Difficulties often emerge while students have to recognize a structure of a complex formula. In particular, it is difficult for students to
- use the brackets to parse the formula from handwritten form to one line form, e.g. for programming ;
- see the steps that should be done first while rearranging a formula;
- use substitutions in chain rule or while solving equations.
Decoding work done
Step 1: Identification of bottleneck
Students have difficulties while recognizing a structure of a formula, not being able to collapse and expand expressions, e.g. not seeing the difference between e^(x^2) which can be collapsed to e^t and (e^x)^2 which can be collapsed to t^2. Some students believe, that to square a+b means to square the elements a and b because they do not think that the sign + is important.
Desired outcome: Students should be able to decide on the essential structure of the formula and read it using operator names, e.g. (a+b)/(2x) is a quotient between the sum and a product. They should be able to blend out the complexity and propose a similar formula/equation with numbers, e.g. C=4 π K R_1R/( R_1−R) with respect to R is like 1=2x/(3-x) with respect to x.
