Building a Math Curriculum for a Computer-Shaped World

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In the penultimate seminar of our series on interdisciplinary computing, we had the pleasure of welcoming Conrad Wolfram (European co-founder/CEO of Wolfram Research).

Conrad Wolfram

Conrad has been an influential figure in the fields of AI, data science and computing for over 30 years. The company he co-founded, Wolfram Research, develops computer technologies, including the Wolfram programming language, used by the Mathematica and WolframAlpha programs. At the seminar, Conrad talked about his work developing a math curriculum “for the age of AI.”

In a computer room, a girl laughs at what she sees on the screen.

Calculus is everywhere

In his talk, Conrad started by talking about the ubiquity of computing. He explained how computation (i.e. an operation that follows conditions to give a definite result) has transformed our daily life and led to the development of whole new sub-disciplines, such as computational medicine, marketing computing and even computing agriculture. He then used the WolframAlpha tool to give several practical examples of applying high-level computing to problem solving in different fields.

A line graph comparing the population of the UK to the number of sheep in New Zealand.
Yes, there are more people in the UK than sheep in New Zealand.

The power of calculation for mathematics

Conrad then turned his attention to the central question of his talk: if calculus has also changed real-world mathematics, how should school-based mathematics education respond to it? He suggested that since numeracy has impacted every aspect of our daily lives, school subjects should be reformed to better prepare students for the careers of the future.

A diagram indicating that manual calculation takes a lot of time in today's math classes.
Manual calculation methods are time consuming.

His greatest criticism was the use of manual calculation methods in the teaching of mathematics. He proposed that a math curriculum that “assumes computers exist” and uses computers (rather than humans) to calculate answers would better help students develop a deep understanding of mathematical concepts and principles. In other words, if students spent less time doing hand-calculation methods, they could spend more time on more complex problems.

What does computer problem solving look like?

An interesting aspect of Conrad’s talk was how he modeled the process of problem solving using calculus. In all of the problem examples, he pointed out that solving computer problems follows the same four-step process:

  1. Define the question: Students reflect on the scope and details of the problem and define questions to be answered.
  2. Abstract form to computable: Using the information provided, students translate the question into a precise abstract form, such as a diagram or an algorithm, so that it can be solved by a computer agent.
  3. The computer responds: Using the power of calculation, students solve the abstract question and solve all the problems during the calculation process.
  4. Interpret the results: Students reinterpret and recontextualize the abstract answer to derive useful results. If problems arise, students refine or correct their work.

Depending on the problem, the process can be repeated several times until the desired solution is reached. Rather than being offered as a static list of results, the process was presented by Conrad as an iterative cycle that resembles an “ascending helix”:

A propeller representing the iterative cycle of computer problem solving.
The helix model of problem solving.

A program for a world with AI

In the final stages of his talk, Conrad talked about developing a new computer program to better define what a modern math curriculum might look like. The platform that hosts the program, called Computer-Based Math (or CBM), emphasizes the need to integrate computational thinking into mathematics in schools. For example, one of the modules, How fast can I do Stage 7 of An Post Rás?, asks students to develop a computational solution to a real-world problem. After the four-step problem-solving process, students apply mathematical models, computational tools, and real-world data to generate a valid solution:

A module of the Computational Mathematics program from Wolfram Research.
Example of Computer Aided Mathematics module. Click to enlarge.

Among the future challenges he mentioned were how a computer-based mathematics curriculum could be integrated into existing curricula or qualifications, at what age computational mathematics should be taught, and what assessment, training and materials would be needed to support teachers. to offer such a program. study programme.

Conrad concluded the presentation by arguing that today’s need for computer literacy is similar to the need for mass literacy and wondering if the UK could lead the push towards a new computer curriculum suitable for learners growing up with AI technologies. This point provided food for thought during our discussion section, especially for teachers interested in integrating computation into their lessons, and for researchers thinking about the impact of AI in different fields. We are grateful to Conrad for speaking about his work and his mission — long may it continue!

You can catch Conrad’s speech with his slides and the speech recording:

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More to explore

Conrad’s book The Math(s) Fix: An Education Blueprint for the Age of AIgives more details on how he thinks data science, AI, and computation could be integrated into the modern math curriculum.

You can also explore Wolfram Research’s Computer Math program, which offers learning materials to help teachers integrate calculus into their math lessons.

Finally, try Wolfram’s tools for solving everyday problems using math. For example, you can ask data-rich questions to WolframAlpha, which the tool converts from text input into a computable problem using natural language processing. (Two of my favorite sample questions are: “How old was Leonardo when the Mona Lisa was painted?” and “What was the weather like when I was born?”)

Join our next seminar

In the final seminar of our Interdisciplinary Computing series, we welcome Dr. Tracy Gardner and Rebecca Franks (Raspberry Pi Foundation) to present their ongoing work on computer science education in non-formal settings. Register now to join us for this session on Tue 8 November:

We will soon be announcing the topic for a brand new series of research seminars starting in January 2023. The seminars will take place online on the first Tuesday of the month from 5.00pm to 6.30pm UK time.

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Sherry J. Basler