I’ve been planning a variety of blog posts for several months, so apologies in advance if this seems like a collection of scattered thoughts.
Our new Mastery Curriculum is now running with first year classes. We began the year by very broadly setting classes based upon two diagnostics – one pre-summer and one post-summer. Five of the classes are embarking upon our Third level course and the other two are looking at a Second level version with a view to moving onto Third Level at a later point. I think we have to be realistic about the starting point of our learners. It’s an uncomfortable truth that 2/7 of the cohort arrive at secondary not in a position to meaningfully engage with Third level, lacking knowledge of times tables and other key ideas, but that is where we are. It wouldn’t be doing these learners any favours to course them into a third level course, when there are so many gaps in their knowledge of Second and, in some cases, First level. We need to get these pupils equipped with the basic skills to meaningfully engage with the Third level course. I’ve seen too many pupils coursed at a level where they are missing substantial pre-requisite knowledge. Advocates of mixed ability may criticise the decision to set at all, however, we are ambitious for all of these learners. We want them to catch up – I have no intention of having ghetto classes of forgotten pupils who are destined to failure. I am delighted to say that the colleagues teaching these pupils share this mindset and I am hopeful, that we can make a difference, with careful planning.
With regard to the other five classes, they may be set, but over time this setting will be by pace of learning – not by ability and not by expected depth of coverage. The bar that learners have to clear in order to achieve what we consider security at Third level is the same for our of our leaners. (Don’t mention Benchmarks!) The rate at which learners progress towards this and achieve this standard will vary. Classes will be flexible and will reflect this. There are no timelines dictating that we spend 2 weeks on fractions etc. We move on when mastery has been achieved by a majority of the class (see previous posts for more details). Learners working at similar paces will be in the same class but there will be relatively frequent movements as and when required. I have the second fastest class – note the use of language- not second top set. We have spent EIGHT weeks on whole numbers. This thinking, on spending time on the essentials, is very much influenced by Bruno Reddy’s work at King Solomon and some of the amazing stuff happening at Michaela. Until learners are secure at the four basic operations then why would we consider moving on?
On Monday two of the classes will be sitting a summative assessment on this topic. Later assessments will be based upon whole phases of the curriculum, encompassing four or more topics, however, for an early indication of where we are and how things are going I felt that an assessment at this point was necessary.
Pupil Ownership
This is a phrase we often hear – but what does it mean? I believe that our curriculum changes are about culture as much as they are mathematics. Our S4/5/6 middle/lower classes are disengaged and underachieving for two many reasons. 1. They lack the pre-requisite knowledge and understanding to engage with the level now being attempted and 2. They have not developed the study habit.
I regularly see kids from oversees arrive at the school and make up two years of progress in one, because they work hard. I want to help all of our leaners to be like this. We are doing a few things to support this in our new curriculum, which will be followed on into S2-6 in each of the subsequent few years.
Stationery packs: Every new S1 is issued with a large zip-lock plastic wallet complete with scientific calculator (Casio fx 83 +), some pencils, pens, a highlighter, protractor, ruler, rubbers, and sharpener. 44% of our learners come from SIMD 1 to 3, despite our leafy location in the fashionable west end. Poverty is real. Indeed only 13% come from SIMD 9 and 10. What the stationery packs mean is that there is an expectation that every pupil turns up to every lesson prepared to work, with the correct resources. This has gone well so far with very few pupils struggling to manage their resources. The kids were delighted with their packs and have looked after them in the main. I love teaching a class where I can now say “take our your highlighters to select the key word” and they all have one! This develops a culture of equity of opportunity but also gives us the chance to have equity of expectation of learners – that everyone comes equipped.
Homework Policy- Every Pupil, Every Night: Homework is going out of fashion, a lot of professionals are suggesting that it has no impact or is pointless! See: Dan Meyer,The news However, given my own experience in secondary maths and widespread evidence, eg: This, I find this a position which I am deeply uncomfortable with. If homework works in one context it is in secondary mathematics.
We have produced booklets for each phase of our curriculum, covering almost every learning intention, with enough short homework tasks to keep our pledge of every pupil every night. Most exercises are single topic based – usually practice and drill. However, we have included some at the back of the booklet for teachers to drop in at appropriate times, which are based upon various topics covered up to that point in the curriculum. This comes from the idea of interleaving and spaced practice. In fact, 5 weeks after doing order of operations I may drop in one of the order of operations exercises for a nightly homework. Thinking about retention is important. Vitally, the homework policy is to ensure that learners are in the study habit. Four pieces of maths homework every week (not counting the formal end of topic exercises or revision materials issued) ensures that every pupil is spending time on maths outside of class. We have supported this with a very transparent homework policy. If a pupil ends up on the fourth occasion not doing homework then a letter goes home (there are sanctions for one, two and three occasions too). I haven’t had to send a single letter home for any S1 pupil after the 36 homework opportunities so far. There are always concerns about pupils copying, but the insistence on showing working and our regular in-class diagnostic testing should almost entirely eradicate this. For example, if a pupil scores 10/10 on an adding integers homework yet scores only 5/10 on a diagnostic in class on the same material then suspicions are obviously raised! We intend to roll the Every Pupil-Every Night policy all the way through the curriculum from Third Level to National 5/Higher in coming years. This culture of doing homework every night – if sustained would make a significant difference to our senior pupils. An extra 30 mins per week of maths, 37 weeks of the year, for 5 years means a total of 92.5 hours extra mathematics work. The equivalent of roughly 2/3 of a school year. Ultimately, if learners are used to doing maths homework then it will take something radical to stop them from working like this. At the moment it often takes something extraordinary in the senior phase to start N4/N5 learners working at the appropriate rate outside of class. The culture is going to be one where everyone does their homework every night from S1 to S6.
Pre Assessment Preparation Policy: Before each formative assessment in our new curriculum, leaners are issued with a self-evaluation grid, which has every learning intention from all of the topics in the assessment. Next to this are questions for pupils to assess if they have this skill/knowledge. At the back of the grid are answers to these questions. If a learner gets the question wrong they are directed to appropriate practice questions in a revision pack. The revision pack is coupled with comprehensive written solutions to every question. We have given no in-class pre-assessment revision lessons prior to Monday’s test. At present I am in favour of continuing this throughout, due to experiences with older kids who muck around and aren’t engaged during these sort of lessons. As @JemmaPDuck said on Twitter, this sort of stuff is a waste of valuable learning and teaching time. Learners have absolutely every physical resource required to do the revision and make a success of it. We should, during normal teaching and homework, be linking topics and developing retention. No in-class revision may sound harsh, but for me it once more comes down to culture. Why revise for yourself if the teacher is going to do it for you anyway? We need to model a culture of high expectation – we need to expect learners to revise. We have equipped them comprehensively to do this. If S1 begin like this, then it can only be a positive in helping them develop the habit. Some of my colleagues disagree – I’m interested in what your views are too, reader. Let me know.
Supported Study: Our learners are lucky that we have a department where on any given night at least one, often two or three, teachers have an open door for an hour or two after school – during which they can come in and work on homework or get extra help with a topic they are struggling with. This is our attempt at removing another barrier to learning, revision and pupil ownership. Some learners do not have a safe/suitable place to revise outside of school. We provide this too. We are encouraging S1/2 to get along and have a specific session for them only – with no older kids, although they can go to any. We want them to get in this habit early. I think this can work in our context, given we are a city school with a high number of kids within easy reach of home. I appreciate this won’t work everywhere.
This four-pronged approach to pupil ownership is, to recap, about equity of expectation and equity of opportunity for every pupil, regardless of home circumstances.
Whole numbers
Our new Mastery Curriculum is now running with first year classes. We began the year by very broadly setting classes based upon two diagnostics – one pre-summer and one post-summer. Five of the classes are embarking upon our Third level course and the other two are looking at a Second level version with a view to moving onto Third Level at a later point. I think we have to be realistic about the starting point of our learners. It’s an uncomfortable truth that 2/7 of the cohort arrive at secondary not in a position to meaningfully engage with Third level, lacking knowledge of times tables and other key ideas, but that is where we are. It wouldn’t be doing these learners any favours to course them into a third level course, when there are so many gaps in their knowledge of Second and, in some cases, First level. We need to get these pupils equipped with the basic skills to meaningfully engage with the Third level course. I’ve seen too many pupils coursed at a level where they are missing substantial pre-requisite knowledge. Advocates of mixed ability may criticise the decision to set at all, however, we are ambitious for all of these learners. We want them to catch up – I have no intention of having ghetto classes of forgotten pupils who are destined to failure. I am delighted to say that the colleagues teaching these pupils share this mindset and I am hopeful, that we can make a difference, with careful planning.
With regard to the other five classes, they may be set, but over time this setting will be by pace of learning – not by ability and not by expected depth of coverage. The bar that learners have to clear in order to achieve what we consider security at Third level is the same for our of our leaners. (Don’t mention Benchmarks!) The rate at which learners progress towards this and achieve this standard will vary. Classes will be flexible and will reflect this. There are no timelines dictating that we spend 2 weeks on fractions etc. We move on when mastery has been achieved by a majority of the class (see previous posts for more details). Learners working at similar paces will be in the same class but there will be relatively frequent movements as and when required. I have the second fastest class – note the use of language- not second top set. We have spent EIGHT weeks on whole numbers. This thinking, on spending time on the essentials, is very much influenced by Bruno Reddy’s work at King Solomon and some of the amazing stuff happening at Michaela. Until learners are secure at the four basic operations then why would we consider moving on?
On Monday two of the classes will be sitting a summative assessment on this topic. Later assessments will be based upon whole phases of the curriculum, encompassing four or more topics, however, for an early indication of where we are and how things are going I felt that an assessment at this point was necessary.
Pupil Ownership
This is a phrase we often hear – but what does it mean? I believe that our curriculum changes are about culture as much as they are mathematics. Our S4/5/6 middle/lower classes are disengaged and underachieving for two many reasons. 1. They lack the pre-requisite knowledge and understanding to engage with the level now being attempted and 2. They have not developed the study habit.
I regularly see kids from oversees arrive at the school and make up two years of progress in one, because they work hard. I want to help all of our leaners to be like this. We are doing a few things to support this in our new curriculum, which will be followed on into S2-6 in each of the subsequent few years.
Stationery packs: Every new S1 is issued with a large zip-lock plastic wallet complete with scientific calculator (Casio fx 83 +), some pencils, pens, a highlighter, protractor, ruler, rubbers, and sharpener. 44% of our learners come from SIMD 1 to 3, despite our leafy location in the fashionable west end. Poverty is real. Indeed only 13% come from SIMD 9 and 10. What the stationery packs mean is that there is an expectation that every pupil turns up to every lesson prepared to work, with the correct resources. This has gone well so far with very few pupils struggling to manage their resources. The kids were delighted with their packs and have looked after them in the main. I love teaching a class where I can now say “take our your highlighters to select the key word” and they all have one! This develops a culture of equity of opportunity but also gives us the chance to have equity of expectation of learners – that everyone comes equipped.
Homework Policy- Every Pupil, Every Night: Homework is going out of fashion, a lot of professionals are suggesting that it has no impact or is pointless! See: Dan Meyer,The news However, given my own experience in secondary maths and widespread evidence, eg: This, I find this a position which I am deeply uncomfortable with. If homework works in one context it is in secondary mathematics.
We have produced booklets for each phase of our curriculum, covering almost every learning intention, with enough short homework tasks to keep our pledge of every pupil every night. Most exercises are single topic based – usually practice and drill. However, we have included some at the back of the booklet for teachers to drop in at appropriate times, which are based upon various topics covered up to that point in the curriculum. This comes from the idea of interleaving and spaced practice. In fact, 5 weeks after doing order of operations I may drop in one of the order of operations exercises for a nightly homework. Thinking about retention is important. Vitally, the homework policy is to ensure that learners are in the study habit. Four pieces of maths homework every week (not counting the formal end of topic exercises or revision materials issued) ensures that every pupil is spending time on maths outside of class. We have supported this with a very transparent homework policy. If a pupil ends up on the fourth occasion not doing homework then a letter goes home (there are sanctions for one, two and three occasions too). I haven’t had to send a single letter home for any S1 pupil after the 36 homework opportunities so far. There are always concerns about pupils copying, but the insistence on showing working and our regular in-class diagnostic testing should almost entirely eradicate this. For example, if a pupil scores 10/10 on an adding integers homework yet scores only 5/10 on a diagnostic in class on the same material then suspicions are obviously raised! We intend to roll the Every Pupil-Every Night policy all the way through the curriculum from Third Level to National 5/Higher in coming years. This culture of doing homework every night – if sustained would make a significant difference to our senior pupils. An extra 30 mins per week of maths, 37 weeks of the year, for 5 years means a total of 92.5 hours extra mathematics work. The equivalent of roughly 2/3 of a school year. Ultimately, if learners are used to doing maths homework then it will take something radical to stop them from working like this. At the moment it often takes something extraordinary in the senior phase to start N4/N5 learners working at the appropriate rate outside of class. The culture is going to be one where everyone does their homework every night from S1 to S6.
Pre Assessment Preparation Policy: Before each formative assessment in our new curriculum, leaners are issued with a self-evaluation grid, which has every learning intention from all of the topics in the assessment. Next to this are questions for pupils to assess if they have this skill/knowledge. At the back of the grid are answers to these questions. If a learner gets the question wrong they are directed to appropriate practice questions in a revision pack. The revision pack is coupled with comprehensive written solutions to every question. We have given no in-class pre-assessment revision lessons prior to Monday’s test. At present I am in favour of continuing this throughout, due to experiences with older kids who muck around and aren’t engaged during these sort of lessons. As @JemmaPDuck said on Twitter, this sort of stuff is a waste of valuable learning and teaching time. Learners have absolutely every physical resource required to do the revision and make a success of it. We should, during normal teaching and homework, be linking topics and developing retention. No in-class revision may sound harsh, but for me it once more comes down to culture. Why revise for yourself if the teacher is going to do it for you anyway? We need to model a culture of high expectation – we need to expect learners to revise. We have equipped them comprehensively to do this. If S1 begin like this, then it can only be a positive in helping them develop the habit. Some of my colleagues disagree – I’m interested in what your views are too, reader. Let me know.
Supported Study: Our learners are lucky that we have a department where on any given night at least one, often two or three, teachers have an open door for an hour or two after school – during which they can come in and work on homework or get extra help with a topic they are struggling with. This is our attempt at removing another barrier to learning, revision and pupil ownership. Some learners do not have a safe/suitable place to revise outside of school. We provide this too. We are encouraging S1/2 to get along and have a specific session for them only – with no older kids, although they can go to any. We want them to get in this habit early. I think this can work in our context, given we are a city school with a high number of kids within easy reach of home. I appreciate this won’t work everywhere.
This four-pronged approach to pupil ownership is, to recap, about equity of expectation and equity of opportunity for every pupil, regardless of home circumstances.
Whole numbers
It’s taken eight weeks to ensure that my class is at a point where I am confident in their handling of the above. Some of the other classes are perhaps two or three weeks away from this point. Fine. These are building block topics that are vital to everything else we will do. Colleagues have been, at times, a little concerened about the slow pace, but our clearly planned pathways all the way to S5 show there is nothing to be worried about in terms of pace relative to making H/N5, as appropriate, by end of S5.
Notice above that multiples are included but no factors or primes. One of our design approaches is to keep minimally separate, often confused topics apart initially. The next topic is negative numbers (1) – which is just adding and subtracting. No multiplication or division until a good while later. Other topics later in the course such as area and perimeter are also kept separate initially.
The results of the whole numbers assessments will be interesting over the coming weeks as classes get to the point of readiness. I am very optimistic that there will be good scores across the board. Pupils will hopefully get used to succeeding in maths, and teachers too, will really begin to believe that all of the learners can succeed.
A typical page in the scheme of work looks like this:
That is, explicit learning intentions, resources for delivery and pupil practice (high quality stuff as previously discussed in other posts), teaching advice if applicable, diagnostic questions and diagnostic assessments, rich tasks and then additional homework tasks – to supplement the booklet mentioned above. The Whole numbers scheme covers six pages of A3. This, perhaps, shows you the scale of development and resourcing we are currently still working on.
The resources are vital. If the schemes of work have good resources, which encourage sound evidence based effective pedagogy, then it makes it easier for teachers to be more effective. The longer I’ve been teaching the lesson planning seems to become more complex- maybe due to my own understanding growing. The examples we use with pupils, the practice that pupils get on each of the specific common cases of a problem and the way pupils get to apply and reason their knowledge all needs to be carefully planned. I’m really interested in the work at Michaela who are creating their own textbook. Perhaps in four or five years time, our compendium of electronic resources could also be made into a department book. Most of our exercises and tasks are sourced from others: take a bow Corbett Maths, Resourceaholic, Median Don Steward, Nrich and Malcolm Swan amongst others. In other cases we have to design our own where we are using, as yet, nationally uncommon approaches (such as algebra tiles for the teaching of integers). We are mindful of Swan’s effective mathematics tasks while also aiming to incorporate the philosophy summarised here, when creating resources and tasks from scratch.
One of the key components of our new curriculum has been the development of teacher capacity – including my own. Masses of reading, research, a lot of trial and error of various approaches in my own classes are being filtered into a scheme of professional development which is running through every department meeting we have this year. Forthcoming sessions I’ll be delivering to colleagues include multiple representation approaches to integers, development of algebraic understanding and fluency, using the bar model effectively for the teaching of fractions and percentages. This follows on from last year where we looked at ideas such as abandoning other forms of solving equations except balancing. My main question is, as ever, how can we help pupils to have more procedural and conceptual fluency with the key topics? The excellent mathagogy blog suggests that just because our conventional methods work for the more able kids, it doesn’t mean the methods are good. It’s a point to consider. I’ve been able to develop fraction skills in many pupils over the years, but also failed miserably to build sustained fraction knowledge in many others. There’s no point being able to teach something to a class who won’t retain it. The learning needs to be deep enough and meaningful enough such that it IS learning, not just instantaneous performance. We need new pedagogy which is evidence based which works for the majority, not just some. So, as well as development of the curriculum and resources, there is a lot of professional learning going on.
The resources are vital. If the schemes of work have good resources, which encourage sound evidence based effective pedagogy, then it makes it easier for teachers to be more effective. The longer I’ve been teaching the lesson planning seems to become more complex- maybe due to my own understanding growing. The examples we use with pupils, the practice that pupils get on each of the specific common cases of a problem and the way pupils get to apply and reason their knowledge all needs to be carefully planned. I’m really interested in the work at Michaela who are creating their own textbook. Perhaps in four or five years time, our compendium of electronic resources could also be made into a department book. Most of our exercises and tasks are sourced from others: take a bow Corbett Maths, Resourceaholic, Median Don Steward, Nrich and Malcolm Swan amongst others. In other cases we have to design our own where we are using, as yet, nationally uncommon approaches (such as algebra tiles for the teaching of integers). We are mindful of Swan’s effective mathematics tasks while also aiming to incorporate the philosophy summarised here, when creating resources and tasks from scratch.
One of the key components of our new curriculum has been the development of teacher capacity – including my own. Masses of reading, research, a lot of trial and error of various approaches in my own classes are being filtered into a scheme of professional development which is running through every department meeting we have this year. Forthcoming sessions I’ll be delivering to colleagues include multiple representation approaches to integers, development of algebraic understanding and fluency, using the bar model effectively for the teaching of fractions and percentages. This follows on from last year where we looked at ideas such as abandoning other forms of solving equations except balancing. My main question is, as ever, how can we help pupils to have more procedural and conceptual fluency with the key topics? The excellent mathagogy blog suggests that just because our conventional methods work for the more able kids, it doesn’t mean the methods are good. It’s a point to consider. I’ve been able to develop fraction skills in many pupils over the years, but also failed miserably to build sustained fraction knowledge in many others. There’s no point being able to teach something to a class who won’t retain it. The learning needs to be deep enough and meaningful enough such that it IS learning, not just instantaneous performance. We need new pedagogy which is evidence based which works for the majority, not just some. So, as well as development of the curriculum and resources, there is a lot of professional learning going on.