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Please see below the answers to some of the questions we have been asked about the Cambridge Mathematics project.
If your question is not answered here, or you would like more information, please contact us.
The Cambridge Mathematics framework is a connected map of the mathematics that students could reasonably expect to encounter between the ages of 5 and 19, although some of the content covers early years (age 3-5 years) too.
No, the framework will be larger than any single curriculum, but content that currently appears in international curricula will be represented within the framework. The framework is informed by research and evidence, mathematics and its applications, and the affordances of digital technology. It is intended as a tool to help people design and develop curricula, resources, CPD and assessment.
Developing the framework is an iterative process and it is changing all the time. Initially, the framework was a set of spreadsheets which rapidly became very complex. The next iteration saw a transfer of the data to a graph database with which the writers interacted directly. More recently, a web-based user interface has been developed to simplify the creation and analysis of content.
Currently the Cambridge Mathematics Framework is hosted on a web page and is powered by a graph database. It has search and tagging functionality and a visualisation window.
We are using Neo4J community edition (www.neo4j.com), an industry standard, open source, graph database management system, and a set of web tools designed in-house for authoring, visualising, and analysing the framework.
Traditionally curricula have been written to be printed out; many curricula mention the importance of connections between mathematical concepts but rarely exemplify them. Our aim, following discussions with experts in the community, was that the framework would capture not only the content itself, but a sense of the connections and the progressions as well. A graph database allows us to capture these connections and generate subsets of the content based on many different criteria, dependent on the intention of the user.
A relational database would also have allowed us to capture connections, but would have been overly restrictive. As our approach is iterative, a graph database suits our needs much better, allowing us to make significant changes to the data structure whenever necessary.
The Framework contains hundreds of nodes and edges that link them together.
Our main type of node is at present called a “waypoint”, which represents a location on the mathematical landscape where a student’s knowledge is added to or adapted.
Each waypoint contains information about the mathematical content as well as a set of student “actions” describing in general terms how the mathematics could be realised through different practices.
We are also developing research nodes encoding the reports, research papers, and expert advice which inform our decisions, plus a glossary of terms to help ensure the language we are using is consistent and accessible.
In the future, we plan to add other nodes to link classroom activities, CPD and assessment directly to our framework.
We are using edges to represent connections in mathematics. Currently we have two types.
Undirected “related to” edges express links between two waypoints that have a shared conceptual basis or common skills/practices.
The second type of edge is directional, expressing a development of or use of ideas.
We anticipate a finer categorisation/delineation of both directed and undirected edges and are in active discussion with the community over the precise nature of the connections we should capture.
At each waypoint, student actions exemplify the content.
Building on the work of the late Professor Malcolm Swan and his colleagues at CRME (Nottingham University) we have adapted their “framework for balanced activities” to describe the skills necessary to understand mathematical content. The list of actions currently comprises Performance, Classification, Representation, Analysis, Argument, Estimate, Model, Solution and Critique.
We are reviewing whether these adequately encompass the ways of interacting with mathematical content.
When publicly launched, teachers and resource developers could use the waypoints and student actions to develop lesson activities that provide a balanced experience for students.
The database will be searchable by keyword, and it will be possible to explore the connections around an individual waypoint, allowing teachers to see how mathematics is linked either as prior knowledge, next steps, or related concepts.
We are working on ways to enable curriculum designers to generate subsets of related content based on a range of criteria. This will help inform a variety of decisions contributing to curriculum design.
Each waypoint will be connected to the research that has informed its development. This could allow us to generate “maps of gaps” showing areas of mathematics education for which we have not identified robust, reliable evidence. Researchers may choose to use the framework to identify topics for further investigation.
We are currently exploring ways in which the content of existing curricula can be mapped to our waypoints. We envisage our framework being used to identify gaps or areas which lack coherence in a curriculum, enabling policy makers to make evidence based decisions when enacting curriculum reform.
If you would like to contribute to the framework, please sign up for our newsletter to be informed of opportunities or contact us.
Work on the project began in 2015 and is initially funded for 5 years. To be kept up to date with news on current development and future plans, please sign up for our newsletter.