In class in week 6 a student answered a question on logarithmic form. The question related to pollution levels in a lake and gave the values of pollution at time t=1 and t=2. Part of the question asked to predict the value at time t=3. One student had converted to logarithmic form, solved the simultaneous equations and built a negative exponential function to predict the value. Her process seemed fine and the answer seemed reasonable (right order of magnitude, etc.). But she had noticed it was wrong; the value she had at t=3 was between the values given at t=1 and t=2. The value at t=3 must be less than that at t=2, since the equation describes a decay. That the student had deduced this really shows an important deep understanding of how the formulae and numbers relate to the real situation.
There can be a tendency in mathematics for the student to believe what the calculator tells them. It is really important when teaching mathematics to those who will be applying it to real situations that they are able to relate the numbers back to the situation they are modelling. It is no good training a plumber who can't tell what's wrong when the calculator tells him to measure out kms of pipe for a central heating system!
