Stats, Common Core Style

I'll begin with a description of today, in "A Day in the Life" format. This is for the special day "Parent Conferences Day." (By the way, in the original Tina Cardone blogging challenge, the special day she chose was "Parent Conferences," not Back to School Night or Open House.) 8:00  -- Unlike Back to School Night, we get a minimum day on Parent Conferences Day. The schedule is just like the monthly Monday minimum days -- in particular, all classes meet starting with first period. I, if you recall, don't have a first period class. 8:40  -- Second period arrives. This is the first of two Ethnostats classes. I'm giving all of my classes a quiz today. The quiz for this class is on Chapter 7 of the text, which is on bivariate data, scatterplots, and correlation coefficients r.  Just like the previous quiz two weeks ago, this quiz contains eight questions -- three multiple choice questions worth five points each and five free response questions wor...

Today in Stats, I begin to prepare the class for the quiz tomorrow. This quiz will cover Chapter 7 of the text, on bivariate data, scatterplots, and correlation coefficients  r.  First of all, I started by having the students calculate a value of  r  for a set of data -- with no calculator! The process isn't too difficult, but it's definitely time-consuming. Here are the data we used for this calculation: (1,10), (2,4), (2,10), (3,10), (4,20), (7,20), (7,26), (12,28), (12,30), (12,32), (15,30) These aren't random values -- instead, they were selected so that the means (7 for the  x -values, 20 for the  y -values) and standard deviations (5 for the  x -values, 10 for the  y -values) are whole numbers. The most difficult calculation is to find 16 * 16 = 256, which I give them in advance. (Some teachers do teach the perfect squares up to at least 16^2). Thus the only numbers that we're required to divide by are 5, 10, and 11 (the number of data point...

There are several irregularities with the schedule the next two weeks. That's because this district has fall Parent Conferences for high school. First of all, Parent Conference Day, on Thursday, is itself a minimum day, so that we can begin calling D and F students at 1:30. In order to keep the block schedule balanced, we have odd periods meeting today and Wednesday, and even periods tomorrow and Friday. But then, like with Back to School Night two months ago (and just like many other districts, including LAUSD and my Orange County district last year), there's  another  minimum day coming (the type where teachers, not just students, get to leave at noon to make up for the late night of conferences). In order to separate the two minimum days, the other early day will be a week from Friday. This in turn affects the block schedule for next week -- Monday and Wednesday are odd periods, Tuesday and Thursday are even. How does all of this affect my blogging schedule, you might ask? ...

Today is the third Thursday in October. Here in California, that means it's time for the Great California Shakeout -- the world's largest earthquake drill. By tradition, the time of the drill matches the date -- and so this year's drill is at 10:21 on 10/21. Back when I was a substitute teacher, I would intentionally avoid subbing on Shakeout Day, since I don't want to be the one to watch the students or figure out where on the field to take them. And if I can't skip it completely, I try to cover a teacher I know has a conference period around drill time. Then I drive off campus around 10:00 and don't return until around 11:00 so as not to be involved. This year's drill occurs during first period -- and recall that my first period  was  the class with just one student, until it collapsed and he was switched to my other class. But even though I do have a prep period during the drill, I already knew coming in (from the teachers meeting on Monday) that I'd ...

Today in Stats, we cover the next six pages of Chapter 7, on bivariate data and scatterplots. On these pages, the students learn how to make a scatterplot on their TI calculators. They also learn correlations, including the correlation coefficient r.  Fortunately, there aren't that many differences between the TI-83 and TI-84 as far as scatterplots and their graphs are concerned. There are no TI-84 surprises of the type that we saw in the previous chapter on Normal distributions. I've heard of the correlation coefficient r  before, but this is the first time I've ever seen the actual formula for calculating it:  r  = sigma/sum z _ x   z _ y /( n  - 1), where z _ x  and z _ y  are the standardized (that is, converted to z -scores) values of x  and y . I like how the text explains it -- standardizing the z -scores centers the plot at the origin. Then if there is a positive correlation, then for most points z _ x  and z _ y  have the s...

I'll begin with a description of today, in "A Day in the Life" format. This is my monthly posting day -- my school has a minimum day on one Monday per month. By the way, the dates of these monthly minimum days aren't announced in advance (so it isn't something simple like "the third Monday of each month," even though today is indeed the third Monday of October). 8:00  -- The school day begins -- but my day doesn't. My original first period class had just one student, and so shortly after the September minimum day, he was moved to my fifth period. And so I no longer have a first period class. 8:15  -- Here in California, Governor Newsom has recently announced a vaccine mandate -- all students eligible for the vaccine will soon be required to take it before stepping onto a K-12 campus. But not everyone agrees with the mandate -- so a statewide walkout/protest is scheduled for this time today. Of course walks out of my first period class -- because I do...

Today in Stats, the students take the Chapter 6 Quiz on Normal distributions. This is the second 75-point quiz of the semester. Once again, I return to the online test bank and choose some questions to post on Illuminate. This time, I select eight questions -- a combination of questions from different quizzes there. Of these eight, three of them are multiple choice -- I make each of these five points each. Then the five constructed response questions can be worth 12 points each (a multiple of four to go along with the Illuminate four-point rubric) to give a total of 75 points possible. I won't grade these until over the weekend, so I don't know how yet well the students fare on them. All I know is what the one-on-one aide of the special ed guy tells me -- while she must provide him with plenty of help, he does seem to understand it better than he did with the Chapter 5 Test. As for the other girl who's struggling slightly in recent weeks, I'm not sure. While the guys ar...

Today in Stats, we cover the next six pages in Chapter 6, on Normal distributions. These pages take us into the review for the upcoming Chapter 6 Quiz on Thursday. I'm wondering how prepared my students will be for this quiz. As usual, of the four students in my fifth period class, two of them are definitely stronger than the other pair. One of the students I'm concerned with is, of course, the special ed guy. His one-on-one has pointed out that at least he appears to understand this chapter better than Chapter 5. Then again, Chapter 5 was heavy on lots of vocabulary terms that he had trouble with. Chapter 6, on the other hand, is more about pressing the right calculator buttons -- knowing when to use normalcdf, invNorm, or just the z-score formula without anything else. Sometimes I have to prompt him too much on using the correct function -- and this will be a liability on quiz day. And the lone girl in the class also struggles with knowing the right formula to use without pro...

Today is Columbus Day, or Indigenous Peoples' Day. While California schools don't close for the holiday, some districts hold a PD day today. My district, of course, had our PD day a week ago. Today in Stats, we cover the next three pages in Chapter 6, on Normal distributions. Here the students learn about finding the area between two z-scores. On the TI-83, this is the invNorm function. As for the TI-84, invNorm is just like the normalpdf and normalcdf functions -- mu and sigma are entered. This lesson goes more smoothly this time, since by now I'm expecting the TI-84 version of invNorm to be beefed-up from the TI-83 version. The exception, though, is in fourth period Ethnostats. For most of Chapter 6, the lessons for general Stats and Ethnostats are nearly identical. But since fourth period is larger than either second or fifth periods, everything goes more slowly. This includes the Warm-Up -- I must keep telling the students to be quiet while I read about the Hispanic Her...

Today in Stats, we cover the next six pages in Chapter 6. The students continue to learn about Normal distributions, including the 68-95-99.7 rule for estimating how many data values lie within one, two, or three standard deviations of the mean. The text also shows how to determine how much data lies between any two  z -scores by use of a function on our TI calculators. But here's the problem -- I have a TI-83, and the text appears to be based on TI-83 (although it's labeled simply as TI). But the class set of calculators are TI-84 -- and the normalpdf and normalcdf functions are more powerful on the TI-84. Whereas the TI-83 assumes that the mean (mu) is zero and the standard deviation (sigma) is one, the TI-84 allows us to enter our own values of mu and sigma as parameters. And this catches me off-guard. The students zip through my prepared material quickly, since they don't need to perform the extra step of standardizing the data into z-scores. At least this gives me extr...

Today in Stats, I begin Chapter 6 of the text, called "What's Normal?" The word "Normal" in the title refers to the Normal distribution (always capitalized in our text). Commonly known as the "bell curve," the Normal distribution is one of the best-known models in Statistics. I cover the first six pages of this chapter today. Most of the chapter is about calculating z -scores -- the idea of standard deviation as a ruler. More than any other chapter in the text thus far, Chapter 6 is fairly heavy on calculations. We spend lots of time on notes and vocabulary, but we must also spend time with markers and whiteboards in order to practice finding z -scores. Upcoming pages in this chapter will also have the students learning how to work with Normal distributions on their calculators. I'm definitely worried about how well my special ed student will do in this chapter. On the Chapter 5 Test that I graded over the weekend, his score is only 44 out of 100. ...