BodyandSoul vs Standard Calculus 1

                                                  Symbols as signs on a blackboard.

The basic principle of the BodyandSoul mathematics education reform program is unification of symbolic and computational mathematic where symbols are given meaning by computational algorithms. The symbol (or sign) $\sqrt{2}$ thus is assigned to the real number with decimal expansion generated by Newton's method for computing a (positive) root of the equation $x^2 = 2$. Further, the symbol 

• $\int_0^t v(s)\, ds$,   

denotes the function $x(t)$ for $t > 0$ satisfying $Dx(t)=v(t)$ for $t > 0$ and $x(0)=0$, where $Dx=\frac{dx}{dt}$ is the derivative of $x(t)$ with respect to $t$, which is constructed by time stepping according to $dx = vdt$. 

Each symbol as a form of soul, thus is carried by a body in the form of a constructive algorithm defining the meaning or numerical value of the symbol.

On the other hand, in a standard presentation of Calculus, symbols are not defined by constructive processes. For example, the symbol $\sqrt{2}$ denotes an object (some form of number) with the property that $\sqrt{2}\times\sqrt{2}=2$, without however carrying any information about its numerical value. Neither does the symbol $\int_0^t v(s)\, ds$ itself carry information about its value.

Standard Calculus mainly consists of symbolic mathematics as symbol manipulation according to given rules, which is what makes Calculus books so thick, while constructive mathematics and numerical algorithms are used only in (the "few exceptional") cases when symbolics fails.

Unification of soul and body can be seen as an expression science, in contrast to religion separating holy soul (symbol) from sinful body (numerical value).

Discussing these aspects with a Standard Calculus teacher is as easy as discussing realities of immaculate conception with a catholic priest. An example is given by the fruitless discussion with teachers at Chalmers claiming to be "inspired by BodyandSoul" while delivering Standard Calculus, as if the central message of BodyandSoul was missed.