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I think part of the problem with some of the negative views on algebra's value is a fundamental misunderstanding of what algebra really is. It is not "different" mathematics from the 2+3 we all do every day. It is a set of rules and notations that helps us do our everyday mathematics. Algebra helps us see trends and predict the next value. It helps to find relationships between cause and effect. And, it gives people a way to communicate their answers and processes to find those answers with others.
A real problem, though, is that many students are not shown the real life applications of the different techniques. They are just given a page of equations to solve. Happily, there is a movement in the mathematics education world to rectify that and require more real life application problems from students. It is slow going, though, because of the time it takes to teach this way.
I think part of the problem with some of the negative views on algebra's value is a fundamental misunderstanding of what algebra really is. It is not "different" mathematics from the 2+3 we all do every day. It is a set of rules and notations that helps us do our everyday mathematics. Algebra helps us see trends and predict the next value. It helps to find relationships between cause and effect. And, it gives people a way to communicate their answers and processes to find those answers with others.
A real problem, though, is that many students are not shown the real life applications of the different techniques. They are just given a page of equations to solve. Happily, there is a movement in the mathematics education world to rectify that and require more real life application problems from students. It is slow going, though, because of the time it takes to teach this way.
Not too long ago, my physics kids told their trig teacher that they understand trig when I teach it because I show them how to use it while he just showed them formulas.
When i was young i did not know that i wouldn't be catching a pass from Joe Namath to win the game for my team.I didn't know that i wouldn't be moving without the ball,...getting a lead pass from Clyde and then a bounce pass to Big Dave or kicking it out to Dollar Bill while me, Willy Reed and the team crashed the boards.
You know what? I have never used those skills i learned to make one dollar.I am however still physically fit a 50.In a pickup game i'm the guy who can run up and down the court all day long.
I am obviously using an analogy.Exercise your body and be physically fit.Exercise your brain and be mentally fit.No well paid athlete gets paid to do situps,pushups,pullups or jumping jacks.Doing those alot will get them to physical excellence,which increases their chances of being well paid.
If your lazy at youth,....physically or mentally it will follow you forever.
I wish I had a teacher who could show me how to apply it to life. Algebra held me back from getting a degree. I was a product of "new math" as a kid and then attended a private school where math was not high on the agenda so I never learned the basics. I tried as an adult and actually made it all the way to intermediate algebra, after 3 tries, and got half way through that before giving up.
I wish I had a teacher who could show me how to apply it to life. Algebra held me back from getting a degree. I was a product of "new math" as a kid and then attended a private school where math was not high on the agenda so I never learned the basics. I tried as an adult and actually made it all the way to intermediate algebra, after 3 tries, and got half way through that before giving up.
Math anxiety is no fun.
This is why I wish I could find a job teaching math. I can't win here. Everyone looks at my chemical engineering degree and my chemistry/physics combination and, suddenly, my math major just vanishes into the background.
I, originally, interviewed for a math position in the school I teach at now. At the end of the interview, which included teaching a lesson, they said "You'd make a fantastic science teacher". Unfortunately, there's no market for science teachers with my certs. So, I can't get the math job because they see a science teacher and I can't get the science job because I have the wrong certs. This just sucks.
My first choice would be to teach math, precisely, because I can make it real world. 20 years in engineering tends to do that. Kids get it when you make it real life.
Maybe someday if the teacher job market ever turns around. Not happening in Michigan though. The district I live in is laying off 90 teachers. I'll be lucky to have a job at all next year. I just hope I don't have to uproot my family to get back into engineering. I really don't want to make my kids switch schools in 10th and 8th grade.
The doctor orders 600 mg of a medication to be given to a patient by injection. The medication comes in 1000 mg (1GM) vials of powder, which has to be reconstittued with 2.2 ml sterile water. When mixed, the vial holds 2.5 ml of fluid. How many ml should the patient receive?
This is a common problem in nursing. If you work in a hospital, it's possible that the pharmacy will do the computation. However, if you work in an office, you may have to figure this out yourself.
Dumb question, probably revealing my ignorance.
60% of the 2.5 -ml solution, right? 1.5 mls? Please tell me if I've just killed our patient.
Pretty good. You can't get the powder out of the vial without diluting it with the water. So you would mix the powder with the 2.2 ml, give 1.5 ml and discard the rest. It's OK to tell anyone you want. You can't save it for another pt.
Okay, another dumb question because the patient lived.
In what way did I specifically use algebra?
I reasoned that, regardless of everything else, you needed to mix the entire gram of medication with 2.2 ml of water and regardless of everything else, you had as a final solution a 2.5 ml solution containing the original gram of medicine, of which you needed only to use 60%. Therefore, it stood to reason that (assuming the medicine was evenly distributed in the solution), that you'd still only need 60% of it.
Therefore, it became a division problem -- what's 60% of 2.5, or rather, a multiplication problem: What's .25 times 6?
I think part of the problem with some of the negative views on algebra's value is a fundamental misunderstanding of what algebra really is. It is not "different" mathematics from the 2+3 we all do every day. It is a set of rules and notations that helps us do our everyday mathematics. Algebra helps us see trends and predict the next value. It helps to find relationships between cause and effect. And, it gives people a way to communicate their answers and processes to find those answers with others.
A real problem, though, is that many students are not shown the real life applications of the different techniques. They are just given a page of equations to solve. Happily, there is a movement in the mathematics education world to rectify that and require more real life application problems from students. It is slow going, though, because of the time it takes to teach this way.
Yes. This is very true. Throughout algebra, I was told that it was "really important" and "a lot of professions use it," but a) they weren't professions I wanted to go in to, and b) it wasn't clear how algebra was used once you WERE in those professions.
Okay, another dumb question because the patient lived.
In what way did I specifically use algebra?
I reasoned that, regardless of everything else, you needed to mix the entire gram of medication with 2.2 ml of water and regardless of everything else, you had as a final solution a 2.5 ml solution containing the original gram of medicine, of which you needed only to use 60%. Therefore, it stood to reason that (assuming the medicine was evenly distributed in the solution), that you'd still only need 60% of it.
Therefore, it became a division problem -- what's 60% of 2.5, or rather, a multiplication problem: What's .25 times 6?
Not sure how that's algebra?
Your solution is about as algebra as you can get without writing an equation.
What is 60% of 2.5? x = .6 * 2.5 (solve for x)
How did you come up with 60%? Finding an unknown? Well, there is algebra again. Algebraic thinking is exactly what you did without writing out all the equations. Writing the equations has the added benefit of letting us quickly repeat this for different amounts. It also gives us a universal way to quickly communicate how we calculated the correct dosage. And, it would let us work backwards for example to see how much of the powder was in the dosage if we only knew the final amount given.
And, although you were easily able to use common sense to figure it out, many students enter college without that skill. We call it number sense or number literacy. Ideally, students can work the problem on paper using formulas and then check themselves using the common sense you did. The sad thing is that too many students just punch numbers into their calculator and never stop to question the answer. They could have typed in the numbers wrong, not account for order of operations, or set the problem up completely wrong (i.e. add 2.2 ml H20 to 60% of the powder.)
Last edited by cabarrusmom; 12-13-2009 at 02:50 PM..
Reason: format fix
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Not too long ago, my physics kids told their trig teacher that they understand trig when I teach it because I show them how to use it while he just showed them formulas.
Unfortunately, there's no market for science teachers with my certs. So, I can't get the math job because they see a science teacher and I can't get the science job because I have the wrong certs. This just sucks.
