Mastery and the Collins Maths Frameworking resources
What is mastery?
The word mastery in relation to mathematics means that students achieve two related things:
Competence the ability to carry out mathematical tasks fluently and accurately
Confidence the ability to work on an unfamiliar problem and use mathematics to solve it
Research into maths teaching in countries in East and South-east Asia, where students achieve highly
in international assessment tests, have identified a number of features which contribute to mastery.
What does teaching for mastery look like?
The National Centre for Excellence in the Teaching of Mathematics (NCETM) has produced a useful
document (October 2014) outlining the features of a teaching approach aimed at helping students to
Teachers have high expectations of what students can achieve
Students in a teaching group progress through the curriculum content at the same pace,
with differentiation achieved by extra challenge and individual support and intervention
A carefully designed curriculum and well planned lessons build student knowledge in a way
that ensures continuity and progression
Practice and consolidation play a central role in developing fluency and confidence
Teachers use questioning in class to make formative assessments so that misconceptions can
quickly be identified and corrected
What are the implications?
Two things are fundamental:
Teaching resources that provide high quality materials that teachers can use with
confidence. Teacher time is best spent in preparing high-quality lessons and not in producing
A detailed and well-designed curriculum will ensure a logical progression in sequenced steps.
It will make links between different areas of the curriculum content and ensure there are no
gaps in learning.
How do Collins Maths Frameworking resources support the achievement of mastery?
Characteristic Collins Maths Frameworking resources
A structured curriculum
The Frameworking pupil books have been meticulously planned to cover the Key Stage 3 programme of study for the National Curriculum. They provide continuity from Key Stage 2 and progression through Key Stage 3 is carefully structured. Each chapter begins by outlining what students should already know. There is a description of why the content of the chapter is useful and this provides motivation and interest. Learning objectives are given at the start of each section and key words are listed and explained as new concepts are introduced.
Detailed lesson plans
The teacher packs provide detailed lesson plans linked to the sections of the pupil books. They provide class activities to introduce new concepts and to encourage discussion. These activities are varied and stimulating and designed to achieve a high level of engagement from the students. Common misconceptions are described together with strategies for remediation.
Exercises in the pupil book are designed to provide a variety of questions. They range from questions that provide practice and consolidation of a new skill to demanding questions that challenge students to apply their knowledge in different ways. Further similarly varied questions are provided in the homework books. As well as the exercises, the pupil books have additional activities in each chapter. These may focus on reasoning or problem solving or provide a challenging task. At the end of each chapter there is a double-page activity which challenges the student to apply his or her mathematical skills in a new context. This wide variety of resources gives a range of interesting and engaging tasks and fosters both conceptual understanding and procedural competence in the student.
Each lesson plan includes a section of probing questions. These are carefully designed to help the teacher to assess students understanding and give immediate feedback. They can provide formative assessment and enable the teacher to act immediately to clarify any misunderstandings. In this way errors are quickly identified and corrected so that the student can progress with confidence.
Students need to be secure in their knowledge before moving on to a new topic. Knowledge in mathematics is cumulative and if understanding is not secure it will cause problems at a later stage. Each chapter of the pupil book ends with a summary of what the student should know and review questions to assess knowledge. By using these both student and teacher can ensure that understanding has been achieved before moving on.
Supporting excellent teaching The reliability and quality of the Maths Frameworking resources pupil books, student books and teacher packs means that teachers can focus their planning on providing high quality teaching in the classroom. This fourth edition has built on 12 years of feedback and good practice in the classroom. Joint planning is a common feature of high-performing education systems and Maths Frameworking supports this. By looking at the lesson plans together, teachers can ensure that there is a common approach. High expectations can be established and less experienced teachers can be supported so that all students receive teaching of the highest quality.