This report, from the Nuffield Foundation, focuses on the crucial period between GCSEs and entrance to higher education, and how mathematical, statistical and quantitative skills develop during this period.
Introductory videos for the Standards Unit: Improving Learning in Mathematics resources featuring Background, Addressing the issues, Developing the approach,The way forward and How to use the resource.
In this DfE Standards Unit resource students learn to interpret and construct distance–time graphs; relating speeds to gradients of the graphs and accelerations to changes in these speeds. Students have often constructed distance–time graphs before. However, experience shows that many still interpret them as if they are pictures of situations rather than abstract representations
In this DfE Standards Unit resource, students interpret linear and non-linear distance-time graphs using the computer programme Traffic. This program provides a simple yet powerful way of helping learners to visualise distance–time graphs from first principles. The program generates situations involving traffic moving up and down a straight section of road. It then allows the user to take ‘photographs’ of this situation at one-second intervals, places these side-by-side, and then gradually transforms this sequence of pictures into a distance–time graph.
In this resource from the DfE Standards Unit, students learn to create and solve their own equations, where the unknown appears once. Most students will have been taught rules for solving equations such as ‘change the side, change the sign’ or ‘you always do the same to both sides’. When used without understanding, such rules result in many errors. ‘Doing the same to both sides’ is the more meaningful method, but there are two difficulties: knowing how to change both sides of an equation so that equality is preserved and knowing which operations lead towards the desired goal.
In this resource from the DfE Standards Unit, students create and solve their own equations where the unknown appears more than once and learn that there may be more than one way of solving such equations.
In this resource from the DfE Standards Unit, students learn to distinguish between and interpret equations, inequations and identities and substitute into algebraic statements in order to test their validity in special cases.
In this DfE Standards Unit resource, students learn to understand the relationship between graphical, algebraic and tabular representations of functions, the nature of proportional, linear, quadratic and inverse functions and doubling and squaring.
This DfE Standards Unit resource enables students to develop their understanding of the laws of logarithms, practise using the laws of logarithms to simplify numerical expressions involving logarithms and apply their knowledge of the laws of logarithms to expressions involving variables
In this resource from the DfE Standards Unit, students explore trigonometrical graphs by recognising translations, stretches and reflections from their equations, sketching the graphs and learning about the period and amplitude
In this resource from the DfE Standards Unit, students convert functions into an appropriate form for differentiating or integrating and then differentiate and integrate negative and fractional powers of x.
In this resource, from the Department for Education Standards Unit, students learn to use past paper examination questions creatively. The questions give them practice in using the equations of motion for constant acceleration and allow them to develop their ability to generalise from specific situations of motion.
In this resource, from the Department for Education Standards Unit, students will learn to understand how Newton’s second law can be applied to a range of different problems. It will encourage learners to link the stages of solutions together and appreciate the purpose and relevance of each stage of a solution.
A collection of ideas from Susan Wall for use in the A-level mathematics classroom. The activities are written in a manner designed to engage student participation, promote discussion and enhance understanding. Each activity is accompanied by teacher notes suggesting how the task should be approached. The tasks are designed to be an integral part of the learning process allowing students to experience the joy of mathematical discovery for themselves.
Cross-curricular work can be incredibly powerful, both in terms of student outcomes and staff Continuing Professional Development. However, it is easy to contemplate, but far more difficult to deliver. Effective planning is the key. At King James’s School, near Huddersfield, members of the mathematics and science departments worked collaboratively to prepare a ‘rockets’ project which was delivered jointly on one of the school’s cross-curricular days, and followed up in subsequent mathematics lessons to provide a high quality and enjoyable learning experience for staff and students alike.