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Do your students actually know their calculators that well?
Of course. We give them a ti83 or 84 as freshman, which they use in their math class, their science class and their naval science class every year.
We are thinking of switching over to ipads instead of the tis since they have all the same functionality plus the textbook thing. The only thing we are still debating is the problem with standardized tests. No ipads on those.
Do your students actually know their calculators that well? And how could you say compound interest is irrelevant? Because all your students are on free lunch and will never have a savings account? It is required to graduate from HS in Arizona, and it probably is in many other States, as well.
Compounding interest problems are irrelevant in SCIENCE class, which is exactly what I stated. No where did I say they were irrelevant in general.
Maybe you should work on your reading comprehension skills, instead of trying to prove how superior you are in math. I am fairly certain people need that skill too.
Do your students actually know their calculators that well? And how could you say compound interest is irrelevant? Because all your students are on free lunch and will never have a savings account? It is required to graduate from HS in Arizona, and it probably is in many other States, as well.
It is irrelevant to the content the person is teaching, not irrelevant to life......
Anyway the key to the problem you posted is not calculator vs. no calculator. The answer is dependent on knowing what the terms annually, and compounded every six months mean.
The formula for compound interest is (1+i)^n. This certainly can be done on a calculator. It can also be done in a spreadsheet. The real key is making sure that you convert the annual interest rate to a semi annual interest rate before you solve the problem.
A few weeks ago, I submitted a problem on this forum, and asked if your kid could do it. We had an interesting discussion, a few people could do it, others argued about terminology, but no one stated their kid could actually do it. Here is another on from the Arizona Standards for high school Math.
My parents can both do it, but I don't think their grandkids can.
Here goes:
Maria opens a savings account with 300 Dollars. The bank will pay her 2% annually. Interest will compound every 6 months. How much will be in the account at the end of one year?
Go ahead, let them use their calculators. They will still (likely) miss it.
i don't get it. Are you arguing against the use of calculators????
Using them too young means they won't properly develop a mathematical mind. however by highschool that part of instruction should be over and they should be instructed on how to use calculators because that's what they'll be expected to in the real world.
I briefly worked for an engineering firm in which we manufactured seals for pumps. you are expected to use complicated computing programs to ensure the seal fits just right... down to one thousandth of a millimeter sometimes.
If my boss saw me doing these calculations in my head or with a pen and pad i'd be fired on the spot. that's not how real life works any more. understanding how to use these devices is important.
besides your whole question is slanted. the reason why children would mess this up is because most kids don't know what it means to compound a 2 percent interest semiannually.
this isn't a problem because of calculators. this is a problem because most children today lack basic life skills like balancing a check book, doing your taxes, changing your motor oil, etc. I remember in college my roomates flipped a circuit breaker while using a blender. i came home and all the lights were out in the kitchen. they told me they had called an electrician!!!! i went down and flipped the breaker back on and told them they were beyond helpless and should be ashamed.
so the real issue with kids not knowing how to do this problem is their lack of understanding of the context... not their use of calculators.
I'm arguing against people who think the calculators are an alternative to understanding Math(s). The AIMS Test doesn't allow calculators anyway. My point is that even with the calculators, most students cannot do these basic business problems. Heaven forbid they make them learn their times tables like the successful generations before them. People that handle money would also get terminated for doing change in their heads, it sure would be good to know if the machine is correct. The others have also pointed out the difficulties with keystroke sequences. It is simply better to have a thorough understanding of numbers and not have it swept under the rug and dismissed as unimportant.
I'm arguing against people who think the calculators are an alternative to understanding Math(s). The AIMS Test doesn't allow calculators anyway. My point is that even with the calculators, most students cannot do these basic business problems. Heaven forbid they make them learn their times tables like the successful generations before them. People that handle money would also get terminated for doing change in their heads, it sure would be good to know if the machine is correct. The others have also pointed out the difficulties with keystroke sequences. It is simply better to have a thorough understanding of numbers and not have it swept under the rug and dismissed as unimportant.
The key to doing this problem correctly does not lie with the calculator though. There are terms that you need to know (annual, compounded every 6 months) that determine whether you do this problem correctly. I worked in finance for years and I have an MBA in finance and any interest calculation will be done by calculator or spreadsheet (because it won't be as simply as the one you presented). The key to getting the correct answer does not lie in knowing how to do ARITHMETIC, but in knowing the correct way to set up the problem. The calculator can only help with the arithmetic it can't tell you HOW to do the problem, which is what you need to know.
For instance, my financial calculator will calculate an mortgage payment for me. I don't need to know the formula (although it is easy enough to look it up). The key to getting the right numbers is in the inputs. The ANNUAL interest rate needs to be divided by 12. The number of payments is 360 for a 30 year mortgage. Doing the arithmetic is just tedious it isn't really the key to getting the right answer though.
i don't get it. Are you arguing against the use of calculators????
this isn't a problem because of calculators. this is a problem because most children today lack basic life skills like balancing a check book, doing your taxes, changing your motor oil, etc. I remember in college my roomates flipped a circuit breaker while using a blender. i came home and all the lights were out in the kitchen. they told me they had called an electrician!!!! i went down and flipped the breaker back on and told them they were beyond helpless and should be ashamed.
After working with young (age 20-25) people for the past 3 years, this scenario doesn't surprise me at all. I'm actually impressed that your roomates called an electrician and not 911 or the fire department!
All but a few of those that I have worked with do lack basic life skills. They seem to have no common sense whatsoever. I'm not entirely sure that they even know how to read. They certainly don't know how to spell or do any kind of basic math calculations.
You can't just hand someone an advanced calculator and expect them to know how to use it. There has to be a fundamental understanding of the formulas and how to apply them in order to use the calculator to solve problems. I don't think they have that fundamental understanding.
As stated by others this particular example is not ruled by calculator or no calculator, but instead by knowledge of how the process works.
When I was growing up my parents and grandmother were in the real estate business. It was their job to compute compounded interest and submit the spreadsheet to the buyers of the house. It was NOT expected for the buyers to know how to do that themselves. I learned from my mother how to do it, not from school. Oh and there were not calculators designed to compute formulas when I was in school. Times aren't that much different now.
Now the thing is, I have an 8 yr old son who could compute the math problem without a calculator, if he was shown how to do, so as his brain has an amazing ability for math. The tricky part would be that he doesn't yet have the understanding of interest bearing accounts or interest owed on mortgages, so he would also want that full understanding before he did it and I'm just not ready to go there.
I also have a 24 yr old daughter who teaches high school math. She struggles with getting her students to understand that type real life concept, yet they can solve that type formula problem easily enough. It has nothing to do with calculators....and all to do with real life application.
A few weeks ago, I submitted a problem on this forum, and asked if your kid could do it. We had an interesting discussion, a few people could do it, others argued about terminology, but no one stated their kid could actually do it. Here is another on from the Arizona Standards for high school Math.
My parents can both do it, but I don't think their grandkids can.
Here goes:
Maria opens a savings account with 300 Dollars. The bank will pay her 2% annually. Interest will compound every 6 months. How much will be in the account at the end of one year?
Go ahead, let them use their calculators. They will still (likely) miss it.
My 7th grader can do this problem.
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