I haven't subbed in this classroom before, but I have been to the continuation school. Indeed, I wrote about the school back in my April 12th post -- the last day before spring break in this district.
Today, the students only need to make up any missing assignments. The only real issue with classroom management is in the fourth class, which is a bit loud. The third class, which counts as homeroom, earns a doughnut party for having one of the best holiday door decorations. (Our door has a poster based on the movie Elf -- as in Buddy the "Elf.")
Both April 12th and today are Fast Fridays -- all students go home early except those with any D's or F's, who must attend tutorial instead. On April 12th, there were only three students who needed tutorial, but today there are a whopping ten. One of them is a girl who somehow has a D-, not in English, but in AVID (the regular teacher's first class). It almost seems as if tutorial is the largest class of the day -- it isn't, but they do outnumber the nine students in the AVID class.
But unlike April 12th, today tutorial is suddenly cancelled. Because I'm a sub, somehow I don't get the message. (Is it sent directly to teachers' email accounts.) Some students receive a text from other friends that they get to leave early, and finally an administrator confirms the cancelling of tutorial. So at 12:40 when I finally get the message, my winter break officially begins.
Today is the third and last day of finals week. It has been my tradition on the blog on the third finals day to post a review of the old semester and preview of the new semester.
Last year, when I was searching for MTBoS blogs, I did find the following blog:
http://cheesemonkeysf.blogspot.com/
The blog belongs to a Northern California high school math teacher. (Apparently the letters "sf" in the URL stand for "San Francisco.") Even though the blog is anonymous, a commenter I quoted yesterday referred to this author as "Elizabeth." Thus I'll refer to cheese monkey by the name Elizabeth (and use feminine pronouns to her).
[2019 update: I wrote this last year, but I wish to preserve this discussion. And I'll also mention one of Elizabeth's posts from this year.]
Anyway, Elizabeth is a Geometry teacher, and she refers to Geometry proofs in these posts:
And so for our review, let's compare our U of Chicago course to Elizabeth's to look for any key similarities and differences.
Let's start with the first semester plan from the U of Chicago text:
1. Points and Lines
2. Definitions and If-then Statements
3. Angles and Lines
4. Reflections
5. Polygons
6. Transformations and Congruence
7. Triangle Congruence
Let's start with the first semester plan from the U of Chicago text:
1. Points and Lines
2. Definitions and If-then Statements
3. Angles and Lines
4. Reflections
5. Polygons
6. Transformations and Congruence
7. Triangle Congruence
In her November 6th post, Elizabeth writes:
So this year, when I had to be out of school for a few days, I designed a Proof Portfolio project for them to do in my absence.
Each day had four small, reasonable proofs students had to do — and they could collaborate on these. But then... they had to write a number of short-answer reflections to analysis questions based on their own proofs in the day's set.
And by "a few days" she means "four days," since she links to four worksheets -- a grand total of sixteen proofs. The first worksheet includes proofs about parallel lines (Chapter 3 of the U of Chicago text), while the other three are the more common triangle congruence proofs (that would have to wait until Chapter 7).
Did Elizabeth's students enjoy the project? Well, that's not exactly the case:
When I returned, there was a great deal of wailing and moaning and gnashing of teeth about How Hard This Project Was and How Hard They All Worked.
Yet she declares the project a success:
But as I'm reading their work, I am blown away by how much they seem to have learned!
The following week, Elizabeth blogs about this project some more:
The complaints and lamentations were filled with drama. "OH MY GOD, DR. S — THAT ASSIGNMENT WAS HARD." But they could tell that they had accomplished something.
(OK, so apparently Elizabeth's last initial is S.) She explains how she grades the assignment:
My assessment strategy was to be rigorous about completion but merciful with points. It was only worth a quiz grade (100 points), and my default score for students who completed every section was a 95. There are rewards for following instructions. Missing sections or components left blank cost more points.
She concludes the post as follows:
I am excited to see what happens on the next major test that includes a proof. Photos of student work to follow.
But unfortunately, she hasn't posted anything on Geometry since then, so we don't know yet how her students fare on the next major test.
Notice that the cornerstone of this project is the peer review. Elizabeth feels that feedback from peers is more effective than that from teachers. Traditionalists would disagree -- they believe that feedback from the teacher (someone who knows math) is better than that from another student (someone who doesn't know as much math). But traditionalists make the assumption that students will actually listen to the teacher just because she says so. Elizabeth's project is based on the possibility that the traditionalists' assumption is false -- that students are more willing to listen to each other than to the "sage on the stage."
Our first semester plan contains some activities, but nothing as ambitious as Elizabeth's four-day proof project.
Here is our second semester plan. We'll begin with Chapter 8:
8. Measurement Formulas (January 7th-13th)
9. Three-Dimensional Figures (January 14th-28th)
10. Surface Areas and Volumes (January 29th-February 12th)
11. Coordinate Geometry (February 13th-27th)
12. Similarity (February 28th-March 12th)
13. Logic and Indirect Reasoning (March 13th-April 2nd)
14. Trigonometry and Vectors (April 3rd-20th)
15. Further Work With Circles (April 21st-May 4th)
Since the new semester begins on Day 86, we start with Lesson 8-6, "Areas of Trapezoids." It means that Lessons 8-3 (rectangles), 8-4 (irregular figures), and 8-5 (triangles) are omitted. But I'll find a way to squeeze in the missing lessons.
Is there anything on Elizabeth's blog about second semester Geometry topics? Well, I did find a link to the following post from over two years ago:
http://cheesemonkeysf.blogspot.com/2017/07/things-that-work-1-regular-vocab.html
This post is all about Geometry vocabulary. Her example is on circles, This appears to be more like the basic circle lessons of Chapter 13 than the more advanced work in Chapter 15 (where we have to deal with inscribed angles, power of a point, and so on).
Our worksheets refer to vocabulary. But Elizabeth takes the extra step of actually giving her students a vocabulary quiz. She writes:
At some level, I recognize that this sounds stultifying. But at another level, it was incredibly empowering for the students. Everybody understood exactly what was being asked and expected. And everybody saw it as an opportunity to earn free points. Students gave each other encouraging written comments and cheered each other on. They saw their scores as information—not as judgment. They used what they knew to make flash cards or Quizlet stacks. They quizzed each other. They helped each other.
And nobody ever complained about the regularly scheduled vocab quiz. It was a ritual of our course.
And apparently, she gives these quizzes every week:
It also ensured that everybody spent a little quality time on the focus task of preparing for the vocab quiz on Thursday or Friday. And this, in turn, meant that everybody was a little more ready to use the correct and appropriate mathematical vocabulary in our work. They noticed more because the owned more.
On the circle answer, Elizabeth gives a term, "2. concyclic points," that doesn't appear anywhere in the U of Chicago text. I believe the correct answer is "N. points that lie on the same circle" -- that is, "concyclic" is to circles as "collinear" is to lines. Also, the answer to "7. party hat situation" is "J. the situation where two tangent segments are drawn to a circle from a point external to the circle." This situation (which does indeed sort of look like a party hat) occurs often on the Pappas calendar, yet the U of Chicago text never gives it a formal name.
Elizabeth writes:
- There should be many more definitions in your right-hand list than there are terms in your left-hand list. Also definitions can be re-used. This way there isn't a zero-sum outcome if someone misses an answer.
Yet in her given circle unit example, there are exactly 16 terms and 16 definitions. But perhaps she follows her own advice on the other vocab quizzes.
I know the importance of vocabulary to any math class, especially Geometry -- particular these days of the Common Core when students must explain their answers. But I've never considered giving students a weekly Geometry quiz.
And Elizabeth has written more about Geometry tips since her endorsement of "word walls" (as the Illinois State text would call them). As I promised, here's one of her posts from this year:
http://cheesemonkeysf.blogspot.com/2019/10/building-feel-for-major-moves-in-proof.html
Here she gives some hints for setting up proofs in Geometry class.
This has meant that we are developing students' intuition that that these sub-assemblies are knowable and predictable. We call these our "major proof moves." Some of our major categories of major proof moves include:
- the relationships between parts & wholes
- a sense of bisectors and "half-ness"
- parallels and the results of parallels
- perpendiculars and their results
- right angles and their results.
It's working out surprisingly well.
There are many other examples of "things that work" on Elizabeth's blog. It definitely gives me something to consider if I ever return to my own classroom someday.
OK, so it's now time for winter break and the holidays. This year, we have not just Christmas but the Jewish Hanukkah, which is so late that it overlaps Festivus, Christmas Eve, Christmas Day, and Boxing Day this year.
Festivus -- that's the name for December 23rd mentioned on the TV show Seinfeld. (It's celebrated with a long metal pole instead of a Christmas tree.) But it's come to my attention that December 23rd is also known by another name: "Christmas Adam." That's because Adam comes before Eve (in the Bible), so Christmas Adam comes before Christmas Eve.
Note that while "Christmas Adam" seems to be a recent invention, it actually goes all the way back to the Middle Ages:
https://aleteia.org/2017/12/24/happy-adam-and-eve-day/
Originally both Adam and Eve were celebrated on December 24th, in order to make a connection to the celebration of Christ on the 25th. With "Christmas Adam," we now have Adam on the 23rd and Eve on the 24th.
So whether you celebrate Festivus, Christmas Adam, Christmas Eve, Christmas Day, Boxing Day, Hanukkah, or any other holiday, I wish you the very best.
Expect three posts this year during winter break this year.
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