On Sun, Jul 29, 2012 at 8:24 AM, Domenico Rosa <DRosa@post.edu> wrote:
<< snip >>
> Lovanio presented the following two examples of the types of problems that may be used for testing 8th-graders. > > 1. She showed an overhead photo of a house on a lot, with a car parked on the driveway. The students are told that the homeowner wants to re-sod the entire lot. The students are to estimate the total cost. [students are given no information about the dimensions of the lot, house and driveway; and no information about the cost of the sod. Part of the assessment is that students must make estimates about these.] >
I like the idea of "an overhead photo" as that's reminiscent of Google Earth, or any similar terraserver. The ability to rotate and zoom in on a globe made from digital photography, at various levels of detail, is a great boon to education and the positive legacy of the Cold War. The ability to zoom in on one's own school or place of residence, then zoom back for a larger context, is a fantastic addition to our curriculum designs. This ability comes at no extra charge once the Internet is presumed, and sufficient hardware (perhaps recycled).
In a STEM setting, it would be OK to let the discussion digress into whether "sodding a lawn" is the most ethical use or even the most practical use of a property. Here in Portland we have the Food Not Lawns work ethic, which hearkens back to UK lifestyles more. Gardening, raising food, versus squandering resources on purely decorative grasses -- what's "more expensive" in terms of waste and chemicals. You can tell I have my thumb on the scale here, am displaying a bias. Teachers are allowed to have a bias, but students are encouraged to counter the teacher in debate, using the rules of the road (rhetoric). The National Forensic League would love this practice to spread.
If you're in a school where teachers are not permitted to share biases and/or students are not allowed to openly debate teachers, making counter points, then your school's curriculum architects might have been from an inferior race (I use the term "race" as a convenience, without any special reference to genetics or biology, as I don't consider the word "race" as a precise term of science).
> 2. She showed a diagram depicting the circumference of the Earth, with children drawn all around the circumference holding hands with their arms extended. The volume of the Earth is given in scientific notation, and the students are to determine how many students would be needed to go all around the Earth. >
Again, starting with Planet Earth is a good idea. Solving the problem in both meters and feet would be a good exercise. The numbers aren't that bad (roughly (25000 x 5280)/5 for the foot solution).
Of course it's ridiculous to take this literally, as if one could do this in practice. The problem should be addressed in the context of similar stories about how many times one drives "to the moon and back" if an average trucker for 30 years, heart beats per average life time, other such trivia / statistics. It's a genre. To ask out of context would seem daft, as students can't stand on the oceans and even trying to link across the continents would be a logistical nightmare resulting in many deaths. We don't want the question to come across as some kind of insane fantasy -- or maybe we do, could be a source of satirical cartoons with the 'Small World After All' soundtrack.
http://youtu.be/2msbfN81Gm0 (related: I was in Italy at the time and I think some of my school mates got into this, whereas in the Philippines they recruited at my school for 'Apocalypse Now')
> At the end of the session, I pointed out that these problems are ill-posed and require students to make too many assumptions. I also asked why she would want 8th-grades to deal with messy numbers as in example 2. she gave some type of absurd answer. > > The point is that the same people who promoted the "standards" and "reform math," without accepting any responsibility for their massive failure, are now peddling the latest rubbish.
So far it looks like STEM teachers might be able to align CCSSM to with their curriculum. The focus on whole Earth thinking looks promising. In places where CCSSM fails to meet STEM standards, we're free to take guidance from other sources, e.g. the physics teaching community. Gotta have V + F == E + 2 if you expect to be taken seriously by your peers. Polyhedrons are core. Does the CCSSM include mention of the Platonic Five? If not, it's way more disgraceful than I realized. Let me go check...
http://www.ms.uky.edu/~lee/mathfest.pdf (Dom you should like slide 11 as it cites textbooks of the 1800s / early 1900s that featured polyhedrons, a topic dropped from high school by the big dummy publishers).
"Polyhedron" does not appear as a term, though standard topics of volume and surface area do. Components, representation and visualization of three-dimensional objects are listed, but not Platonic solids or Euler's formula.
Carl Lee (UK) Polyhedra in Math Ed MathFest | August 2011 21 ===
Yikes, Platonic Five are not mentioned. I look forward to telling my students the CCSSM is for morons at best (a biased position, they're free to debate me).
Opportunities Other Ideas?
Ah c'mon. Concentric hierarchy duh. Gotta have it. Shocking to see no mention. But then the UK is mostly stuck in old ways, contributes to why east coasters are such slow pokes. Glad we look to Asia more. Our concentric hierarchy posters were published in Singapore (1979).