How much mathematics do we need today?

arthwollipot said:
Obviously, some professions need more understanding of mathematics than others. The question was "how much mathematics do we need today?"

Anecdote alert: I can get by with basic arithmetic, because I'm not an engineer, a scientist or a programmer. I've never encountered a situation in my life where I've needed even the simplest algebra. I've yet to see a good argument for me to learn more mathematics than I already know, especially since I don't appear to be particularly good at it (I stumble somewhere before simultaneous equations). Seems to me that people who are already interested in, and good at, mathematics tend to gravitate towards those professions where they can use that ability. The rest of us make coffee for them.

Actually, the rest of us do a lot of valuable work. Just not mathematical work. :D
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As others have pointed out you are using mathematical skills and 'doing' mathematics practically every hour of every day of your life... maybe you just dont realise it (or more likely for the general public dont recognise it as such).

When my kids ask me about algebra my first explanation is "finding something you dont know" - you paid for a choccy with a fiver and got £2.20 in change...how much did it cost? does that stack up against your expectations?

Deciding on a route - decision mathematics (or graph theory)

Working out if you can cross the road before being splatted by the car - kinematics and probability

Putting your lunch in the lunchbox - very difficult problem in maths - packing

we could go on throughout your daily routine...

Whether you choose to accept or recognise it as mathematics is another matter...

You can also extend this argument to much higher level mathematics but of course most people cannot use this in their day to day life because they dont understand it and therefore cant see its use or application!

(today one of my further maths students was asking me about cardiods and we got side tracked into art, design, logos, print briefs etc)
 
How many people use mathematical logic when packing a lunchbox? I just put the biggest thing in first, then pack the smaller things around it without worrying too much about working out how many square centimetres a banana occupies.

Process like this can be mathematised, in order to find an ideal solution. That's what your GPS does when it finds a route for you. Me, I just go whichever way seems best at the time. It might not be the most efficient way, but I rarely stop to think about what is the most efficient way. There's no need, even before I had GPS.

I don't calculate the position of the ball before I catch it. Though this is technically a mathematical process, I don't use maths to catch the ball. I just catch it.
 
DrDave said:
You've never needed algebra? I find that hard to believe.

If you've ever worked out anything like "I have $500, and need to pay $300 rent and $50 a week for food. How many books can I afford to buy each week if they are $7 on average and it's 2 weeks till payday" you're algebraing.
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Ain't there apps for such algebra, I know there is Gutenberg for free books.
 
arthwollipot said:
How many people use mathematical logic when packing a lunchbox? I just put the biggest thing in first, then pack the smaller things around it without worrying too much about working out how many square centimetres a banana occupies.

Process like this can be mathematised, in order to find an ideal solution. That's what your GPS does when it finds a route for you. Me, I just go whichever way seems best at the time. It might not be the most efficient way, but I rarely stop to think about what is the most efficient way. There's no need, even before I had GPS.

I don't calculate the position of the ball before I catch it. Though this is technically a mathematical process, I don't use maths to catch the ball. I just catch it.
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But that is my point.

I would contend you ARE using maths... you may not sit down and write out some stuff on a piece of paper (and likely neither would I)... but you/your brain/your body is using mathematics and the skills involved in mathematics to solve that problem.

Mathematics is more universal than most people would perceive (in my opinion)...

Some examples just from yesterday (contrived slightly in that I am a maths teacher)...

One of my Further Mathematics girls was asking for help on sketching cardiods... investigating this led us into a discussion on spirals, the logos of certain companies, how to specify fully the shape of the curve to protect a trademark and to produce a design brief..

Another was asking about asymptotes and we got side tracked into a discussion on zero sheep in the field as opposed to no sheep in the field..

Another was asking about simultaneous equations in solving a problem in buying combinations of items in the way that would be the best value for money

One class was looking at lottery numbers and the frequency in which they came up and starting to look at whether knowing that can effect future outcomes and therefore influence their potential winnings

My year 10s were working out the length of a go kart track using circles and sectors.

Some younger ones were working out how much paint they need to paint their bedroom, how much it would cost, how to build in some contingency plans for estimating the amounts correctly, what was the best way to buy the paint...

We also looked at ratios in recipes
Understanding the ticket prices on a car parking ticket machine
Working out profit margins for a cafe
Estimating journey times on a visit to family members
Looking at the cheapest mobile phone tariff
Looking at bus timetables
Working out the cheapest way to buy soap powder
Working out how long it takes to heat some water up
Working out how long it takes to empty a sink



Ok, fair enough, my Year 7, 8, and 9 all had end of year tests this week and my Year 11, 12 and 13 are all in their exam period, but the point is this was JUST the discussions I had in a single day.

My wife is the best person to ask probably. She constantly bemoans the way in which I have to incorporate maths and science into the most mundane aspects of life!



Also.. on Wednesday our girls had a talk from a bloke at Cambridge University about how to gain entrance to the top unis in the UK. He was constantly banging on about mathematics (A level maths and Further Maths)... it struck them quite a bit when he listed the top things they look for in arts and humanities entries - english lit, history, geography and maths. He explained why .. it wasnt just about the direct skills, it was about the way it taught you to think, to rationalise, to analyse, to model, to experiment, to trial, to solve, to break down, to generalise, to prove.. a logical, systematic method...

Take a look at the following (and related articles from that link) and see if you are still convince you dont need/use higher maths in everyday life.

http://www.mathscareers.org.uk/viewItem.cfm?cit_id=382712
 
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DazzaD said:
But that is my point.

I would contend you ARE using maths... you may not sit down and write out some stuff on a piece of paper (and likely neither would I)... but you/your brain/your body is using mathematics and the skills involved in mathematics to solve that problem.
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Nope. When I catch a ball, that's muscle memory and physical training. Purely physical. Ask any baseball player whether they even know what a parabola is. I'd bet that not one of them calculate an x2 in their heads when they catch a fly ball. Instead, they rely on their physical training. The path of the ball can be calculated mathematically, but no-one does that when they're catching it.
 
I use math, including simple calculus and statistics quite often. I haven't solved a differential equation for a while though. I do really enjoy what some expertise in a good spreadsheet program lets you do these days.
 
arthwollipot said:
Nope. When I catch a ball, that's muscle memory and physical training. Purely physical. Ask any baseball player whether they even know what a parabola is. I'd bet that not one of them calculate an x2 in their heads when they catch a fly ball. Instead, they rely on their physical training. The path of the ball can be calculated mathematically, but no-one does that when they're catching it.
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My point is you are using maths at some level. Of course neither of us would sit and calculate the path using projectile mechanics.. but you know the ball wont swerve back up, you can predict its path by the very nature of its parabolic path, and of course experience and practice improves this but nonetheless you have an inkling of what to do the firs time you go to "catch a ball" or something new as an adult because of the predictive and analytical nature of the maths involved.

Maths is more than just writing sums down on a page.
 
How much mathematics do we need today?

6.5 grams per day is enough for most people. Higher amounts may cause cancer.
 
DazzaD said:
My point is you are using maths at some level. Of course neither of us would sit and calculate the path using projectile mechanics.. but you know the ball wont swerve back up, you can predict its path by the very nature of its parabolic path, and of course experience and practice improves this but nonetheless you have an inkling of what to do the firs time you go to "catch a ball" or something new as an adult because of the predictive and analytical nature of the maths involved.

Maths is more than just writing sums down on a page.
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Okay, clearly we're talking past each other here. :rolleyes:
 
On second thought, I would like to amend my earlier post as follows: The value of mathematics reaches across so many disciplines within the sciences, the crafts, the arts, business and virtually all aspects of everyday life. So, I have no idea why one would not want to know as much mathematics as he/she has the time and capacity to learn. In addition (for some of us) mathematics is also rewarding in and of itself.
 
arthwollipot said:
Obviously, some professions need more understanding of mathematics than others. The question was "how much mathematics do we need today?"
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Yes, and as I said, if you go back to post #36 most of Myriad's examples don't apply to any particular profession.
 
arthwollipot said:
Nope. When I catch a ball, that's muscle memory and physical training. Purely physical. Ask any baseball player whether they even know what a parabola is. I'd bet that not one of them calculate an x2 in their heads when they catch a fly ball. Instead, they rely on their physical training. The path of the ball can be calculated mathematically, but no-one does that when they're catching it.
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How to catch a ball in a two dimensional world (Up/down and back and forward)
1. Look at the ball. If it is moving downwards accelerate forwards.
2. Look at the ball. If it is moving upwards accelerate backwards.
3. Look at the ball. If it will hit you within seconds get ready to catch the ball, then catch it. Exit the ball catching routine.
4. Go to step 1.


No maths involved.

Edit. Upwards and downwards refer to the angle you see the ball.
 
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rjh01 said:
How to catch a ball in a two dimensional world (Up/down and back and forward)
1. Look at the ball. If it is moving downwards accelerate forwards.
2. Look at the ball. If it is moving upwards accelerate backwards.
3. Look at the ball. If it will hit you within seconds get ready to catch the ball, then catch it. Exit the ball catching routine.
4. Go to step 1.


No maths involved.

Edit. Upwards and downwards refer to the angle you see the ball.
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I've hilited some of the maths for you...
 
rjh01 said:
How to catch a ball in a two dimensional world (Up/down and back and forward)
1. Look at the ball. If it is moving downwards accelerate forwards.
2. Look at the ball. If it is moving upwards accelerate backwards.
3. Look at the ball. If it will hit you within seconds get ready to catch the ball, then catch it. Exit the ball catching routine.
4. Go to step 1.


No maths involved.

Edit. Upwards and downwards refer to the angle you see the ball.
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The algorithmic approach is a key mathematical skill.

It may not say "learn how to apply the skill of algorithmic ways of thinking" in most mathematics exam syllabus but nonetheless it is something that is "taught" in mathematics.

Looking at the ball requires the concept of position, which probably relates to a coordinate system of some kind.

The movement involves some sort of translation, or angle approach, or vectors.

Acceleration obviously is a vector quantity that depends upon looking at changes in velocity with respect to time (calculus, rate of of change of one variable with respect to another).


I think, in this thread, the opinions are skewed by each persons personal interpretation of what "maths is". Those who have not had the luxury of studying maths at a high level may have the misconception that it is solving hard sums or doing big calculations or adding 50 different terms in an algebraic expression. In my experience the higher the level of maths studied the wider the appreciation of just what maths is.

(e.g. why is a negative number times a negative number a positive number in school? why? what blooming use is that? who would use that now in real life?)
 
arthwollipot said:
Nope. When I catch a ball, that's muscle memory and physical training. Purely physical. Ask any baseball player whether they even know what a parabola is. I'd bet that not one of them calculate an x2 in their heads when they catch a fly ball. Instead, they rely on their physical training. The path of the ball can be calculated mathematically, but no-one does that when they're catching it.
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Am I right in thinking that the top baseball teams do hire sports scientists to aid their training and skills?
 
Roboramma said:
Yes, and as I said, if you go back to post #36 most of Myriad's examples don't apply to any particular profession.
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So graphics programming, circuit design and game design are things that everybody is expected to be able to do?

Home improvements I will grant, but only inasmuch as it is basic arithmetic, with perhaps a little trigonometry or very simple algebra.
 
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