Mathematics Subject Leader In-Depth Study Module 3 (3 hours)
Ensure that the pedagogy is suitable and that pupils can learn mathematics efficiently and effectively
By studying this module you will consider ideas about leading a mathematics department that is attempting to ensure that the pedagogy it uses is suitable so that pupils can learn mathematics efficiently and effectively. In particular you will come to know more about:
- the characteristics of pupils and the mathematics they need to learn;
- models for thinking about pupil difference;
- managing behaviour;
- creating a positive learning environment;
- assessment that works for pupils;
- the pupil voice;
- working across the school and with other departments.
The sections can be studied in the order presented here or you can click on one of the sections below to take you to a section that particularly interests you:
- Looking at the characteristics of pupils and the mathematics they need to learn - models for thinking about pupil difference (30 mins)
- Managing behaviour (30 mins)
- Creating a positive learning environment (30 mins)
- Assessment that works for pupils (and staff) (30 mins)
- What does personalisation mean? (10 mins)
- The pupil voice (20 mins)
- Working across the school and with other departments (20 mins)
- Reviewing the module (10 mins)
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1. Looking at the characteristics of pupils and the mathematics they need to learn
Pupils display many different characteristics when they come to learn about mathematics. Some of them are helpful, some of them can be helpful if the lesson is presented in a different way. Some pupils have characteristics will take some ingenuity for the teachers in your department to help those pupils learn. Other characteristics pupils don’t yet have and teachers can help them learn. Click the title of the section that you want to study:
The characteristics of pupils and the mathematics that they learn.
What are the characteristics of your pupils?
There are many characteristics typical of learners of mathematics.
We may want learners of mathematics to display the following characteristics
Think of a pupil that you have taught for some time. List the characteristics that they display when trying to learn mathematics.
Now think of yourself and list your characteristics as a learner of mathematics.
What are the differences?
What does this mean in terms of teaching in your department?
There are many desirable characteristics of a mathematical student. Obviously not all learners of mathematics will display all of these characteristics all the time. For example, some will be persistent when engaged in certain tasks and not in others.
Developing the characteristics of a mathematical learner
Reflect on these characteristics: are there any others that you would like to add to the list?
Is it the job of a mathematics teacher to help pupils develop these characteristics?
Choose two of the characteristics and devise a lesson that would help students to develop those two characteristics.
Here is a shortened summary of the Key Concepts and Processes of Mathematics.
Developing characteristics of mathematical learners in the key concepts and processes
Use the summary above.
Using Folio 3.1.1 to consider which concept or process uses and/or develops the desirable characteristics of mathematical learners – don’t forget to add in your own desirable characteristics.
Models for describing characteristics of pupils learning mathematics, VAK(R) Gardener, Steinberg, thinking skills
Different models of intelligence
Use Folio 3.1.2 to reflect on different models of characterising intelligence
1. What types of intelligence do you test in your department?
2. What does it mean to help pupils develop Sternberg’s:
• analytical Intelligence
• experiential / creative intelligence
• contextual / practical intelligence
in mathematics lessons?
3. What about Gardner’s seven intelligences detailed in Folio 3.1.4?
Many people think of these types of intelligence as a learning disposition.
VAK in maths
VAK is a way of thinking about learning dispositions.
• Use the VAK test Folio 3.1.5 to establish your own learning type
• Reflect on what this means in terms of learning in your department?
Why do some pupils misbehave?
Explaining behaviour and misbehaviour
Use the ideas discussed in this session to construct an explanation of why a pupil you know well sometimes ( possibly frequently) misbehaves and why another behaves appropriately
Use Folio 3.1.6
- First explain what the pupils do that you count as good behaviour and misbehaviour
- Then try to think of explanations that might help you understand why one pupil behaves whilst another pupil misbehaves
- Then think of ideas to help all pupils exhibit learning behaviour in the classroom.
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2. Managing behaviour
Often managing behaviour in a department is about developing assertiveness in all the staff. You will need to model positive working relationships both with students and staff, treating everyone with respect while maintaining your standards and being consistent. You will use a great deal of emotional intelligence in doing this as you make demands on your staff that they manage pupils behaviour whilst supporting them. In this section we will look at what developing assertiveness means and how a subject leader can plan to support staff in managing the behaviour of pupils in the department. Homework can be a problem when discussing behaviour, senior management and many parents demand that it is set, but what happens when it is not done? Click the title of the section that you want to study:
Developing Assertiveness in your staff
Assertiveness is part of building positive working relationships in a department. It is part of taking appropriate responsibility for your own actions and treating people with respect. It is an ‘emotionally intelligent’ way to act with other people. Assertiveness is vital in teachers who need it to take control in their classroom. However some teachers achieve discipline through dominating pupils, and some do not achieve an appropriate discipline in their classrooms. Both extremes could benefit from learning more about assertiveness.
Assertiveness taken to extremes can look like dominance or bullying, getting one’s own way at other’s expense. Often as a leader you will not want to be assertive, but inclusive and developmental. However, even if all your staff are working with you there will situations when you need to use assertiveness techniques.
Assertive communication is emotionally intelligent and can strengthen your relationships, reducing stress from conflict and providing you with social support when facing difficult times. Assertive communication can help you handle difficulties more easily, reducing drama and stress. Assertiveness is not natural behaviour for many people who are often passive or after a quiet life. However teachers have to gain control over their classes and therefore have to be assertive, particularly when pupils are assertive themselves.
When behaving assertively always:
- make sure your body reflects confidence: stand up straight, look people in the eye, and relax;
- remember everyone deserves respect, including you;
- use a firm, but pleasant, tone;
- don’t assume you know what the other person’s motives are, especially if you think they’re negative;
- when in a discussion, don’t forget to listen and ask questions! It’s important to understand the other person’s point of view as well;
- try to think win-win: see if you can find a compromise or a way for both of you to get your needs met.
Assertiveness is often in the words that you use, using factual descriptions rather than judgements, using I rather than you and so
Use Folio 3.2.1 to learn more about talking assertively.
Being an assertive subject leader
As subject leader you will need to be assertive with your staff and pupils, and be assertive with other members of the school, making sure that your department gets access to the resources that it needs and deserves.
Sometimes in acting assertively you will be modelling good practice for staff and students alike and showing how to achieve positive working relationships throughout the department.
Assertiveness in other areas of your work
Are you as assertive as you might be in meetings with staff, parents or other members of the community? Do you model positive working relationships outside the department?
Use Folio 3.2.2 to find out more about assertiveness in other areas of your work.
Emotional Intelligence is part of being a good leader as we saw in Module 1.
Daniel Goleman (1995) in ‘Emotional Intelligence’ identified the five ‘domains’ of Emotional Intelligence (EQ) as:
- knowing your emotions;
- managing your own emotions;
- motivating yourself;
- recognising and understanding other people’s emotions;
- managing relationships, ie, managing the emotions of others.
Emotional Intelligence (EQ) obviously overlaps with acting assertively, knowing and managing your own emotions and recognising and managing the emotion of others. EQ embraces and draws from numerous other branches of behavioural, emotional and communications theories, such as NLP (Neuro-Linguistic Programming), Transactional Analysis, and empathy. By developing our Emotional Intelligence in the five EQ domains we can become more productive and successful at what we do, and help others to be more productive and successful. The process and outcomes of Emotional Intelligence development also contain many elements known to reduce stress for individuals and organisations, by decreasing conflict, improving relationships and understanding, and increasing stability, continuity and harmony.
Read more about Emotional Intelligence on the BusinessBalls website.
Planning to support staff in managing behaviour
There are many complex ideas about managing behaviour in the department. Encouraging all staff to act assertively and not aggressively will develop positive working relationships. Setting clear expectations of behaviour within the department and showing your appreciation of those that adhere to those expectations will go a long way to encourage good behaviour. There will be those that do not and will not conform and you need to plan an approach for those that can be consistently applied by all staff
Planning rules and consequences
Consistency is the most important factor in achieving a well ordered and disciplined department and school. Obviously your department’s rules and consequences must fit in with the school, but it is worth discussing and setting out clearly both what is acceptable and what is not and what happens when a pupil oversteps the mark
A Classroom Discipline Plan may be composed of three parts:
A Sample Classroom Discipline Plan can be found here.
- rules that students must follow at all times;
- consequences that result when students choose not to follow the rules;
- rewards for when students do follow the rules.
Many departments or schools send a note home to parents explaining that these are the rules in their classrooms and are in effect at all times. Severe misbehaviour, such as unsafe or disruptive behaviour and verbal abuse will result in the immediate imposition of the Severe Clause. These rules are discussed with the pupils and some teachers chose students to roll play the teacher and various misbehaving students to make sure everyone understands. There is a tear off section of the letter that the parent signs and returns to say they have talked to their child about the discipline plan.
Make your own department discipline plan
Use Folio 3.2.3 to devise your own rules, consequences and rewards.
Then share them with your department and ask for their ideas to improve the plan.
Display the agreed plan in each classroom.
Plan how you intend to make sure that the agreed classroom discipline plan is used consistently.
Homework and getting it done
Homework can be a big issue for teachers. Some pupils do it willingly others would rather not. Some teachers want to set it believing that it helps their pupils learn, others think that it is not worth the hassle of making pupils complete it. It can be a source of conflict and can spoil the ethos of the department unless it is well managed.
As department leader you will have your own opinions, be responsible for consistency within the department and be working within school policies that you will have some say in devising or reviewing. Therefore it is worth spending some time reflecting on the issues and deciding your approach to homework.
Setting Out your Department Homework Policy
1. Find out your school homework policy. Some schools develop a tradition that teachers think is the ‘policy’ but when they investigate they find the policy is flexible and allows departments a great deal of flexibility. Find out the exact wording of your school’s policy.
2. Find out exactly what your department does and ask them what they want to do. How far does what they do and / or want to do fit in with school policy? Can you make the two coincide with a little creative tinkering? Or will you have to talk to your SMT about making changes?
3. Think about marking homework as well as setting homework. We know that if homework is checked and /or marked and used in the next lesson, the pupils are much more likely to do it. Will the way that homework is set allow your teachers time to mark work in the way they want to? What other ways might there be to set and mark homework? Reflect on the advantages and disadvantages of the ideas in Folio 3.2.4.
4. When homework is set it should be part of the scheme of work and the whole learning experience – therefore it must be done. What consequences will there be for homework that is not done? What is acceptable in terms of ‘trying’ and what is not? These must be agreed across the department as consistency here is as important as in everything to do with expectations of pupil behaviour.
5. Investigate what other departments do – talk to heads of department within your school and in other schools
6. Draft your policy, ask the rest of the department for comments and the redraft it and put it into practice. Remember to keep talking about the policy within the department and redraft the policy as soon as it becomes necessary. A policy must be consistently applied but can be changed to suit different circumstances.
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3. Creating a Positive Learning Climate
It is important that your mathematics department is an effective learning environment for pupils. That means taking account of the physical environment, the organisation of classrooms as well as wall displays and so on, as well as the way that pupils are encouraged to learn in the department. Click the title of the section that you want to study:
Looking at the physical environment
Take a ‘Learning Walk’
Developing a growth mindset in pupils
Walk through your department and try to see it as someone new to the school might see it.
- Look at the entrance to the department and the corridors
- what do they say about the department?
- how could they be improved?
- Look at the classrooms
- what climate do they engender?
- how could they work better for the pupils?
- Take a walk around another department and answer the previous two questions.
- Now decide what should be done to make the department more:
- welcoming, to pupils and other people?
- mathematical – is it obvious that it is a maths department?
- a place where ICT is a tool for learning?
The Fixed Mindset
People with a fixed mindset...
Believe that their abilities are carved in stone. They cannot improve by working hard or any thing else
Have an urgency to prove themselves over and over
Seek short term success to prove to themselves that they are ‘smart’
Dislike struggle and making mistakes as they can ‘prove’ how limited their ‘fixed’ intelligence is
Want to stick with what they know in case they are tried and found wanting
Tend to give up as difficulties prove that they are reaching the limit of their potential
The Growth Mindset
People with a growth mindset...
Believe your basic qualities can be cultivated through your own efforts. They know that they can understand more and improve their skills through application and hard work
Seek to work with others as they know that people can learn from one another
Say ‘why waste time proving over and over how good you are when you could be getting better?’
Consider that hiding deficiencies and / or lack of understanding is pointless when they could be overcoming them?
Think, why stick with the tried and true when you could be challenging yourself with experiences that will stretch you?
Are able to grow and thrive through all challenges.
How do you encourage a growth mindset?
This has a great deal to do with what you say.
Use Folio 3.3.1 to reflect on what comments will engender a fixed mindset and whihch will engender a growth mindset.
How praise works and how it doesn’t
Praise and rewards do not always have the effect that we think they will. The best teachers are known to praise less than their less-effective colleagues. If praise is given randomly then it is quickly devalued. If you give a reward for underlining a title what are you going to do when that same student solves five difficult problems on Pythagoras in 3D? Rewards make everything a success or a failure, you get a sticker or you don’t, and often it is just that you are lucky or you are unlucky.
Praise works when it is:
- specific, that is says exactly what has been done well;
- targeted, that is about a specific piece of work or process completed; and
- about the task not the pupil.
Praise should always be about something that the pupil has made an effort to change, so not about a neat book when the pupil always has a neat book. Praising the process and not the outcome is also important, you want your students to focus on thinking things through, reasoning, trying and sometimes failing so those are what you praise. Remember mistakes are good because that is where you start to learn!
Use praise to improve behaviour
Praise is similar to providing positive feedback. Praise has an important part to play in building a positive ethos. The repeated process of positively acknowledging desirable acts helps to build a positive distinctive character. Pupils are less likely to misbehave in environments in which they feel positive.
Remember to acknowledge those who come to school and day-in-day out do what they are expected to do. This group of students do not usually get the same degree of attention that poorly behaved students get, but if the technique of positively recognising and praising desired behaviours is used, it reverses the situation and also makes a significant contribution to developing a positive ethos.
Praise students for doing what they are asked to do. For instance a command like ‘stop what you are doing, face the front and pay attention’ is followed by immediately praising those students who stop what they were doing, face the front and pay attention. This produces a ripple effect because other students want the positive attention as well.
Use a high level of positive language - this in turn contributes to developing a positive ethos which in turn contributes to improved behaviour because students are less likely to be disruptive in an environment in which they feel positive.
Planning for a classroom ethos that helps manage behaviour
Creating a positive classroom ethos
Read Folio 3.3.2
Assessment for Learning and managing behaviour
Reflect on how to help your teachers develop a classroom ethos that helps them maintain good behaviour in their classrooms.
Would it be useful to have a summary document about the ideas on developing a positive learning environment alongside your department behaviour policy to ensure consistency in this aspect as well?
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4. Assessment what works for pupils (and for you)
Assessments that are used in your department should work hard to help pupils move their learning forward. All too often assessment measures the pupils without helping them know how to improve.
‘It is no use spending so much time weighing the pig that you don’t have enough time to feed it!’
This section looks at using assessment in a way that enables the students to know where they are and know how to improve without causing too much work for teachers. Click the title of the section that you want to study:
Using Peer- and Self-Assessment
Peer and self assessment are an important set of approaches for a teacher. They help develop the pupils abilities to know what is required in a piece of work and to develop the discernment to self-assess – an important life skill.
Peer- and Self-Assessment are useful because...
- they encourage students to listen to one another
- they encourage students to ask questions about the quality of work that can be produced
- they extend students' repertoire of ways to tackle a task and helps them to learn more effective or efficient strategies
- others' work may contain a wide range of imperfections and misconceptions through which a student may explore their own
- they show students different ways of completing the work
- they encourage a co-operative learning environment in the classroom
- they ask students to use criteria to comment on others' work through which they can come to a better understanding of the criteria
- they enable students to have an overview of what it means to complete a task to a high standard
- it is possible to become more conscious of what you are trying to achieve yourself when you have to explain to other people
- students can obtain an objectivity through peer-assessment that they can then apply to their own work
- students can become more involved in and responsible for their learning
- they help in creating a better and more productive relationship between students and teacher.
Using Peer- and Self-Assessment
Look at the 'short sharp' suggestions in Folio 3.4.1.
Which could be useful in your department?
Look at the longer, more formal ideas - how could those be used?
Formative use of summative assessment
When tests are used formatively
- tests can help pupils learn;
- pupils see tests as a positive part of the learning process;
- pupils see the tests as a check-up on where they are and a pointer to where they need to go.
Teachers need to think of tests as:
- part of the learning process not the end of it;
- as “check-ups” on the road to learning not as an end in themselves;
- timed so that any problems that are disclosed by the test can be dealt with.
Some teachers make up tests from a selection of questions from a database or write them themselves. Such tests are useful as they allow the teacher and the pupil themselves to know how well the students can answer exam questions, or at least those exam questions. If the test is followed up with time set aside to sort out any problems encountered then it can be useful in the learning process. Remember tests only tell anyone what the pupil can achieve with those questions, at that time. Much more information will be needed to know if the work they are doing in class is challenging them appropriately.
Testing systems can be set up that work for pupils for example:
- tests are followed up by a group activity to find out and solve any problems encountered;
- pupils using exam board mark schemes to peer mark others’ tests. This system allows all the pupils to gain a greater understanding of what is needed to score high marks;
- pupils writing their own questions and mark schemes for a test. Pupils who write their own questions are known to outperform those who just do practice questions.
Thinking about using summative assessment formatively
Use Folio 3.4.2
to review some ideas for using summative assessment formatively and decide which to use in your department.
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5. Personalising the curriculum
What does Personalisation mean?
As defined in the Report of the Teaching and Learning in 2020 Review Group: "Put simply, personalised learning and teaching means taking a highly structured and responsive approach to each child's and young person's learning, in order that all are able to progress, achieve and participate. It means strengthening the link between learning and teaching by engaging pupils - and their parents - as partners in learning."
Personalised learning is the challenge to meet more of the needs of more pupils more fully than has been achieved in the past. It is about ensuring that more pupils achieve their full potential during their school years and are better prepared for lifelong learning. It is concerned with a transformation of education and schooling that is fit for citizens in the 21st century
“Personalised learning is about tailoring education to ensure that every pupil reaches their full potential...it is not individualised learning, where children work alone, nor is it pupils being left to their own devices. It means shaping teaching around the different ways children learn.”
Explore the internet for the latest ideas on personalisation, put the words, ‘personalisation’, ‘personalised learning’ and ‘personalising learning’ into a search engine.
Try and answer these questions from what you find:
- what are the key ideas for personalisation from your perspective?
- what does it mean to personalise the curriculum in your department?
- how can different groups be helped to learn more effectively?
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6. The pupil voice
There are many ways that schools use to enable them to hear what the pupils want from their school and how they think their learning can best be organised
To find out more, watch Pupil Voice (duration 30 minutes) on Teachers TV, part of the series School Matters.
Reflect on listening to the Pupil Voice
- what are the advantages of listening to the pupils?
- what are the disadvantages?
- what ways can you use to take the best advantage of ‘the pupil voice’ to improve learning mathematics?
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7. Working across the school and with other departments
There are many ways that as subject leader in mathematics you might work across the school. You may take an interest in promoting numeracy across the curriculum, highlighting the way that maths supports and extends learning across the curriculum. You might also use the opportunities presented by the new national curriculum to work across the school. Click the title of the section that you want to study:
Numeracy across the curriculum – making use of the opportunities
Who should be in charge?
Some schools assume that someone from the maths department should be in charge of the ‘Numeracy Across the Curriculum’ initiative in school but that is not always the case. There are advantages and disadvantages of using a mathematics teacher that should be considered.
Whether it is a maths teacher or another teacher that takes charge of promoting numeracy across the curriculum, it can raise the status of mathematics and stimulate an interest across the school. Be ready with ideas to take advantage of this.
In thinking about working across the curriculum do you know where other subjects use maths?
There are examples and ideas in the National Curriculum (2007) for how you might work across the curriculum. However there are questions to ask of departments.
Reflect – do you know what mathematics is present in other department’s schemes of work?
Where and when do Science, Art, History and Design and Technology use mathematics?
There is mathematics in most subjects if you work to find it, for example dates, calculations and negative numbers in History and statistics and graphs in Geography. Finding out what needs teaching and reaching a compromise on when to teach it with other departments can make for a more coherent experience for the pupils and make optimum use of curriculum time – why teach speed, distance, time in both Science and Maths?
Task – Working across the curriculum
Over the next two terms, interview as many heads of other departments as you can.
Talk about the maths that they use.
Try to agree re-timings of teaching topics, or joint teaching of topics and/or exciting ways to learn the maths and write it in both schemes of work for the next academic year.
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8. Reviewing the module
In completing this module you will have considered:
1. Looking at the characteristics of pupils and the mathematics they need to learn
2. Managing behaviour
- the characteristics of pupils and the maths they need to learn.
- models for describing characteristics of pupils learning mathematics.
- why do some pupils misbehave?
3. Creating a positive learning climate
- developing assertiveness in your staff.
- planning to support staff in managing behaviour.
- homework – getting it done.
4. Assessment that works for pupils (and you)
- looking at the physical environment.
- developing a growth mindset in pupils.
- planning for a classroom ethos that helps manage behaviour.
5. What does Personalisation mean?
- peer- and self-assessment.
- formative use of summative assessment.
6. The pupil voice
7. Working across the school and with other departments
Each of these sections is intended to add to your knowledge of how to help all staff involved in the teaching of mathematics to ensure that the pedagogy they use is suitable and that pupils can learn mathematics efficiently and effectively.
Review the ideas that you have gained from each of the sections and reflect on which of the sections will make a short term difference to your department and which will add to your long term plans.