How Difficult?

It seems to me that the advent of calculators many years ago and their widespread use in secondary schools has caused a steady erosion in basic math skills and the understanding of math in general.
Some of the high school students that I teach are often unable to comprehend basic math concepts related to fractions, decimals, and percentages.

So how difficult would it be for a random adult to perform the calculation 12/0.125 and come up with an answer in their head within 15 seconds?

Would it be more likely for someone to be able to do this, or to be able to achieve an undergrad Math or Physics degree assuming they work extremely hard and only need a bare minimum pass?

[Bez]

96

The question is easy if you recognise 0.125 as 1/8. If it was 12/.123, I don't know many people who could do that in their head without a pen and paper in <15 seconds. But I think most people could learn with enough practice. In comparison I think less than 50% of people could complete a physics degree.

[ QUOTE ]
It seems to me that the advent of calculators many years ago and their widespread use in secondary schools has caused a steady erosion in basic math skills and the understanding of math in general.

[/ QUOTE ]
I think calculators are a scapegoat here; the real culprit is poor teaching methods. A similar decline has occurred in grammar and spelling.

The problem is a lack of rigour. Learning this stuff requires disciplined practice, putting people on the spot regularly, and demanding mastery of each of the basic skills before moving up. Having this kind of training has benefits beyond maths class as well.

[ QUOTE ]
The question is easy if you recognise 0.125 as 1/8. If it was 12/.123, I don't know many people who could do that in their head without a pen and paper in <15 seconds. But I think most people could learn with enough practice. In comparison I think less than 50% of people could complete a physics degree.

[/ QUOTE ]

I think you kind of missed my point a bit here. I wouldn't expect anyone to be able to do the question if it was 0.123 instead of 0.125. I'm just curious what percentage of people would be able to recognize 0.125 as 1/8, divide by a fraction correctly, and know their 12 times table all within a short period of time. I don't think it would be as easy as you say assuming no prior knowledge of what the question would be like. I think your 50% is a bit high, but I think more people could do the undergrad degree than answer that question without paper/pencil. I'd be surprised if more than 10% of the general population could do it.

[ QUOTE ]
It seems to me that the advent of calculators many years ago and their widespread use in secondary schools has caused a steady erosion in basic math skills and the understanding of math in general.

[/ QUOTE ]
I think calculators are a scapegoat here; the real culprit is poor teaching methods. A similar decline has occurred in grammar and spelling.

The problem is a lack of rigour. Learning this stuff requires disciplined practice, putting people on the spot regularly, and demanding mastery of each of the basic skills before moving up. Having this kind of training has benefits beyond maths class as well.

[/ QUOTE ]

I agree with you to a point. Still, the focus of Math education has changed a bit in the past 10-15 years. Where 20 years ago students needed to draw their own graphs and perform more rudimentary calculations, todays curiculum focuses more on using technology such as graphing calculators and spreadsheets to supposedly prepare students for the reality of the work place. Contrary to this, most University math professors don't allow students to use calculators at all on their tests.

I do agree that the amount of rigour and practice has decreased. Students are asked to "think" on an abstract level to solve word problems without a firm grasp of the basics.

[ QUOTE ]
I think you kind of missed my point a bit here

[/ QUOTE ]
I saw what you were saying, wasn't sure if it was deliberate so I change my initial reply. I agree with your 10% figure.

Do you really believe <50% of students could pass a math/physics degree? I'm surprised at that. Having done one myself (finished three years ago) and spent three years tutoring, it is difficult, but perfectly amenable to hard work with quality teachers. The standards for passing are ridiculously low.

[ QUOTE ]
The focus of Math education has changed a bit in the past 10-15 years.

[/ QUOTE ]
Whatever the focus, this basic teaching should be completed by the end of Year 7. A thorough grounding in basics is best done at a young age. That's precisely what the first seven years of school are for.

[ QUOTE ]
Students are asked to "think" on an abstract level to solve word problems without a firm grasp of the basics.

[/ QUOTE ]
I like the quote marks. IMO all students do is memorise certain abstract concepts that are fed to them. It's basically a memory exercise. It's not designed to develop or sharpen skills, but rather to impart a 'math vocabulary', if that makes sense. As a tutor nearly every student I've come across has appallingly underdeveloped problem solving skills. A couple of weeks of putting them on the spot and drilling them hard, and they're tacking new material on their own. And starting to enjoy learning. There's absolutely no reason this can't be done in the classroom.

Regardless of what the focus of math education is today, so little extra time is required for mastery of basic concepts that the two shouldn't be mutually exclusive. But it does require a dedicated and skilled teacher willing to step on some toes. [img]/images/graemlins/grin.gif[/img]

Not all who could pass math could pass physics.

I don't think the inability to recognize .125=1/8 means people are incapable, it just means they are not quick with numbers. So, while I believe your example is flawed, I agree with your sentiment.

[ QUOTE ]

Not all who could pass math could pass physics.

[/ QUOTE ]

It seems to be the general sentiment of this board that University level Physics is more difficult than Math. It's funny, as that wasn't my experience at all. I did equally well in high school Math and Physics, but did significantly better in Physics at University. Part of it might have been that I had better Physics professors who made the courses more interesting and enjoyable. I also enjoyed and excelled at the laboratory component of the Physics classes.

[ QUOTE ]
Do you really believe <50% of students could pass a math/physics degree? I'm surprised at that. Having done one myself (finished three years ago) and spent three years tutoring, it is difficult, but perfectly amenable to hard work with quality teachers. The standards for passing are ridiculously low.

[/ QUOTE ]

I think it depends on what you mean by "student" If you are talking about anyone starting school at the age of 6, I believe it's much much lower than 50% If you are talking about a high school student who has made it as far as grade 12 and is doing matriculation level courses then your estimate might be close. Even then, I think it is a bit high.