“The truly painful thing about the way mathematics is taught in school is not what is missing – the fact that there is no actual mathematics being done in our mathematics classes – but what is there in its place: the confused heap of destructive disinformation known as “the mathematics curriculum.”
This is intimately connected to what I call the “ladder myth”— the idea that mathematics can be arranged as a sequence of “subjects” each being in some way more advanced, or “higher” than the previous. The effect is to make school mathematics into a race – some students are “ahead” of others, and parents worry that their child is “falling behind.”
I think it’s simply that we as a culture don’t know what mathematics is. The impression we are given is of something very cold and highly technical, that no one could possibly understand – a self-fulfilling prophesy if there ever was one. Mathematics is viewed by the culture as some sort of tool for science and technology.
School boards do not understand what math is, neither do educators, textbook authors, publishing companies, and sadly, neither do most of our math teachers. We learn things because they interest us now, not because they might be useful later. But this is exactly what we are asking children to do with math.
Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration. Mathematics is and always has been about ideas. Math is not about following directions, it’s about making new directions. Mathematics is not a language, it’s an adventure.
In place of discovery and exploration, we have rules and regulations. The problem is not that the students can’t handle it, it’s that none of the teachers can. The point is you don’t start with definitions, you start with problems.”
In “A Mathematician’s Lament”, Paul Lockhart