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During the week of 11 July, the Cambridge Mathematics team will be sharing a great deal of our work. We will explore some of our design principles, describe a variety of implementations of the Cambridge Mathematics Framework, and give educators the opportunity to engage with a range of our resources. We will also be talking about how educators, policy makers and colleagues around the world can access our services.
Cambridge Mathematics works in partnership with teachers, schools, districts, jurisdictions, ministries, and research institutes. The team offers support in any and all areas of maths education including professional development, curriculum review and design, policy formation and thought leadership. This is achieved through maximising the experience and expertise of the team as well as using the Cambridge Mathematics Framework, which is based in evidence and research, as a foundation on which to build.
Two crucial characteristics of our consultancy work are its bespoke and collaborative nature. Anything we do is not an “off the shelf” product; we work closely with partners to ensure that we understand their aims and purpose, and the challenges they face. This helps us ensure that the outcomes meet the objectives and have an impact. At the same time, we challenge and question choices from a mathematical and educational perspective while our partners contribute their knowledge of their individual situations, so that together we come to informed decisions. This also means that we don’t have the answer – we present ideas to, collaborate with, support, and enable others.
In the last few years, we have worked with educators across the world using the Framework as the basis of our advice and support. This has included the development of curricula from scratch, the design of scope and sequencing documentation to form the basis of new textbook schemes, and the redevelopment of course outlines.
One element of this range of collaboration is curriculum review, where we consider collections or entire sets of learning objectives, creating connections between individual statements and the Framework’s waypoints.
Figure 1. A small selection of curriculum statements (in purple) connected to waypoints within the Framework
Initially this can mean creating minimal maps, connecting in content that we feel is explicitly stated in the learning objective or statement. These maps are then explored and qualitatively analysed – we search for connected and unconnected content, for agreement or disagreement with orderings, and explore how a curriculum collects and connects content.
This may include looking at a particular topic or subsection in a particular grade or year, or the development of a topic over several years, or the entire content of one year.
Figure 2. A larger collection of curriculum statements specific to one college-level calculus course mapped to waypoints within the Framework
Often these minimal maps are disjoint, where natural steps between learning objectives are not identified.
Figure 3. A mapping of curriculum statements within a topic, showing different connected sub-collections of waypoints, unconnected waypoints and a mismatch in the learning statement ordering when compared to the Framework
This doesn’t necessarily mean that more needs to be added; the additional information may be presented in teacher guides, resources or other means. Through exploring the connections and pathways joining them we help organisations decide if adaptations need to be made within and between particular topics, as well as within and between teaching years. Often this results in reworded learning outcomes.
To learn more about how these ideas have been implemented in a range of situations do join us during Journey Week.