DIGITAL LEARNING
answer from abstract form using the most appropriate methodology ; and interpret the result in the context of the question . Most curricula currently focus almost exclusively on the third step , which made sense before computers were available , but this is no longer the case ; in the real-world , computers do almost all the calculating , whereas in schools , students bear this responsibility with little delegation to computational tools . The crucial analytical and decision-making process about ways to solve the problem , which information is relevant , and acceptable computational expense , are often unexamined parts of the thinking process .
When scientists were faced with a rapidly emerging pandemic in 2020 , the data were scarce , uncertain , and noisy , but scientists had approximately four decades of mathematical tools developed for other outbreaks to draw from . Thus , the task was as follows : consider the questions of interest , such as the virus ’ transmissibility , which groups were high-risk , and whether to close schools ; evaluate which methods were most applicable to the public health questions of interest ; compute the required answers with as much accuracy as possible given the constraints ; and interpret these answers for policy-makers , whilst acknowledging the strengths , limitations , and uncertainties within the methods and results . If we distil this process to its core components , we arrive at the four-stage Wolfram ( 2020 ) model for how mathematics curricula should evolve in the age of AI . Again , this is not to render current curricula entirely irrelevant ; for students pursuing careers in STEM subjects , computers can only be programmed if the programmer sufficiently understands the mathematics behind the code , but the key point is that not all students are being prepared for the mathematical demands of post-school life by current curricula .
Encouragingly , two sixth form courses are beginning to recognise this gap . In the IB Applications and Interpretation course , students are required to use technology to solve practical problems , and although the execution is currently limited , future iterations of the course hold great potential .
In my opinion , however , the best and most progressive UK curriculum is the Further Pure with Technology option within MEI A level Further Mathematics . This module covers investigating properties of curves , exploring differential equations , and number theory , but does so with a greater emphasis on understanding and interpreting mathematical problems than simply undertaking routine calculations , and students are required to use Python to solve questions that would be too time-consuming or challenging by hand . In this module , “ the emphasis is on students having an understanding of the mathematics and for the technology to support them in this ” ( Lee and Button ,
2020 ) and is a direct response to the Smith review of post-16 mathematics , in which use of technology was highlighted as a key priority to respond to a rapidly-changing world ( Department of Education , 2017 ). In 2024 / 25 , the Mathematics Department at Sevenoaks School will pilot a new Year 8 curriculum that follows the progressive ethos of the Further Pure with Technology option by teaching students how to code in Python and requiring them to use their programming skills , plus AI and other technology , to solve open-ended mathematical problems and , where possible , check these by hand ; if successful , the plan is to extend this approach to more sets and year groups .
As technology advances and computers can readily automate tasks previously undertaken by humans , it is crucial for education to evolve at the same pace . Students should be empowered to assess how they can work with technology and evaluate ‘ who does what ’; in essence , we must educate them about how to simultaneously exploit the strengths of human thinking with the power of computational doing .
DEFINE questions
1 2 ABSTRACT 3 COMPUTE 4 INTERPRET
Think through the scope and details of the problem , defining manageable questions to tackle . Identify the information you have or will need to obtain in order to solve the problem . to computational
Transform the question into an abstract precise form , such as code , diagrams or algorithms ready for computation . Choose the concepts and tools to use to derive a solution . answers
Turn an abstract question into an abstract answer using the power of computation , usually with computers . Identify and resolve operational issues during the computation . results
Take the abstract answer and interpret the results , recontextualising them in the scope of your original questions and sceptically verifying them . Take another turn to fix or refine .
Figure 1 . Wolfram 2020
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