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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?
You can set it up as a proportion problem. I don't know how to show it on the computer, but you end up with X/2.5 = 600/1000. Cancel out your 0s, cross mulitply and you have 10X=15.0, or X=1.5. I don't do those problems that way at work, but some people do.
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%?
The original called for 600 mg of medicine to be administered out of a 1000mg dose. 600/1000 = 60%. Waiting tables and tending bar taught me how to do percentages.
Quote:
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.)
I asked my students to calculate their percentage given #correct/45 total. You would've thought I'd asked them to dissect themselves and remove their own appendices.
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.
When did you begin to study this new math? I think that my brother and I were also part of this experiment. In the Fifth Grade, we were introduced to New Math and it didn't help to prepare us to navigate Algebra 1 in the Ninth Grade like they thought it would. We did finally "get" Algebra, but it was more a function of lots of homework and growing up a bit. I graduated high school in 1974, so wonder if you are in the same generation.
My experience early in my teaching career helped me to understand the issue with Algebra. I had a very bright student who burned through all of her math subjects up until she began Algebra 1. She was only about 12 at the time. She just could not "get" Algebra 1, so I suggested to her mother that we wait six months. After six months, we began again, and she "got it". I think that it has to do with the age at which a brain can begin to understand abstract concepts.
Little children can understand 1 + 2 = 3, but they do not understand 1 + x = 3. Why not? The idea that a symbol replaces a number does not make sense to children, it seems.
The original called for 600 mg of medicine to be administered out of a 1000mg dose. 600/1000 = 60%. Waiting tables and tending bar taught me how to do percentages.
Sorry to not be more clear - that question was a reflective question for you to see how you were solving for an unknown, not asking where the 60% came from.
Quote:
Originally Posted by Charles Wallace
I asked my students to calculate their percentage given #correct/45 total. You would've thought I'd asked them to dissect themselves and remove their own appendices.
How very algebraic of you using an equation with a variable!
Honestly, I am very worried about many of my students' complete lack of math sense. I could go on for pages listing some of the basics that are missing. Multiplication is one example. Third graders here are taught that multiplication means to add over and over. Then they get totally confused when they are taught fractions! Not all students struggle with this, of course, but many do.
Little children can understand 1 + 2 = 3, but they do not understand 1 + x = 3. Why not? The idea that a symbol replaces a number does not make sense to children, it seems.
That is true for some students. What is amazing is how many that cannot tell you what x means in 1 + x =3, can solve this:
It was the battle I did fight and maybe Waterloo? I never did like it but it may of helped me?
I did ignore X and Y maybe I was wrong? Oh well Merry Christmas to the X and Y and the plus and minus! I fought this battle so hard I did end into summer
school when I got a good grade. I had a great teacher also why I could deal with it and get a good mark!
Last edited by maggiekate; 12-13-2009 at 10:16 PM..
I use Algebra, Calculus, Statistics, and Differential Equations on a daily to weekly basis. Even on things like building structures, I find a use for high level math (Calculus, especially) when the object being built is curvy and varies according to height/length/width. It works wonders measuring volume of a cup that isn't a perfect cylinder.
My mom didn't like Algebra, but she says she wished she had paid more attention because as she got better jobs, it required it (this is in regulatory/accounting).
That is true for some students. What is amazing is how many that cannot tell you what x means in 1 + x =3, can solve this:
What number goes in the blank? 1 + ___ = 3
Same thing, just phrased differently!
With my Malay engineering students (who are very weak in Algebra), I use a question mark, and that seems to help them in the same manner as your underscore.
1 + ? = 3
But, of course, engineering students are well past simple addition. Their issues are with algebraic ratios in trigonometry and geometry.
Everyone should gain competence in algebra, statistics/probability....and basic economics and personal finance in K-12
Many of those whose low-skill jobs are shipped away to lowest cost place haven't a clue about why...much like many lib arts college grads who wonder why, despite a 4-yr, $250K college "education", they have such irrelevant skills for a modern, globalized, tech/quant-centric economy
I don't doubt that technical/maths skills are one causitive factor with regard to jobs being shipped overseas, but let's not forget that profit margin also plays but one of many other factors in that issue. College-educated people rightly expect that the extra effort they've provided to go through four years (or more) of college should afford them higher wages as well.
Also consider those folks who are not particularly adept at telling the teacher how Algebra works, yet are incredibly capable workers who are intelligent, hard working, and can figure most anything out using critical thinking skills that are unrelated to their Algebra education (or lack thereof).
Algebra is used in everyday life for sure, but I certainly do believe that maths are being over emphasized with writing and spelling being left in the dust, and to me, that is more problematic when you want to develop "critical thinking skills." IMHO, one needs to be able to accurately assess facts on both sides of an issue before they can come to an informed decision about how they feel on any particular matter.
When did you begin to study this new math? I think that my brother and I were also part of this experiment. In the Fifth Grade, we were introduced to New Math and it didn't help to prepare us to navigate Algebra 1 in the Ninth Grade like they thought it would. We did finally "get" Algebra, but it was more a function of lots of homework and growing up a bit. I graduated high school in 1974, so wonder if you are in the same generation.
My experience early in my teaching career helped me to understand the issue with Algebra. I had a very bright student who burned through all of her math subjects up until she began Algebra 1. She was only about 12 at the time. She just could not "get" Algebra 1, so I suggested to her mother that we wait six months. After six months, we began again, and she "got it". I think that it has to do with the age at which a brain can begin to understand abstract concepts.
Little children can understand 1 + 2 = 3, but they do not understand 1 + x = 3. Why not? The idea that a symbol replaces a number does not make sense to children, it seems.
DD was being quizzed by a sister and her teen daughters when she was four years old and threw this in there. We never taught her how to do this but she got the right answers. It depends on how logical a child is.
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DD was being quizzed by a sister and her teen daughters when she was four years old and threw this in there. We never taught her how to do this but she got the right answers. It depends on how logical a child is.
