It’s 80% a different subject from what is required in the real world. Computers have mechanised computation beyond previous imagination, yet today’s maths education spends 80% of the curriculum time gaining expertise in hand-calculation methods rather than using a computer to do the calculating. The curriculum is ordered by the difficulty of the skills necessary to complete the calculation, rather than the difficulty of understanding the complexity of the topic. Computational difficulty rather than conceptional difficulty.
The very reason mathematics is seen as so important in education today is because mathematical or computational thinking skills appear so widespread and deeply embedded in all walks of life. But his is a relatively new phenomenon. Before mechanised computing, the use of mathematics above very basic arithmetic was much narrower and only applicable to fields such as some areas of physics and accountancy. It did not work well on anything requiring larger amounts of data, or messier or less immediately quantitative problems. Computers have made this fundamental change and without them many other current and rapidly emerging fields would not exist.
Students solve problems using the Computational Thinking Process (CTP). This is a process in which one creatively applies a four-step problem-solving cycle to real-world problems in order to develop and test solutions. The emphasis is learning how to take real-life situations and abstract them to a computational setting - often code - so that a computer can calculate the answer. Some problems may require going through the cycle multiple times. It is helpful to represent this iteration as ascending a helix made up of a roadway of the four steps, repeating in sequence until “success” is declared.
1) Define Questions
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.
2) Abstract to Computable Form
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.
3) Compute Answers
Turn the abstract question into a n abstract answer using the power of computation, usually with computers. Identify and resolve operational issues during the computation.
4) Interpret 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 redefine.
Our curriculum follows an 11-category draft set out of outcomes to reflect the needs of modern society. Our outcomes follow four core principles:
1. They cover “thinking”
Outcomes should explicitly abstract out the thinking skills needed to tackle real-world problems using real-world technology. Skills like the ability to critique and verify a solution, or to generalise a model.
2. They fit to the Computational Thinking Process
Outcomes come in varying levels of granularity. One outcome might be about the whole process; another might be about one step o fit; another might be about just one small part within a step.
3. They scope beyond individual toolsets
The Computational Thinking Process is iterative, multi-layered and complex. Outcomes should be broad, not limited to the concepts and tools fo a specific problem.
4. They are not dependent upon assessment
If current assessment methodology cannot measure an outcome, that should not be a reason to remove it from the curriculum.
Two key outcomes: Concepts and Tools - the Computational Outcomes. Being computer based, the computational toolset vastly increases in depth and complexity. Levels of “knowing” are substantially different to hand-calculation toolsets. When we think about which actual concepts and tools we should include, we start with actual problems that students need to solve, working back to the concepts and tools they need to solve them.
Our curriculum falls into five broad sectors (although these are by no means strict divisions):
Traditional curricula are built upon outdated collections of mathematical concepts, making them poor representations of the problems people face in the world today. The have taken the reverse approach: carefully choosing a selection of modern, real-world problems, then. Seeing how they map. Across mathematical concepts. By doing this, only concepts useful in the real world make the cut. Our curriculum goes beyond the innovations required in the PISA 2021 Mathematics Framework.
Rather than separately specifying the curriculum and then building deliverables, building deliverables is part of our curriculum specification. Each deliverable, or module, is problem-centred, with students focusing on an overarching question that they can understand. Models can be delivered with the CBM Teacher Platform or as self-study versions, both leading learners through the Computational Thinking Process to solve a problem. Within the compute step, students learn to drive the computer, so coding is integral to our approach. The Wolfram Language has the advantages of being easily understandable and having real-world knowledge built in. At the end of each module, there is a final project where students independently transfer their skills and knowledge to another related context. Each module comes with a certificate of completion and opportunities for assessment of the CBM outcomes.