What is the nature of the mathematics curriculum?
- How would you describe Maths?
- What is vital to knowing about Maths?
- What would you describe as mathematical thinking?
What is mathematics?
Mathematics as habit 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 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.
Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy.
Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all pupils when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Children who are functional in mathematics and financially capable are able to think independently in applied and abstract ways, and can reason, solve problems and assess risk.
Mathematics is a creative discipline. The language of mathematics is international. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.
Reflect on the Importance of Mathematics. The above 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?
John Mason is Professor of Maths Educaiton at the Open University. Listen to him reflecting on The Nature of Mathematics (length10.39) John – so what is mathematics learning? John strongly believes that generalisation is the key to negotiating through the world – seeing the general through the particular and seeing the particular in the general. As you listen, make some notes about what John is advocating for the classroom. Do your learners have multiplicity of perspective? Listen to this further reflection (length 10.23) John – The Nature of Maths. John talks about three worlds, the material, virtual and symbolic. He believes in the importance of the power to imagine and the power to express what we imagine.
Developing mathematical Habits of Mind in primary-aged children
For each habit of mind identify how you could recognise it in children in your class and how you could help them to develop it. This activity can be downloaded here.
Review the notes you made while listening to John Mason. Do you feel inspired to make any changes in your classroom? Record your thoughts on mathematics as a habit of mind in your Personal Learning Space. If you use the activity in a staff meeting, how do your ideas compare with your colleagues?
If you would like to find out more about mathematics as a habit of mind, read the Mathemapedia entry Habits of Mind, or you can download it in full from the Educational Development Center website.
The National Strategies site offers this definition of mathematics.
Record your thoughts about this definition of mathematics in your Personal Learning Space. What surprised you? What raised questions for you? How could you find the answers to your questions?
Carry out an internet search on the definition of mathematics. Put the words ‘define mathematics’ into a search engine of your choice and browse the results.
Record your thoughts about the further definition of mathematics in your Personal Learning Space. Did any of the additional definitions surprise you or raise further questions? How could you find the answers to your questions?
Why is mathematics important?
The 2004 report into mathematics education Making Mathematics Count, led by Professor Adrian Smith, offered several reasons why mathematics is important:
The acquisition of at least basic mathematical skills - commonly referred to as "numeracy"- is vital to the life opportunities and achievements of individual citizens. Research shows that problems with basic skills have a continuing adverse effect on people's lives and that problems with numeracy lead to the greatest disadvantages for the individual in the labour market and in terms of general social exclusion. Individuals with limited basic mathematical skills are less likely to be employed and, if they are employed, are less likely to have been promoted or to have received further training.
Mathematics is of central importance to modern society. It provides the vital underpinning of the knowledge economy. It is essential in the physical sciences, technology, business, financial services and many areas of ICT. It is also of growing importance in biology, medicine and many of the social sciences. Mathematics forms the basis of most scientific and industrial research and development. Increasingly, many complex systems and structures in the modern world can only be understood using mathematics and much of the design and control of high-technology systems depends on mathematical inputs and outputs.
Mathematics provides a powerful universal language and intellectual toolkit for abstraction, generalisation and synthesis. It is the language of science and technology. It enables us to probe the natural universe and to develop new technologies that have helped us control and master our environment, and change societal expectations and standards of living. Mathematical skills are highly valued and sought after. Mathematical training disciplines the mind, develops logical and critical reasoning and develops analytical and problem-solving skills to a high degree.
Mathematics makes an extensive contribution to society, and has always done so. The study of mathematics develops the mind, honing the cognitive skills desired by many employers. Proficiency with mathematics is a significant life skill.
Children begin to acquire basic mathematical skills from an early age. The Early Years Foundation Stage and Primary curricula extend and develop these skills. The ability to analyse information and to solve problems are key skills embedded in the primary curriculum. These key skills are in demand. Children leave primary school well equipped to make further progress towards success in the global marketplace.
The mathematics curriculum
In the EiML materials Core Responsibilities (Primary): Developing a common purpose and a shared culture, you will have considered whether all teaching staff have a clear sense of why mathematics is important for the development of all children. At what level did you place your school? If you have not yet studied this section, it would be useful to do so now. If you have already studied this section, review progress made to date and consider next steps.
Do all teaching staff have a clear sense of why mathematics is important for the development of all children? Is progress being made? What are the next steps? Who is responsible for ensuring that progress is maintained? What is your role in this and your next steps? Record your thoughts on your school’s position in your Personal Learning Space.
In the EiML materials Key Elements (Primary): Curriculum and Lesson Planning you will have worked through an effective structure for mathematics curriculum planning. Following this structural approach will have helped you to reflect on the nature of the mathematics curriculum.
Revisit the notes you made when you reflected on the nature of the mathematics curriculum. Has your thinking developed further? Record your thoughts on your school's position in your Mathematics Subject Leader file.
The Primary Mathematics Framework was considered to be a spiral curriculum. The Mathemapedia entry Spiral Curriculum considers just what a spiral curriculum is:
A spiral curriculum is constructed to help the learner revisit, extend and deepen their knowledge, understanding and skills. Using a spiral model for a mathematics curriculum is often thought to be helpful in helping learners make greater progress in their learning.
A spiral curriculum is based on the principle that efficient and effective learning is a matter of overlaying multiple layers, multiple exposures to the same ideas but getting ever deeper and richer. A spiral curriculum arranges that the same topic, the same idea, the same mathematical theme
, is encountered many times, each time slightly differently, or probing more deeply.
The framework See–Experience–Master
was formulated to act as a reminder to teachers that learners don’t master ideas on first exposure. They require ongoing experience over time so that they become more and more familiar with the idea and its ramifications. This fits with the framework Manipulating–Getting-a-sense-of–Articulating
which can act as a reminder that it is through manipulating confidence-inspiring familiar objects that learners can get a sense of the meaning and import of a conjecture or assertion, and that over a period of time their attempts to refine how they articulate that sense can become more and more succinct and sensible. [see alg-babble
A spiral curriculum
contrasts with a step-by-step mastery curriculum [see mastery learning
] in which each step is mastered before proceeding.
Reflect on what you have read about the spiral curriculum. How much of what you have read do you agree with? How much do you disagree with? Was the new primary mathematics curriculum a spiral curriculum?
Does what you have read about the spiral curriculum have implications for your own practice? Record your thoughts in your Personal Learning Space.
What is a rich task?
A phrase you will often hear when teachers and practitioners talk about mathematics is ‘Rich Tasks.’ So just what is a ‘Rich Task’? And does the term have any relevance in the primary sector?
‘I would describe a rich task as having a range of characteristics, offering different opportunities to meet the different needs of learners at different times. What is also apparent to me is that much of what it takes to make a rich task "rich" is the environment in which it is presented, which includes the support and questioning that is used by the teacher and the roles that learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent, assertive constructors of their own understanding who challenge and reflect. On its own a rich task is not rich - it is only what is made of it that allows it to fulfil its potential.’
Having read this description, you might be surprised to hear that the writer goes on to talk about Key Stage 4. If this is a good description of what a rich task is, then the term does indeed have relevance in the primary sector.
The writer of the above definition offers more detail in an article on the NRICH site. Jennifer Piggott lists some of the characteristics of a rich task (or good problems). She goes on to explain that it is for the teacher to look at a task and recognise its potential then present it in a way and in a forum which makes it "rich".
The NRICH site also offers a series of professional development resources designed to support embedding rich tasks into the KS1/2 curriculum. Activity 1.1 in this series is called What makes a task rich? The series goes on to examine higher order thinking skills, using rich tasks in the classroom, integrating rich tasks into the curriculum and finally, reflection and review. All are appropriate for reflecting on the nature of mathematics and the mathematics curriculum. Browse the materials and assess their suitability for use in future professional development meetings in your school.
If you would like to explore Rich Tasks further, read Mathematics Knowledge Networks (MKNs) - Exploring rich mathematical tasks. The project is an investigation into what constitutes a rich mathematical task and what kind of tools, resources and classroom practice can support the use of such tasks in classrooms.
Discuss what you have found out about Rich Tasks with a member of your senior management team. Consider any evidence of rich tasks being used in mathematics in your school. Could this be a way of developing the mathematics curriculum in your school?
Could some work on Rich Tasks in professional development meetings be a way of developing the mathematics curriculum in your school? Would you be happy to lead some sessions on this area or would you prefer to invite someone else to lead the sessions? What would the role of the senior leadership team be? What would your own role be – before, during and after the professional development meetings? Record your thoughts in your Maths Subject Leader file.