A little MatheMagic is needed!

The University of Queensland's Faculty of Engineering  held a networking forum for teachers on 5th November 2013. They expressed a number of concerns regarding the High School graduates entering  the first year engineering course, and I think it's worthwhile highlighting one of those concerns here.

The main academic concern is that High School graduates do not have an adequate background in mathematics to cope with engineering. Now, they were very upfront about this, admitting that part of the problem was that they reduced the prerequisite from Maths C to Maths B in order to attract more school graduates to engineering. For those not familiar with the Queensland education "system", students present 6 final subjects, Maths B is one subject and Maths C is a separate , more advanced subject. Previously, engineering hopefuls would study Physics, Chemistry, Maths B, Maths C, English + 1 other subject. Now, they can present Physics, Chemistry, Maths B, English + 2 other subjects. The assembled teachers weren't very sympathetic to start with, why don't you just raise the prerequisite to Maths C again? Until we were presented with examples of the kind of maths some of the students seemed to be struggling with.
One of the examples we were given was that there were students who believed that if
a + b = -1 then that means that a = -b
and that is a huge concern! But raising the prerequisite wouldn't help, simply because any Maths student in senior high school should have no trouble realizing that a = -1 - b

I've had a similar discussion with a friend of mine who is a lecturer in nursing (at a different university). Her complaint is that High School graduates entering first year nursing often have difficulty with calculations involving drug doses. For instance, students have to decide how many tablets to give a patient given that a doctor has prescribed 100 mg of drug A four times a day, and that the hospital supplies brand X tablets each containing 50 mg of drug A.

High School chemistry and physics teachers are very familiar with this problem. There always seem to be atleast a few students in each class who appear to be quite good at maths judging by their report cards, but who don't seem able to handle fairly simply algebra when they leave the maths class.

Now, before the maths teachers start feeling indignant, let me say that this problem is not restricted to maths, and, unfortunately, it isn't even restricted to students. After the Engineering Faculty's presentation, I was chatting to a science teacher who was telling me about developments in the silicon chip industry that required "water that is so pure it is acidic".Curious, I followed up with a few questions, thinking that this teacher may have been using a definition of acid that I wasn't familiar with, but no, this teacher seemed to be using a Bronsted-Lowry definition.

So, the problem in a nutshell is that we are graduating students from schools with reasonable grades in maths who are not capable of rearranging an equation (and the much worse problem that there are teachers teaching science who don't seem to understand the concept of equilibrium and neutrality).
Clearly, any "learning" that has taken place is only at a very superficial level. How can we address this problem?