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 X2. SYSTEMATIC TEACHING STRATEGIES FOR AMOUNT OF SUBSTANCE 

Teaching calculations in chemistry or physics, like any other form of teaching, has to be structured to be effective; it has to be logical and it has to be systematic.  Priority order and logical sequence are of the utmost importance.  Should an instructor deliver two facets out of logical sequence, understanding and subsequent learning become more difficult because they make less sense. 

masses

Module C(2020)

Through carefully graduated practice, students/pupils need to gain experience in chemistry of the various calculation types involving first of all single substances, working with:

volumes of gases

Module E(2021)

concentrations of solutions

Module F(2022)

However, much teaching is based on the misguided notion that practice makes perfect.  That is not necessarily so.  Practice make permanent and that fact applies with equal certainty to both good and bad practice.  Incorrect practice will eventually produce permanent bad habits, ones that are virtually impossible to eradicate.

Although  n = m / M  calculations are usually those dealt with first of all, there is no good reason why the order of treatment above cannot be adjusted.  Doing so could provide advantages on the practical front should, say, concentration units be required early on for a reaction rate investigation.  

Dealing initially with the simplest calculations involving solutions or gases removes the requirement to have dealt with molar masses earlier on.  It also provides the opportunity for pupils to see higher numerical values of (amount) concentration manifest themselves in more intensely coloured solutions of  copper(II) sulfate  or  potassium permanganate , for instance.  Such visual stimuli offer

CuSO4_stoppered_phials_two_concentrations.jpg
KMnO4_dilutions.jpg

some physical significance for meaning attached to the derived unit  mol / L,  i.e., varying amounts of solute per unit volume of solution, something which  g / mol  struggles to convey quite so readily.

The main disadvantage in dealing initially with gas volume or solution concentration calculations is that it precludes tackling the progression to two-step calculations requiring molar mass values. This would be the case, for example, either in calculating

(i) the mass of a given volume of gas or

(ii) the mass of solute required to make a given

volume of solution of specified concentration.

Of course, when dealing with gas volumes, an opportunity arises to complement material being covered in corresponding physics classes, where properties of gases are considered.  Such curriculum coordination in chemistry and physics should be routine.

Moreover, the sciences and mathematics departments in schools ought to be in much closer liaison than is typically the case, one of the key themes emerging from a two-year study carried out by Marianne Cutler, funded by the Nuffield Foundation from 2014-16.  The primary document arising from this study should not be ignored.

The Language of Mathematics in Science:
A Guide for Teachers of 11-16 Science

Language of Mathematics in Science - Guide for Teachers of 11-16 Science (ASE 2016)_p1_cov

It identifies:

  • where ideas in secondary school mathematics coincide with their application in the sciences;

  • key mathematical terms and explains these in easily understandable language;

  • good technical practice in applying the ideas of mathematics to science.

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