Lesson 0.8 of Serra's Discovering Geometry is called "Perspective." This is the second of two sections appearing in the Second Edition but not in the modern editions. Serra begins:
"Many of the paintings created by European artists during the Middle Ages were commissioned by the Roman Catholic Church. The art was symbolic; that is, people and objects in the paintings were symbols representing religious ideas."
Unlike Lesson 0.5 on mandalas, which we choose to include on the blog even though it's "missing" from the modern editions, Lesson 0.8 can just be left out altogether. This is because we'll be starting the U of Chicago text next week, and that text already has a lesson on perspective (Lesson 1-5), so Day 15 would just be a repeat of Day 8.
Then again, we recall that in my class last year, the students in all grades had trouble drawing cubes even though those were on isometric paper rather than in true perspective). So we might wish to teach perspective on both Day 8 and Day 15. True perspective drawings should most likely be completed on plain unlined white paper, with a straightedge to draw lines toward the vanishing point. Lined notebook paper for one-point perspective drawing may also be acceptable -- but not for two-point perspective (the subject of today's worksheet).
The worksheet below comes from "marcandersonarts" and "Daisuke Motogi."
Here is the Blaugust prompt for today:
What’s a practice you keep doing year after year? Either something that works great or something that maybe needs examining. Why do you keep doing it?
Well, I was only in the classroom for one year, so I can't say "year after year." But I can find some practices that I did during that single year. In fact, I found a January 2017 post in which I found both "something that works great" and "something that needs examining."
The thing that works great is the music break. Here I describe a music break during sixth grade math:
In my classes, I often sing songs in order to break-up the monotony of our 80-minute blocks. Today's song is called GCF, since the sixth graders were learning about greatest common factor yesterday:
GCF!
Greatest Common Factor
GCF!
List every factor
GCF!
Circle the ones in common
GCF!
Choose the biggest one
LCM!
Least Common Multiple
LCM!
List some multiples
LCM!
Circle the ones in common
LCM!
Choose the smallest one
I made up the tune as I played it on my guitar. Of course, I couldn't resist the temptation of basing the tune on the actual musical notes G, C, and F.
And the song works because the students enjoy singing along with it -- and the lyrics of the song are the steps to finding the GCF or LCM. On the other hand, something that doesn't work is -- you guessed it -- the way I teach eighth grade science:
But first, let me provide some explanation. My small charter school has no middle school science teacher -- instead, I, as the math teacher, must include some science into the lesson. Notice that some STEM projects, like the ones I gave sixth and seventh, already contain some science. But I want to be sure that the eighth graders receive sufficient science content since this is a tested subject here in California.
And so I go to our online software that we use for science, and download a worksheet based on questions that they may see on the state test. The hope is that next week, they can go to the online program itself and answer the questions correctly. The lesson is on the environment, because there is an upcoming science unit that will begin next month. It is called Green Team, and the students will be learning about energy and water conservation.
But then one girl -- the top student in math -- begins to complain. She argues that at the very least, science should be project-based, and so she wants to have some project rather than a worksheet. I assume that she had her hopes up all week when she saw that we'd be doing science, only to be disappointed when she sees the worksheet today. She says that she enjoys the science projects that she performed at her old school, before she transferred to our school over a month ago.
There are several issues at play here. In sixth and seventh grades we have the Illinois State "STEM" projects in math, but "STEM" projects are not actually science projects. At our charter school, there is neither a science teacher nor a specially designated time for science. But at our sister charter, there is an actual science period, even though there's no separate science teacher there either. At our last meeting, the math/science teacher at the other school tells me that there are separate texts published by Illinois State for actual science projects, distinct from the STEM projects. She says that her students enjoy the real science projects more than the STEM projects.
My top student wants to do actual science projects. She isn't satisfied by the STEM projects -- which isn't surprising, since the students at the sister charter feel the same way.
As I reflect on this discussion (and the student mentioned here is the "special cousin," by the way), I can easily point out one big mistake I made there. I shouldn't have downloaded the worksheet from the Study Island website. Instead, I should have had the students do the assignment online. It wasn't until I saw the Edgeniuty website last summer that I realized that this is the age we now live in -- entire assignments can be given online. Even though the special cousin was hoping for a project, she probably would have liked answering the questions online better than on the printed copy.
Today we check out another Blaugust participant -- Kim (no last name), a middle school teacher:
http://logicalpoetry.blogspot.com/2018/08/daily-warmups.html
If we were to ask Kim about a practice she does year after year, surely "Daily Warmups," the topic of this post, would be her answer.
But Kim's warmups are very different from mine. Her warmups are based on the day of the week:
- Number talk Monday
- Today's number Tuesday
- Which one doesn't belong? Wednesday
- Clothesline Thursday
- Reflection Friday
Because she was out yesterday, she doesn't fully explain how all of these warmups work. But one that I am familiar with is "Which one doesn't belong?"
You see, WODB? is another one of those open-ended questions. Students are given four choices (numbers, geometric figures, etc.) and asked the question "Which one doesn't belong?" It's definitely open-ended because arguably, any of the four choices may be described as not belonging.
For example, Kim's WODB? problem in the link gives four figures as the choices. The most obvious answer to WODB? is the lower-left corner -- unlike the others, it's not "filled in." (To be more precise, the other three are polygonal regions while this one is just a polygon.) The figure in the upper-left corner is another obvious choice -- it's a triangle while the others are all rhombi. The figure in the upper-right doesn't belong -- it's the only figure containing right angles. And even the figure in the lower-right doesn't belong -- it's the only figure with a horizontal base (bottom) while the others all have a vertex as its lowest point.
Here's an example of WODB? containing numbers -- 3, 27, 123, 31:
- 3 doesn't belong, because it's the only single-digit number.
- 27 doesn't belong, because it's the only perfect cube.
- 123 doesn't belong, because it's the only triple-digit number.
- 31 doesn't belong, because it isn't two more than a perfect square. (Ha! I bet you thought I was going to say "it isn't a multiple of three" or "it's the only prime.")
As I mentioned in yesterday's post, the purpose of open-ended questions is to get the students thinking about math without fear of the teacher saying "You're wrong."
Returning to Kim's warmup list, another one of them is "Number talk Monday." In this post she provides an example of a "number talk" but doesn't fully explain what it is. I can only glean from her post that the assignment is that each set of symbols (dots and lines) has the value of 7, and students must figure out what each symbol stands for.
Meanwhile Shelli -- the leader of the Blaugust challenge -- also mentions number talks in her own post (her latest installment in the "My Fav Friday" series):
One of the number talks looks identical to Kim's (7, 7, 7, 7), but Shelli also posts two more examples, which are 10, 10, 13 and 14, 14, 14, 14.
Hmm. I tried a Google search for mtbos number talks. I notice that the first two results are both by Sara VanDerWerf, whose blog I mentioned early this week. And in one of the links, VanDerWerf even links back to the Queen of the MTBoS, Fawn Nguyen. But nothing on either of those blogs look like the "number talks" of Shelli and Kim.
In the following link, VanDerWerf makes her opinion of "number talks" clear:
Every, yes every, 6-12 Math Teacher should be doing Number Talks regularly in the core mathematics classes they teach. If a secondary teacher wants all students to make growth in their classrooms then Number Talks MUST be a part of what they are doing in their classrooms.
In this post of my top ideas for support classes I advocated doing a number talk every single day if a student has a second math class. I’d love to advocate for the same frequency in a core math class but I know this is unrealistic for many. So here is my challenge to you for the 2016-17 school year in your 6-12 core math classrooms. Commit to doing at least 30 number talks over the course of the year. Commit that at least 10 of the 30 will be done 1 per day for a two week time.
I know, I know what you are going to say. I don’t have time. I have so much material to cover. I can’t do this.
She mentions "I don't have time" and other excuses for not giving the number talks. My excuse was that I still don't know exactly what they are now (much less in 2016-17). I still don't know whether Shelli's and Kim's number talks have anything to do with VanDerWerf's.
Whatever "number talks" are, they sure don't look like anything traditionalists would approve of.
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