Wednesday, November 2, 2016

Student Journal: Intro to Functions (Days 53-54)

Let's see -- another Wednesday, another Wednesday schedule. Today, I begin the day with the sixth graders, and thinking there would be no music, I send them off to the history room and get the eighth graders instead. This way, I can use the extra period when the eighth graders would have had music to use the computers instead.

But then right at that moment, the music teacher arrives! I am already starting to take out the laptops, so I have to put them back. Since the eighth graders normally have music in the history classroom, I prepare to send them to that room. Then the music teacher says that it's too much trouble to have the students move, so he just begins the music lesson in my room. This is in addition to the seventh grade music lessons which normally occur in my room.

My original plan is to use the extra time for the eighth graders to use our online software -- but it wouldn't have been for science. Instead, it was going to be for an online Benchmark Test -- and this is not the same Benchmark as the Illinois State test that I've been mentioning all week! Apparently now there's another Benchmark test that's supposed to align exactly with the Common Core SBAC. But this test is even worse than the Illinois State Benchmark, since this test apparently covers the entire year's worth of standards (in both English and math) even though we give it every trimester.

Both the English teacher and I have extra periods of time on Wednesdays for this online program. On the weird Wednesday schedule, she doesn't see eighth graders at all, and so she devotes the entire day to the online program rather than English. Therefore, she gives both the English and math test to the sixth and seventh graders (and based on the preliminary results, all of them score terribly, just as you would expect this early in the year). This leaves me to give both math and English to the eighth graders -- and due to music, I'll have to give the test tomorrow during IXL (the other online program we use) instead.

Now let's get back to the main Benchmark Test from Illinois State. Today I decide to begin the next strand to be covered on the Benchmark Test, which is on Functions. According to the Benchmark Test itself, the standard to be covered is:

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Notice that the word "slope" isn't mentioned anywhere in this standard, and indeed, the questions on the Benchmark have nothing to do with slope. But when I try to get problems from the Student Journal on this standard, all of those questions mention slope! Obviously, the last thing I want to do is rush through the topic of slope, so instead I pulled questions from the previous standard:

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

In many ways, it all depends on how one interprets 8.F.A.2. The main part of the standard mentions only the properties of functions -- only later on does it mention "rate of change." Apparently the Benchmark Test interprets the standard as requiring slope, while the Student Journal doesn't (even though both come from Illinois State).

With everything going on now, science is the last topic on my mind. I've been linking to Sarah Carter's blog as a resource for science. Well, now I'm linking to her blog for math, since as it turns out, her Algebra I class is now learning about functions:

According to Carter, "rate of change" is actually a distinct topic from slope:

I defined rate of change for my students as the change in the dependent variable divided by the change of the independent variable.  This is the first time I have ever taught rate of change independently from slope, and I LOVE it!  My students are finding the slope, but they don't know that yet.  Most of my 9th graders come in my room with a history of either loving slope or hating slope from their middle school years.  By focusing only on rate of change and not slope, I'm giving them each a fresh start.

Then again, the function questions on our Benchmark only ask about the definition of a function and filling in values, so this isn't really "rate of change," much less slope. This is why to me, the standard actually being tested in 8.F.A.1, not 8.F.A.2.

By the way, today her classes reach one of my favorite Carter-isms -- DIX-ROY. Actually, I forget that now she calls it DIXI-ROYD:

Domain and range aren't on our Benchmark either. If and when they appear, I plan on teaching them DIXI-ROYD as well, since as I said, I think this Carter-ism is very effective.

Meanwhile I'm continuing integers and opposites with seventh grade. Notice that both functions and opposites are two easy topics that can be squeezed in before the Benchmarks. The real problem is my sixth grade lesson -- long division.

Both the Student Journal and the Benchmark Test itself focus on dividing a four-digit number by a two-digit number. But division by a two-digit number isn't easy, especially not for those who are just beginning to divide. So naturally I want to squeeze in some one-digit divisors as well so that students can actually learn the process of divide, multiply, subtract, and bring down.

If you remember from the many discussions on the blog, this standard is one of the battlegrounds between the traditionalist and progressive philosophies. Traditionalists believe that this standard should be taught in a lower grade, certainly no higher than fifth grade. It's obvious that some students have already seen long division, and these students keep calling out the answers. Other students are clearly seeing this for the first time -- indeed, a few students are just mindlessly copying my work on the board. These students end up writing down all of the work, but not the actual quotient!

Believe it or not, there is no "Day in the Life" blogger for the second of the month! So today, I want to link to two of the blogs I like to fall back on. The first I've already mentioned -- Sarah Carter, the math and science teacher. The other is middle school teacher Fawn Nguyen, as she wrote a new post last week:

Two weeks ago I presented at an independent school that’s Preschool through Grade 8 [...] My school is Kindergarten through Grade 8, and the similarity between my school and this independent school pretty much ends there. I teach four classes, my smallest class has 23 8th graders, the other three, all 6th graders, have 32, 35, and 36 students.We’re a Title 1 public school.
And of course, my own school is also K-8, and it has nothing in common with either Nguyen's home school or the one at which she gave her presentation. My school isn't a public school or a private school, but rather a charter school. But just like Nguyen's class, my smallest class is 8th grade.

Just as I'm struggling with grades, Nguyen talks about what she grades in her class:

I don’t grade textbook exercises, i.e., homework, because I can’t think of a bigger waste of my time. I post the answers [in Google Classroom] the day after I assign them. I don’t grade PS [Problem Solving -- dw] because that’s when I ask students to take a risk, persevere, appreciate the struggle. I don’t grade warm-up because I don’t like cats.

Notice that at my school I'm required to count homework as 15% of the grade, so the idea of not grading homework isn't an option. Furthermore, I include my Warm-Up and Exit Passes as part of the 20% that I'm required to count as participation.

I’m finally comfortable with this, something I’ve been fine-tuning each year (more like each grading period) for the last 5 years.

And I'm already having to fine-tune my own grading this first trimester. The main problem is how to incorporate the Benchmark Tests into my grades.

As I think about it more and more, the less I like the idea of counting the Benchmark as a 100-point test similar to the other tests. I speak to the fifth grade teacher today, and she tells me that her students probably won't fare well on their Benchmark due to so many missing standards.

So most likely, I'll count one of the previous tests as less than 100 points -- exactly 100 minus the number of points the Benchmark ends up being worth. Again, this is equivalent to simply declaring the Benchmark to be extra credit.

I'm also confused as to whether to count the online Benchmark I mentioned in this post as a grade. I may end up doing the same thing with this test. This is why I can't make any changes to the grades now, since I don't know how many points I'll use for both Benchmark Tests.

This is a two-day post. My next post will be Friday.

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