I finally figured out how to format code nicely. Kudos to Blaine for posting HTML showing some properly indented code, which I plag^?^?^?^? researched to fix all my previous posts.
PS: Yes, Tom Lehrer again, this time the Lobachevsky song.
Sunday, March 06, 2005
James referenced my post on innumeracy, and some of the comments in his blog made me think about doing numbers in my head.
I thought that I like doing it, and I also remembered some of my classmates who definitely didn't like it.
The comparison brought the question: what is it that I like about it? At first I felt it but couldn't put it into words - a feeling of excitement, of being able to see through the fog. And now I have it.
Being able to do numbers like that allows me to firmly grasp onto my own ideas and onto what I think about the world. To me, the world without mathematics is like life without language.
And it's full circle back to distinctions, to putting labels onto each distinction, how meaning is derived from the relationship between these distinctions. Numbers are labels of a set of distinctions that, on aggregate, have many interesting properties. If you know the properties, then whatever you label in terms of numbers also has the properties. Think of it as thinking in terms of traits - you have the "numbers" trait, and the richer it is, the more understanding you can get from applying the labels to things that are labeled differently.
To us humans, it's all about the labels and the distinctions. That's why Smalltalk is so cool: it gives you a lot of freedom to do label/distinction management stuff right out of the box. It is geared towards letting you think in powerful terms. That's why I like it so much.
While I don't see exactly how this is fun for me, the fact that it is fun remains.
Posted by Andrés at 21:53
I had the opportunity to read this today:
According to the No Child Left Behind Act, schools are required to give the military each student’s name, age, address and phone number. No other organization has access to this information besides the military, and military recruiters cannot be barred from recruiting in any school event.
Besides considering this is an invasion of my family's privacy, I find this disturbing because most of the targets of this advertisement, our sons and daughters, cannot use math in real-life, life-threatening problems. How can they make the decision to join properly?
I wonder how much do innumeracy and joining the armed forces correlate with each other.
Now go back to the early 60s and listen to Tom Lehrer's Send the Marines. It appears we have not learned much.
Posted by Andrés at 14:06
Wednesday, March 02, 2005
I usually quote that about 30% of the US adult population cannot deal with percentages, and that about 20% cannot even work out a change for a purchase. But tonight I wondered where did those figures come from.
After a while of Google, I found this table of mathematical proficiency of 8-graders for the year 2000 compared to 1990. I was unable to find the most current data, or data for 12-graders, but even then the numbers hurt big time to read. Go down to the bottom, and you will see that if you are supposed to be proficient at math to the point that you can use it on real-life problems, you need to be in the column that says proficient or above \4\. If you fall into the two columns to the left, you cannot use math for real-life problems.
Now this is data from 2000, but again I do not think that things have changed that much since then. Look at the first four columns. If from 1990 to 2000 it is the case that average proficiencies have not improved by more than 10% in general terms, I think it's more or less safe to assume they have not improved more than 10% in general terms from 2000 to 2005. So what follows should be more or less accurate to within 10%.
Now let's take some examples of what the data in the table means.
In 2000, the state with students with the best mathematics proficiency percentage was Minnesota with 40%. That means that the best we could do in 2000 was 60% of 8-graders unable to apply mathematics to real-life problems.
This is a sorry state of affairs. But there's more.
The District of Columbia, where so many important decisions are made, produced just 6% of mathematically proficient 8-graders in the year 2000. Isn't it scorchingly painful to realize that, where things like taxes are decided, 94% of 8-graders could not apply math to real-life problems? Only Guam and American Samoa scored lower, with 4% and 1% respectively.
Other states score double-digits, except Mississippi with 8%. So the national average, considering the population of each state, is somewhere between 1% and 40% - let's say 25%. Are we really ok with 75% of mathematical lack of proficiency?
I wish I could find the data for adults, because some books mention that 4-graders usually score above international average, 8-graders usually score equivalently to international average, and 12-graders usually score worse than international average.
The responsibility to take care of what our previous generations have built and worked for is falling on progressively weaker shoulders. That responsibility calls for mathematical proficiency because of things like our yearly individual and national budget.
So without the skills, what can we expect to be successful at? And before we put all the blame on students or schools, see also how we have managed to get textbooks written.
How is this going to be different from Europe's Dark Age? Keep in mind that this time we have nuclear weapons to play our crusade/holy inquisition games with.
Posted by Andrés at 20:39