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 two years ago. If you recall from that 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.
Here is the Blaugust prompt for today:
How do you support struggling students? What intervention strategies have you used?
Before I answer this question, let me announce that today is the first day of school in the district where I receive most of my subbing calls. Therefore, I expect that next week will mark my return to the classroom as a sub.
Meanwhile, yesterday was the 100th birthday of Katherine Johnson -- the NASA mathematician who was the main subject of the movie Hidden Figures. She celebrated the weekend of her centennial at her alma mater, West Virginia State University, where a statue was erected in her honor. I can't help but think back to our field trip to the movie theater during my year at the charter middle school.
To respond to today's Blaugust prompt, as usual, I think back to two years ago. Since I'm already thinking about the Hidden Figures field trip from January 2017, let's look at old some posts from around that time.
January 12th, 2017:
I need to mention my eighth grade class today, especially since they're learning about transformations on this Common Core Geometry blog. In the end, I decided to delay the science lesson to tomorrow and teach transformations today.
This means that this week I had three full days to cover the three transformations. On the first two days, the translations and reflections went well, and most students appeared to understand. But I worried as today's lesson approached, because rotations are probably the most difficult of the three transformations for students to understand.
Now keep in mind that I'm using the Student Journals that are part of the Illinois State text. We know that rotations can be centered either at the origin or away from the origin. Rotations centered at the origin have easier formulas -- for example, the rotation of 180 degrees centered at the origin maps the point (x, y) to the point (-x, -y).
But none of the rotations mentioned in the Illinois State text are centered at the origin. Most of the questions direct a student to rotate a line segment around one of its endpoints. This at least makes it a little easier, since every rotation maps its center to itself.
And so here's what I did today -- on the first page, the students are asked to rotate
Of course the students are confused by this at first, but in the end, I believe that they're starting to get the hang of this. I like teaching rotations this way because it sets them up nicely to learn the slopes of perpendicular lines later on. By the end of class, I think the most confusion came from changing all the questions in the Illinois State text, which were geared towards the rotation centered at A rather than the origin.
So that's one possible answer to the Blaugust prompt -- I help struggling students by making the questions in the text easier.
January 23rd, 2017:
Meanwhile, today is a coding Monday. In case you're curious, sixth graders create logos for an imaginary company, while seventh graders learn about spreadsheets. The students learn about various Excel functions, including mean, median, and mode. I don't normally have music break on coding Mondays, but I couldn't help singing the Measures of Center song from last month to jog the students' memory.
I notice that often when I wrote that my class "struggled" on something, that something was actually the Monday coding assignment, not math! But in this case, the coding lesson was math-related -- and my solution was to sing a song to remind them of what they had learned.
I admit that in both of these cases, the students simply shut down. They didn't realize why learning math was worth the effort. I used the field trip to inspire them -- I reminded them (especially the girls) that if they studied hard in math, they could become the next Katherine Johnson.
Today we'll check out the blog of another Blaugust participant, Sarah Giek:
https://riseoverrunblog.wordpress.com/2018/08/27/perfect-squares-and-perfect-cubes/
Sarah Giek is a Virginia high school Algebra I teacher. (Actually, she teaches in Charlottesville -- a town that made the news last year for all the wrong reasons.)
In this post, Giek writes about what she does when her students struggle. In this case, her students are learning about basic exponents. She writes:
Right now we’re working on the Order of Operations. Last year I jumped right in with good old Aunt Sally, but this year I’m taking a different approach. We started with the four basic operations and parentheses, the next day we learned about exponents, and now we’re working on square roots and cube roots. In an effort to really help my students understand these concepts, we broke out the colored blocks and starting making squares and cubes. After recording the number of blocks needed to make the various shapes and solids, we talked about perfect squares and perfect cubes and how these names related to the exponential form.
Recall that the Illinois State curriculum also encourages the use of manipulatives similar to the ones mentioned here in Giek's post -- DIDAX manipulatives. These were supposed to be used as part of Learning Centers, but of course I didn't use them properly.
I must admit that more often than not, I failed to use the DIDAX manipulatives because I didn't know how to use them. It never occurred to me to use the blocks to make squares and cubes the same way that Giek does in this post.
That's one problem with many of these visual aids. They might help our students very, very much -- but only if the teachers know what to do with them. That applies not just to DIDAX manipulatives, but something I mentioned in my last post -- Number Talks.
This month once again marks Educator Appreciation Days at Barnes & Noble. I intended to purchase a book that has nothing to do with math, but I couldn't help but notice a book in the education with "Number Talks" in the title -- Making Number Talks Matter by Cathy Humphreys & Ruth Parker.
I didn't necessarily want to purchase the book. The Number Talks book is on the expensive side -- and for some reason, it's not eligible for the Educator Appreciation discount (while ironically, the non-math, non-education book I bought was eligible for the discount). But after reading so much about Number Talks in several MTBoS Blaugust posts, it piqued my curiosity. And so I gave in and bought the book.
The subtitle is Developing Mathematical Practices and Deepening Understanding, Grades 4-10. I notice that Sara VanDerWerf recommends Number Talks for all secondary teachers -- Grades 4-10 is a slightly lower grade range. The important thing is that the middle school grades that I taught two years ago are smack dab in the middle of the recommended range in either case. And I found the example from Shelli's and Kim's blog in Chapter 2, so this confirms that the "Number Talks" on their blogs are indeed the same as VanDerWerf's.
I'm wondering whether I should make Parker's book my next side-along reading book. (I'll list Parker as the main author rather than Humphreys, since Parker is one of the creators of Number Talks.) I wasn't planning on starting another side-along reading book so soon after finishing Van Brummelen.
But notice that many MTBoS bloggers read books on the side and discuss them on their blogs. But they're much more likely to cite a book that leads to better math teaching, such as Parker's, than a book that teaches higher math such as Van Brummelen's.
Of course, Number Talks aren't for reading about -- they're for doing in the classroom. I'll be much more likely to read and discuss Number Talks if I had a classroom in which to do Number Talks. Two years ago, I could have done Number Talks, but manipulatives were probably better (if only because DIDAX manipulatives, not Number Talks, are part of the Illinois State curriculum).
But if I ever get my own classroom, I'll definitely consider Number Talks -- especially after having spent the money on the book! Will Number Talks help my students. I don't know -- but once again, notice that the teachers giving Number Talks are still teaching this year, whereas I am not teaching in a classroom this year. So once again, I must assume that those successful teachers know much more than I do about what helps students learn math.
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