Re: Math...
 

Where is the point that we become dependent on the tools that we create and what are the reasons (read that - excuses) that we create for that dependency? And how do those reasons (read that - excuses) ripple out into society and the decisions made as a consequence or result?

Offering some food for thought...

Jane

Re: Math...
 

This is how I was taught until 8th grade...

Re: Math...
 

whip up a simple simulation, crunch a few billion numerical integration floating-point calculations in a matter of seconds, and instantly plot a time-graph of the results (in color!),

create a spreadsheet and play with the inputs to see how they affect the outputs,

instantly plot a complex non-linear equation to visualize its behavior and help find its roots,

do a monte-carlo simulation of a probability or statistics problem,

fit a model to a set of experimental data,

etc etc etc

Using calculators, and especially personal computers, opens up worlds of understanding for those who will use these tools to gain insight, and not as a substitute for thinking.

Re: Math...
 

And you let them????

Is this what is known as a teachable moment?

Next time we are in the same town overnight, introduce me to those students so that I can assist with their education.

I'll teach them the importance of several branches of mathematics, the importance of being good at unassisted arthimetic, and help them figure out whether or not the universe is going to wait for them to wake up and smell the coffee.

I suspect they will remember the lesson for the rest of their lives, and in later years will consider the experience a beneficial one.

Blake
PS: Folks - Red dot me if you care to - Don't be shy - I'll pay attention, but I won't be upset

Re: Math...
 

Interesting. My high school devoted almost 50% of its space to Career and Technical Education. We had an auto shop, a machine shop, a video production studio, a CISCO networking class, classes for all types of computer software...etc. These classes were often the saving grace of those students who hated math and science; they still found a passion and training in a useful technical skill in the CTE department.

Not everyone has a passion for math and science. But everyone has a passion for something, and everyone can become good at anything with enough motivation. The poster in the OP is comparing the brightest engineers in the world of forty years ago to the average schoolchild of today. That's an unfairly biased comparison. We still have NASA today, and the people who work there are still just as bright and passionate.

Also, the students of today have FIRST...:)

Re: Math...
 

Personally, I'm not that great at math and going into FIRST I didn't really care for it. But after working on designing and building a robot and seeing what practical application knowing Algebra, Geometry, and Calculus was and experiencing it first hand and after that I felt that I understood it better.

I think that the issue today is that students are pretty much educated in a vacuum, students learn about the theroy and how to perform it, but not so much the actual practice. Put it this way if you went into FRC and had someone explain how to build a robot without you personally laying hands on any tools, would you have any interest in it?

Going hands-on with a subject sometimes rather than just relying on a textbook is what can get a student to see the value in a subject, the Apollo Program wasn't just a bunch of guys sitting around a table discussing how one would go to the moon it was about actually achieving that goal.

On the slide rule subject, one of those has got to be easier than using some of my TI-83's higher functions

Re: Math...
 

Niether is excelling. I have three daughters who have excelled in mathematics (all have passed through FRC (the youngest still active), but their passion for math predated robotics). Not all current students are math dummies. Not all 1960's students were math geniuses either.

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The journey is the reward. :)


-dave




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Re: Math...
 

In dealing with math this is so true.

I do have to bring up the point though, is it really the student's fault they don't want to do their homework? I am going to quote from a paper I was reading when I clicked into this thread (isn't random coincidence funny?).

By sheer chance I was reading that paper yesterday (I am really taking my time to digest it) when a friend mentioned they were struggling with their math course. Their main sticking point was they did not understand what they were finding, when asked what a derivative was they rattled off some equation they had been told to memorize. Figuring I had just asked the question in a bad manner I tried again by asking what it represented. They merely shrugged and said they didn't know.

I guess, in my mind, students not wanting to do homework is a symptom of something far more disturbing. Math education seems to be so focused on wrote memorization instead of passionate exploration.

Re: Math...
 

This reminds me of some information our team coach likes to tell us, I don't have his sources.

80% of high school drop outs had passing grades. When the reason to their removal was investigated, they said they saw no application to what they were learning.

Re: Math...
 

In my experience, this is a systemic and massive problem that goes back to primary education. People are told "when you see this, do this" because it's easier and faster to teach that way, rather than defining what the symbols actually mean. Once you get past calculus, math gets taught the way it should be, with strict definitions based on other mathematical terms, and it throws so many math whizzes for a loop simply because they got through high school memorizing everything and taking an "if this do that" approach to math. So many students struggle with math classes because they can't make themselves do the what without knowing the why, rather than because they're inherently bad at math.

A bit depressing if you think about it too much...

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Differential equations are covered in two classes at Cal Poly; one professor taught how most teachers would, the other strictly taught using practical examples (even on the first day! So we're making this circuit, which you guys know nothing about, but pretend you do.... Or, An engineer is analyzing the vibration of this beam...). It made quite a difference, and was a heck of a lot more interesting.

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The future is ours to set, change, determine - FIRST has a great way of influencing careers and there are a great many teachers and future teachers that are being influenced, empowered, and entrusted with helping to shape and define this awesome adventure that is the future.

That is no small thing.

Jane

Re: Math...
 

Coming from an above-average math student in HS (whatever that's worth in todays standards...), I think the root of the problem is in the student's willingness to work for their grades.

A few days ago we were working on a worksheet about numerical patterns (Algebra 2). I finished the whole page in 3 minutes while the rest of the class was still on question #2 (Guess why it's so easy - programming for FRC), so the teacher told me to help the 2 students behind me. As soon as I turned around, they asked me "Can I just copy down your answers?". After saying no many times, they finally started actually working on the problems. Still, they would continually try to just copy my answers, even trying to trick me into giving them ("Hey can I have your paper to check my answers to #1-4"), to the point where they were working harder on cheating than on actually thinking about the questions. Think about it: Students in an honors class trying harder to cheat than to figure out the answers themselves. I don't even know why it deserves to be called an honors class.

There also is a problem in the way we see teaching the students. Our district just passed a new rule that says teachers cannot fail students because they don't do homework (basically, if their homework grades put them below the fail threshold, then they still pass the class). We got that rule because too many students have been failing courses for not doing their homework...why don't they come up with some other way to get students to do homework? Or there are other problems like when a student who can't handle an honors class and refuses for come in on their free time for extra help is told by the teacher that the student needs to go to a regents level, the parent then calls and blames the teacher for not helping the student enough and forces the student to stay in honors class (I've seen it happen). What about sports? The rules in our district say that a student can have all their grades be C- (possibly even D+) and still be allowed to participate freely in sports. Why are the expectations so low?

My point is, why does the school and district do so little to provide incentives for the students to do well in their classes and even occasionally provide free passes to students who don't deserve to be in the class at all?

Re: Math...
 

The fact that we're not going back to the moon has nothing to do with education, computation skills or expertise.

We're landing vehicles on Mars. Consider the math involved.

Not going to the moon is a question of funding and political clout / deficits. There is no political will to go back to the moon.