve. If anything, it has catalysed other teachers and SLT members in schools around the country to stop and think: teachers can have an impact, mobilising the poorest children to have the best life chances, if we change the current priorities of teachers and SLT members insofar as they are merely Ofsted-pleasing.

Here, in my placement school, there were layers of bureaucracy, triple marking, duplicative data entries and many other ridiculous tasks which made me an ineffective teacher. My CPD, subject knowledge development and ability to behaviour-manage a room of children with low aspirations and expectations of themselves were not priority number 1, and frankly they were never going to be because I did not have the time or the energy to make this a priority. How could it have been, when I was told to prioritise elements of my workload by SLT members of my placement school driven by the desire to get an Outstanding by Ofsted? It didn’t matter that children were running riot, or that our expectations of children were so low that they could be taken out of the classroom to have a breather because they had ‘anger issues’ when actually they had no self-control because pupils’ bad behaviour was appeased.

I now work at Michaela Community School. Teachers have the following priorities:

• Have high expectations of pupils and as a result have excellent and consistent behaviour management;
• Excellent subject knowledge as a result create high quality resources and develop explicit and concise language when delivering worked examples; and
• Strong warm-strict relationships with pupils.

How is this possible? It is because we have a visionary Headmistress with an incredible SLT who explicitly state what the teacher priorities are at Michaela Community School. We do not mark or even triple mark. We do not do multiply data entries. Every single decision made by Katharine, Barry and Joe considers the impact it will have on teacher workload. Why? Because teachers are important: they need to be taken care of rather than driven into the ground with ridiculous Ofsted-pleasing administrative and bureaucratic tasks.

Michaela Community School is a revolution and a product of the education beliefs of the New Blob. Teachers write blogs sharing good teaching practice, evidencing the impact of different efforts taken to improve the teaching and learning of children of all socio-economic backgrounds.

It is the vision and belief that education can improve the life chances of the poorest children in the country that is changing the priorities of schools today. Is your curriculum tailored to provide children with the best education possible? Is your behaviour management consistent and, as a result, does it mould your pupils to be good, well behaved, respectable, self-controlled and responsible young people with good character? Is this task that you are asking teachers to do helping the pupil that is ultimately being taught?

The New Blob of educational commentators has empowered teachers around the country to change a status quo in existence for decades. It is now ever more important for the New Blob to be shouting from the rooftops about the ludicrous expectations of teachers to be triple marking and writing three-page lesson plans. What the difference between Mary Bousted and people within the New Blob is that the latter group of people are actually changing the status quo. It is all well and good talking about how absurd the current situation is for teachers. However, if it were not for the New Blob ‘spouting nonsense’ from the DfE then Michaela Community School wouldn’t even exist, National Mathematics Conference wouldn’t exist, King Solomon Academy wouldn’t exist etc.

It is the New Blob of educational commentators that have changed the lives of the poorest children in this country, and they shall continue to do so. It is the New Blob of teachers who have introduced and set up some of the incredible free schools which are now leading the way. The New Blob is a change to the existing status quo. I am not going to stop ‘spouting nonsense’ when what I am saying is having an impact. We can change the lives of the poorest; we just need to get on with the job – which is, as it always was, to teach.

So, I believe that Mary’s article incorrectly points fingers at a large group of people who have, for the last ten years, had a significant positive impact on education. Credit should be given where credit is due, rather than passively-aggressively threatening a group of people that you are watching them. Times are changing. Teacher workload doesn’t have to be the norm. Children from the poorest communities need to be held to an even higher standard of expectations in terms of their academic study and attitude to learning. Education is the window of opportunity to change a child’s life chances. I believe that the New Blob are increasing the chances of the poorest succeeding, and that the leaders of education in this country need to be learning from people such as Max Haimendorf, Katharine Birbalsingh and many more.

My first half term at Michaela Community School has come to an end. I have really enjoyed it but it has also been very difficult. It has been difficult in terms of the mindset change I have had to make, as a teacher, and also in my teaching two subjects, including one which I had never taught before, Science (alongside teaching Maths).

I joined Michaela because I wanted to learn about curriculum design, as well as developing my pedagogy in terms of subject knowledge and sequencing of problem types. I am going to share the problem types that I have come up with (through discussing it all with the team – Bodil and Dani) whilst spending Saturday planning for next half term. I am going to start with solving one step equations and two step equations.

First, an important point: I was initially struggling to understand whether the following problem types are three step or two step equations. However, following Kris helping me to realise that they are two step equations – because we rearrange over the equal signs twice to achieve the numerical value of the unknown – I’d manage to resolve this. And so, let’s get cracking.

Solving one step equations (addition and subtraction):

I have found that, in order to induce our children to be more successful academically, in exams, and also in developing greater interconnections between different topics such as solving one step equations and fractions, we need to show them a variety of problem types. I would, formerly, teach three or four very similar problem types such as below. Now, after Craig Jeavons’ and Bruno Reddy’s talk on Shanghai pedagogy I have branched out to teach a variety of different problem types, but all with the same thread of thought. The procedure of solving one step and two step equations is made clearly visible to the children, through the carefully selected and crafted worked examples used.

The children, following this, then try a few problems on their mini whiteboards, in order for me to check their understanding. Here, I ask more questions to ensure that after each and every question more and more children are getting the correct solution. I am, effectively, trying to close the gap. Through this, I am sure that the children will find the practise of such questions listed below more meaningful, because they are applying their knowledge of the problem and procedure to questions that have a different level of surface knowledge but the depth behind solving the equation is similar in all the problem types shown above.  This is what I have learnt in making these nuanced problem types on Saturday afternoon.

I hope this has been useful. I have attached a lesson plan of how I structure my teaching for a lesson. Enjoy!

Usually I would blog in detail about the wonderful workshops I had attended and what I had learnt from each one. This post does not do that, and instead it highlights something different; something interesting. Every maths teacher should attend Mathsconf6.

Mark McCourt. What Mark has achieved by establishing a National Mathematics conference is incredibly powerful. It is, in short, a movement. Mark and his team at La Salle have effectively united thousands of maths teachers and educators in one location on a Saturday to do great things. Very experienced and intelligent teachers hold several workshops to share good practice from the likes of Bruno Reddy, Craig Barton, Kris Boulton, Jo Morgan, Amir to name just a few. Here, various topics are discussed such as the new AQA specification and its implications, diagnostic questioning and the use of Multiple-choice questions, the stories of Mathematics, Singaporean Teaching and Bar Modelling etc.

I believe that Mathsconf can be said to be a movement because its teachers are being empowered by learning about the many changes to come within education, but also by learning what has been working effectively in the past. Teachers are growing and developing from each other. There is a space for this to happen. Teachers from all around the country who have different amounts of experience in the classroom, who have entered teaching via different ITT routes, are getting together and we are talking: we are learning.

I attended the first maths conference as an unqualified Teach First participant and it revolutionised my teaching practice. I have now attended all five conferences held so far. My pedagogy is developing because of the workshops I attended and everything I had learnt was smoothly applied in the classroom. For example, I attended a workshop by Robert Wilne who made it increasingly aware to me that my teaching was not enabling my pupils to develop the procedural fluency mathematically to access some of the nuanced problem types to come in AQA’s new specification. His workshop taught me that intelligent lesson planning was composed of a selection of carefully crafted and logically sequenced worked examples. At Bruno Reddy’s workshop, I learnt that I needed to ensure that I taught minimally different concepts such as area and perimeter far apart. At Kris Boulton’s workshop, I learnt that Pythagoras had learnt a lot from the mathematician Talmus – who knew?

Through these regular Maths conferences, new Hubs have started such as Lime Oldham run by the brilliant duo Lindsey Bennett and Richard Deakin. This, in turn, catalysed Lime Brent to come into force by Bodil Isaksen and Lime North Yorkshire by Neil Turner.

A Twitter network of teachers has blossomed, with a significant amount of credit to be given to Old Andrew for his blogs and tweeting. Teachers all around the country are able to share informative sound bites from these events, further engendering communication amongst teachers throughout the country. Did I mention that I’d gained my current reaching post through Twitter!?! I.e., only because I met Bodil Isaksen at mathsconf2 – the social network is so very empowering.

I look back at my ITT with such regret because pedagogy was not at the centre of my teacher training. Whereas pedagogy is at the forefront at each workshop held at mathsconf.  At ITT, the majority of my time was spent talking about behaviour management, and asking unqualified teachers to discuss how to plan a lesson with no knowledge of how to. It did not teach me how to use bar models as a pictoral aid to teach ratio or solving one and two step equations. My ITT did not teach me how to sequence the teaching of different topics such as teaching fractional indices before teaching surds. What on earth was the point of my ITT?

What I have learnt continues to contribute to my becoming an impactful teacher; from the workshops I attended at Mathsconf as well as my efforts to develop independently my teaching through reading a selection of blogs and books. This has also allowed many teachers around the country to develop and grow. I feel empowered after attending a La Salle Education conference. Such mathconfs are practically essential even more so at at a time where so much is changing within the field of education. There is so much expertise in one room that the possibilities are endless. Even more so at a time where so much is changing within the field of Education. There is so much talk going on about Mathematics Mastery, Shanghai, Maths Hubs, AQA New Specification and teachers all around the country are trying to work out what this all means for them in the classroom. Mark has established a space for teachers to become well-informed: it is a space where different thoughts, opinions and ideologies regarding education can be discussed.

Lastly, I believe it has provided me with well informed opinions about the current state of education. I do think that the current quality of ITT is shambolic. I do think that there is a huge disparity in the quality of teaching delivered in different parts of the country, as a result of ITT. I do think teachers are not aware of the complexities of pedagogy in terms of the sequencing in teaching of different topics after each other, or the CPA framework in teaching concepts such as ratio. Mathsconf is providing some support in overcoming such problems. More importantly, one cannot necessarily know of such problems without breaking out of one’s bubble and see what is happening on Saturday 5^th March in Peterborough. For this reason I think it is essential for more maths teachers to attend conferences like mathsconf.

We are constantly learning. We need to continue developing because changes are coming and they will continue to come. To allow our pupils to be successful we need to be informed of these changes. We need to adapt to these changes not for their sake but because these changes will impact our pupils. So, I’ll see you all on Saturday 5^th March!

This year, I finished my first two years of teaching on Teach First’s Leadership Development Programme. I said bye to my placement school and I now look forward to beginning work at Michaela Community School in Wembley Park from September.

This blog post will outline the biggest impact I had as a teacher. It is specific to my second year of teaching after learning from one of – if not – the biggest mistake I had made, during my first year of teaching. I did not set up my Y10 students for academic success in Y11 during my first year, because

1. a) I did not know of the huge positive impact it has in Y11 and;
2. b) I did not know how to either.

This is not to say that you should not set up each and every class. I say this because at my placement school, and this is the case in many schools if not all, is that you carry on teaching your Y10 class into the following year for Y11.

The biggest impact I had was in setting up 10X1 (Set 1) with a well thought out two year plan. I do believe that KS4 is a 5 year plan but that is a different blog post. 10X1 are my favourite class. They taught me so much. They enabled me to be the best teacher I could be. There was not one lesson where I had not thought, at the end of the 60 minutes, that each and every of the 28 girls were exceptional, intelligent, confident and inspirational. I am going to share my success with 10X1 with you. It is valuable and it will help you prepare your Y10 class if you are just starting to teach this September, or even if you have been teaching for years.

1) Scheme of Work Mapping

This sounds daunting and time consuming. It isn’t. Look at the topics that your scheme of work suggests for you to teach your class in Y10 and Y11. Restructure the order to ensure that each topic lends itself nicely to the next inasmuch as each concept taught previously can be developed or linked to the concept being taught next. For example, teaching fractional indices before moving onto teaching surds.

The benefits behind remapping the sequencing and order in which topics are taught are extensive. Firstly, it gives you an idea of the bigger picture so you can see how all the concepts link; you can also explain and teach the connections to your students. If you teach fractional powers months later or before teaching surds then students will see the concepts as too fragmented and isolated concepts. Teaching one before the other allows students to recognise the connection between the two concepts. This betters their conceptual understanding, and through continual recall of fractional indicies in relation to surds it will also strengthen their understanding in their long-term memory. (It is more complex than this – please refer to previous blog post)

2) Knowledge framework

In this context, a knowledge framework is a web of connected pieces of factual knowledge (Figure 2). The stronger the connection between different pieces of factual knowledge the more accurate one’s conceptual understanding, lending to the ability to manipulate complex problems. For example:

Figure 1 – GCSE 1H 2015 Exam question Q22(b)

This question (Figure 1) can be solved through a clear and accurate understanding of different pieces of connected factual and procedural knowledge. Look at the amount of knowledge students need to know to attempt this question, and more importantly the interplay and connections between these different pieces of knowledge:

Figure 2 – Example of a Knowledge Framework outlining the factual and procedural knowledge required for students to attempt such a question. Also an example of a problem type where two concepts are linked.

As teachers we can only enable our students to think critically if:

1. a) they have a clear understanding of the factual knowledge and procedural knowledge behind a concept;
2. b) they have a clear understanding of how to apply such factual knowledge and procedural knowledge to different categories of problem types;
3. c) they are given sufficient time to practise categories of different problem types in an organised fashion; and
4. d) they are taught and given the time to practise unusual complex problem types, where the necessary factual and procedural knowledge is interleaved throughout the problem in question.

I would really recommend for you to have a go at remapping and sequencing the different topics for the year and look at the first three topics that you will be teaching in half term 1. How are these topics connected mathematically? How can I teach these topics in an interconnected fashion so students can see the connection between index rules, index notation and surd notation, improper fractions and mixed numbers? How can I structure my teaching to enable essential recall and consolidation of prior knowledge necessary for students to access the topic being taught? What are the unusual problem types which I can expose my students to, in order for them to apply their knowledge of what has been taught in turn enabling them to think critically?

My next blog post will outline the practical and consistent practice I put in place in order to allow students to retain their learning for the long term.

This summer, I have been reflecting deeply on my first two years of teaching whilst also I looking toward my next step career-wise at Michaela Community School (MCS). The experience will be very different. Whilst being at dinner with Katie Ashford, Head of Inclusion at MCS, I said something which made her raise her eyebrows. I said “Teachers really do not want to work.” This blog post will explain what I meant by that.

Essentially, teachers plan lessons, deliver lessons, mark books etc. However, we spend the majority of our time writing two-to-three page lesson plans, standing at the printer to print resources on different colour cards for differentiation, organising paperwork for performance management, writing schemes of work every summer, calling parents, dealing with behaviour, chasing up incomplete homework from students etc.

Does the above sound familiar?

We complete a significant amount of other tasks aside from planning our lessons and delivering them. Surely, we should spend most of our time doing the latter set of activities? Why? Because they have the biggest impact on the children’s learning. I am not implying that we are at fault but that something is going wrong. We spend a significant amount of our time completing a variety of administrative or bureaucratic tasks in order to meet the requirements and demands of SLT, in anticipation of a phone call from Ofsted informing us of its impending visit.

Teachers work incredibly hard but on a selection of tasks which may be described as

1.  administrative;
2.  purposeless in the long run;
3.  adding no value or benefit to the children we teach and
4.  having an output is relatively small in comparison to the input of effort required.

In some instances, it wouldn’t be unfair to say that some teachers are seen to be effective because they are able to complete everything on their to-do list everyday. However, I believe that the work that we do which makes us effective teachers is sometimes intangible, and is unable to be measured, or that it is not necessarily impactful straight away. Reading books, going to conferences, spending hours thinking about the assessment you are preparing for your year 9 class, spending hours thinking on how to restructure and design an existing unit of the curriculum: we do so much which adds value to our CPD and provides our students with high quality teaching. Again, this is not necessarily work that is tangible.

I have been that teacher that has tried to do both, to-do list and high quality planning, to the best of my ability and I could never avoid my students saying “Miss, are you ok? You are looking really tired recently.”

After completing all the necessary admin, we then have no energy or time to really work on that which actually allows children to learn. Teachers do not have the energy, nor the time, to effectively sit down, think and plan high quality lessons with excellent pedagogy and subject knowledge at the core of their planning. And it is not out fault! For this reason I believe that teachers do not have the time to really work. Even though we really want to spend our time on making excellent lessons and producing high quality assessments but we simply do not have the time because of our growing administrative workload. Productivity is seen as the result of completing a to-do list of administrative tasks as well as other tasks (of which I would question how purposeful they really are) instead of thinking and planning a structured and impactful lesson. Can we cut out the admin?

The teachers that do both burn out. They leave teaching. Schools that have a high attrition rate see it is a good thing because we are bringing fresh new teachers with new ideas in regularly. In the cruel reality of the situation, we are churning and spitting teachers out of the profession. We are investing time and money into teachers to develop a skills set which is not put to effective use (for very long) because they leave the profession. SLT need to acknowledge this. Let’s try an experiment:

Go to your diary and categorise your tasks in either being admin or T+L and you shall be surprised. This is not a blog to name and shame teachers. This is to get all of us to reflect on our workload and to seriously think of how we can start working again ready for September. Here is a plan of action:

1. a) Write a to-do list of tasks;
2. b) Categorise them into administrative tasks and into T+L tasks;
3. c) Keep the tasks which meet the following conditions, are these tasks

– purposeful?; do they

– result in an equivalent or greater amount of desired output in comparison to the effort inputted?; and do they

– add value to my practice and/or add value to the learning experience of the children I am teaching?

You will surprise yourself with the list of tasks you kept on the to-do list you started off with.

HAPPY SUMMER FELLOW TEACHERS! I just finished being an AT (Assosciate Tutor) at Teach First’s Summer Institute .This blog is inspired by the amazing participants I have come across so far. Here is my advice to you, and it is on lesson planning. Keep it simple!

You have come across so many resources from card sorts, interactive games, metre square demonstrations etc. These are all very valuable and serve an academic purpose in supporting and engaging pupils but, to make your life easier for the first term, just keep your lessons simple.

What this means is keeping the structure of your lesson simple. You don’t have to make it complicated. You are just starting out – you have time to experiment and try new things: it doesn’t have to all be done within the first half term. So this is what I suggest.

1) Starter (Do Now)

Figure 1 – Example of a Starter (Do Now)

This is a 7 – 10 minute activity for students to attempt within the first 10 minutes of the lesson in complete silence. This is to ensure that even if students come in dribs and drabs, those that are early are not wasting time, and that those that are late are still entering the lesson in a purposeful manner rather than disrupting those already learning. You need silence in the first 10 minutes to get all pupils into the academic mindset that they are entering a learning environment. Learning begins when they enter the classroom. You do not want the chaos of the corridor cutting into your teaching time. Demand it. Don’t budge!

I usually have an A5 print out of the activity for students to complete in their exercise book or on the sheet.  I hand this to them as they enter the room – greeting them Good Morning/Afternoon. (See Figure 1) It has the date, title, level (depends on your whole school policy if still required) and C/W. This is because it is not academically purposeful for students to write it and underline it (Except for Wales) It saves learning time. They complete the activity, mark it and stick it in. Done!

2) Lesson brief and success criteria

“Thank you for completing your starter in silence and for marking your work with your green pen. Now, SLANT.”

I explain to students what I will be teaching them this lesson. (See Figure 2) I will elaborate on what we have learnt, and how what we are learning today is a continuation of that, and what we will learn in the following lessons too. This is to give students an awareness of the bigger picture. They like to know where they are going. I will have a success criteria to follow with examples so students can see what exactly their learning looks like. (See Figure 3)

Figure 2 (Learning objective and outcomes) and Figure 3 (Success criteria)

This takes 3 minutes.

3) Exposition of worked examples

As a new teacher, it is best to assume as little as possible of what students can do. This is not to say you have low expectations of your pupils. I shall go into this in a follow up blog.

There is nothing wrong in teaching your students. Stand at the front at the board, teach your pupils how to calculate the area of a circle through a selection of well–sequenced worked examples.

Example 1: Calculating the area of a circle using the radius (Figure 4)

Example 2: Calculating the area of a circle using the radius (repeat for consolidation) (Figure 5)

Example 3: Calculating the area of a circle using the diameter (Figure 6)

Teacher talk is not a bad thing. Do not assume that Y9 Set 2 have been taught how to calculate the area of a circle. Mine had not. If you demonstrate how to calculate the area of a circle through a selection of examples then students will make fewer mistakes because you have taught them. It is really simple. However, make sure their notes are exactly the same as yours (Board = paper – Teach Like a Champion Technique) because misconceptions come from misinterpretations of your exposition. They will not make mistakes if they duplicate what you have taught them. Later on, as their teacher, you can explore different calculations to the same correct answer but only, and I repeat only, after they have one concrete example.

 In attempting a few questions independently, another benefit lies in students being able to use their worked example as an accurate reference point – they are becoming independent learners, slowly but surely.

4) AFL – Hinge Questioning – Mini – whiteboard activity

AFL (Assessment For Learning) serves the purpose of providing the teacher a sense of what has been learned. Using mini whiteboards is the best way to do that.

You ask a question. Students attempt it independently. They hide their answer. You countdown 5 – 4 – 3 – 2 – 1 and reveal. The whole class show their answers and you can identify who has understood what has been taught and who hasn’t understood the main teaching point. You clarify any misconceptions and then ask students to complete another question.

You should note that after 5 – 6 questions a greater percentage of students are getting the calculations and answers correct. If there are a few still struggling you go to them individually or gather them together to support them through the independent activity. This is a form of differentiation – See Bodil Isaksen’s blog for further reference.

5) Independent Task

“It is time for our independent task. I would like you all to complete all 20 questions in your exercise book. Demonstrate your thinking by showing all your working out. Refer to your worked example. I would like this to be completed in silence for the next 20 minutes. If you require any help then raise your hand and I shall come and help.”

This is the time for students to apply their understanding of the topic from the worked example by themselves. For thinking to really take place it needs to be conducted in silence. If we want our pupils to be independent learners we need to give them the time to work independently.

The value of this task is in the careful selection of questions. Do not give a bunch of random questions on the topic being assessed. Have 10 questions testing one element of their understanding. For example, calculating the area of a circle provided the radius. (Figure 6) Then change one variable, and now give them 10 questions on calculating the area of a circle provided the diameter. (Figure 7) Then in the next 10 questions, vary the questions on calculating the area of a circle given the radius then the diameter so students have to now differentiate which calculation they need to carry out in order to calculate the answer depending on what information is provided by the question. (Figure 8)

This was discussed by Kris Boulton during his lectures at Summer Institute, he talked about the variability effect. 

Figure 6 – Independent Task 1 – Calculating the area of a circle given the radius.

Figure 7 – Independent Task 2 – Calculating the area of a circle given the diameter.

Figure 8 – Independent Task 3 – Calculating the area of a circle given the diameter or the radius.

Their ability to differentiate between how to start the problem is only possible through trying 10 questions straight on calculating the area of a circle using the radius, then 10 questions using the diameter.

Consolidation is not a bad thing. Students learn through repetition.

6) Self or Peer assessment with green pens.

Go through the answers – or display the calculations.

“3 or more correct then please raise your hand, 6 or more correct, 9 or more correct etc…”

I learnt this from my KSA interview and I will never forget it. Students who got only a few correct or a few completed feel great when their hand stays up with the rest of the class. Once you carry on it is more noticeable to you  the children whose hand goes down. Students feel great when they are keeping their hand up because they got so many questions right. Rather than counting the opposite way.

7) Exit ticket – this can be your plenary effectively.

This is another form of AFL. It is one or two questions. It tests them on what has been taught. For example, one question on calculating the area of a circle using the radius, and another with the diameter. Pupils complete it in silence. They write their name on it. You collect it and mark it. It takes 5 minutes to mark a class set and it informs you how each pupil has performed in that lesson. You can then support students the following lesson or clarify any whole class misconceptions in the starter. (Figure 9 – see below)

It is simple if you keep it simple. Bring in everything you have learnt when it is required and where it serves an academic purpose for your pupils. You will be great. Be confident. Work hard.