A New Course in Development
Awaken Your Inner Mathematician
From Procedural Mathematics to Independent Mathematical Reasoning
How This Course Came About
This course was born from a deep longing to understand mathematics more deeply.
During my school years, mathematics was explained to me procedurally. However, whenever I wanted to investigate the why behind all the formulas, my questions remained unanswered and were even laughed at. Eventually I stopped asking, and then I lost interest in the classes. I fell behind.
Somehow I managed to obtain a university pass and enrolled for first-year mathematics – still hoping that perhaps here I would find what I was looking for. Wonder of wonders, I managed to pass Math 1 and even Math 2 first semester.
Then I crashed.
My lack of understanding caught up with me, and I couldn’t make the grades no matter how hard I studied or tried.
I ended up completing my degree with other majors but left university feeling like a bigger failure than ever before.
I left mathematics alone and followed other routes, exploring languages, my love for music and spirituality. Then I met Waldorf education and became a Waldorf teacher. It was through the Waldorf mathematics curriculum, and more specifically Jamie York’s work, that the light finally broke through.
At last here was someone who explained the why behind procedures. Where they came from. I saw the beauty behind the structures and was able to connect the dots.
This didn’t mean that I suddenly understood all mathematical procedures – far from it – but I understood the journey. I got a glimpse of the big why. And that made all the difference.
It lit a fire inside of me. Yes, this I could work with. This was the path to deeper investigation into reality. I felt a deep surge of energy and life inside of me and a sense that nothing was more important.
Fast forward many years and the passion remains.
About two years ago, I stopped teaching and was looking for a new direction in my career. I was thinking of pursuing mathematics full time but had to find a way to do this. I loved the why behind mathematics, and when I came across Prof Keith Devlin’s course, Introduction to Mathematical Thinking, I decided to enrol.
I loved every minute of it and decided that I definitely wanted to go much deeper into what he was teaching. I wasn’t sure what form this would take.
Eventually I decided to start a Substack blog focusing on exploring the why behind mathematics. I called it Sacred Math and eventually it became Sacred Mathematics. I started extensive conversations and research with ChatGPT around this topic.
This led to the first articles on Mathematics and Language and Healing Our Relationship with Mathematics. This in turn led to the series of articles on Euclid’s Elements, Book I.
These articles grew into a substantial body of work tracing the development of mathematics from the formation of words to axioms, postulates and definitions, and the building of mathematical systems where conclusions can be derived from logical assumptions by following logical rules.
I started thinking about how different my mathematical journey would have been if I had been taught these things during my school years.
And I started wondering: what would be the best way to make this knowledge available, not only to matric students, but to anyone who wanted to understand the bigger picture when it comes to mathematics?
Eventually I decided on two avenues.
The first avenue would be the articles. The direction here is to map the history of mathematics and its development, and secondly to continue exploring mathematical thinking through the study of Euclid’s Elements.
The second avenue would be the development of a course to aid the transition between school mathematics and university mathematics. The course would also be valuable for anyone interested in going beyond procedural mathematics. It would focus on reasoning skills and could help not only with understanding how to reason mathematically, but also with developing habits of thought that are useful in everyday life.
And so the course Awaken Your Inner Mathematician was born.
Why is this course necessary?
The transition from procedural mathematics to independent mathematical reasoning is a difficult one for many students. The shift from following procedures to understanding definitions, reasoning through arguments and constructing proofs asks for a very different kind of thinking.
This gap is not always easy to cross without support. Students may need more hands-on guidance, more time to work through the thinking process and someone who can help identify where the chain of reasoning begins to break down. This is the gap that Awaken Your Inner Mathematician will attempt to address.
In the following notes, I will explain the difference between procedural and conceptual mathematics and also how mathematical reasoning fits into the picture.
This will enable you to begin to understand the difference between school- and university-level mathematics.