Values and Variables: Mathematics Education in High-Performing Countries
This report, commissioned by the Nuffield Foundation, addresses two questions: • What is the range and type of research evidence from countries with high performance in mathematics that gives insights into the reasons for their relatively high position? • What constitutes high performance in mathematics learning and…
Mathematics in A Level Assessments
A report produced by the Nuffield Foundation on the mathematical content of A level assessments in business studies, computing, economics, geography, psychology and sociology. In the UK fewer students engage with mathematics after the age of 16 than do their peers in other countries. One way of addressing this issue is to consider…
Key Understanding in Mathematics Learning: Paper 1 Overview
This review, published by the Nuffield Foundation, presents a synthesis of research on mathematics learning by children from the age of five to the age of sixteen years and identifies the issues that are fundamental to understanding children’s mathematics learning. The report concentrates on three main questions regarding key…
An International Comparison of Upper Secondary Mathematics Education: 24 Country Profiles
This report, published by the Nuffield Foundation in 2010, provides an international comparison of upper secondary mathematics education in 24 countries, including England, Scotland, Wales and Northern Ireland. It is based on data collected as part of a research review, which was subsequently validated and supplemented by national…
Global Grant-Making: a Review of UK Foundations' Funding for International Development
This report published by the Nuffield Foundation in January 2012 provides an up-to-date picture of the scale of UK foundation resources devoted to international development. It also identifies how these resources are distributed across region and need, and how foundations approach international funding activities. Commissioned…
Towards Universal Participation in Post-16 Mathematics: Lessons from High-performing Countries
This study, from the Nuffield Foundation, is a follow-up to the report 'Is the UK an outlier?', which examined mathematics education provision in 24 different countries and revealed that England, Wales and Northern Ireland have the lowest levels of participation in upper secondary mathematics. They were the only countries…
Mathematics in A level Assessments
This report, from Nuffield Foundation, presents the findings of a research project which mapped the mathematical and statistical content in the assessment of six A level subjects: business studies, computing, economics, geography, psychology and sociology. Analysis of the summer 2010 examination papers from AQA, CCEA, Edexcel,…
Key Understandings in Mathematics Learning
These resources are provided by the Nuffield Foundation who, in 2007, commissioned a team from the University of Oxford to review the available research literature on how children learn mathematics. The resulting review is presented in a series of eight papers. Paper 1 Overview - summarises findings from detailed analysis of a…
Is the UK an Outlier? an International Comparison of Upper Secondary Mathematics Education
Participation in mathematics education, when it becomes optional at the age of 16, has been a consistent subject for debate in the United Kingdom over the past decade. The research in this resource, from the Nuffield Foundation, addresses a number of questions about policy and participation in upper secondary mathematics education…
Credit Cards
This activity from the Nuffield Foundation shows students how to use a recurrence relation to work out how long it takes to pay off a credit card loan and how much it costs. They can use a graphic calculator or spreadsheet to do the working. After working through the given example, where a customer spends £1250 and repays…
Parking Permits
In this activity from the Nuffield Foundation, which uses a scenario of parking permits at a college to introduce the topic, students learn about collecting data by stratified sampling and designing a questionnaire. A full review of relevant statistical terms is provided, together with instructions of how to select a representative…
Runaway Train
In this activity from the Nuffield Foundation, students carry out an experiment to collect data about a trolley rolling down a slope. They then use this data to simulate the motion of a train by fitting a quadratic curve to their data, using a graphic calculator or spreadsheet. The slideshow provides an introduction to the activity…
Chinese Postman Problems
In this activity from the Nuffield Foundation students use the Chinese postman algorithm, also called the Route Inspection Problem, to solve practical problems. The College Open Day problem provides an introduction to the concept, and asks students to investigate the minimum distance someone would have to travel to deliver leaflets…
Anthropometric Data
This resource from the Nuffield Foundation allows students to investigate relationships between anthropometric variables and write a report on their findings, which may include the use of scatter diagrams, lines of best fit, regression lines, and correlation coefficients. The spreadsheet contains anthropometric data from a sample…
Derivative Matching
The Nuffield Foundation provides this activity which can be used to review students' knowledge of the derivatives of quadratic and cubic functions and their graphs. The slideshow provides an introduction by considering a quadratic example and a cubic example. There are 12 sets of cards, each set containing a polynomial function,…
Ozone Hole
The Nuffield Foundation provides this activity where students suggest types of function to model ozone hole data, before using a graphic calculator or spreadsheet to find at least two particular models. They then consider how well their functions model the data and what they predict for the future. The slideshow includes web…
Gas Guzzlers
The Nuffield Foundation provide this activity which uses graphical methods to find a suitable model to connect two sets of data. There are a variety of ways in which the data could be used, depending on the focus required. It is possible to use a log graph to find an exponential model, which is the intended focus of this activity,…
House Prices Moving Averages
This activity from the Nuffield Foundation introduces the use of moving averages and weighted moving averages to smooth out seasonal fluctuations in UK house prices, enabling the yearly trend to be identified. The data provided is adapted from The Halifax House Price Index spreadsheet and although the arithmetic required to complete…
Successful HE Students
The Nuffield Foundation provide this resource which enables students to carry out significance tests on proportions and test hypotheses about successful applicants to higher education. The data provided on information sheet A is simulated but similar to real data available on the UCAS website. Information sheet B outlines…
Model the Motion
In this activity from the Nuffield Foundation, students match descriptions of a variety of real scenarios involving motion with the corresponding velocity–time and displacement–time graphs. Several issues will be discussed while completing this task and students will also have to consider how realistic or unrealistic…
Cable TV
This activity from the Nuffield Foundation shows students how to use Kruskal’s and Prim’s algorithms to solve minimum connector problems. A cable TV company wants to lay cables to connect the towns, laying the cable along the roads shown on a map of the Isle of Wight. They want to connect all of these towns to their…
Stature
The Nuffield Foundation provide this resource where students use simulated stature data for men and women in eight countries to draw histograms and look for general results, as manufacturers need to take these into account when they design products. This is mainly intended as an introduction to the normal distribution, but the…
Coastal Erosion
The Nuffield Foundation provides this resource which shows students how, given a set of measurements along an irregular coastline, it is possible to approximate the area of land which is lost to coastal erosion over a period of time. Coastal erosion A - this activity uses the context of coastal erosion to introduce the trapezium…
Climate Prediction
The Nuffield Foundation provides this activity which students use to create spreadsheets that model what would happen to the temperature of the Earth if there were to be a sudden change in the amount of radiation entering or leaving the planet. Students then investigate polynomial and exponential functions to find the best model. Before…
Mathematics Reader
The Nuffield Advanced Mathematics reader provided articles as background or extensions to topics covered elsewhere in the course. The aim was to encourage students to make further study of the development and applications of the ideas about which they were learning. This was one of the ways by which the course team illustrated how…
Nuffield Advanced Mathematics Resources File
The Nuffield Advanced Mathematics Resources file provided supporting material for four types of calculator and for the spreadsheet, Excel. The program listings in the calculator sections were designed to be transparent and easy to understand. They followed the algorithms in the Nuffield texts as closely as possible, and they used…
Mathematics, Music and Art
This Nuffield Advanced Mathematics option consisted of two units of work on different themes. A likely model for coursework was that students would develop an aspect of interest from one of the themes into a longer project. There are a variety of types of topic within the chapters of this book. In the ‘Music and mathematics’…
The History of Mathematics
This Nuffield Advanced Mathematics option consists of six units of work, each on a different theme. Students had the opportunity, as part of their coursework, to develop an aspect of interest from one of the themes into a longer project. These topics were chosen to relate the learning in an A-level mathematics course and to deepen…
Surfaces
The Nuffield Advanced Mathematics course took advantage of computer graphics programmes to introduce into the A-level course an option of studying surfaces, their gradients and other properties. This field had traditionally been the subject of first year university courses. Students who attempted this option were encouraged to use…
Discrete Mathematics
A substantial part of this Nuffield Advanced Mathematics option was about algorithms. Students used calculators, or computers with a structured programming language, to turn algorithms into programs. They were introduced to various aspects of discrete mathematics and, in particular, they were shown how many of these relate to important…
Complex Numbers and Numerical Methods
The two units in this Nuffield Advanced Mathematics option were independent of one another, and of unequal in length. ‘Complex numbers’ needed more time than ‘Numerical methods’. The unit on complex numbers developed the arithmetic and geometry of complex numbers and led up to a section on fractals. The…
Statistics
The emphasis in this Nuffield Advanced Mathematics option was on non-parametric methods to help students to gain a good understanding of statistical processes. Students required access to a computer with a professional statistics package to gain the full benefit from this option. Contents 1. Introduction 2. Collecting real…