What I did about the math...
Okay, so sometimes a thorny problem turns out to be deceptively simple.
The math difficulty that I was describing below was more a problem with the children's division skills than it with their ability to calculate an average. You see, I had all the kids walk as fast as they could for the length of the hallway (distance = 42 m) while a friend timed them. They came out with a number in seconds and hundredths of seconds, which we rounded to a whole number to keep things relatively simple. Then they divided distance by time. This is where the problem started - many of the kids are still accustomed to dividing and getting a remainder (2 r 4 m/s) rather than continuing to divide and getting a decimal answer (2.2 m/s). But if you have a string of numbers like 2 r 3, 2 r 7, 3 r 1, finding the average is really tricky, and the kids rightly asked me how to do it. Most knew how to compute an average using whole numbers, they just didn't know what to do using numbers with remainders.
So, I decided that the simplest solution, and best for their long-term ability to do useful things with data, would be to learn how to divide out to decimal places rather than using a remainder. I taught the whole class how to graph their data on a distance-time graph, then I asked those students who had used remainders or wanted a brush-up to sit at the front three tables, and moved the kids who already knew how to divide using decimals to the back to start making their graphs. I taught the front group the steps to divide out to tenths of a m/s, we did a couple together, and then they spent the rest of the period recalculating the speeds.
I'll see when I get their lab reports whether or not it worked, but I think it did for most of them. I realized when I thought about it more that they already knew the steps for long division, and they really just needed to be shown what to do with the decimal point and how to add zeroes so you can "bring down the zero." We talked briefly about how 42 is the same as 42.00, and then we just went ahead and started dividing.
I see it as an important part of my job to incorporate math into science class, but I really prefer to let them learn new ideas in math class, and just to reinforce what they've already learned and to demonstrate the ways that scientists use math in my class. I don't feel like that's a cop-out, I think it's just realistic.
The math difficulty that I was describing below was more a problem with the children's division skills than it with their ability to calculate an average. You see, I had all the kids walk as fast as they could for the length of the hallway (distance = 42 m) while a friend timed them. They came out with a number in seconds and hundredths of seconds, which we rounded to a whole number to keep things relatively simple. Then they divided distance by time. This is where the problem started - many of the kids are still accustomed to dividing and getting a remainder (2 r 4 m/s) rather than continuing to divide and getting a decimal answer (2.2 m/s). But if you have a string of numbers like 2 r 3, 2 r 7, 3 r 1, finding the average is really tricky, and the kids rightly asked me how to do it. Most knew how to compute an average using whole numbers, they just didn't know what to do using numbers with remainders.
So, I decided that the simplest solution, and best for their long-term ability to do useful things with data, would be to learn how to divide out to decimal places rather than using a remainder. I taught the whole class how to graph their data on a distance-time graph, then I asked those students who had used remainders or wanted a brush-up to sit at the front three tables, and moved the kids who already knew how to divide using decimals to the back to start making their graphs. I taught the front group the steps to divide out to tenths of a m/s, we did a couple together, and then they spent the rest of the period recalculating the speeds.
I'll see when I get their lab reports whether or not it worked, but I think it did for most of them. I realized when I thought about it more that they already knew the steps for long division, and they really just needed to be shown what to do with the decimal point and how to add zeroes so you can "bring down the zero." We talked briefly about how 42 is the same as 42.00, and then we just went ahead and started dividing.
I see it as an important part of my job to incorporate math into science class, but I really prefer to let them learn new ideas in math class, and just to reinforce what they've already learned and to demonstrate the ways that scientists use math in my class. I don't feel like that's a cop-out, I think it's just realistic.
posted by ms. v. at 12:25 PM
3 Comments:
sounds like a reasonable solution, and their math benefits.
Warning - I'm getting out my soapbox:
NYS has been shifting the borders between math and science in strange ways, and both areas have lost out as a result. I am at the high school level, and am more aware of the bizarreness there.
- On the Math B exam, students are expected to add force vectors or displacement vectors using the law of cosines, rather than by resolving into components.
- Again, on the Math B exam, over ten percent of the points on last June's exam could be lost for rounding errors, (traditionally rounding had ben taught in science).
- On every HS Math Regents exam since 2000, students have been instructed to round to arbitrary places and ignore rules of significant digits.
- On every high school math regents since 2000, between 10 and 20% of the exam has been made up of questions from earth science, biology, chemistry, or especially physics.
At regular intervals I pose to the State the necessity of coordintating thier standards and content for math and science so that we are not REQUIRED to teach mutually contradictory things in math and science classes; I will ask the State's math contact person the same question next weekend.
In the meantime,
it would be good to talk to the math people you teach with to help dilineate where your school's boundaries should be. in some cases you may find that math teachers are not allowed to teach math that the kids need (i am not making this up) and that the math teacher would love you to review a particular skill.
math and science teachers need to talk more, much more, and not assume that we know what the other one is doing.
Ahem, stepping off my high horse, I know that many teachers are busy up to here and barely have time to sleep, plan, grade, and eat, let alone engage in extra conversations with equally harried colleagues. But if time can be found... It's one of my issues, sorry for running on.
Jonathan
ps. this new format forced me to open a blog accuont to comment? not sure if i will use it yet
it's to prevent comment spam, sorry about that
not a problem, and sorry about the rant.
We'll se if I actually start a blog. Scary stuff.
Jonathan
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