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Have you ever read through a maths textbook from school and wondered what on earth they were talking about?

It’s no wonder problem solving isn’t more streamlined with the ridiculous conundrums they decide hold enough significance to be worth noting for high school maths problems.

Steve has £5.65; four one-pound coins, two fifty pence pieces, three twenty pence’s and a five pence coin. If Steve needs to go shopping and the oranges cost 50p each, the cabbages cost 45p each, and he has to get four oranges and three cabbages – what money does Steve have left?

Firstly, where the hell is Steve’s contactless card? They’ve put the limit up to £100, so can he stop messing around holding the queue up whilst he counts out his germ-ridden pennies?

Secondly, why is Steve shopping if he has to go through this farce every time? He could simply take more than enough money – a nice and tidy ten-pound note – then just accept the change he’s given and move on with his day. He could even, shock horror, do an online shop—an exceptional idea during our times of Covid.

 

Maths problems: The need for context and objectives

 

The real point I’m getting at here is that these problems are infuriating for the rational-minded human. And if a student asks for context, teachers often get impatient as they just want you to answer the question without the need to explain the reasoning behind said conundrum.

And this problem doesn’t stop at school. When you move on to employment – you’re often meant to do the task without asking why. But you can’t solve a problem without context. And every solution starts with a stated objective.

In the case of poor Steve, the rational objective – it would seem from the little context introduced by the somewhat lacking storyline – is that he needs to address his need for nutritional consumption in the form of fruit and vegetable shopping. Reasonable so far. Yes, that’s a requirement of life.

But then, can we not ascertain that the objective is merely Steve shopping. Therefore, the efficient answer here is (as noted above):

  • Use a contactless credit or debit card
  • Take more money than you need
  • Do an online shop

That’s a quick and easy solution to the objective. And – let us not forget – there’s the invention of the calculator in…

Well, I’ll be damned – the first calculator, called the Pascaline, was actually invented in 1642! (Had to look that up). Although, I don’t think you’d want to pull this out at the check out in Lidl, whilst the cashier launches your shopping at you like their auditioning for a part on the Supermarket Sweep team.

Pascaline

But, back to the modern era – who doesn’t have a phone with a calculator on it? In fact, you can just ask Google.

 

Science: teaching maths problems in a useful context

 

When I advanced my education after school, I had a much better experience. Completing a science degree meant that any mathematical question posed was done so within the context of a distinct problem to solve. This, to me, made the subject much more accessible.

When you’re asked to calculate the rate of half-life decay of a radioactive element as you wish to know how long it is until it reaches a safe level – this makes sense. There’s only one solution here, and the problem is something significant worth addressing. Nuclear energy is a clean energy source when it comes to emissions. The problem with it lies in the radioactive waste. Not something to overlook.

Better yet, the context is there. You have a society dependent upon energy to survive in its current economic state. The production of energy has negative consequences for our environment – a system, no matter how inconvenient – needs protecting at all costs, as there is only ONE. So, how do we reduce or eliminate the waste that’s damaging the environment?

nuclear power

Firstly, to understand the importance of the problem, it needs quantifying. So, the question, “how long is the substance radioactive for?” can be further broken down to ask, “and with X quantity, at Y half-life, how long does it take to safely dispose of the by-product required to produce 2 gigawatts of energy?” This is enough energy to power a city the size of New York for 26 minutes – which is also (consequently) how much energy is produced in a thunderstorm 11.4 km above sea level, with an area of approximately 380 km2 and travelling at 60 km/hr.

Something to think about.

Thunder storm

Now, can you see the difference between these two problems? When looked at objectively, they have vastly different solutions. One problem appears worth taking the time to complete a calculation for (and yes, you can even use a calculator if you’re not a maths whizz, the objective is getting an answer). The other is a waste of reasonable time.

What would society look like if we addressed significant problems in maths textbooks that held a worthy objective? No longer would time be wasted on needing to understand why we’re learning how to complete a fruit and vegetable shop in a maths lesson, but instead solve the worlds energy and environmental crisis.

Just a thought.

 

Read more >> 15 Exceptional Quotes from Albert Einstein

 

Advice for the teachers of ASD students

 

So, if you’re a teacher, and you have a student who routinely questions you over the ridiculous tasks you hand out to them (albeit – at the fault of the dictated syllabus material) – please don’t lose patience with them.

Please see that they are – in fact – the sane ones in this society and likely to go on to solve significant problems. Even more so if you can appreciate that they’re just being reasonable in their interrogation of the context to the problem and reward them for it. After all, you can’t solve a problem without an objective. Otherwise, how do you know if what you have is indeed the answer?

 

So, what’s the problem with maths problems?

 

There’s an age-old idiom that best describes the issue with textbook maths problems:

“Ask a stupid question, and you’ll get a stupid answer.”

 

Many people, adults and children alike, with Autism, ASD and Asperger’s, require a context for the problem. Without it, the whole activity is void of meaning. Show admiration for those who question the context, not impatience for their inability to simply “do as you’re told”, which, without wanting to go off on another tangent, is horrific advice. Where’s the advice for children that states:

“Assume a lower base of intelligence for all people (regardless of age) before following instructions. Validate any information relayed through independent research and check the credentials of the informer. If all appears reliable from this point, feel free to come to your own conclusions after whatever amount of independent research seems adequate for the issue at hand. But remember – your decisions and actions are ultimately your own responsibility.”

There – much better advice.

 

Final thoughts

 

I’m sure my daughter’s teachers won’t thank me for such advice. But I am grateful and rest safely in the displays of my daughter’s ingenuity. Every time she comes home from school and relays a conversational dispute, she has partaken in with a teacher or TA, in doing nothing more than questioning some obscure request that they’ve made.

No, I don’t reprimand her. Instead, I explain why, in terms of ‘societal norms’ and manners, some behaviour elicits certain responses and what is deemed an ‘acceptable response’ in the situation. However, I always applaud her for her use of thinking for herself, and to date, she has not raised an irrational question.

 

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