Developing Mathematical Learning For Teachers and Pupils
In England, the current National Curriculum (2014), says, amongst other things: “The expectation is that the majority of children will move through the programmes of study at broadly the same pace. … Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before acceleration through new content.” and Ofsted : “as part pf pupils’ progress inspectors will consider the growth in pupils’ security, breadth and depth of knowledge, understanding and skills.” Ofsted Handbook 2015
This can be challenging. It demands much of teacher’s skills, knowledge and pedagogy. Many teachers will have the necessary in depth maths knowledge to enable them to fulfil the expectations of both the maths Curriculum (2014) and Ofsted (2015) but some may not.
The aim of the Curriculum is to build reasoning, fluency and problem solving into every lesson. Much exposure is needed, at all levels, using concrete apparatus to embed concepts before moving onto written and abstract methods. Once a concept has been thoroughly understood the challenge for the teacher is to broaden the pupils understanding, not to quickly move on to the next ‘topic’. Good questioning skills, and the ability to make links between topics are essential to meeting the aims of the curriculum.
Problem solving is seen by many as ‘word problems’ however it is much, much more than this. Polya ( G. Polya, “How to Solve It”, 2nd edition., Princeton University Press, 1957,) says that it is:
- seeking solutions not just memorising procedures
- exploring patterns not just memorising formulas
- formulating conjectures, not just doing exercises
The final report from the Commission on Assessment without Levels goes on to say
In mathematics lessons, teachers can assess mastery through formative questions that focus on the different aspects of the concept being assessed. The questions can be used to uncover a pupil’s reasoning behind the answers. It can sometimes be helpful for teachers to focus on the wrong answers, which can be used to explore the concept in greater depth and to identify and address any misconceptions
These all have the potential to present a significant challenge to teachers.
Our aim is to support teachers in meeting these challenges, enabling them to develop their own knowledge, skills and pedagogy thereby enabling their students to become resilient maths learners, developing their curiosity, enjoyment and greater success in maths. One of the courses that has been developed specifically to provide this kind of support is Primary Mathematics: Building Teacher’s Maths Subject Knowledge for the New Curriculum. It is a comprehensive four day course designed to improve teacher’s pedagogy, subject knowledge and skills and give a detailed understanding of the requirements of the Maths curriculum. It is an intense course covering in greater depth areas which concern teachers practice; fractions, simple algebra and geometry.
One of the areas of intense focus in Mathematics is Mathematical Mastery. Although the phrase has been used in a number of different ways, it principally denotes a deeper understanding.
The new national curriculum is premised on this kind of understanding of mastery, as something which every child can aspire to and every teacher should promote.
[Final report of the Commission on Assessment without Levels September 2015]
To provide an insight into what is meant by a Maths Mastery curriculum we have developed a course entitled “Mastering Mathematics in the Primary Classroom” It explores ways of delivering maths lessons from a maths mastery standpoint. By the end of the course participants will have insight into:
- what mastery of maths means in terms of the new curriculum,
- how and why to teach concrete and pictorial representations of mathematics,
- how to develop their students deep structural knowledge,
- how to make connections between different mathematical areas,
- how to plan learning that makes the best use of time, puts an investigative attitude at the heart of all maths learning, and meets the needs of the curriculum.
For more information regarding the range of maths courses available to help and support your school, please go to PBM Literacy and Mathematics Courses