Logic in puzzle solving

Maths is a method for solving problems and puzzles using logic. When I was at school we were encouraged to reason our way through a maths problem, and taught to write out the problem again and again as we reasoned our way through them. I would like to show an example of a maths problem from Chemistry. It deals with mols. ( The weight in grams of Avogadro's number of atoms of a chemical). This is considered to be so difficult that it has been removed from the double award science specification (syllabus). But approached in the right way it is simplicity itself. All that the student must learn is that a chemical formula is not a shorthand for the name of the chemical but represents a SPECIFIC QUANTITY of that chemical. Then using the chemical equation for a reaction, the pupil can determine what weights of the products are created by what weights of the reagents, a feat that is accomplished simply by looking up the weights of each element involved on the Periodic Table and adding them together. Thereafter it is just verbal reasoning along the lines of:
100g of Calcium Carbonate produces 44g of Carbon dioxide
therefore: 1 g of Calcium carbonate produces 44/100 g of Carbon dioxide
therefore: x g of Calcium carbonate produces 44x/100g of Carbon dioxide.

Once when I was tutoring a pupil in chemistry the pupil claimed inability to do these calculations. But she was not writing any English along with her numbers. This told me that she wasn't reasoning logically, because doing so involves the use of language. Once I prevailed on her to write out the small amount of English that is contained in the sentences above, she immediately found that she could solve this type of problem. At Puppet Maths we teach verbal reasoning as part of maths. We believe that maths is there to solve real life problems not as some mystery that pupils must be subjected to.