Mathematics Subject Leader In-Depth Study Module 1 (3 hours)
Providing an appropriate curriculum for all pupils, in order that they might achieve their potential
By studying this module you will consider ideas about what it means to lead a mathematics department, and what aspects have to be considered in developing a curriculum that allows everyone to develop their potential. In particular you will come to know more about:
- what it means to take a lead on curriculum issues
- the nature of mathematics
- some learning theories and their effect on the curriculum
- how to create an effective climate for learning
- how to assess and monitor the curriculum
- how to design a curriculum to enable your pupils to learn mathematics to their full potential
- some difficulties in learning mathematics
The sections can be studied in the order presented here or you can choose one of the sections below to take you to a section that particularly interests you:
- Taking the lead on the curriculum (30 mins)
- The Nature of Maths (20 mins)
- Learning theories - creating a climate for learning (30 mins)
- Assessing and monitoring the curriculum (20 mins)
- Designing the curriculum (20 mins)
- Developing potential (20 mins)
- Difficulties in learning maths (30 mins)
- Reviewing the module (10 mins)
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1. Taking a lead on curriculum issues
One of the main responsibilities of a head of department is to take a lead on curriculum issues. In this section we shall look at the areas where you have to take a lead, what it means to lead and how you might develop your leadership style. Click the title of the section that you want to study:
Where will you take a lead?
There are four main areas in which you will take a lead as Head of Department:
- Curriculum organisation: what is taught and how it is taught is explored at length in Module 2;
- Developing and improving pedagogy appropriate to the pupils;
- Creating the team and group climate, mores and habits;
- CPD - evaluating what CPD is needed, how it is provided and how useful it is.
Reflect on which area of leadership you see as most interesting and rewarding and which you see as most difficult.
Keep a note of your thoughts so that you can return to them at the end of the module.
What does it mean to lead?
Taking a lead can be done in many ways:
Autocratic – dictator
What I say goes…
Do it because I say so!
Often considered aggressive but sometimes necessary to get something done quickly or to make people try something when they are reluctant to do so..
Democratic - consensual
Let's agree on how we will move forward
We all need to agree that our next move will help
Often takes a great deal of patience and time
Can allow one dissenter to spoil the work of the whole team.
Each person takes on responsibility according to their own skills and interests
Develops everyone’s leadership skills and allows the best use of the skills and experience in the team.
People sometimes say ‘You’re paid to do it, not me’.
Requires a charismatic leader.
Inspiration can come from outside, a speaker, trainer, book or video.
Inspiration often short lived therefore it is imperative to act quickly if changes are to be made.
Can be exhausting always to have to inspire your team.
I need to check everything to make sure it is right.
Everything is completed in the way that the leader wants
Can disempower the rest of the team
If people are always reminded and checked up on then there is no need to remember or think about things themselves.
Leader is exhausted and the team often feel that they don’t have any say..
I take on the leadership role needed for the task
Is flexible and can be appropriate for each task.
Can confuse the team ‘I never know where I am with her’
Each leader finds some styles more natural than others and this can lead to only using one or two styles and thinking they are acting according to what the task needs.
Which leadership style do you use when?
Leadership must be fit for purpose: think of a time when you would need to use each of the above styles. For example:
- Asbestos has been found in the roof and the contractors are coming tomorrow, the room needs to be cleared – no discussion: it needs to be done!
- A new style of report has been introduced, the Head is very keen that both grammar and vocabulary used is good and he seems to think the Maths department will let him down. The Micro-managerial style is needed here, your team’s reputation is at stake.
Think of examples where the other styles would be appropriate.
Developing your Leadership Style
Look at the way leadership styles are described on Folio 1.1.1
and Folio 1.1.2
Reflect: How do these ideas extend your ideas on leadership? Which will build your team in the way that you want to build it?
What type of leader do you want to be? Make notes on your preferred leadership style. When do you have to act outside your comfort zone? Why?
Quotes from other leaders
"It is amazing what you can accomplish if you do not care who gets the credit." (President Harry S Truman)
"I not only use all the brains I have, but all I can borrow." (Woodrow Wilson)
"A dream is just a dream. A goal is a dream with a plan and a deadline." (Harvey Mackay)
"Ideas are like rabbits. You get a couple, learn how to look after them, and pretty soon you have a dozen." (John Steinbeck)
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2. The Nature of Mathematics
How would you describe Maths? What is vital to knowing about Maths? What would you describe as mathematical thinking. In this section we will begin to unpick and explore some of these ideas. Click the title of the section that you want to study:
The Importance of Mathematics
Read the Importance of Mathematics from the National Curriculum.
Reflect on the Importance of Mathematics
This statement tells you that Maths is a Habit of Mind, a way of thinking, what else does it tell you? Does this statement change your thoughts on what Maths is?
The Nature of Mathematics
Listen to the Vox.
Reflect on the following:
- How does John view the nature of maths?
- How does this fit with your views?
Mathematical Habits of Mind
Read Habits of Mind.
Why habits of mind?
The mathematics developed in this century will be the basis for the technological and scientific innovations developed in the next one. The thought processes, the ways of looking at things, the habits of mind used by mathematicians, computer scientists and scientists will be mirrored in systems that will influence almost every aspect of our daily lives.
If we really want to empower our students for life after school, we need to prepare them to be able to use, understand, control and modify a class of technology that doesn’t yet exist. That means we have to help them develop genuinely mathematical ways of thinking. In this paper, we’ve tried to describe some of these mental habits. Our curriculum development efforts will attempt to provide students with the kinds of experiences that will help develop these habits and put them into practice.
Considering Habits of Mind
Use Folio 1.2.1
For each habit of mind, identify the important aspects for your teaching and what you could do to develop this habit of mind in your students.
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3. Learning Theories
There are many theoretical positions on how and why learning happens. In this section you will study the main ones and consider how that effects the way that your department creates a climate for learning. Click the title of the section that you want to study:
The Main Theories of Learning
The main theories to consider are:
- Radical Construction
- Social Construction
- Situated Cognition
Considering theories of learning
Read about these in Folio 1.3.1
Make notes about the important aspects of each idea on Folio 1.3.2
Creating a Climate for Learning
Some of the theories will make sense to you, others may surprise you and some you will disagree with or discount. All of them have something to say about how people learn and therefore how a climate for learning should be created.
Creating a Climate for Learning
Using your reading about the learning theories and Folio 1.3.3
to make notes on the important aspecrs of a classroom climate that fosters learning.
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4. Assessing and Monitoring the Curriculum
Assessing and monitoring the curriculum is an important aspect of your role as a head of department. You must know what goes on in classrooms in your department so that you can act to ensure that every pupil is able to learn mathematics as well as they possibly can. Click the title of the section that you want to study:
Finding out what goes on in the classroom
There are many sources of information about what goes on in a department.
Sources of Information
What can a source of information tell you and what can't it tell you?
Use Folio 1.4.1
to reflect on the information you can and cannot gain form the various sources of information.
will give you some suggestions.
Who Assesses and Monitors the curriculum?
Assessing and monitoring the curriculum and the way that it works is the responsibility of the Head of Department but it may not always be the Head of Department who does it. Delegating this aspect is possible as with most other jobs.
Who Assesses and Monitors the Curriculum?
Questions to reflect on or discuss:
- Does the subject leader have to do all the assessing and monitoring? Who else could do it? Are there observations that a subject leader has to make? Could there be a learning and teaching specialist role in a department?
- How else can we know ‘what works’ in terms of learning and teaching in the department? Could there be a role for meetings in doing this? Some departments use an ‘open door policy’ or ‘tea and cakes’ to facilitate the sharing of good practice, could either of these work in your department?
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5. Designing the curriculum - putting the vision together
The leader of a mathematics department must have a vision, a vision of what it means to learn maths, a vision of the importance of mathematics and a vision of how teachers in the department should act in the classroom. Begin to map out your vision by reflecting on, discussing with colleagues and completing the statements in this task box.
Task: Getting the vision
1. Expressions of how your department sees maths and why people want to learn about maths
- maths is exciting and interesting because …
- maths is important because …
2. Statements about how your department decides what to teach when.
- we recognise that maths concepts build and depend on one another therefore …
- we know that people learn at different rates and therefore we will ensure successful learning before moving on by …
3. Statements about the principles behind the way the department teaches
- we use active and involving teaching approaches because …
- we actively encourage reflection on learning because …
- we use rich questioning and discussion because …
- we take time over each new concept so that …
- students need to use and apply their mathematical knowledge therefore …
- everyone has the right to achieve success in maths irrespective of specific learning difficulties, disability, gender and racial grouping therefore we …
4. An articulation of how the department continues to improve
- we seek to use and extend every teachers experiences by …
- where there are specific skills in the department we seek to share them by …
- we use data to …
What is the most important aspect of your vision, what will you keep reminding your department about?
What other ideas do you need to include in your vision for your department?
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6. Developing Potential
Part of your role as Head of Department is to ensure that all pupils achieve as much as they can. Pupils can fail to develop their potential for many reasons, possibly because
- the climate is not one where learning is valued but rather competing to be the best
- challenge is not part of every lesson and therefore challenging yourself seems unusual
- independent learning is not encouraged
Or for many other reasons.
Click on the highlighted words in the circle below to read more about the seven characteristics of effective teaching for gifted and talented learners:
When you have studied the seven characteristics of teaching that develops the potential for pupils to excel in mathematics, complete the following task:
Developing your department’s ability to cater for gifted and talented mathematicians
- Reflect on the seven characteristics of effective teaching.
- Which one is easiest for your department to implement?
- Which characteristic is most urgent for your department to work on?
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7. Difficulties in learning maths
Many people have difficulties with learning mathematics. Some of these difficulties are caused by anxiety or poor teaching but others can be classed as special educational needs. Click the title of the section that you want to study:
What are Special Educational Needs?
Children have special educational needs if they have a learning difficulty which calls for special educational provision to be made for them.
Children have a learning difficulty if they:
(a) have a significantly greater difficulty in learning than the majority of children of the same age; or
(b) have a disability which prevents or hinders them from making use of educational facilities of a kind generally provided for children of the same age in schools within the area of the local education authority.
Special Educational Needs can be categorised as:
- communication and interaction
- cognition and learning
- behaviour, emotional and social development
- sensory and/or physical.
It is important to recognise that difficulties can easily fall within two or more of these categories.
What does this mean for a mathematics department?
Melissa Rodd (2005) identifies problems in learning maths under:
- Speech language and communication
- Specific learning difficulties
- Deafness, hearing impairment
- Autistic spectrum
- Emotional and behavioural difficulties
- Moderate learning difficulties
- Physical impairment
- Visual impairment
Beginning to remove barriers to learning
Read about the types of learning difficulty on Folio 1.7.1
Reflect on these difficulties in terms of particular pupils at your school.
Use Folio 1.7.2
to record your thoughts on the actions needed to remove barriers to learning for these pupils.
How can we understand the difficulties and reduce the barriers to learning?
The following task is designed to help you begin to understand some of the barriers to learning that pupils in your school encounter everyday so that you and the teachers in your department can imagine ways to help those pupils overcome those barriers and enjoy learning mathematics.
1. Go to the PBS Misunderstood Minds site and try the arithmetic, spatial and sequence activity. Reflect on what you have learned from these activities about the way that some people could experience difficulties in learning mathematics and what you could do to help.
2. Choose a pupil that you do not teach who has been identified with special educational needs. Research how the pupil’s needs were established. Sit in one or two maths lessons with this pupil and observe how they go about learning. How does the maths department need to react in order to meet this pupils needs?
3. Think about all the special needs identified above, are all the teachers in the department prepared to meet the needs of all the pupils that might be in the school? How could this aspect be improved?
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8. Reviewing the Module
In completing this module you will have:
1. Considered what it means to take a lead on curriculum issues
- where will you take a lead
- what does it mean to lead?
- developing your leadership style
2. Considered critically the nature of mathematics and the essential concepts, processes and skills within it.
- the importance of mathematics
- the nature of mathematics
- mathematical habits of mind
3. Explored some learning theories and their effect on the curriculum
- the main theories of learning
- creating a climate for learning
4. Considered how to assess and monitor the curriculum
- finding out what goes on in the classroom
- who assess and monitors the curriculum?
5. Designed a curriculum by beginning to put a vision together
6. Considered how to design a curriculum to enable your pupils to develop their potential to learn mathematics
7. Explored some difficulties in learning mathematics
- what are special educational needs
- what does this mean for the mathematics department?
- How can we understand the difficulties and begin to remove the barriers to learning?
Each of these sections is intended to add to your knowledge of how to provide an appropriate curriculum for all pupils in order that they might achieve their potential.
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.