Friday, August 18, 2017

Lesson 0-3: Daisy Designs (Day 3)

This is what Theoni Pappas writes on page 230 of her Magic of Mathematics:

"In addition, they form macromolecules (enormous molecules made up of thousands of atoms strung together) such as lipids, starches, cellulose and the even more complex nucleic acids and proteins. The DNA molecule with its genes provides the blueprint for the life of a cell."

I think back to my own days as a student. A classic project is for the students to construct a model of a DNA molecule, and I did so as a sophomore taking Integrated Science II.

I don't know whether the Illinois State text includes a DNA molecule project or not. The Illinois State science text was divided into three volumes -- earth, life, and physical science -- and the life science text was the last to arrive at my school. Therefore I was less familiar with the projects in this text than in the other two science texts.

In fact, part of the reason for my failure to teach science was the lack of science texts. You see, Illinois State didn't supply us with enough science texts (as opposed to math texts) -- in fact, the students never received science texts. There were teachers editions of the earth and physical science texts -- and they were both delivered to our sister charter school.

The thing about our sister charter is that they didn't have any eighth graders. This made a huge difference when looking at their bell schedule. (See my November 9th post for more information.) At both schools, the day was divided into four main blocks followed by P.E. time. Over there, sixth and seventh graders had two blocks with my counterpart teacher -- one for math, the other for science. At my school, meanwhile, I had each grade for one STEM block and the last block was for IXL with one of the grades.

I think this was what confused me about teaching science. The administrators intended me to start teaching science, possibly by going to the Illinois State website for science materials. But I didn't, because I thought that the STEM projects in the Illinois State math text counted as science! Notice that some of the math projects in each text could double as science projects (e.g., research projects in Grades 6-7, solar system project in the eighth grade text). But in reality, I should have taught science using the Illinois State materials -- online only until my teachers editions arrived.

So there was a perfect storm of confusion regarding why I didn't teach science properly:

-- lack of science texts at start of year
-- nonappearance of science on daily schedule (replaced by mystic "STEM" block)
-- projects in math "STEM" text resembling science projects
-- lack of other middle school science teachers on campus to ask for info
-- counterpart on other campus unhelpful as she didn't teach eighth grade (the critical testing year)
-- counterpart on other campus unhelpful as her specialty wasn't science (it was really kindergarten!)
-- transition from California Science Standards to NGSS

My earth and physical science texts finally arrived at some point -- I don't recall exactly when (though it might have been close to that aforementioned November 9th date). Neither my counterpart nor I had a life science text. In fact, she ended up using the earth science text for sixth grade (which she knew matched the old standards) and thus, by default, physical science for seventh grade. (Some physical science topics, such as atoms and molecules, do appear in the seventh grade NGSS.)

Of course, I knew that at the very least, my eighth graders needed science for the state test. One day, some eighth graders complained, "Why aren't you teaching us science? In fact, do we even have any science textbooks?"

There were some old texts near the back of the classroom -- but unfortunately, they were only for sixth (earth) and seventh (life) grades. Then I tried to teach an eighth grade NGSS lesson from the seventh grade text -- but of course they rejected the lesson. And of course, no one accepted my explanation of what NGSS was, or why Illinois State didn't provide any student texts. Interestingly enough, science and math suddenly appeared on PowerSchool just in time for me to assign separate grades at the end of the second trimester (as opposed to the first trimester, when the students received only a "STEM" block grade).

Notice that it was right around the end of the first trimester when the Illinois State teacher texts arrived -- perhaps that should have been the hint that skipping science first trimester was understandable without the texts, but as soon as I had them, that was the time to begin teaching science -- to all three grades.

Well, I did start teaching science to the eighth graders at that point -- the DNA lesson. And this takes us back to Pappas. She writes about the importance of the shape of the sugars in the molecule:

"It is the pentagonal shape of deoxyribose which makes the shape of the spiral and requires 10 rungs to complete a turn."

Later on, she explains:

"When gene copying (or DNA replication) takes place the DNA double helix is unwound at breakneck speeds of over 8000 rpm, and splits along the bases separating into two strands."

Again, I could have tried to keep the mathematical models of DNA structure and replication in mind as I taught this lesson to the proper grade level -- the seventh graders.

Lesson 0.3 of Michael Serra's Discovering Geometry is called "Daisy Designs." Yesterday the students used rulers or straightedges to make designs, and today they'll use a compass.

Serra begins:

"The compass is a geometric tool used to construct circles. You can make some very nice designs with only a compass."

The students are then directed to create a "daisy" using a single compass setting. Serra points out that this construction is related to that of a regular hexagon -- which is required under the Common Core.

On today's worksheet, I take one question from the exercises  -- and the other, as usual, is taken from the project. I found a website that teaches students how to form the daisy designs:

http://geometry2014.weebly.com/daisy-design.html

(The creator of this website is Monica Zimmers, a New York high school teacher.)

The second question directs the students to use a graphing calculator to graph r = a sin (n theta) in polar coordinates, for various values of a and n. The graph of these are, well, "daisies." Of course, I don't expect all students to have graphing calculators (though I do expect them to have compasses).



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