STEM Knowledge Networks
This booklet provides twelve case studies from STEM Knowledge Networks. These were projects supported by the National STEM Centre in partnership with the National Centre for the Excellence in Teaching Mathematics (NCETM). Schools were required to enable at least two or more STEM departments to work collaboratively by releasing teachers…
Mathematics Within A Level Science 2010 Examinations
A report by Science Community Representing Education (SCORE) designed to address the growing concern across the science community about the use of mathematical assessments in science qualifications. SCORE’s overall objective for this project was to gather evidence on the type, extent and difficulty of mathematics assessed…
Post-16 in 2016
A report produced by the Advisory Committee on Mathematics Education (ACME), published in July 2010, discussing the proposals for 16-19 mathematics in anticipation of the review of qualifications scheduled for 2013 with resulting changes to be implemented from 2016. The report proposes that: • Three Level 3 pathways in Mathematics…
Travelling Salesperson
The aim of a travelling salesperson problem is to visit every vertex of the network and return to the starting vertex using the route that has the minimum total weight. The problem requires students to find the best route for a courier to take to deliver parcels to a number of towns and return back to base. Travelling salesperson…
Route Inspection
The aim of the route inspection problem is to find a route that is as short as possible yet goes down every road once and returns to the starting point. The task informs students that there has been a heavy snowfall overnight and that the students are required to clear the roads in the town centre as quickly as possible, then return…
Planarity
Many topological graphs have edges that cross. The aim is to re-draw the graph in such a way that none of the edges cross. The task informs students they are required to design a printed circuit board and since the wires are not insulated they must not cross. Planarity: presentation - an introduction to the problem outlining the…
Minimum Spanning Tree
The aim of a minimum spanning tree is to connect every vertex of the network using the edges having the least possible total weight. The task requires students to analyse information about a town centre and suggest which roads should be pedestrianized. Minimum spanning tree: presentation - an introduction to the problem outlining…
Matchings
A matching is a set of edges on a bipartite graph in which no two edges share a common vertex. A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y. A matching in a bipartite graph is the pairing of some or all of the vertices in X with some or all of the vertices in Y. If…
Linear Programming
Linear Programming involves creating a function that represents a real life problem. The aim is to optimise this function given certain constraints. Simple examples of linear programming will have few variables and constraints, however, real life situations will have many more variables and constraints that will need to be considered. Problems…
Flows
The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services. The problem involves students analysing the plan of a school canteen and deciding whether, given relevant…
Dijkstra's Algorithm
Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the source to…
Critical Path Analysis
Critical path analysis is a project management technique and is used to lay out all of the activities which are needed to complete a task. Starting some activities will depend on completing others first, while independent activities can be started any time. Critical path analysis helps to predict the project completion time. The…
Bin Packing
The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD. Bin packing:…
Linear Functions
This resource, from Susan Wall, contains a number of advanced level activities designed to practise and strengthen understanding of linear functions. Although students have worked with linear functions at GCSE connections between properties, equations and diagrams are not always secure. At advanced level students need to move from…
Review of Vocational Education - the Wolf Report
This report, by Dr Alison Wolf and published in March 2011, was commissioned to investigate the state of vocational education for young people aged 14 to 19. It was found that many courses offered very little value, offering no route to further education or prospects for meaningful employment. Many prospective students cannot…
Improving Young People's Engagement with Science, Technology, Engineering and Mathematics (STEM)
This paper, published to coincide with Science and Engineering Week 2013, presents evidence from research carried out by the National Foundation for Educational Research (NFER) to explore how to encourage further engagement in, and take-up of, STEM subjects. It discusses why STEM education is important and looks at how policymakers,…
Tunnelworks: Introductory Video
Tunnelworks is a series of teaching and learning resources linking mathematics and science to the Thames Tideway Tunnel project, a major new sewer that will help protect the River Thames from increasing pollution. Background to the project is given in this introductory video which explains when and how the sewer system, which still…
Maths and Science Education: the Supply of High Achievers at A Level
This paper, from the Department of Education (DfE), presented a comprehensive set of statistical analyses building up a picture of the production function for the supply of young people in England with good A levels in mathematics and science. In this way, the questions addressed are focused towards high attainers in these subjects,…
Mathematics: Made to Measure
This Ofsted report is based predominantly on evidence from inspections of mathematics between January 2008 and July 2011 in maintained schools in England. Inspectors visited 160 primary and 160 secondary schools and observed more than 470 primary and 1,200 secondary mathematics lessons. The report draws attention to serious inequalities…
A World-class Mathematics Education for All our Young People
This report was the result of a request to Carol Vorderman from David Cameron and Michael Gove for advice on mathematics education at the time the Conservative Party was in opposition. A small voluntary task force was formed and worked with organisations and individuals (including students and parents) in the course of the completion…
Supporting Scotland's STEM Education and Culture: Second Report
This report, published by the Science and Engineering Education Advisory Group in January 2012, addresses many of the challenges and opportunities arising in implementation of the Scottish Curriculum for Excellence (CfE) as it affects the delivery of STEM education and engagement. It examines the ways in which STEM education may…
Subject Progression from GCSE to AS Level and Continuation to A Level
This report, by the Department for Education, provides an analysis of the proportion of students taking GCSE and progressing to AS Level in the same subject (that is, progression rates), focussing on English Baccalaureate subject areas. The report then follows the same cohort through from AS to full A level achievement. Data…
Second Report of the Independent Review of Teachers' Standards
This report sets out the recommendations of an independent Review of Teachers’ Standards, chaired by Sally Coates. The review was launched by the Secretary of State in March 2011 with a remit to review the existing framework of professional standards for teachers. The Review Group comprises excellent teachers, head teachers…
Ready to Grow: Business Priorities for Education and Skills
This is the third education and skills survey published by the Confederation of British Industry (CBI). The survey provides an authoritative barometer of business opinion on key education and skills issues. It was conducted in February 2010, with responses received from 694 employers, collectively employing over 2.4 million people,…
Educating the Next Generation of Scientists
This report was published by the National Audit Office in 2010 and evaluates progress by the Department for Education in increasing take-up and achievement in maths and science up to age 18. It also reviews the extent to which specific programmes to raise the quality of school science facilities, recruit and retain science and maths…
STEM Careers Review 2010
This review of STEM careers, led by John Holman, was funded by the Gatsby Charitable Foundation in February 2010. The review covered provision of STEM careers education, information, advice and guidance in England. The report focused on secondary and further education, but recommended the need to commence careers related work from…
New Challenges, New Changes: Further Education and Skills System Reform Plan - Building a World-Class Skills System
This document was published by the Department of Business, Innovation and Skills in December 2011, and sets out the programme of work required to take forward the reform of FE and skills system for adults aged 19 and over in England. The report was based on the principles set out in Skills for Sustainable Growth and took account…
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…
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…
Evaluation of the Wellcome Trust Camden STEM Initiative
This report, published in March 2012 by the National Foundation for Educational Research, presents the findings of an evaluation of the Wellcome Trust’s Camden Science, Technology, Engineering and Mathematics (STEM) Initiative which provided funding to eight Camden schools to develop interdisciplinary projects. Projects…
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