Our focus is now the U of Chicago text. Just like the Serra text, it's an old Second Edition (1991), and there are newer editions in which the chapters are ordered differently. Since my plan this year is to follow the order strictly, let's revisit the chapter order in my text:
Table of Contents
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
8. Measurement Formulas
9. Three-Dimensional Figures
10. Surface Areas and Volume
11. Coordinate Geometry
12. Similarity
13. Logic and Indirect Reasoning
14. Trigonometry and Vectors
15. Further Work With Circles
Let's compare this to the modern Third Edition of the U of Chicago text. The first thing we notice is that the new text has only 14 chapters, not 15. We observe that the first twelve chapters are more or less the same in each text, and so it's Chapter 13 that is omitted in the new version. Instead, the material from the old Chapter 13 has been distributed among several different chapters.
You might recall that in the past when I used to juggle the lessons around, it was Chapter 13 that I moved around the most. So you could argue that when I was breaking up Chapter 13, I was actually adhering to the order in the new Third Edition -- unwittingly, of course!
Let's look at Chapter 13 in the old text, and I'll give the lesson in the new text to which the old Chapter 13 material has been moved:
- Lessons 13-1 through 13-4 (on indirect proof) are now the first three lessons of Chapter 11, just before coordinate proofs. (Lesson 13-2, "Negations," is no longer a separate lesson in the new text.)
- Lesson 13-5, "Tangents to Circles and Spheres," is now Lesson 14-4, in the circles chapter.
- Lesson 13-6 through 13-8 (on exterior angles of polygons) have been incorporated into Lessons 5-6 and 5-7 (on Triangle Sum).
Some of these changes are those I once made by myself -- for example, including tangents to circles with the other circle lessons.
Besides the breakup of Chapter 13, here are the other major changes made in the Third Edition:
- Chapters 4 through 6 exhibit many changes. In my old version, reflections appear in Chapter 4, while the other isometries don't appear until Chapter 6. In the new version, all isometries are defined in Chapter 4. With this, the definition of congruence (and some of its basic properties) have now moved up from Chapter 6 to Chapter 5. Only Triangle Sum remains in Chapter 5 -- the properties of isosceles triangles and quadrilaterals have been pushed back to Chapter 6.
- With this, Chapter 3 has a few new sections. Two transformations are actually introduced in this chapter, namely rotations and dilations. This may seem strange, since rotations are still defined as Chapter 4 as a composite of reflections in intersecting lines -- and reflections themselves don't appear until Chapter 4. It appears that the purpose of rotations in the new Lesson 3-2 is to introduce rotations informally, as well as tie them more strongly to the angles of Lesson 3-1. (Rotations appear before reflections in Hung-Hsi Wu, but Wu does for different reasons.) Arcs also now appear in Lesson 3-1 instead of having to wait until 8-8. Meanwhile, the new Lesson 3-7 on dilations (which are still called "size transformations") is essentially the old Lesson 12-1 and 12-2. Again this is only an intro -- dilations are still studied in earnest only in Chapter 12.
- Chapter 7 is basically the same as the old text, especially the first five sections (except that SsA in Lesson 7-5 now has an actual proof). The new Lesson 7-6 is the old Lesson 8-2 on tessellations. I see two new lessons in this chapter, Lesson 7-9 on diagonals of quadrilaterals and Lesson 7-10 on the validity of constructions. (David Joyce would approve of this -- but he'd take it a step forward and not even introduce the constructions until this lesson.) Meanwhile, the old Lesson 7-8 on the SAS Inequality (or "Hinge Theorem") no longer appears in the new text.
- Chapter 8 has only one new section -- Lesson 8-7, "Special Right Triangles," is the old 14-1. This is so that special right triangles are closely connected to the Pythagorean Theorem.
- Chapter 9 was always a flimsy chapter in the old book -- it's on 3D figures, yet most of the important info on 3D figures (surface area and volume) don't appear until Chapter 10. Now surface area has moved up to Chapter 9, reserving Chapter 10 for volume (except for the surface area of a sphere, which remains in Chapter 10). The old Lesson 9-8 on the Four-Color Theorem has been dropped, but that was always a lesson that was "just for fun."
- The last section of the old Chapter 12 (side-splitter) is now the first section of Chapter 13, which is the new trig chapter. Lesson 13-2 is a new lesson on the Angle Bisector Theorem, and Lesson 13-4 is a new lesson on the golden ratio. I've actually seen these ideas used before -- including on the Pappas Mathematical Calendar -- but this is the first time I've seen them in a text as separate lessons. This is followed by lessons on the three trig ratios. Vectors, meanwhile, have moved up to Lesson 4-6, so that they can be closely connected to translations.
- Chapter 14 should be like the old Chapter 15, but there are a few changes here as well. Ironically, I, like the text, moved tangents to circles to this chapter (Lesson 14-4) so that it would be closer to the other important circle theorem, the Inscribed Angle Theorem. But inscribed angles have been moved up in the new text to Lesson 6-3. This places that lesson closer to the Isosceles Triangle Theorem, which is used in the proof of the theorem. Meanwhile, Lesson 14-6 technically corresponds to 15-4 ("Locating the Center of a Circle") of the old text, but it has been beefed up. Instead of just the circumcenter, it discusses the other three concurrency theorems (important for Common Core) as well as the nine-point circle of a triangle.
Meanwhile, of immediate concern are Chapters 1 and 2 of the new text. Unlike the others, these chapters haven't changed much from the old text. The only difference in Chapter 2 is that Lesson 2-3, on if-then statements in BASIC, has been dropped. (After all, who uses BASIC anymore, except on the Mocha computer emulator for music?) In its place is a new lesson on making conjectures.
Two of the lessons of Chapter 1 have been dropped. One of them is actually today's Lesson 1-1, as its material has been combined with the old Lesson 1-4. Meanwhile, Lesson 1-5, on perspective, has been delayed to Chapter 9 (which makes sense as perspective is definitely related to 3D). The last lesson in Chapter 1 is on technology -- a "dynamic geometry system," or DGS. (That's right -- goodbye BASIC, hello DGS!) Officially, it still corresponds to the last lesson of the old Chapter 1, since this lesson still introduces the Triangle Inequality Postulate (but now students can test out this postulate for themselves on the DGS).
On the blog, I'll continue to follow the old Second Edition of the U of Chicago text. But if I ever get to sub in a classroom again, the classroom has priority over the U of Chicago order. In this case, if an important lesson is skipped, I could sneak the lesson in by following the Third Edition order instead.
Okay, without further ado, let's finally start the U of Chicago text!
Lesson 1-1 of the U of Chicago text is called "Dots as Points." This lesson has the first description of a point:
First description of a point:
A point is a dot.
This is the start of a new school year. Many students enter Geometry having struggled throughout their Algebra I class. Now they come to us in Geometry, and after all the frustration they experienced last year, the first question they ask is, "Why do we have to study Geometry?" Well, the answer is:
A point is a dot.
The old U of Chicago text writes about dot-matrix printers. This isn't relevant to the 21st century, and indeed they don't appear in the modern edition. But here's another question to ask students -- if you didn't have to take math, what would you do at home instead of math homework? And if the answer is "play video games," then guess what -- video game graphics consists of millions of dots. Or, more accurately, they consist of millions of points, since:
A point is a dot.
Images on video games don't come out of nowhere -- someone had to program in the millions of dots, treating them as points -- therefore using Geometry. So without Geometry, video games don't exist. If you want to answer that question -- "What would you do if there was no math?" -- then next time choose something that doesn't require math to build.
In the modern version of the text, there is a brief mention of pixels as part of both computer images and digital camera images. Again, it's not emphasized as much, since "dots as points" must share the new Lesson 1-3 with "network nodes as points."
Here is the Blaugust prompt for today:
A peek into my classroom - show us your classroom or describe a typical day / hour
Well, yesterday I wrote that I don't have any videos of my teaching. And only once did I take any photos of my classroom (not counting photos submitted to Illinois State). For the sake of this Blaugust post, I'll post those pictures again today.
As for a typical hour, I did write about what I originally wanted a typical 80-minute block to look like, about three weeks before the first day of school:
10 minutes: Warm-Up
10 minutes: Go over homework/previous day's lesson
20 minutes: New lesson (Foldable note taking)
10 minutes: Music break
20 minutes: Guided practice
10 minutes: Closure/Exit Pass
This was set up for a traditional lesson. Of course, soon I learned more about the Illinois State text and its nontraditional lessons. Many parts of this 80-minute plan changed -- but I always kept some form of a Warm-Up, music break, and Exit Pass.
Here are the changes to this plan caused by Illinois State. First of all, the Warm-Up turned into the Illinois State Daily Assessment, which is supposed to take only five minutes, not ten. Going over HW and the previous day's lesson were awkward since there was supposed to be only one traditional lesson per week, and the HW was to be done online. Most of the time, I had the students take notes directly into the Student Journals, which was also where the guided practice was. Thus in the end, the typical 80-minute block became:
5 minutes: Warm-Up (Illinois State Daily Assessment)
10 minutes: Review previous week's lesson (from Illinois State)
20 minutes: New lesson (Illinois State Student Journals)
10 minutes: Music break
25 minutes: Guided practice (Illinois State Student Journals)
10 minutes: Closure/Exit Pass
If I remember correctly, the Illinois State pacing guide assigned one hour to the traditional lesson, and notice that the Illinois State parts of this lesson do add up to one hour. The only non-Illinois State parts of this lesson plan are the music break and Exit Pass.
The traditional lesson, as I wrote earlier, would be one day per week. As I realized much too late, the ideal weekly plan would have been something like this:
Monday: Coding (with coding teacher)
Tuesday: Traditional Lesson
Wednesday: Learning Centers
Thursday: Science
Friday: Weekly Assessment
Meanwhile, Shelli -- the leader of the Blaugust challenge -- has her own weekly plan:
http://statteacher.blogspot.com/2018/08/evolutions-in-teaching.html
Even though today is Wednesday, Shelli's post today is all about Multiple Choice Monday. Notice that she doesn't merely ask her students to answer five MC questions. She actually hands her students a worksheet for the students to choose a letter and then reflect on each question -- and it's taken her over three years to develop this worksheet.
Recall that I should have created more worksheets similar to this for more student accountability. In fact, Shelli's weekly plan somewhat fits my own. I could have made the "Monday Five" worksheet into multiple choice (by providing the students with answers choices) and then had them fill out a reflection form while waiting for the coding teacher to arrive. She also mentions a "Terms Tuesday" and "Words Wednesday" for vocabulary practice. This fits the Illinois State curriculum, which encourages teachers to create "word walls" but doesn't explicitly include them in the pacing plan. In any case, I must always be sure to have the proper photocopies when I need them.
Sarah Giek also writes about a typical week in her post today:
https://riseoverrunblog.wordpress.com/2018/08/29/sanity-saving-planning-guide/
Even though Giek teaches high school, her classes are probably the most similar to my old middle school classes from two years ago:
For the first time in my teaching career, I have 4 different classes to prepare for, although most days it feels like 5 because the needs of my ELL students are very different than my non-ELL students.
Two years ago, I had three preps -- and that's part of the reason I was reluctant to delve into science, since my load would have felt more like six preps. Giek continues:
Each course I teach is given a section with 15 rows, with each row representing 5 minutes.
Let's see -- 15 * 5 is 75, so her classes are 75 minutes each. That's not significantly different from my own 80-minute classes.
Giek shows a picture of her lesson-planning spreadsheet, but it's scrolling up so fast that it's difficult to see all the details. I do like how she highlights the cells to indicate whether she has all of the materials for the lesson. That was another reason I was hesitant to teach science -- fear that I wouldn't have all of the materials.
In fact, if I'd had a planning spreadsheet similar to Giek's, then I could have shown it to my staff support aide -- who also could have helped me out more effectively with copies and materials. And moreover, I wonder whether the administrators would have accepted the weekly lesson plans (that we were required to submit) in spreadsheet format.
But here are those pictures from my classroom two years ago to fulfill first part of the Blaugust prompt, followed by the Lesson 1-1 worksheet.
END
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