High School and Math

[Them Bones]

A few threads ago one member challenged another member with a simple integral. The challenger said that high schoolers should be learning calculus. Well, I agree.

I'm pretty sure most high schools at least offer calculus, which is good.

The problem is, you have to want to learn calculus in order to learn calculus. I failed algebra II in my senior year of high school, now I professionally tutor people in math up through differential equations and linear algebra.

As a culture we are going to have to start holding intelligence and learning above everything else before most kids will want to learn calculus. Until then, us math lovers will just be closet geeks. And even then, there are a lot of people whose minds just dont think along those lines.

Don't think a person is unsophisticated just because they cant wrap their minds around math.

[Le Type Français]

Learning is often cherished more when you get older. In high school, it felt like a chore to do the work. Great teachers also help keep it interesting.

[betheny]

Some people don't have math brains. (I'm holding up my hand.) My brother could do math and chemistry half-asleep, I always struggled with them. Conversely, an English lit paper would kick Del's butt and I could ace them in my sleep.

We used to joke that if we put both our brains together, we would have one excellent one!

[Lindox]

The differences in our brains is the main reason we live in social groups vs. solidarity.

Trying to make a peach tree out of a cherry tree is pretty much a waste of time when both fruits are delicious and nutritious and different.

It's like trying to become left handed when you are right handed. Sure it can be done..but will what you produce from the left hand be as wonderful as if you had used your right hand to it's highest ability?

Maybe if in the schools a persons natural tendencies were more appreciated and developed..we would have more people doing amazing things..instead of dropping out of life. And joining the drug scene and the gangs and other forms of living.

Let's compare say Dr. Wise and say me in the art of science and the brain cells devoted to incorportate the information..I compare these two brains to say the olfactory cells devoted to smell in humans (me) to the olfactory cells devoted to smell in bloodhounds (Dr. Wise).

But I am pretty certain I have a comparative group of brain cells in another area of thought. So go for what you mentally are..instead of fighting it.

[rfbdorf]

Definitely, people have different innate abilities for mathematics, language, social interactions, music, driving, athletics, dress design, you name it. However there are also powerful social pressures at play here - remember the Barbie that said "math is hard" - that direct our interests. That is neither all bad nor all good. I rather suspect that would explain a lot of the difference between you and your brother in terms of math and language skills, Betheny.

Them Bones makes the excellent point that our society needs to encourage learning, and I decry the state to which the active discouragement of learning and disparagement of the learned has brought our country (for example, a presidential candidate who correctly pronounces the word "nuclear" is at a disadvantage with the electorate). On the other hand, has there ever been an older generation that has not said the same?

Them Bones other point - that there is not necessarily a 1:1 relationship between intelligence and learning - is also on the spot. Learning without intelligence is rare (but it happens - I wasn't very impressed with one math Ph.D I knew, and one grad student who worked for me some years ago was pretty bad!), but the converse is the norm. I've known very intelligent people who have had less than a high school education.

Lindox - I agree, but the hard part is finding out what it is for which one is well suited. Social pressures are important here, too, however the society only has a place for so many basketball players. Sometimes an effort should also be placed into finding the area for which one is second-best suited.

- Richard

[rollin64]

reading "MATH FOR DUMMIES" wouldn't do me any good. i need a calculator for most math equations.

[Lindox]

Yes, Richard maybe even three or four specialties.
The problem though that I have seen is a student gets A's in math, art and geography. BUT gets C's and lower in English lit. and say World History.

That student is more adviced on improving the lit and history grades..even though he is celebrated to some degree on his A's his C's become the focus point.

Then in a few semesters his D's and C's may raise to C+'s and C's from D's..but at the same time his A's have lowered to B's. Why is this?

[rfbdorf]

I don't know. Could it be that a side effect of pushing him on the one subject have a depressive effect on the other subject? That is, he hears "I want to see better grades in history" and interprets it as including "I don't care if you get As in math"?

I was very good in math & science in school, just average in social studies. I found history, etc. boring and an unpleasant chore. Now I find it fascinating. If I had had an excellent teacher, I'm sure I would have enjoyed it at the time, and so would have done better.

- Richard

[kate]

Some people don't have math brains.

I don't know . . . I taught it for 12 years, and I think there is always a way to make things clear. In the end I think anybody can learn anything--and at the same time it's possible to make any subject boring.

I had kids who stuck it out through calculus even though their parents would come to conference after conference and tell me that their kids were terrible at math and could I please stop encouraging them!

At the other end were kids whose parents were determined that they be good at this stuff--it was funny, because you could see the kid just choosing to passively resist and play dumb.

I had other kids who didn't even need to open the book to "get it"--I was one of those myself about a zillion years ago, so I had sympathy for them and worked not to let things get tedious.

I think the way learning actually works is that a teacher makes some kind of connection with a student, and then if other baggage doesn't get in the way, together they can fire the old synapses in new ways.

And I still love math--but I love writing more. :)

[Wise Young]

In my opinion, the essential part of mathematics for the public is really a language and should be taught like a language. It is simply a symbolic representation of relationships. Scientists may need a different level of understanding of mathematics in order to use it to describe phenomena and mathematicians need to be exposed to cutting edge thinking in order to advance mathematics but every educated person must be "math-literate" in the same way that they must be English-literate.

The difference of math literacy in the United States and the rest of the world is disappointing. For example, if I show a simple line equation in a lecture in the United States, most people don't recognize it. Even after I describe the equation and point out the y-intercept and slope variables, some still don't get it. So, when I say correlation coefficient, they just don't understand. However, when I show the same equation to a Japanese or Chinese audience, a majority of the audience get it.

I believe that math literacy must be taught in the same way that language is taught. There is a vocabulary, a grammar, and pattern recognition. People must use it, practice it, and apply it to different situations, as much as they can. They must be able to recognize the symbols, the rules of operation, and the correct ways of expressing relationships. A lot of this is rote learning and experience.

When my daughter was going to elementary school, they were teaching at least an hour of English grammar, reading, and literature every day of the week but they were doing math only for an hour 2 or 3 days a week. I urged the school to have a minimum of 5 days of math. In the same way that you cannot master French doing just 2-3 hours a week, you cannot master mathematics with such limited exposure.

Students should not be able to say that they are not mathematically inclined or that math is hard, and allowed to skip math. If a student is unable to read, we treat it as a real problem, diagnose the problem, and put the student through remedial training. We should do the same for math. Not being able to understand and express relationships in mathematical language is a real handicap in the same way being illiterate is a handicap.

In the same way we would not want a student to graduate from high school without being able to read a newspaper, we should not want students to graduate from high schools without being able to understand the symbology of mathematics. Students must have confidence in their ability to understand and use mathematics as if their lives or lives of others depend on it.

Let me give an example. I ask my students to calculate the volume of pentobarbital (an anesthetic drug) to give to a rat, if they have a bottle of solution that contains 50 mg/ml pentobarbital and they need to give 45 mg/kg to a rat that weighs 250 grams. I tell them that the life of the rat literally depends on their calculation and that they have as much time as they want to come out with the right answer. A significant number of students cannot come up with an answer. Many come up with an answer that is an order of magnitude off. Some come up with an right answer but when I press them on it, they are uncertain.

They must have confidence in their mathematics. If they become a doctor, they will likely kill somebody someday because they cannot calculate or cannot recognize a wrong solution to a calculation. By the way, even if they don't become a doctor, they may kill somebody one day because they cannot use mathematics. We use mathematics in everything that we do, whether it is business, engineering, or computers.

Wise.

[Steven Edwards]

I'm bored.

Let me give an example. I ask my students to calculate the volume of pentobarbital (an anesthetic drug) to give to a rat, if they have a bottle of solution that contains 50 mg/ml pentobarbital and they need to give 45 mg/kg to a rat that weighs 250 grams. I tell them that the life of the rat literally depends on their calculation and that they have as much time as they want to come out with the right answer. .045mg/g * 250g = 11.25mg

11.25mg/50mg = 0.225ml

Does the rat live? :)

[Le Type Français]

I agree with Wise. You can make Math understandable and it should be taught like a language.

My Algebra teacher and I had a silent feud going because I used to teach my fellow classmates easier ways to solve problems than the typical way she taught them. But of course, I could have been in the wrong by using shortcuts instead of following the text book formula.

[Lindox]

Dr. Wise has wonderful ideas..now how to implement them to help change our drop out rates.
As the testing shows in the fourth grade 80% are doing grade level and above math..then you get to the eigth
grade and 60% are doing grade level and above..then it just gets worse. Could it be the 20% from the fourth grade were so lost? And another 20% joined them along the way?

It's easy very easy to teach a child that has the aptitude for the subject you are teaching.
Now the hard part is to teach the ones without the aptitude..this isn't being done thus fewer and fewer will go onto the higher forms of math..no matter how you teach it..they won't be there. The same 60% will be there.

By the time a child is in the eigth grade..well if they are too far behind in the basics they will drop out in one way or another. We have the proof of this..now we need the proof of the progressive teaching methods being successful in the learning of math by the 40%.

Just like reading skills..you can test people for anything..but what do you do to change the results of an individuals inability to learn. You can't test that away and that is pretty much what the schools do. Pass the child onto the next teacher/grade..or flunk them and teach them the same thing in the same way and wonder why they still don't get it.

Another future drop out..of course when they start to deal in drugs they will find math interesting. And will know exactly how many bags can be sold from a kilo of coke. Or how to measure the ingredients that are needed to produce crystal meth.

[Wise Young]

I'm bored.

.045mg/g * 250g = 11.25mg

11.25mg/50mg = 0.225ml

Does the rat live? :)

Steven,

Hmmmmm, are you sure? :)

Actually, that is what I say and the students look insecure. I then tell them that they must be certain of their answer because the life of their patient depends on it.

There are two ways of gaining confidence. The first is to go through the calculation as you outlined it, check the assumptions and relationships. A second way is to test the answer in several other ways. What many students have not learned to do is to test the answer to gain confidence in the answer.

For example, let's take your answer 0.225 ml. We know that a ml contains 50 mg of pentobarbital. A quarter of that amount to about 12 mg. If the rat weighs one kilogram, you would give 45 mg to that rat. A quarter of that would be close to 12 mg. Therefore, your answer is correct and I would be willing to stake my life (and the rat's life) on it.

Wise.

[Steven Edwards]

Steven,

Hmmmmm, are you sure? :) Is .99999... = 1? :) (The ... designates a repeating decimal.)

Of course I'm sure. I bet you didn't know that English is my second language; math is my first. :D

[1 Fine Spine RN]

Geeks are hot.

PS Wisey when the rats go into rat pentobarb comas do they get little rat continuous EEGs?

[adi chicago]

to became a good doctor you have to study hard .dr.wise is right.

[Wise Young]

Is .99999... = 1? :) (The ... designates a repeating decimal.)

Of course I'm sure. I bet you didn't know that English is my second language; math is my first. :D

Steven,

I trust your math language skills.

By the way, I wanted Pascal to be my children's second language but it probably would have been cruel and unusual punishment.

Wise.

[Steven Edwards]

Wise,

It could be worse: You could have taught them Hypercard. :eek:

Steven

[adi chicago]

what about 1+1=3 or more.....the biology has the answer .

[rdf]

When I was in college in the 90s, I loved math. I went as high as was available, but calculus (both eng and business) and finite math were my favorites, after algebra. Stats was also fun, and I tutored stats because nobody else in the school could be found to tutor it.

I noticed so many high school kids' in their first year of college get discouraged over math. I'm talking about basic algebra, which it seems some people just can't grasp. I saw so many broken hearted kids who quit school altogether because they couldn't get over the algebra hump, from which most higher math courses use as their foundation.

But there was one teacher, can't remember her name, who'd sit for hours after her work day and help out kids with algebra. She had a really cool method for teaching them factoring, and it seemed to help many of them get over the hump and continue on with their education.

I love math, some hate it, but it's needed in today's world more than ever it was in the past, and I wish there was a way to make algebra easier for those who don't get it right away, or sometimes never...because once a person understands algebra, then IMO they can do any math there is.