"Ten dimensions seems out of the question. But if one thinks of dimensions as descriptive numbers that pinpoint the locations and characteristics of an object in the universe, they become more comprehensible."
Here Pappas is taking us from knot theory to string theory. According to string theory, the universe contains more than just the three ordinary spatial dimensions and one time dimension. Instead, as Pappas writes, there could be nine spatial dimensions and one time dimension, for a total of ten.
I've alluded to string theory in the past on the blog, in posts devoted to the works of David Kung and Mario Livio. And of course, Eugenia Cheng wrote about higher dimensions. Like Pappas, Cheng informs us that a "dimension" is nothing more than a "descriptive number" -- a coordinate -- so the idea of there being ten of them isn't as far-fetched.
Pappas tells us that string theory is related to the possibility of a TOE -- theory of everything. Of course, I've written about the movie Theory of Everything here on the blog before. This movie is the story of Stephen Hawking, a physicist who studied string theory and sought out a TOE.
Pappas continues:
"The ideas of TOE have been evolving for over 20 years [as of 1994]....The results have been most convincing."
Here is a link to a string theory website:
http://superstringtheory.com/
And this is what it has to say about the extra dimensions:
http://superstringtheory.com/experm/exper5.html
It's not so hard to construct higher dimensional worlds using the Einstein equations. But the question is then: WHY BOTHER?
It's because physicists dream of a unified theory [a TOE -- dw] : a single mathematical framework in which all fundamental forces and units of matter can be described together in a manner that is internally consistent and consistent with current and future observation.
And it turns out that having extra dimensions of space makes it possible to build candidates for such a theory.
In string theory, the extra dimensions are very tiny -- in other words, they're "rolled up" in a certain way into "strings."
String theory is obviously not a middle school science topic, nor is it a high school science topic. As of now, string theory still lies at the frontier of our knowledge. Even though we now see how knot theory ties in to science, it still has nothing to do with the science I should have taught last year.
Lesson 0.9 of Michael Serra's Discovering Geometry is labeled "Chapter Review." In the Second Edition, chapter reviews have their own lesson numbers, but in the modern editions (just as in the U of Chicago text), the chapter reviews are unnumbered.
At this point, we may wonder, should there be a Chapter 0 Test? If there were a Chapter 0 Test tomorrow, then this would allow us to start Lesson 1-1 of the U of Chicago text on Day 11, which would be Wednesday.
Some teachers may point out that Chapter 0 consists of just introductory activities and so it shouldn't be tested -- and besides, a Chapter 0 test would be so soon after the first day of school, when many students are still requesting schedule changes from their counselors.
On the other hand, without a Chapter 0 Test, the first test would be the Chapter 1 Test on Day 20. At some schools, grades must be submitted every quaver (i.e., twice a quarter). Day 20 would be very close to the end of the first quaver -- and at many schools, grades are due a few days before the mathematical end of the quaver. So whether or not there should be a Chapter 0 Test depends on how often a school issues progress reports, as well as whether a teacher wants to give a solid test before those first progress reports are issued.
As far as this blog is concerned, my decision is to follow what my old school did last year. If you recall from last year, the first test I gave my students was called a "Benchmark Test." This was, of course, a diagnostic pre-test to determine what the students already knew, and what they would need to learn in the coming year.
Therefore tomorrow I will post some Benchmark Tests for Geometry. It will preview lessons to be covered the entire year. Nonetheless, today's worksheet is based on review questions from Lesson 0.9 of Serra's text.
In all these posts, I've been continuing to think about how I should have taught science last year. No, I wouldn't have taught string theory, but thinking about last year's Benchmark Tests are causing me to think about how the class was organized again.
Recall that the basic structure of the class, as envisioned by Illinois State, looked like this:
-- Monday: Coding
-- Tuesday: STEM Project
-- Wednesday: Traditional Lesson
-- Thursday: Learning Centers
-- Friday: Weekly Assessment
But there were several problems with this weekly plan. Most notably, seventh graders didn't attend my class on Wednesdays, when the traditional lesson ought to be taught. This usually meant that the traditional lesson was pushed back to Thursday -- the day before the assessment on Friday. Clearly, this isn't learning at all.
A better weekly plan would look like this:
-- Monday: Coding
-- Tuesday: Traditional Lesson
-- Wednesday: Learning Centers
-- Thursday: Science Project
-- Friday: Weekly Assessment
Not only do the seventh graders now have a traditional lesson, but all the grades benefit from having an extra day between the lesson and the assessment. Meanwhile, the project is now explicitly listed as a science project. This keeps the math class more or less traditional while the science projects prepare students for laboratory science -- required in high school under the a-g requirements for college. All the seventh graders end up missing are the learning centers -- which, frankly, are less important than the Tuesday math lesson and the Thursday science lesson.
So now I've established Thursday as my science day. It's also likely that I would have included some science as part of the Wednesday learning centers, but for the most part science is on Thursday.
Now science for Grades 7-8 are based on the old California science standards, and so I take projects from the life and physical science texts found on the Illinois State website. But sixth grade is based on the new NGSS standards, which I find on the Study Island website. I no longer have access to these websites, so I can't quite be sure how I would have divided the class into units.
But if I recall correctly, the sixth grade curriculum was divided into nine units, with a pre-test in Unit 1, the main curriculum in Units 2-8, and a post-test in Unit 9. This corresponds roughly to months, so Unit 1 is in August, Unit 2 in September, all the way up to Unit 9 in April (and then May can be used for test review). Notice that the Unit 1 Pre-Test in August fits nicely into Benchmark Testing Week -- and in fact, I could give that pre-test on Thursday of that week, to fit the pattern to be established.
Science projects can be given every other Thursday, to meet the requirement that we submit project photos to Illinois State every fortnight. I admit that the idea of having to prepare so many projects intimidated me a little. It might have been good to give the mousetrap car project that first Thursday in September (as it appears in the math STEM texts for all three grades), but then switch to science projects only, starting with our second project.
On the non-project Thursdays, I have the students take Foldable notes. And on the last Thursday of the month, I give the science test. Most likely, the first real science test (for Unit 2) wouldn't have been given until the last Thursday in September, due to other distractions earlier in the month (holidays, a field trip, and Back to School Night). The only problem is that this was after grades for the first progress report were due (echoing the problem I mentioned earlier in this post). Fortunately, at that point there were no separate grades for math and science (just a "STEM grade"), so I could get away with having no science grades until after the first progress report.
Yes, it's tricky to figure out how to grade these assignments. We weren't told about PowerSchool and the weighting percentages until October, and so I probably would have winged it with the grades until being made aware of the weights. At that point, I most likely would have squeezed all science into the 40% reserved for "Formal Assessment and Projects." Of course, late in the second trimester, PowerSchool was changed again so that I needed to give separate grades for math and science.
In weeks when there is a formal assessment in science on Thursday, the weekly math assessment on Friday changes to a Dren Quiz instead, so that the students don't have two hard tests in a row. The Dren Quiz number can correspond to the Study Island unit number, so the first real science test is followed by the 2's Dren Quiz. The pre-test during Benchmark Testing Week could be followed by a 1's Dren Quiz (which doesn't count, since no tests during that week count in the grades), or if that's too goofy, I could keep the 10's Dren Quiz (which was my first actual Dren Quiz).
In fact, the idea that the second week of school should follow the same pattern as the rest of the school year extends back to the first week of school. For example, the Opening Week Activity for Thursday should lean more towards science, and so on.
But of course, this is all a dream. This is what my class could have looked like if I had taught science properly, but unfortunately I didn't teach it properly.
As of today, the Japanese artist mentioned on the worksheet, Kunito Nagaoka, is still alive.
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