In case you haven't figured it out by now with the song I wrote earlier this week, yes, today we go on a field trip to the LA County Fair in Pomona.
By the way, since the original song Meet Me in St. Louis has a second verse, I decided to add another verse to the song I wrote this week. Here is the full version:
MEET ME IN POMONA, MONA
First Verse:
When Mona came up to the school, as she sat,
She hung up her coat and her hat.
She gazed around, but no teacher she found,
So she said "Where can the class be at?"
She remembered the noted, she flipped,
She saw it was a permission slip.
It said, "Hear, hear, it's too slow to learn here,
So let's go on this crazy field trip.
Refrain:
Meet me in Pomona, Mona,
Meet me at the fair.
Don't tell me that I'll learn science,
Any place but there.
The barn will have goats and worms soon,
Kangaroos at the crazy lagoon.
Meet me in Pomona, Mona,
Meet me at the fair!
Second Verse:
To the fair Mona wanted to go,
To see the monkey named Mojo,.
Peacocks and giraffes and a whole lot of laughs,
But how to get there she didn't know.
"What, Mona," the janitor said,
"The bus will leave just ahead,
"What good is that?" Mona said, "Read that,"
And the janitor smiled as he read:
(Repeat Refrain)
Obviously, there isn't much math for me to write about today. But there is a little bit of science, since today we really do see some of the animals I mention in the song, including giraffes and Mojo the monkey, but unfortunately my group of half a dozen sixth graders never make it to the barn. As I wrote earlier this week, today's field trip provides a little bit of Life Science for my seventh graders (so I hope those groups get to see all the animals).
I might as well keep this post relatively brief, since I must prepare for my big monthly post on Sunday the 18th for "A Day in the Life." Speaking of which, here is a link to Matt Baker, who's monthly post is scheduled for today, the 16th:
pythagoraswasanerd.wordpress.com
Unfortunately, as of the time of this post he hadn't made his September 16th post yet. (Pythagoras was a nerd, really? Well, I guess if he was a nerd, he must have been the first nerd!)
Baker did recently make his First Day of School post:
https://pythagoraswasanerd.wordpress.com/2016/09/09/ditlife-first-day-of-school/
As it turns out, Baker is a New York high school teacher. He teaches both Algebra II and a special IB (International Baccalaureate) class for seniors. He began his IB classes with a "Three Act Lesson," which refers to the ideas of Dan Meyer, the king of the MTBoS.
My next post will be my own monthly post, Sunday, September 18th, a day of reflection.
Friday, September 16, 2016
Wednesday, September 14, 2016
Learning Module 2: Show Me the Numbers and Quiz #1 (Days 20-21)
Learning Module 2 of the Illinois State text is called "Show Me the Numbers." Recall that the first four modules are identical in all three grade-level texts.
In this project, students are to take wheels of various sizes and shapes. They measure how far the wheel goes from one to five revolutions, and then display the information on a graph. And so just as the first module has them practicing tables, the second has them practicing their graphing.
Today I decide to do the project only with eighth graders. This is because the sixth graders are having some major behavior issues, and the seventh graders meet only for music on mixed-up Wednesdays. I have only two types of objects with wheels -- some small Hot Wheels and some larger toy cars that I purchased at the 99 cents store for a quarter each.
Again, the reason for doing projects is that it's always more interesting to record data and graph it than it is to just to graph some meaningless numbers. This is why I hope that not allowing the sixth graders to participate will be an effective punishment -- I tell them about all the fun the older students are having and they're missing because of their behavior.
As it turns out, the Hot Wheels are sized such that after five revolutions, the car will have traveled a little less than ten inches. So each revolution is about two inches, and the students end up graphing the points (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) -- in other words, the equation y = 2x. If the students are using the centimeter side, then five revolutions are almost 25 centimeters, and so the points end up being (1, 5), (2, 10), (3, 15), (4, 20), and (5, 25) -- the equation y = 5x.
The bigger cars are a little harder to measure. I believe that five revolutions are supposed to be about 35 centimeters, so the points should be (1, 7), (2, 14), (3, 21), (4, 28), and (5, 35) -- in other words, the equation y = 7x. But the problem is that the students often placed the back wheels at zero but measured the distance from the front wheels. The length of the car is about 10 cm, and so the graphed points were closer to (1, 17), (2, 24), (3, 31), (4, 38), and (5, 45). But this is no problem -- now the students are graphing linear equations like y = 7x + 10 that don't pass through the origin!
One group finishes quickly, and so I decide to have them use the mousetrap cars from Module 1 as a third set of wheels to measure. The mousetrap cars have three wheels -- one tiny wheel in front and two larger wheels in rear. I tell this group to measure using the larger rear wheels, since the front wheel will probably give a graph much like that for Hot Wheels. As it turns out, five revolutions using these larger wheels are almost two meters! So the graph ends up being (1, 40), (2, 80), (3, 120), (4, 160), and (5, 200). I tell the students to graph them on the same set of axes -- so if the graph is just large enough to graph (5, 45) from the previous car, it can barely show (1, 40).
The plan is for the seventh graders to perform the project tomorrow. The sixth graders will still make a graph -- except it's using the older kids' data, since they won't be allowed to use the toy cars.
In fact, the next page in the sixth grade traditional text after is a graph for some strange reason. Out of the blue, the students are asked to graph y = x + 5 and y = 7x. So today, I have the students graph the equation y = x + 5 as an introduction to graphing -- that is, I told them all about what the x and y-axes are as well as the origin.
I don't have time to show them y = 7x today -- but then again, tomorrow I'm giving them the data from the toy cars, and hey, isn't one of them y = 7x (if measured from zero correctly)? So in the end, I really am having them graph y = 7x from the text!
Recall that on Wednesdays, I give my eighth graders a science period. Today I decide to go to the next physical science lesson from Sarah Carter, on scientific notation:
http://mathequalslove.blogspot.com/2016/09/scientific-notation-ordering-cards.html
Some students figure out the order quickly after just one hint -- when I tell them that if the exponent is positive, the number is greater than one. Oops -- I probably should have done what Carter suggested and had a second set of cards ready for them.
Today is a two-day post, so let me give my plans for tomorrow. It's an assessment day -- eighth graders get a General Quiz, seventh graders get a Dren Quiz, and sixth graders get a test (after we finish graphing). The eighth grade test will be on converting rational numbers from decimal to fraction form and back -- and includes one question where they must name an irrational number.
Each day, I will continue to link to the "A Day in the Life" poster assigned to today. Again, there are many middle school teachers participating, but the poster for the 14th is a high school teacher -- in fact, it's none other than Tina Cardone, the creator of the "A Day in the Life" challenge. Here is her post for September 14th:
http://drawingonmath.blogspot.com/2016/09/day-in-life-sept-14.html
Cardone writes that she gives her Honors Algebra I students a "challenging puzzle" -- it took me a while to figure out that she's referring to the famous "four fours" puzzle, where one tries to write the numbers from 1 to 100 using four fours.
Also, I think it's interesting that Cardone has even fewer students than I do -- just 60, which must be a rarity at a public high school such as hers.
My next post will be on Friday.
In this project, students are to take wheels of various sizes and shapes. They measure how far the wheel goes from one to five revolutions, and then display the information on a graph. And so just as the first module has them practicing tables, the second has them practicing their graphing.
Today I decide to do the project only with eighth graders. This is because the sixth graders are having some major behavior issues, and the seventh graders meet only for music on mixed-up Wednesdays. I have only two types of objects with wheels -- some small Hot Wheels and some larger toy cars that I purchased at the 99 cents store for a quarter each.
Again, the reason for doing projects is that it's always more interesting to record data and graph it than it is to just to graph some meaningless numbers. This is why I hope that not allowing the sixth graders to participate will be an effective punishment -- I tell them about all the fun the older students are having and they're missing because of their behavior.
As it turns out, the Hot Wheels are sized such that after five revolutions, the car will have traveled a little less than ten inches. So each revolution is about two inches, and the students end up graphing the points (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) -- in other words, the equation y = 2x. If the students are using the centimeter side, then five revolutions are almost 25 centimeters, and so the points end up being (1, 5), (2, 10), (3, 15), (4, 20), and (5, 25) -- the equation y = 5x.
The bigger cars are a little harder to measure. I believe that five revolutions are supposed to be about 35 centimeters, so the points should be (1, 7), (2, 14), (3, 21), (4, 28), and (5, 35) -- in other words, the equation y = 7x. But the problem is that the students often placed the back wheels at zero but measured the distance from the front wheels. The length of the car is about 10 cm, and so the graphed points were closer to (1, 17), (2, 24), (3, 31), (4, 38), and (5, 45). But this is no problem -- now the students are graphing linear equations like y = 7x + 10 that don't pass through the origin!
One group finishes quickly, and so I decide to have them use the mousetrap cars from Module 1 as a third set of wheels to measure. The mousetrap cars have three wheels -- one tiny wheel in front and two larger wheels in rear. I tell this group to measure using the larger rear wheels, since the front wheel will probably give a graph much like that for Hot Wheels. As it turns out, five revolutions using these larger wheels are almost two meters! So the graph ends up being (1, 40), (2, 80), (3, 120), (4, 160), and (5, 200). I tell the students to graph them on the same set of axes -- so if the graph is just large enough to graph (5, 45) from the previous car, it can barely show (1, 40).
The plan is for the seventh graders to perform the project tomorrow. The sixth graders will still make a graph -- except it's using the older kids' data, since they won't be allowed to use the toy cars.
In fact, the next page in the sixth grade traditional text after is a graph for some strange reason. Out of the blue, the students are asked to graph y = x + 5 and y = 7x. So today, I have the students graph the equation y = x + 5 as an introduction to graphing -- that is, I told them all about what the x and y-axes are as well as the origin.
I don't have time to show them y = 7x today -- but then again, tomorrow I'm giving them the data from the toy cars, and hey, isn't one of them y = 7x (if measured from zero correctly)? So in the end, I really am having them graph y = 7x from the text!
Recall that on Wednesdays, I give my eighth graders a science period. Today I decide to go to the next physical science lesson from Sarah Carter, on scientific notation:
http://mathequalslove.blogspot.com/2016/09/scientific-notation-ordering-cards.html
Some students figure out the order quickly after just one hint -- when I tell them that if the exponent is positive, the number is greater than one. Oops -- I probably should have done what Carter suggested and had a second set of cards ready for them.
Today is a two-day post, so let me give my plans for tomorrow. It's an assessment day -- eighth graders get a General Quiz, seventh graders get a Dren Quiz, and sixth graders get a test (after we finish graphing). The eighth grade test will be on converting rational numbers from decimal to fraction form and back -- and includes one question where they must name an irrational number.
Each day, I will continue to link to the "A Day in the Life" poster assigned to today. Again, there are many middle school teachers participating, but the poster for the 14th is a high school teacher -- in fact, it's none other than Tina Cardone, the creator of the "A Day in the Life" challenge. Here is her post for September 14th:
http://drawingonmath.blogspot.com/2016/09/day-in-life-sept-14.html
Cardone writes that she gives her Honors Algebra I students a "challenging puzzle" -- it took me a while to figure out that she's referring to the famous "four fours" puzzle, where one tries to write the numbers from 1 to 100 using four fours.
Also, I think it's interesting that Cardone has even fewer students than I do -- just 60, which must be a rarity at a public high school such as hers.
My next post will be on Friday.
Tuesday, September 13, 2016
Student Assessment Page (Day 19)
Well, I'm officially a part of the "A Day in the Life" MTBoS blog challenge. But there are a few things that I want to point out about this challenge.
First of all, I chose the 18th as the date of my monthly post. I first stumbled onto this project on September 7th, so I was hoping that the 7th would be my date. But as it turns out, not only is the 7th already taken, but so are all dates from the 8th through the 17th. Again -- that's what I get for arriving late to the party. And so I chose the next available date after today's date -- the 18th. If I want to be included in the final project, I had to select a day that isn't already chosen.
Going back in time, this change means that August 18th -- unlike August 7th -- is past the first day of school, which means that my first monthly post should be for August 18th, not September 18th. To rectify this, I went back and edited my post in order to conform to the challenge requirements. Notice that August 18th was the third day of school -- as well as my first skipped day, since I don't post on school days that are multiples of three. So I had to go back to August 19th (Day 4) and edit in "A Day in the Life" for August 18th.
I also decided to go back to edit my August 12th post, which is supposed to satisfy the "week before students arrive (a PD day)" challenge requirement. As I wrote earlier, this post contains several pages of links (to other MTBoS members) before I finally mention the PD day. This is unacceptable for a post that's to be included in a book, so I indeed edited out all the links.
And so I submitted three posts -- August 12th (a PD day), August 16th (Day 1), and August 18th (my monthly post, which also happens to be Day 3) -- directly to Tina Cardone, the challenge leader. Here is a link to the edited versions of the three submitted posts (actually I left the post on the 16th intact):
A PD Day
Day 1
August 18th (Day 3)
Looking ahead, it turns out that the 18th is a great choice for my monthly posting day. Notice that the 18th doesn't fall on a Monday for a full year -- not until September 18th, 2017, after "A Day in the Life" is completed. Monday is my worst posting day, since the coding teacher takes over. I doubt that Cardone and the other readers want to see "8:25 -- I watch the coding teacher arrive to teach the seventh graders, 10:05 -- I watch the coding teacher arrive to teach the eighth graders," and so on.
On the other hand, notice that my next monthly posting day -- September 18th, 2016, happens to fall on a Sunday. This, at first glance, would seem to be worse than Monday, since on Sunday I won't even be watching anyone teach.
But Cardone actually provides us with five special Reflection Questions, and recommends that we answer those questions instead when our chosen day falls on the weekend. Of course, there's nothing stopping me from answering the Reflection Questions in a Monday post, but there's less time. In short, Monday is the worst of both worlds -- I don't actually teach anything, yet I must go through the motions, thus taking time away from the Reflection Questions.
Oh, and by the way, I usually don't post on the weekend, especially not during the school year. And yes, I know that my "August 18th" post is actually dated the 19th, but that was before I knew about the challenge. From now on, I want to post on the actual 18th of the month to avoid confusing the challenge readers. So expect a rare weekend post on Sunday, September 18th.
For now, let's leave the challenge with a link to one of the other participants. Since today is the 13th, here's a link to Kit Golan, the blogger who chose the 13th as his monthly posting day:
https://teachdomore.wordpress.com/
Golan teaches at a New York middle school -- that's right, middle school! Actually, a quick glance at some of the other participants reveals a few other middle school bloggers. That's what I like about these MTBoS challenges -- before them, I had all sorts of trouble finding middle school blogs.
Golan writes that for years, he taught only eighth grade, but now he has both 6th and 7th graders. He writes that he works at a small school that is co-located with another school. This sounds just like the situation with my own charter school -- except it appears the California equivalent of his school would be a magnet, not a charter. Unlike me, Golan doesn't have a support staff aide, but he does have a student teacher.
As of the time of this post, Golan hasn't written his September 13th post, but here's a link to his special First Day of School post:
https://teachdomore.wordpress.com/2016/09/11/day-in-the-life-first-day-of-school-2-days-actually/
In this post, Golan writes that his first day is focused on procedures, including a paper-passing procedure that comes from the Wongs and their The First Days of School book. It's a bit confusing though, since so many students arrive and leave at different times.
By the way, here is a link to where Cardone's finished project will eventually go:
http://ditlife.tumblr.com/
So far, none of the posts I submitted have appeared here yet.
Okay, that's enough about MTBoS challenges. Today is the final day of Learning Module 1. With my younger students, I check their foldable notes. For the eighth graders, I will check the traditional texts to see how many pages they have filled in. They should have reached the last page of the current lesson in the traditional text, labeled "Student Assessment."
The main thing I want to mention in this post is my song for Music Break. Coming up with all of the various songs that I sing for music break is quite difficult. As I've written before, I first use a random number generator and convert the numbers into notes, then I come up with a song that both fits the notes and describes what we are learning in math or science.
Now consider the two songs that seem to be the most popular with the students -- Fraction Fever and Count on It. These songs were also the two easiest for me to come up with. The tune of Fraction Fever came from an old computer game -- even though the song has no lyrics and I hadn't heard the tune in over 20 years, it's still easier to add lyrics to a tune that has already been created. And of course Count on It was even simpler, as the entire song comes from Square One TV, so all I had to do was find the song on YouTube and the lyrics from a fan of the old TV show.
Because of this, there will be some days when -- rather than attempt to invent a tune and lyrics from scratch -- I will sing a parody of an established song during my Music Break.
Parodies of popular songs changed for math or science are quite popular. I've mentioned before that several artists have changed Rebecca Black's Friday to "Pi Day," and of course there are also several versions of "American Pi."
For today's parody, I have chosen the classic Meet Me in St. Louis, Louis, My version will change "St. Louis" to "Pomona," because my song will refer to the LA County Fair that takes place in the city of Pomona every September.
At first, I just wanted to repeat the last two syllables, "Meet Me in Pomona-mona," as this directly parodies "St. Louis, Louis." But as I observe the lyrics of St. Louis (in preparation for parodying them), I notice that the second "Louis" is actually a person's name. Fortunately, "Mona" is also a person's name, so the title stands at "Meet Me in Pomona, Mona." In this song, I'm telling an imaginary girl named Mona about all of the science she'll learn by going to the fair. Some of the things that Mona sees at the fair come from the following link:
http://tlcfairplex.org/fair/home
And here is the parody:
MEET ME IN POMONA, MONA
When Mona came up to the school, as she sat,
She hung up her coat and her hat.
She gazed around, but no teacher she found,
So she said "Where can the class be at?"
She remembered the noted, she flipped,
She saw it was a permission slip.
It said, "Hear, hear, it's too slow to learn here,
So let's go on this crazy field trip.
Refrain:
Meet me in Pomona, Mona,
Meet me at the fair.
Don't tell me that I'll learn science,
Any place but there.
The barn will have goats and worms soon,
Kangaroos at the crazy lagoon.
Meet me in Pomona, Mona,
Meet me at the fair!
One thing notable about this song is that, as a science song, the focus is obviously on the animals (and plants) that people can see at the fair. This hopefully will help out my seventh graders, who ought to be focusing on Life Science this year. The science I'll teach them is limited to the projects that appear in the Illinois State text, which seem to be heavier on Physical Science than Life Science.
At the end of the lesson, I give the eighth graders an Exit Pass based on the page that comes right after the Student Assessment Page -- a repeat of the introduction about how some mathematicians were upset to find out that some numbers are irrational. And so my Exit Pass directed the students to write about the discoverer of the irrationality of sqrt(2) -- Pythagoras. One student did remember my story about how he killed the person who gave away the secret. But as the students are still struggling to convert between fractions and decimals, and so I spend more time making sure they can convert than talking about the specific Pythagoras proof.
Well, let's find out how popular my "Meet Me in Pomona" song turns out to be!
First of all, I chose the 18th as the date of my monthly post. I first stumbled onto this project on September 7th, so I was hoping that the 7th would be my date. But as it turns out, not only is the 7th already taken, but so are all dates from the 8th through the 17th. Again -- that's what I get for arriving late to the party. And so I chose the next available date after today's date -- the 18th. If I want to be included in the final project, I had to select a day that isn't already chosen.
Going back in time, this change means that August 18th -- unlike August 7th -- is past the first day of school, which means that my first monthly post should be for August 18th, not September 18th. To rectify this, I went back and edited my post in order to conform to the challenge requirements. Notice that August 18th was the third day of school -- as well as my first skipped day, since I don't post on school days that are multiples of three. So I had to go back to August 19th (Day 4) and edit in "A Day in the Life" for August 18th.
I also decided to go back to edit my August 12th post, which is supposed to satisfy the "week before students arrive (a PD day)" challenge requirement. As I wrote earlier, this post contains several pages of links (to other MTBoS members) before I finally mention the PD day. This is unacceptable for a post that's to be included in a book, so I indeed edited out all the links.
And so I submitted three posts -- August 12th (a PD day), August 16th (Day 1), and August 18th (my monthly post, which also happens to be Day 3) -- directly to Tina Cardone, the challenge leader. Here is a link to the edited versions of the three submitted posts (actually I left the post on the 16th intact):
A PD Day
Day 1
August 18th (Day 3)
Looking ahead, it turns out that the 18th is a great choice for my monthly posting day. Notice that the 18th doesn't fall on a Monday for a full year -- not until September 18th, 2017, after "A Day in the Life" is completed. Monday is my worst posting day, since the coding teacher takes over. I doubt that Cardone and the other readers want to see "8:25 -- I watch the coding teacher arrive to teach the seventh graders, 10:05 -- I watch the coding teacher arrive to teach the eighth graders," and so on.
On the other hand, notice that my next monthly posting day -- September 18th, 2016, happens to fall on a Sunday. This, at first glance, would seem to be worse than Monday, since on Sunday I won't even be watching anyone teach.
But Cardone actually provides us with five special Reflection Questions, and recommends that we answer those questions instead when our chosen day falls on the weekend. Of course, there's nothing stopping me from answering the Reflection Questions in a Monday post, but there's less time. In short, Monday is the worst of both worlds -- I don't actually teach anything, yet I must go through the motions, thus taking time away from the Reflection Questions.
Oh, and by the way, I usually don't post on the weekend, especially not during the school year. And yes, I know that my "August 18th" post is actually dated the 19th, but that was before I knew about the challenge. From now on, I want to post on the actual 18th of the month to avoid confusing the challenge readers. So expect a rare weekend post on Sunday, September 18th.
For now, let's leave the challenge with a link to one of the other participants. Since today is the 13th, here's a link to Kit Golan, the blogger who chose the 13th as his monthly posting day:
https://teachdomore.wordpress.com/
Golan teaches at a New York middle school -- that's right, middle school! Actually, a quick glance at some of the other participants reveals a few other middle school bloggers. That's what I like about these MTBoS challenges -- before them, I had all sorts of trouble finding middle school blogs.
Golan writes that for years, he taught only eighth grade, but now he has both 6th and 7th graders. He writes that he works at a small school that is co-located with another school. This sounds just like the situation with my own charter school -- except it appears the California equivalent of his school would be a magnet, not a charter. Unlike me, Golan doesn't have a support staff aide, but he does have a student teacher.
As of the time of this post, Golan hasn't written his September 13th post, but here's a link to his special First Day of School post:
https://teachdomore.wordpress.com/2016/09/11/day-in-the-life-first-day-of-school-2-days-actually/
In this post, Golan writes that his first day is focused on procedures, including a paper-passing procedure that comes from the Wongs and their The First Days of School book. It's a bit confusing though, since so many students arrive and leave at different times.
By the way, here is a link to where Cardone's finished project will eventually go:
http://ditlife.tumblr.com/
So far, none of the posts I submitted have appeared here yet.
Okay, that's enough about MTBoS challenges. Today is the final day of Learning Module 1. With my younger students, I check their foldable notes. For the eighth graders, I will check the traditional texts to see how many pages they have filled in. They should have reached the last page of the current lesson in the traditional text, labeled "Student Assessment."
The main thing I want to mention in this post is my song for Music Break. Coming up with all of the various songs that I sing for music break is quite difficult. As I've written before, I first use a random number generator and convert the numbers into notes, then I come up with a song that both fits the notes and describes what we are learning in math or science.
Now consider the two songs that seem to be the most popular with the students -- Fraction Fever and Count on It. These songs were also the two easiest for me to come up with. The tune of Fraction Fever came from an old computer game -- even though the song has no lyrics and I hadn't heard the tune in over 20 years, it's still easier to add lyrics to a tune that has already been created. And of course Count on It was even simpler, as the entire song comes from Square One TV, so all I had to do was find the song on YouTube and the lyrics from a fan of the old TV show.
Because of this, there will be some days when -- rather than attempt to invent a tune and lyrics from scratch -- I will sing a parody of an established song during my Music Break.
Parodies of popular songs changed for math or science are quite popular. I've mentioned before that several artists have changed Rebecca Black's Friday to "Pi Day," and of course there are also several versions of "American Pi."
For today's parody, I have chosen the classic Meet Me in St. Louis, Louis, My version will change "St. Louis" to "Pomona," because my song will refer to the LA County Fair that takes place in the city of Pomona every September.
At first, I just wanted to repeat the last two syllables, "Meet Me in Pomona-mona," as this directly parodies "St. Louis, Louis." But as I observe the lyrics of St. Louis (in preparation for parodying them), I notice that the second "Louis" is actually a person's name. Fortunately, "Mona" is also a person's name, so the title stands at "Meet Me in Pomona, Mona." In this song, I'm telling an imaginary girl named Mona about all of the science she'll learn by going to the fair. Some of the things that Mona sees at the fair come from the following link:
http://tlcfairplex.org/fair/home
And here is the parody:
MEET ME IN POMONA, MONA
When Mona came up to the school, as she sat,
She hung up her coat and her hat.
She gazed around, but no teacher she found,
So she said "Where can the class be at?"
She remembered the noted, she flipped,
She saw it was a permission slip.
It said, "Hear, hear, it's too slow to learn here,
So let's go on this crazy field trip.
Refrain:
Meet me in Pomona, Mona,
Meet me at the fair.
Don't tell me that I'll learn science,
Any place but there.
The barn will have goats and worms soon,
Kangaroos at the crazy lagoon.
Meet me in Pomona, Mona,
Meet me at the fair!
One thing notable about this song is that, as a science song, the focus is obviously on the animals (and plants) that people can see at the fair. This hopefully will help out my seventh graders, who ought to be focusing on Life Science this year. The science I'll teach them is limited to the projects that appear in the Illinois State text, which seem to be heavier on Physical Science than Life Science.
At the end of the lesson, I give the eighth graders an Exit Pass based on the page that comes right after the Student Assessment Page -- a repeat of the introduction about how some mathematicians were upset to find out that some numbers are irrational. And so my Exit Pass directed the students to write about the discoverer of the irrationality of sqrt(2) -- Pythagoras. One student did remember my story about how he killed the person who gave away the secret. But as the students are still struggling to convert between fractions and decimals, and so I spend more time making sure they can convert than talking about the specific Pythagoras proof.
Well, let's find out how popular my "Meet Me in Pomona" song turns out to be!
Friday, September 9, 2016
Dren Quiz #1 (Days 17-18)
Today the eighth graders take their first Dren Quiz of the year. Recall that a Dren Quiz is my name for the basic multiplication quiz that I give from time to time in my classes.
Of course, I don't devote the entire 80-minute block to the Dren Quiz. After the Warm-Up and collecting the homework, I return to converting repeating decimals to fractions. But now I begin with a very famous problem:
Convert 0.999... to a rational number.
Let's use the method that I showed the students earlier this week:
x = 0.999...
10x = 9.999...
-x = -0.999...
9x = 9
x = 1
And so we see that 0.999... is actually equal to 1. This counter-intuitive result has been discussed time and time again at various websites, for example, Cut the Knot:
http://www.cut-the-knot.org/arithmetic/999999.shtml
and Metamath:
http://us.metamath.org/mpegif/0.999....html
The proof that 0.999... = 1 is as rock-solid as the proof that 2+2 = 4 -- but according to the above link, 40% of the respondents to a certain poll disagreed with 0.999... = 1.
The famous YouTube star Vi Hart even created a video about 0.999... = 1:
Meanwhile, at Math Forum, debaters like to discuss 0.999... all the time. Here is a link to the most recent 0.999... debate:
http://mathforum.org/kb/message.jspa?messageID=9964374
Notice that the original dissenter created his own video on why 0.999... should not equal 1. I tell my students that people like John Gabriel, the video creator, and Wolfgang Muckenheim -- who is, believe it or not, a professor at a German university -- are called not "drens," but cranks due to their inability to accept a simple proof -- and that if they understand this proof, they are already smarter than a German professor!
After talking about 0.999... = 1, I sing my latest song at music break. Notice that this song has a separate verse for each grade level, in order to reflect what they are learning:
ANOTHER RATIO SONG
6th Grade:
What can we do with fractions?
What can we do with fractions?
As everyone knows
We write ratios.
You can do no worse
If you write the 1st one 1st.
In between write dots
Then the 2nd -- that's a lot
We can do with fractions!
7th Grade:
What can we do with fractions?
What can we do with fractions?
We see over there
With ratios we can compare.
The fractions to divide
Flip the 2nd & multiply.
Remember to simplify
And now you know why
We can use fractions!
8th Grade:
What can we do with fractions?
What can we do with fractions?
We can make them decimal
And that is not all.
Another major feat
Is that decimals repeat.
They go on forever.
Know that whenever
We can use fractions!
After the break, I like to lead into the Dren Quiz by discussing various traditionalists who emphasize the need to learn basic skills. I've said before that I want to emphasize the website of Barry Garelick especially since now he's a middle school teacher himself. His most recent post does discuss the need to learn basic math -- but as usual, it's SteveH who makes the specific comment:
https://traditionalmath.wordpress.com/2016/09/06/developmentally-appropriateinappropriate-dept/
SteveH:
In my son’s fifth grade class, many bright students still didn’t know the times table and some had to add 7+8 using their fingers.
Notice that SteveH doesn't blame the students for being drens, rather the school and its curriculum -- the U of Chicago elementary text that many traditionalists despise.
I say that part of the issue is about the generation gap:
1945 = End of World War II
1946-1964 = Baby Boomers
1964-1982 = Generation X
1982-2000 = Generation Y, or Millennials
2000-present = Generation Z
1978-2008 = The "Dumbest Generation" of Mark Bauerlein
Naturally my students don't like hearing a Boomer like Bauerlein tell them that they are in the "Dumbest Generation" -- but then again, I tell them that I myself am part of this generation as well. I try to be careful enough to use pronouns "we" and "us" in explaining why we're considered part of the Dumbest Generation.
By the way, the boundaries between the generations have been much debated. Next week, the CBS show Survivor will feature tribes made up of Gen X'ers and Millennials. The oldest player on the Gen X tribe is 52 and the youngest is 33, which matches well with the dates listed above. I always knew that I myself on the cusp of two generations. By this definition I'm a late Gen X'er, as I'm older than the youngest member of the Gen X tribe. Of course, I and the other youngest Gen X'ers are fully included in Bauerlein's "Dumbest Generation."
http://www.joannejacobs.com/2009/04/calculators-dont-answer/
http://www.joannejacobs.com/2009/05/confused-bothered-and-befuddled/
Earlier I said that I wouldn't quote Bill at the Joanne Jacobs site this year -- and I don't. I only read the quotes by two science teachers -- nothing by Bill:
Miller T. Smith:
I have honors chemistry students who have passed three high school level math classes who can’t do fractions, scienctfic notation, don’t kow the mutipliction tables, can’t graph on paper, can’t multiply fractions, on and on.
Physics Teacher:
I want to make sure that the students see some comments about the inability to multiply by ten right before their first Dren Quiz, which is on multiplying by ten. The idea is that the students should be motivated to prove people like the two science teachers and Bauerlein wrong.
As today is the first Dren Quiz, everyone should be starting with their tens today. But last week, two students had trouble logging into the computer system and so they couldn't use the online program that they were supposed to be using. These two girls were still upset that they hadn't fared well on the eighth grade test I'd given them earlier that day -- but then they found a stack of Dren Quizzes left over from the sixth grade lying on my desk. So they just took the quiz right then and there.
The top student in my class -- the girl I'm hoping to teach Algebra I this year -- is wondering why I'm insulting her by giving her a lowly Dren Quiz. On the other hand, the bottom student in my class enjoys the Dren Quiz and is hoping that I'll give another such quiz soon.
This is a two-day post, officially covering today and Monday. But Mondays are coding days with very little math taught, so there wouldn't be much for me to write about Monday anyway.
But notice that Monday -- Day 18 -- marks the end of the first 10% of the year, which I've designated as the Willis Unit (or Wong Unit). During the Willis Unit, I've learned the names of all my students as well as their strengths and weaknesses, while the students have learned all about me as a teacher.
I've made several changes to my plans during the Willis Unit. I've rotated my Dren Quizzes, general quizzes, and tests during the Willis Unit, but now my plan is to switch to giving them to all three grades on the same days.
I've also decided, after switching from local Participation Points to Scholar Dollars for the entire school, to return to Participation Points. What happened was that a few seventh graders ended up stealing a large number of Scholar Dollars, and my supply of them hasn't been replenished because I can't be trusted with them. So I'd rather return to Participation Points -- which I just record as marks on a sheet of paper.
By the way, speaking of the younger grades, I decided to let my seventh graders use their Foldables on the harder test, but the sixth graders couldn't use them on the easier quiz. But one sixth grader tries to use a Foldable anyway -- forcing me to give the student a zero and make a parent phone call.
My next post will be on Tuesday.
Of course, I don't devote the entire 80-minute block to the Dren Quiz. After the Warm-Up and collecting the homework, I return to converting repeating decimals to fractions. But now I begin with a very famous problem:
Convert 0.999... to a rational number.
Let's use the method that I showed the students earlier this week:
x = 0.999...
10x = 9.999...
-x = -0.999...
9x = 9
x = 1
And so we see that 0.999... is actually equal to 1. This counter-intuitive result has been discussed time and time again at various websites, for example, Cut the Knot:
http://www.cut-the-knot.org/arithmetic/999999.shtml
and Metamath:
http://us.metamath.org/mpegif/0.999....html
The proof that 0.999... = 1 is as rock-solid as the proof that 2+2 = 4 -- but according to the above link, 40% of the respondents to a certain poll disagreed with 0.999... = 1.
The famous YouTube star Vi Hart even created a video about 0.999... = 1:
Meanwhile, at Math Forum, debaters like to discuss 0.999... all the time. Here is a link to the most recent 0.999... debate:
http://mathforum.org/kb/message.jspa?messageID=9964374
Notice that the original dissenter created his own video on why 0.999... should not equal 1. I tell my students that people like John Gabriel, the video creator, and Wolfgang Muckenheim -- who is, believe it or not, a professor at a German university -- are called not "drens," but cranks due to their inability to accept a simple proof -- and that if they understand this proof, they are already smarter than a German professor!
After talking about 0.999... = 1, I sing my latest song at music break. Notice that this song has a separate verse for each grade level, in order to reflect what they are learning:
ANOTHER RATIO SONG
6th Grade:
What can we do with fractions?
What can we do with fractions?
As everyone knows
We write ratios.
You can do no worse
If you write the 1st one 1st.
In between write dots
Then the 2nd -- that's a lot
We can do with fractions!
7th Grade:
What can we do with fractions?
What can we do with fractions?
We see over there
With ratios we can compare.
The fractions to divide
Flip the 2nd & multiply.
Remember to simplify
And now you know why
We can use fractions!
8th Grade:
What can we do with fractions?
What can we do with fractions?
We can make them decimal
And that is not all.
Another major feat
Is that decimals repeat.
They go on forever.
Know that whenever
We can use fractions!
After the break, I like to lead into the Dren Quiz by discussing various traditionalists who emphasize the need to learn basic skills. I've said before that I want to emphasize the website of Barry Garelick especially since now he's a middle school teacher himself. His most recent post does discuss the need to learn basic math -- but as usual, it's SteveH who makes the specific comment:
https://traditionalmath.wordpress.com/2016/09/06/developmentally-appropriateinappropriate-dept/
SteveH:
In my son’s fifth grade class, many bright students still didn’t know the times table and some had to add 7+8 using their fingers.
Notice that SteveH doesn't blame the students for being drens, rather the school and its curriculum -- the U of Chicago elementary text that many traditionalists despise.
I say that part of the issue is about the generation gap:
1945 = End of World War II
1946-1964 = Baby Boomers
1964-1982 = Generation X
1982-2000 = Generation Y, or Millennials
2000-present = Generation Z
1978-2008 = The "Dumbest Generation" of Mark Bauerlein
Naturally my students don't like hearing a Boomer like Bauerlein tell them that they are in the "Dumbest Generation" -- but then again, I tell them that I myself am part of this generation as well. I try to be careful enough to use pronouns "we" and "us" in explaining why we're considered part of the Dumbest Generation.
By the way, the boundaries between the generations have been much debated. Next week, the CBS show Survivor will feature tribes made up of Gen X'ers and Millennials. The oldest player on the Gen X tribe is 52 and the youngest is 33, which matches well with the dates listed above. I always knew that I myself on the cusp of two generations. By this definition I'm a late Gen X'er, as I'm older than the youngest member of the Gen X tribe. Of course, I and the other youngest Gen X'ers are fully included in Bauerlein's "Dumbest Generation."
http://www.joannejacobs.com/2009/04/calculators-dont-answer/
http://www.joannejacobs.com/2009/05/confused-bothered-and-befuddled/
Earlier I said that I wouldn't quote Bill at the Joanne Jacobs site this year -- and I don't. I only read the quotes by two science teachers -- nothing by Bill:
Miller T. Smith:
I have honors chemistry students who have passed three high school level math classes who can’t do fractions, scienctfic notation, don’t kow the mutipliction tables, can’t graph on paper, can’t multiply fractions, on and on.
Physics Teacher:
I’ve had kids who can’t multiply by ten or divide by one.
How are these students supposed to grasp the idea of momentum if vector quantities are completely beyond there grasp?
I want to make sure that the students see some comments about the inability to multiply by ten right before their first Dren Quiz, which is on multiplying by ten. The idea is that the students should be motivated to prove people like the two science teachers and Bauerlein wrong.
As today is the first Dren Quiz, everyone should be starting with their tens today. But last week, two students had trouble logging into the computer system and so they couldn't use the online program that they were supposed to be using. These two girls were still upset that they hadn't fared well on the eighth grade test I'd given them earlier that day -- but then they found a stack of Dren Quizzes left over from the sixth grade lying on my desk. So they just took the quiz right then and there.
The top student in my class -- the girl I'm hoping to teach Algebra I this year -- is wondering why I'm insulting her by giving her a lowly Dren Quiz. On the other hand, the bottom student in my class enjoys the Dren Quiz and is hoping that I'll give another such quiz soon.
This is a two-day post, officially covering today and Monday. But Mondays are coding days with very little math taught, so there wouldn't be much for me to write about Monday anyway.
But notice that Monday -- Day 18 -- marks the end of the first 10% of the year, which I've designated as the Willis Unit (or Wong Unit). During the Willis Unit, I've learned the names of all my students as well as their strengths and weaknesses, while the students have learned all about me as a teacher.
I've made several changes to my plans during the Willis Unit. I've rotated my Dren Quizzes, general quizzes, and tests during the Willis Unit, but now my plan is to switch to giving them to all three grades on the same days.
I've also decided, after switching from local Participation Points to Scholar Dollars for the entire school, to return to Participation Points. What happened was that a few seventh graders ended up stealing a large number of Scholar Dollars, and my supply of them hasn't been replenished because I can't be trusted with them. So I'd rather return to Participation Points -- which I just record as marks on a sheet of paper.
By the way, speaking of the younger grades, I decided to let my seventh graders use their Foldables on the harder test, but the sixth graders couldn't use them on the easier quiz. But one sixth grader tries to use a Foldable anyway -- forcing me to give the student a zero and make a parent phone call.
My next post will be on Tuesday.
Thursday, September 8, 2016
Whiteboard Lesson: Converting Rational Numbers (Day 16)
Let me begin this post by introducing my next MTBoS challenge -- and suddenly you're thinking, there's yet another MTBoS challenge? So Blaugust isn't enough for us -- now we need Septemblog, Octoblog, Novemblog, Decemblog, and so on?
Actually, this is a different sort of challenge. Instead of posting everyday for a month, this challenge involves posting once a month for a year:
http://drawingonmath.blogspot.com/2016/08/day-in-life-book-plan.html
The creator of this challenge is Tina Cardone, a Massachusetts high school math teacher. I've written about Cardone before -- she came up with some of the prompts for the 2016 Blogging Initiative back in January. Here is Cardone's description of the challenge:
Each author will pick a different date and write on the same day of the month each month.
Additional key days where all authors will write:
Now I live in Southern California, so of course I won't write about a "Snow Day," but I can write on all the other days -- perhaps I can include a "Rain Day" as the California equivalent. According to Cardone, the prompt for each day is "A Day in the Life of...."
As is always the case, I'm late to the party. Cardone tells us that she may include some of our posts in a book that she's writing -- but not mine, since I joined too late. And two of the days in the list have already passed -- "A teacher day..." and the first day of school. But I did write posts for each of those first two days:
A teacher day the week before students arrive
This post is very long -- I began the post with a disclaimer, followed by a Blaugust prompt, and then links to various other teacher websites. Scroll down to "More on the Illinois State text" -- this and the following sections mention teacher meetings and some of the information I learned there. It is not written in "A Day in the Life of..." format -- but I can always go back and edit that post if I need to to satisfy the challenge requirement.
First day of school
I actually did write this post in "A Day in the Life of..." format, so it should already meet challenge requirements as it is. Here's another example of what "A Day in the Life of..." posts look like, based on yesterday:
7:45 -- I arrive at my school.
8:15 -- I report to the playground, where many of my students are beginning to arrive. The students are told to gather in a circle for the flag salute. But this time, the sixth graders and I are in charge of leading the morning circle routine.
8:25 -- My first class, a sixth grade class, begins. This class has grown so that there are now 26 students in this class. I continue an easy lesson on ratios, and the students take foldable notes.
9:20 -- My sixth graders leave and my eighth graders arrive. Now I admit that on Wednesdays, which is our Common Planning day, the schedule is very confusing -- and in fact, the other middle school teachers and I are still trying to work out the kinks. The eighth graders are supposed to be here for two periods -- the first to do a computer lesson, the second for math.
My plan is that I would use the computer period for science. But I don't have the students go to the computer, because I knew that all the computer questions were on lessons they haven't learned -- the students would just guess all the answers and use the rest of the time for free computer play. The students need to learn science. So I decide to give them a science lesson from the famous MTBoS blogger Sarah Carter, on accuracy and precision:
http://mathequalslove.blogspot.com/2016/09/accuracy-precision-error-and-percent.html
I have the students throw balls of crumpled paper into the trash can in order to determine the accuracy and precision. Today (that is, Thursday), I notice that Carter has written another post about her accuracy and precision assignment:
http://mathequalslove.blogspot.com/2016/09/accuracy-and-precision-posters.html
Returning to Wednesday, many of the students are still upset that they are required to be in my room for so long, with no computer time to break it up. During the math lesson, which was on converting rational numbers between fraction and decimal form, one student even tried to throw a small rubber ball at me. I don't know who the culprit is, but one girl accuses another of being the one. I don't believe the accuser, because I know that the one she's accusing is often picked on by the others -- they would say that the poor girl is guilty whether or not it's true.
11:05 -- Nutrition finally arrives. I dismiss only the students who have been working on science -- as it turns out, both the accuser and accused failed to finish. The accused girl stays to finish it, but the accuser leaves without permission -- apparently to go straight to the office and repeat her accusation of the poor girl. I receive a phone call that I must send the girl to the office. Apparently the administrators believe the accusation, and the girl is forced to leave the school early -- along with another group of eighth grade girls who often cause trouble (but not the "whistle blower").
During nutrition, I meet my predecessor -- the previous middle school math teacher. As it turns out, he is now teaching at a nearby high school. He tells me that last year, a great way to engage the students is to get them working on whiteboards, since we can't trust them to work at any other time -- especially not on the homework. And so I include whiteboards in my plans for Thursday.
11:25 -- My seventh graders arrive, but due to the mixed-up Wednesday schedule, they come to my room only for music, not for math. The music teacher gives them a test on various instruments and informs them that they will begin playing the piano next week.
12:15 -- This time is officially called "advisory." The students are very confused as to where they were supposed to go. I inform the other middle school teachers that I want to see the sixth graders at this time, so that we can prepare for tomorrow's morning circle routine.
At this time, the sixth graders are very loud, and some of them play with rubber bands. I assign lunch detention to three of the students.
12:45 -- I release the students to lunch. Two of the students report to the lunch detention table, but one boy tries to hide. The girl he's hiding behind tells me that he isn't there -- and so I give that girl lunch detention as well. She is very upset and says that she'll inform her mother that I'm giving her a detention for no reason. I inform her that she should not protect a troublemaker, and that the best thing to say when I'm looking for a student other than her is nothing at all.
1:15 -- The middle school students go home right after lunch. I've noticed that usually when there is a troublesome situation, younger kids (like 6th graders) tend to tattle-tale, while older kids (like 8th graders) prefer not to snitch and instead protect the misbehaving student. In the end, it's ironic that the two biggest troublemakers of the day are an eighth grader who tattle-tales and a sixth grader who protects another student!
But of course my day is nowhere near over yet. It's a Common Planning day, and so I must wait for the 2:00 meeting to begin.
1:50 -- I decide to check my email -- and discover that the meeting is at our sister campus (as our charter school has two different locations), nearly ten miles away. Oops!
2:15 -- I finally arrive at the other campus. I speak to my counterpart -- the math and science teacher at the other school. She is in a rush to leave, but she briefly tells me that she's also been struggling with the Illinois State text. Some of the answers given in the teacher edition are wrong, while the student edition expects sixth graders to graph linear equations without explanation.
2:35 -- The meeting begins. So in the end, it doesn't really matter that I am late, since the meetings never start on time anyway. I'm not the only one who has trouble traveling to the other campus.
During the meeting, we teachers are introduced to the software that we are supposed to use to take attendance and grades -- and this is the fourth week of school.
4:00 -- After the meeting, I am assigned a laptop, since the one I'd been assigned at the start of the year never worked.
And so in many ways this was what the first day of school should have been like. I finally obtain a working laptop and have access to the software we need. I meet with my predecessor so that I know what and how to teach. Our Wednesday schedule is finally beginning to stabilize (but it needs fixing).
Then again, in the old days Wednesday really would have been the first day of school. For years the LAUSD -- whose calendar our charter largely follows -- begin the Wednesday after Labor Day. It was four years ago when the LAUSD adopted the Early Start Calendar.
I actually don't have much to say about today, Thursday, except to say that I do indeed give the whiteboard lesson to all three grades today. For the eighth graders, it's a chance for them to practice converting decimals into fractions, including repeating decimals.
Actually, this is a different sort of challenge. Instead of posting everyday for a month, this challenge involves posting once a month for a year:
http://drawingonmath.blogspot.com/2016/08/day-in-life-book-plan.html
The creator of this challenge is Tina Cardone, a Massachusetts high school math teacher. I've written about Cardone before -- she came up with some of the prompts for the 2016 Blogging Initiative back in January. Here is Cardone's description of the challenge:
Each author will pick a different date and write on the same day of the month each month.
Additional key days where all authors will write:
- A teacher day the week before students arrive
- First day of school
- Parent Conferences day
- Day before Thanksgiving break? (are people more worn out before Thanksgiving or Christmas break?)
- Before and after Christmas break
- Snow day
- State test day (pick one)
- Last day of school
- A day you work during the summer (you mean teachers don’t take the entire summer off?)
Now I live in Southern California, so of course I won't write about a "Snow Day," but I can write on all the other days -- perhaps I can include a "Rain Day" as the California equivalent. According to Cardone, the prompt for each day is "A Day in the Life of...."
As is always the case, I'm late to the party. Cardone tells us that she may include some of our posts in a book that she's writing -- but not mine, since I joined too late. And two of the days in the list have already passed -- "A teacher day..." and the first day of school. But I did write posts for each of those first two days:
A teacher day the week before students arrive
This post is very long -- I began the post with a disclaimer, followed by a Blaugust prompt, and then links to various other teacher websites. Scroll down to "More on the Illinois State text" -- this and the following sections mention teacher meetings and some of the information I learned there. It is not written in "A Day in the Life of..." format -- but I can always go back and edit that post if I need to to satisfy the challenge requirement.
First day of school
I actually did write this post in "A Day in the Life of..." format, so it should already meet challenge requirements as it is. Here's another example of what "A Day in the Life of..." posts look like, based on yesterday:
7:45 -- I arrive at my school.
8:15 -- I report to the playground, where many of my students are beginning to arrive. The students are told to gather in a circle for the flag salute. But this time, the sixth graders and I are in charge of leading the morning circle routine.
8:25 -- My first class, a sixth grade class, begins. This class has grown so that there are now 26 students in this class. I continue an easy lesson on ratios, and the students take foldable notes.
9:20 -- My sixth graders leave and my eighth graders arrive. Now I admit that on Wednesdays, which is our Common Planning day, the schedule is very confusing -- and in fact, the other middle school teachers and I are still trying to work out the kinks. The eighth graders are supposed to be here for two periods -- the first to do a computer lesson, the second for math.
My plan is that I would use the computer period for science. But I don't have the students go to the computer, because I knew that all the computer questions were on lessons they haven't learned -- the students would just guess all the answers and use the rest of the time for free computer play. The students need to learn science. So I decide to give them a science lesson from the famous MTBoS blogger Sarah Carter, on accuracy and precision:
http://mathequalslove.blogspot.com/2016/09/accuracy-precision-error-and-percent.html
I have the students throw balls of crumpled paper into the trash can in order to determine the accuracy and precision. Today (that is, Thursday), I notice that Carter has written another post about her accuracy and precision assignment:
http://mathequalslove.blogspot.com/2016/09/accuracy-and-precision-posters.html
Returning to Wednesday, many of the students are still upset that they are required to be in my room for so long, with no computer time to break it up. During the math lesson, which was on converting rational numbers between fraction and decimal form, one student even tried to throw a small rubber ball at me. I don't know who the culprit is, but one girl accuses another of being the one. I don't believe the accuser, because I know that the one she's accusing is often picked on by the others -- they would say that the poor girl is guilty whether or not it's true.
11:05 -- Nutrition finally arrives. I dismiss only the students who have been working on science -- as it turns out, both the accuser and accused failed to finish. The accused girl stays to finish it, but the accuser leaves without permission -- apparently to go straight to the office and repeat her accusation of the poor girl. I receive a phone call that I must send the girl to the office. Apparently the administrators believe the accusation, and the girl is forced to leave the school early -- along with another group of eighth grade girls who often cause trouble (but not the "whistle blower").
During nutrition, I meet my predecessor -- the previous middle school math teacher. As it turns out, he is now teaching at a nearby high school. He tells me that last year, a great way to engage the students is to get them working on whiteboards, since we can't trust them to work at any other time -- especially not on the homework. And so I include whiteboards in my plans for Thursday.
11:25 -- My seventh graders arrive, but due to the mixed-up Wednesday schedule, they come to my room only for music, not for math. The music teacher gives them a test on various instruments and informs them that they will begin playing the piano next week.
12:15 -- This time is officially called "advisory." The students are very confused as to where they were supposed to go. I inform the other middle school teachers that I want to see the sixth graders at this time, so that we can prepare for tomorrow's morning circle routine.
At this time, the sixth graders are very loud, and some of them play with rubber bands. I assign lunch detention to three of the students.
12:45 -- I release the students to lunch. Two of the students report to the lunch detention table, but one boy tries to hide. The girl he's hiding behind tells me that he isn't there -- and so I give that girl lunch detention as well. She is very upset and says that she'll inform her mother that I'm giving her a detention for no reason. I inform her that she should not protect a troublemaker, and that the best thing to say when I'm looking for a student other than her is nothing at all.
1:15 -- The middle school students go home right after lunch. I've noticed that usually when there is a troublesome situation, younger kids (like 6th graders) tend to tattle-tale, while older kids (like 8th graders) prefer not to snitch and instead protect the misbehaving student. In the end, it's ironic that the two biggest troublemakers of the day are an eighth grader who tattle-tales and a sixth grader who protects another student!
But of course my day is nowhere near over yet. It's a Common Planning day, and so I must wait for the 2:00 meeting to begin.
1:50 -- I decide to check my email -- and discover that the meeting is at our sister campus (as our charter school has two different locations), nearly ten miles away. Oops!
2:15 -- I finally arrive at the other campus. I speak to my counterpart -- the math and science teacher at the other school. She is in a rush to leave, but she briefly tells me that she's also been struggling with the Illinois State text. Some of the answers given in the teacher edition are wrong, while the student edition expects sixth graders to graph linear equations without explanation.
2:35 -- The meeting begins. So in the end, it doesn't really matter that I am late, since the meetings never start on time anyway. I'm not the only one who has trouble traveling to the other campus.
During the meeting, we teachers are introduced to the software that we are supposed to use to take attendance and grades -- and this is the fourth week of school.
4:00 -- After the meeting, I am assigned a laptop, since the one I'd been assigned at the start of the year never worked.
And so in many ways this was what the first day of school should have been like. I finally obtain a working laptop and have access to the software we need. I meet with my predecessor so that I know what and how to teach. Our Wednesday schedule is finally beginning to stabilize (but it needs fixing).
Then again, in the old days Wednesday really would have been the first day of school. For years the LAUSD -- whose calendar our charter largely follows -- begin the Wednesday after Labor Day. It was four years ago when the LAUSD adopted the Early Start Calendar.
I actually don't have much to say about today, Thursday, except to say that I do indeed give the whiteboard lesson to all three grades today. For the eighth graders, it's a chance for them to practice converting decimals into fractions, including repeating decimals.
Tuesday, September 6, 2016
Traditional Lesson: Rational and Irrational Numbers (Days 14-15)
The first project in my classes -- the mousetrap cars -- are complete. After each project, the Illinois State text provides us with a traditional textbook from which we should give lessons.
But over the long Admission-Labor Day weekend, I've been thinking long and hard about how I should be assessing the students. As I mentioned in my last post, my original plan was to rotate among a Dren Quiz, general quiz, and test, which the eighth graders starting with a test. Yet I believe that the students were not prepared for this test, since the days leading up to it were spent on the mousetrap project rather than the traditional text.
As it turned out, of my 14 eighth graders, exactly half passed the test and half failed. I'd argue that later in the year -- when the math starts to get tough -- as many as half passing is great. But at the start of the year, during the Willis (or Wong) Unit, I don't want half the class feeling frustrated. I want to set the tone for success, and that means most of the class should pass the first test.
Indeed, let's think back to the Wongs and their book, The First Days of School. According to the Wongs, there are several poor reasons for giving assessments, such as "the passage of time" and "points on a curve." Now my rotation plan sounds dangerously like giving tests just because of "the passage of time" -- tests were to be given every three weeks. My rationale for this schedule was that I didn't want too many tests to grade at one time -- but that's yet another pro-teacher reason for giving the tests. Instead, according to the Wongs, I need to show how my testing benefits the students and their learning.
I also said that I gave tests every three weeks as a student teacher. But my master teacher did warn me that I shouldn't just blindly give tests every three weeks or after every chapter -- in fact, it just so happened that those students were ready for tests every three weeks. On the other hand, my students were clearly not ready for a test right after spending all week on the project.
Notice that "because I don't want too many tests to grade at once" could be a pro-student reason for the timing of a test -- for example, because the teacher wants to give the students prompt feedback on how well they are doing. But, as I wrote before, that doesn't apply to my situation -- I work at a small charter school, so it's not as if I have nearly 200 students or anything like that.
Regarding the Wongs and their comments about "points on a curve," I would argue that transparency in grading is a pro-student reason for making sure that there are the correct number of tests worth the proper number of points. I still think back to my student teaching and the computer grading system, where the homework could be worth 10 points and a test worth 100, yet the test is worth much more than 10 homework assignments because one homework point is not equal to one test point (as points are instead weighted so that homework is 10% and tests 40% of the grade).
I've decided that in my class, homework will remain 10%, but classwork, quizzes, and tests will each comprise 30% of the grade. Classwork has been elevated to equal tests since there are so many projects that require considerable effort. The idea is that the whole trimester is worth 1000 points, and so I can give three tests each worth 100 points, which total 300 points, or 30% of the grade.
So here's my plan -- unfortunately I already began this rotation plan, so I should follow it through one complete rotation. This means that eighth graders will rotate to a Dren Quiz this week and a general quiz next week. Meanwhile, a test will be given to the seventh graders this week and the sixth graders next week. I will make sure through this week's traditional lessons that my younger students are prepared for the tests.
After my sixth graders take their test, I will abandon my rotation and switch to what I hope will be a more student-friendly assessment plan. Notice that the Illinois State text itself provides assessments that line up with each Learning Module. But simply giving a test at the end of every Module will result in too many tests -- for example, I wish to finish Module 5 this trimester, but I only want to give three tests this trimester, not five.
Instead, I could come up with a new sort of rotation -- one which shows which types of assessments occur during each module:
(Module 1: Dren Quiz, General Quiz)
Module 2: Dren Quiz, Test
Module 3: General Quiz, Test
Module 4: Dren Quiz, General Quiz
Module 5: Dren Quiz, Test
and so on. This plan has several advantages. It reemphasizes what I wrote last week -- if I'd followed this plan from the start, all the students would have started with a Dren Quiz, which is more logical than a test after spending so much time on the project (and I probably should have waited until today to give said Dren Quiz, so that all students had the opportunity to work of the project). In fact, here Dren Quizzes always occur in the middle of a unit, while tests always occur at the end -- after traditional lessons. If a General Quiz occurs in the middle of a module, I will make sure that all information needed for the quiz can be derived from working on the project.
Because I gave an extra test at the start of the year, this means that there will be four tests this trimester rather than three. But I don't mind having a fourth test, since whenever there are four tests, I can drop the score of the lowest test. This could help that half of my eighth grade class that failed this first test.
According to the pattern, Module 16 will contain a Dren Quiz and a general quiz, but definitely not a major test. This is good, because Module 16 will be taught during the SBAC. And so this appears to be a strong assessment plan that will help the students learn throughout the year.
All three grades test at the same time on this plan. The eighth grader who had been the most upset on Friday about the test asked me today whether the other grades have tested yet or not. Technically, I'm within my rights to push the eighth graders harder and test them more because they're older. But actually, after this first rotation, all three grades will test at the same time.
All three grades test at the same time on this plan. The eighth grader who had been the most upset on Friday about the test asked me today whether the other grades have tested yet or not. Technically, I'm within my rights to push the eighth graders harder and test them more because they're older. But actually, after this first rotation, all three grades will test at the same time.
This week, the students will work out of a traditional text. Notice that while the first four modules of the main Illinois State text (the STEM project book) are identical for all three grades, the traditional texts are different for sixth, seventh, and eighth grade. The traditional texts are arranged by naively preserving the order of Common Core Standards themselves. Therefore the sixth and seventh grade texts begin with Ratios and Proportional Thinking followed by the Number System, while the eighth grade text, which doesn't have a Ratios strand, goes directly to the Number System.
Illinois State provides the teachers with a "pacing plan" which tells us which traditional lesson corresponds to each STEM project. But not only is this pacing plan cumbersome to read, but the first four modules ("Tools for Learning") -- despite appearing in the STEM text for all three grades -- are only assigned traditional lessons in the sixth grade text!
I have no problem with jumping around in the traditional text -- after all, consider the order in which I posted lessons to the blog last year! Still, starting at the beginning of the text is logical for both sixth and seventh grades, since Module 1 is The Need for Speed, and speed definitely is a ratio -- namely the ratio of distance to time.
The eighth grade traditional text doesn't have a lesson on ratio. But the lesson at the start of the book is about rational numbers -- specifically the existence of numbers that aren't rational. So in a way it's at least somewhat related to ratios. As usual, this blog focuses on my eighth grade class, so let's look at this lesson in more detail. The first Common Core Math 8 standard is:
CCSS.MATH.CONTENT.8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Back in my Square Root Day posts, I wrote about the irrationality of sqrt(2) on the blog. Before I took Algebra I, I had always heard that sqrt(2) was irrational, but I never realized that this was something that we could prove until I saw a form of the proof in my Algebra I text.
I might give my students a proof of the irrationality of sqrt(2). In fact, I'd love to tell the story such as the math YouTube star Vi Hart does:
In her video, Hart discusses how Pythagoras and his disciples eschewed beans. I definitely like Hart's pun about how one of the followers "spilled the beans" about the irrationality proof!
Today I start to tell the story about Pythagoras, but my eighth graders are a little confused as to why I'm telling them this story. I ask them what sqrt(2) is, and one student tries 1, until I tell them that 1 times 1 is 1. And of course they shouldn't even bother with 2, since 2 times 2 is 4. Someone suggests 1 1/2, or 3/2, which is a good guess, but its square is 9/4, which is a little more than 2.
But then the story falls apart when I try to suggest 7/5, or 1.4, as the next guess, since the students are confused where these numbers come from. And besides, the story works better when sticking to fractions, rather than decimals -- otherwise, students may wonder why sqrt(2) is "impossible" when 1.414213562... is apparently sqrt(2). (Though in the end, one student does figure out what my story is leading up to.)
The Common Core Standard requires students to know that rational numbers have repeating decimals as well as how to convert these repeating decimals into fractions. The Illinois State text teaches the following method:
x = 0.333...
10x = 3.333...
9x = 3
x = 3/9
x = 1/3
Perhaps my students would have appreciated the story of Pythagoras more if I had waited to tell the story after having them convert between fractions and decimals. Then it would have been more obvious where 7/5 and 1.4 come from.
As I wrote earlier, the lower two grades are working on ratios. Because I don't have enough textbooks for all of my sixth and seventh graders yet, I have these students take foldable notes instead. (The eighth graders don't need foldables since all Illinois State texts are consumable.) The students are required to copy what I write on the board into the foldable -- but then some students claim that they can't see what I'm writing!
Recall that the idea behind foldables is that students are more likely to take notes on the foldable than on notebook paper. But here we see the students are still coming up with excuses. Another idea is for the students to take guided notes where they fill in the blanks -- the words to fill in are right in front of them, so that's no longer an excuse (but of course, some students will come up with any reason why they can't take notes). But I want to avoid guided notes since they take extra time to prepare as well as require overuse of the Xerox machine.
In all classes, this is the song that I sing:
RATIOS:
Ratios are everywhere.
Ratios surround you,
Probably here and there.
For every "for every"
There's a ratio.
Divide at the colon,
And away we go.
That's all there is
To a ratio!
Bridge:
Ratios are everywhere,
But not everything's rational.
Square root of two and pi,
Are proved to be irrational.
By the way, since this is a two-day post, I'm thinking ahead to Wednesday's lesson, when I want to return to science. In the past few days my go-to for science, Sarah Carter, posted some lessons on accuracy vs. precision and scientific notation:
http://mathequalslove.blogspot.com/2016/09/accuracy-precision-error-and-percent.html
http://mathequalslove.blogspot.com/2016/09/scientific-notation-inb-pages.html
http://mathequalslove.blogspot.com/2016/09/scientific-notation-ordering-cards.html
I'm torn between giving these lessons from Carter and continuing with the online website that I've been using for science. On the website I was hoping for some simple speed and velocity questions, but most of the mechanics questions for eighth grade deal with force -- a concept that will confuse and frustrate students if I teach it this week. Indeed, force will make sense if I teach it along with Module 3, where the STEM project involves measuring force. So it's probably better for me to give Carter's lessons this week.
Notice that Carter -- who originally championed the idea of using foldables -- has now switched to using what she calls an "interactive notebook." In many way, an interactive notebook combines some of the ideas of foldables and guided notes -- students cut and paste pages into their notebooks. As of now I have no plans to use interactive notebooks, but I may consider it in the future.
My next post will be on Thursday.
I might give my students a proof of the irrationality of sqrt(2). In fact, I'd love to tell the story such as the math YouTube star Vi Hart does:
In her video, Hart discusses how Pythagoras and his disciples eschewed beans. I definitely like Hart's pun about how one of the followers "spilled the beans" about the irrationality proof!
Today I start to tell the story about Pythagoras, but my eighth graders are a little confused as to why I'm telling them this story. I ask them what sqrt(2) is, and one student tries 1, until I tell them that 1 times 1 is 1. And of course they shouldn't even bother with 2, since 2 times 2 is 4. Someone suggests 1 1/2, or 3/2, which is a good guess, but its square is 9/4, which is a little more than 2.
But then the story falls apart when I try to suggest 7/5, or 1.4, as the next guess, since the students are confused where these numbers come from. And besides, the story works better when sticking to fractions, rather than decimals -- otherwise, students may wonder why sqrt(2) is "impossible" when 1.414213562... is apparently sqrt(2). (Though in the end, one student does figure out what my story is leading up to.)
The Common Core Standard requires students to know that rational numbers have repeating decimals as well as how to convert these repeating decimals into fractions. The Illinois State text teaches the following method:
x = 0.333...
10x = 3.333...
9x = 3
x = 3/9
x = 1/3
Perhaps my students would have appreciated the story of Pythagoras more if I had waited to tell the story after having them convert between fractions and decimals. Then it would have been more obvious where 7/5 and 1.4 come from.
As I wrote earlier, the lower two grades are working on ratios. Because I don't have enough textbooks for all of my sixth and seventh graders yet, I have these students take foldable notes instead. (The eighth graders don't need foldables since all Illinois State texts are consumable.) The students are required to copy what I write on the board into the foldable -- but then some students claim that they can't see what I'm writing!
Recall that the idea behind foldables is that students are more likely to take notes on the foldable than on notebook paper. But here we see the students are still coming up with excuses. Another idea is for the students to take guided notes where they fill in the blanks -- the words to fill in are right in front of them, so that's no longer an excuse (but of course, some students will come up with any reason why they can't take notes). But I want to avoid guided notes since they take extra time to prepare as well as require overuse of the Xerox machine.
In all classes, this is the song that I sing:
RATIOS:
Ratios are everywhere.
Ratios surround you,
Probably here and there.
For every "for every"
There's a ratio.
Divide at the colon,
And away we go.
That's all there is
To a ratio!
Bridge:
Ratios are everywhere,
But not everything's rational.
Square root of two and pi,
Are proved to be irrational.
By the way, since this is a two-day post, I'm thinking ahead to Wednesday's lesson, when I want to return to science. In the past few days my go-to for science, Sarah Carter, posted some lessons on accuracy vs. precision and scientific notation:
http://mathequalslove.blogspot.com/2016/09/accuracy-precision-error-and-percent.html
http://mathequalslove.blogspot.com/2016/09/scientific-notation-inb-pages.html
http://mathequalslove.blogspot.com/2016/09/scientific-notation-ordering-cards.html
I'm torn between giving these lessons from Carter and continuing with the online website that I've been using for science. On the website I was hoping for some simple speed and velocity questions, but most of the mechanics questions for eighth grade deal with force -- a concept that will confuse and frustrate students if I teach it this week. Indeed, force will make sense if I teach it along with Module 3, where the STEM project involves measuring force. So it's probably better for me to give Carter's lessons this week.
Notice that Carter -- who originally championed the idea of using foldables -- has now switched to using what she calls an "interactive notebook." In many way, an interactive notebook combines some of the ideas of foldables and guided notes -- students cut and paste pages into their notebooks. As of now I have no plans to use interactive notebooks, but I may consider it in the future.
My next post will be on Thursday.
Thursday, September 1, 2016
Test #1 (Day 13)
My home state of California was admitted the 31st state in the union on September 9th, 1850. Many states celebrate a special holiday called Admission Day, to commemorate the day that they were admitted to the union, and California is no exception.
Admission Day is theoretically, a holiday with no school. But having no school on September 9th is a bit awkward, especially under the Labor Day Start Calendar. Imagine a year when Labor Day is on its latest possible date, the 7th, So Monday would be Labor Day holiday, Tuesday the first day of school, and then Wednesday the Admission Day holiday! Even in a year such as this one, with Labor Day on the 5th, we'd have a three-day first week, Tuesday through Thursday.
So Admission Day has been redefined as the Friday before Labor Day. I'd argue that defining it as the Tuesday after Labor Day would be more logical, since that would be closer to the 9th, while the Friday before Labor Day is sometimes in August. But under the current definition, schools with Labor Day Starts would have their offices closed the Friday before the first day of school -- which goes largely unnoticed.
But now many California schools are moving towards the Early Start Calendar. The LAUSD, whose calendar my charter school largely follows, has a four-day weekend from Admission Day to Labor Day, meaning that today is the last day before the holiday.
Some California districts cheat and declare "Admission Day" to be nowhere near September. I know at least two districts that use "Admission Day" to add an extra day to spring break -- for example Good Friday in a district that takes the week after Easter off, or Easter Monday in a district that takes the week before Easter off.
By the way, I'm not sure how prevalent closing schools on Admission Days in other states is. For example, five states (Vermont, Ohio, Maine, Florida, and Nebraska) have Admission Days during the first half of March. A holiday at that point would be welcome to break up the long block between President's Day and Easter. Yet I wasn't able to find a school closed on Admission Day in any of those states.
Since tomorrow is Admission Day, I give the first test to my eighth graders today, as part of the plan I mentioned earlier on the blog to rotate tests among the three grades. The test is supposed to have nine questions on speed/velocity (worth 10 points each) and the other ten questions coming from the Next Generation Science Standards, as a sort of benchmark (worth 1 point each), just like last week's Benchmark Tests. But unfortunately, the test turns out to be a disaster. Students are completely confused as to how to answer the speed questions.
By the way, I took the questions from the following website:
http://www.softschools.com/quizzes/physics/speed_and_velocity/quiz5366.html
As you can see, the questions are straightforward -- all the students had to do is divide each distance by each time to find the answer -- and the distance is always given before the time. So why did my students have so much trouble with the test?
Well, let's reflect back on the week I had. Monday was coding, and on Tuesday the students built the mousetrap cars from the Illinois State text. And the mousetrap car project bled into Wednesday -- and somewhat into today as well. And I gave the test today knowing that there's no school tomorrow. So the students hardly had any actual practice calculating speeds and velocity before today's test.
I think back to why I came up with the idea of testing the eighth graders the third week of school. It all goes back to my student teaching, when I had two preps, Algebra I and Algebra II. My Algebra II students took their first test during the third week of school, with Algebra I taking their first test a week later. It wasn't planned this way, but it ended up being that Algebra II was tested every third week of school, with Algebra I taking a test a week after Algebra II did. So as soon as I found out I had three preps, I immediately came up with a testing schedule where I would rotate tests, quizzes, and Dren Quizzes among the three grades. The main idea was that I wouldn't have to grade tests for all three grade levels the same weekend.
But as I think about it more, I realize that all of the reasons I came up with for rotating the testing schedule are no longer applicable. First, even with my classes continuing to grow, I still have far fewer students than I would at a public school, so I shouldn't have compared student teaching at a public school to teaching at a charter school. Second, I obviously didn't take Monday coding into consideration when I came up with the plan. Third, I didn't take into account the fact that I have a support staff aide to help me grade papers, so grading all three grade levels isn't an issue. Usually, she can grade for two of my classes before she leaves, so I have only one class I need to grade. Fourth, I knew that I'd be teaching out of the Illinois State text which is full of projects, yet I didn't truly consider how these projects would affect my teaching and assessing.
When I met the Illinois State curriculum developers as part of training week, they pointed out that these projects are meant to motivate students who would be turned off by a traditional text. Yet the Illinois State text doesn't begin Learning Module 1 with the students building mousetrap cars. Instead the text has the students fill out charts. First the columns are labeled "Column 1," "Column 2," and "Column 3," and the students are supposed to discover that the first column divided by the second column is the third column (but not many did). Then another chart is given with the headings now changed to "Distance," "Time," and "Speed." It's not until after those charts are given that the students are instructed to build the cars.
On Tuesday, it took half the period -- all the way until my music break -- to fill out the charts. I recall one student who struggled to fill out the charts and was completely unmotivated. She put her head down during my music break and groaned afterward when I was trying to explain what the next part of the project was -- until she found out that it was building mousetrap cars. I could tell that she enjoyed the building part of the project. But this appeared to be the opposite of what the Illinois State developers had told us -- that the exciting part of the project was supposed to come first!
And of course all that time wasted on completing the charts meant that there was less time for the students to finish the cars. This meant that car building continued into Wednesday -- meaning that there was less time for the students to roll them down the ramp and measure their speed. So the students didn't practice calculating speeds much before Thursday's test.
If I could do this whole week over again, how would I teach it? Of course, at this point a traditionalist would tell me just to drop the project and have the students calculate speeds over and over again until they got it. But that's not what I believe I should have done -- the students, after all, were motivated to build the cars, so the idea is to extend that motivation into the calculation.
Here's what the ideal week would have looked like:
Monday -- Coding -- I have no power to change that.
Tuesday -- Just have the students build the mousetrap cars. Ignore the charts that the Illinois State text insists be completed before the construction. This is an 80-minute block and the Illinois State text states that the construction should take one approximately 50-minute period. (Yeah, but did they take filling in the charts into consideration?) So the students should have more than enough time to finish the construction.
Wednesday -- Now start looking at the charts. To motivate the students, I could offer a participation point to the first student who discovers the pattern among the columns. (Actually, my school offers something called "Scholar Dollars" to the best students, and so I have folded my participation points system into the Scholar Dollars.) The offer of a Scholar Dollar might be sufficient to get the students to keep looking at the charts until they figure them out. After changing the columns to "Distance," "Time," and "Speed," I could say, "If only there were something in this room that we could move to measure its speed," in the hopes that the students answer, "Mousetrap cars!"
Thursday -- By now the students have been calculating speeds, so they might be able to perform well on the test. Still, it's probably better not to give the test today. Instead, I could give just a quiz -- or better yet, a Dren Quiz. If I had only one prep, my first assessment would be the Dren Quiz -- the whole idea of starting with anything other than a Dren Quiz was merely to stagger the tests. Since the first Dren Quiz (on the 10's times tables) would be so fast, there would be plenty of time left to finish the mousetrap car project if they needed it.
There are still a few issues with the events of this week. After the students complain that they don't know how to calculate speed, I point out that I did give them several opportunities to figure out speed during the week, including the Warm-Ups. The problem, though, is that many students didn't actually calculate any speeds during the week -- instead, they merely wrote down the date, since my Warm-Up questions follow the Theoni Pappas pattern.
When I first came up with the idea of having the answer always be the date, I already knew that some students would try to get away with just writing the date. My rationalization was that I require the students to write down the intermediate steps -- the date, then, was a self-check to make sure that the students are on the right track. The problem, though, is that calculating speed is a one-step process, so there are no intermediate steps, unless I forced the students to do long division or something rather than use a calculator.
I notice that the Illinois State text actually provides some Warm-Up questions (online). I might have the students work on these instead -- the answer will then almost never just be the date. I could return to giving questions where the answer is the date in October -- by which point the students will be working on more multi-step problems.
By the way, I'm not the only teacher who tried making the date into a math problem (teacher, so I'm not referring to Pappas herself). The following link is to a teacher who uses the date this way:
http://windywilsons.blogspot.com/2009/04/take-ride-in-time-machine-enter-fourth.html
This post is dated 2009. I thought I saw another teacher do the same sometime last month, but as usual I can't find the link when I need to.
Here's the other issue -- so far, I've only mentioned my eighth grade class. Well, today I let my younger classes attempt the mousetrap cars, and they do, with mixed success. Actually, my sixth graders perform the construction better than my seventh graders -- but this is most likely because I actually give the sixth graders a Dren Quiz, while I give my seventh graders a general quiz.
This gives the sixth graders more time for construction, but there's still one problem. Recall that on Dren Quizzes, any grade less than a "A" (or 45 out of 50) is a failing grade. One of my sixth graders is upset when she finds out that she has failed the Dren Quiz. Her problem is that she continued to write 10 times 10 as 110, and this question appears five times. I say that six mistakes is failing -- and her sixth mistake is when she writes 10 times 5 as 5. She tells me that she makes this error because she feels under pressure by the other students, who want her to hurry up so that they can begin the mousetrap cars! She begs me to let her retake the Dren Quiz right away -- but unfortunately, my policy is that she will retake her 10's Dren Quiz in three weeks, when the other students move on to the 2's Dren Quiz. Anyway, there might still be a problem with giving Dren Quizzes on project days.
It might have been possible to let all three grades build mousetrap cars simultaneously. Originally, I saw the three boxes of mousetrap cars and thought that each box contained one car, which is why I had my smallest class, the eighth graders, work on them first. But each box actually contained enough material for six cars! I probably should have opened one of the boxes on Monday night, but I hadn't because, again, I'd thought there was only one car in the box and I didn't want to lose any pieces by opening the box.
Instead, I opened all three boxes during the eighth grade class -- and because of this, many of the tiny washers and other pieces got lost. We contacted Illinois State, who told us that it was OK to have the eighth graders take their cars apart so that the younger students could rebuild them. This would mean that the best strategy would have been to have just one class build them first. But again, if I'd opened only one box in each grade, the parts might not have gotten lost -- meaning that I could have had all three grades work at the same time after all.
In the end, I'm trying to figure out what to do about next week. Next week, the eighth graders are scheduled to have a Dren Quiz, the seventh graders a test, and the sixth graders a general quiz. But after seeing the eighth graders struggle, I now wonder whether it's best just to scrap the whole idea of staggering the tests and just assess all three grades at the same time -- especially through the first four Learning Modules of the Illinois State text, which is the same for all three grades.
Of course, this means that I will have changed my mind yet again -- which can only confuse the readers of this blog. But I am a teacher, and so my priority is helping students learn. Given a choice between frustrating my blog readers and frustrating my students, I will always choose to frustrate my blog readers. And so if I write something (such as an assessment schedule) and I see that my students learn better when I do something else, I will contradict what I write on the blog and do what appears to be best for my students.
Happy Admission Day and Labor Day! My next post will be on, Tuesday, September 6th.
Admission Day is theoretically, a holiday with no school. But having no school on September 9th is a bit awkward, especially under the Labor Day Start Calendar. Imagine a year when Labor Day is on its latest possible date, the 7th, So Monday would be Labor Day holiday, Tuesday the first day of school, and then Wednesday the Admission Day holiday! Even in a year such as this one, with Labor Day on the 5th, we'd have a three-day first week, Tuesday through Thursday.
So Admission Day has been redefined as the Friday before Labor Day. I'd argue that defining it as the Tuesday after Labor Day would be more logical, since that would be closer to the 9th, while the Friday before Labor Day is sometimes in August. But under the current definition, schools with Labor Day Starts would have their offices closed the Friday before the first day of school -- which goes largely unnoticed.
But now many California schools are moving towards the Early Start Calendar. The LAUSD, whose calendar my charter school largely follows, has a four-day weekend from Admission Day to Labor Day, meaning that today is the last day before the holiday.
Some California districts cheat and declare "Admission Day" to be nowhere near September. I know at least two districts that use "Admission Day" to add an extra day to spring break -- for example Good Friday in a district that takes the week after Easter off, or Easter Monday in a district that takes the week before Easter off.
By the way, I'm not sure how prevalent closing schools on Admission Days in other states is. For example, five states (Vermont, Ohio, Maine, Florida, and Nebraska) have Admission Days during the first half of March. A holiday at that point would be welcome to break up the long block between President's Day and Easter. Yet I wasn't able to find a school closed on Admission Day in any of those states.
Since tomorrow is Admission Day, I give the first test to my eighth graders today, as part of the plan I mentioned earlier on the blog to rotate tests among the three grades. The test is supposed to have nine questions on speed/velocity (worth 10 points each) and the other ten questions coming from the Next Generation Science Standards, as a sort of benchmark (worth 1 point each), just like last week's Benchmark Tests. But unfortunately, the test turns out to be a disaster. Students are completely confused as to how to answer the speed questions.
By the way, I took the questions from the following website:
http://www.softschools.com/quizzes/physics/speed_and_velocity/quiz5366.html
As you can see, the questions are straightforward -- all the students had to do is divide each distance by each time to find the answer -- and the distance is always given before the time. So why did my students have so much trouble with the test?
Well, let's reflect back on the week I had. Monday was coding, and on Tuesday the students built the mousetrap cars from the Illinois State text. And the mousetrap car project bled into Wednesday -- and somewhat into today as well. And I gave the test today knowing that there's no school tomorrow. So the students hardly had any actual practice calculating speeds and velocity before today's test.
I think back to why I came up with the idea of testing the eighth graders the third week of school. It all goes back to my student teaching, when I had two preps, Algebra I and Algebra II. My Algebra II students took their first test during the third week of school, with Algebra I taking their first test a week later. It wasn't planned this way, but it ended up being that Algebra II was tested every third week of school, with Algebra I taking a test a week after Algebra II did. So as soon as I found out I had three preps, I immediately came up with a testing schedule where I would rotate tests, quizzes, and Dren Quizzes among the three grades. The main idea was that I wouldn't have to grade tests for all three grade levels the same weekend.
But as I think about it more, I realize that all of the reasons I came up with for rotating the testing schedule are no longer applicable. First, even with my classes continuing to grow, I still have far fewer students than I would at a public school, so I shouldn't have compared student teaching at a public school to teaching at a charter school. Second, I obviously didn't take Monday coding into consideration when I came up with the plan. Third, I didn't take into account the fact that I have a support staff aide to help me grade papers, so grading all three grade levels isn't an issue. Usually, she can grade for two of my classes before she leaves, so I have only one class I need to grade. Fourth, I knew that I'd be teaching out of the Illinois State text which is full of projects, yet I didn't truly consider how these projects would affect my teaching and assessing.
When I met the Illinois State curriculum developers as part of training week, they pointed out that these projects are meant to motivate students who would be turned off by a traditional text. Yet the Illinois State text doesn't begin Learning Module 1 with the students building mousetrap cars. Instead the text has the students fill out charts. First the columns are labeled "Column 1," "Column 2," and "Column 3," and the students are supposed to discover that the first column divided by the second column is the third column (but not many did). Then another chart is given with the headings now changed to "Distance," "Time," and "Speed." It's not until after those charts are given that the students are instructed to build the cars.
On Tuesday, it took half the period -- all the way until my music break -- to fill out the charts. I recall one student who struggled to fill out the charts and was completely unmotivated. She put her head down during my music break and groaned afterward when I was trying to explain what the next part of the project was -- until she found out that it was building mousetrap cars. I could tell that she enjoyed the building part of the project. But this appeared to be the opposite of what the Illinois State developers had told us -- that the exciting part of the project was supposed to come first!
And of course all that time wasted on completing the charts meant that there was less time for the students to finish the cars. This meant that car building continued into Wednesday -- meaning that there was less time for the students to roll them down the ramp and measure their speed. So the students didn't practice calculating speeds much before Thursday's test.
If I could do this whole week over again, how would I teach it? Of course, at this point a traditionalist would tell me just to drop the project and have the students calculate speeds over and over again until they got it. But that's not what I believe I should have done -- the students, after all, were motivated to build the cars, so the idea is to extend that motivation into the calculation.
Here's what the ideal week would have looked like:
Monday -- Coding -- I have no power to change that.
Tuesday -- Just have the students build the mousetrap cars. Ignore the charts that the Illinois State text insists be completed before the construction. This is an 80-minute block and the Illinois State text states that the construction should take one approximately 50-minute period. (Yeah, but did they take filling in the charts into consideration?) So the students should have more than enough time to finish the construction.
Wednesday -- Now start looking at the charts. To motivate the students, I could offer a participation point to the first student who discovers the pattern among the columns. (Actually, my school offers something called "Scholar Dollars" to the best students, and so I have folded my participation points system into the Scholar Dollars.) The offer of a Scholar Dollar might be sufficient to get the students to keep looking at the charts until they figure them out. After changing the columns to "Distance," "Time," and "Speed," I could say, "If only there were something in this room that we could move to measure its speed," in the hopes that the students answer, "Mousetrap cars!"
Thursday -- By now the students have been calculating speeds, so they might be able to perform well on the test. Still, it's probably better not to give the test today. Instead, I could give just a quiz -- or better yet, a Dren Quiz. If I had only one prep, my first assessment would be the Dren Quiz -- the whole idea of starting with anything other than a Dren Quiz was merely to stagger the tests. Since the first Dren Quiz (on the 10's times tables) would be so fast, there would be plenty of time left to finish the mousetrap car project if they needed it.
There are still a few issues with the events of this week. After the students complain that they don't know how to calculate speed, I point out that I did give them several opportunities to figure out speed during the week, including the Warm-Ups. The problem, though, is that many students didn't actually calculate any speeds during the week -- instead, they merely wrote down the date, since my Warm-Up questions follow the Theoni Pappas pattern.
When I first came up with the idea of having the answer always be the date, I already knew that some students would try to get away with just writing the date. My rationalization was that I require the students to write down the intermediate steps -- the date, then, was a self-check to make sure that the students are on the right track. The problem, though, is that calculating speed is a one-step process, so there are no intermediate steps, unless I forced the students to do long division or something rather than use a calculator.
I notice that the Illinois State text actually provides some Warm-Up questions (online). I might have the students work on these instead -- the answer will then almost never just be the date. I could return to giving questions where the answer is the date in October -- by which point the students will be working on more multi-step problems.
By the way, I'm not the only teacher who tried making the date into a math problem (teacher, so I'm not referring to Pappas herself). The following link is to a teacher who uses the date this way:
http://windywilsons.blogspot.com/2009/04/take-ride-in-time-machine-enter-fourth.html
This post is dated 2009. I thought I saw another teacher do the same sometime last month, but as usual I can't find the link when I need to.
Here's the other issue -- so far, I've only mentioned my eighth grade class. Well, today I let my younger classes attempt the mousetrap cars, and they do, with mixed success. Actually, my sixth graders perform the construction better than my seventh graders -- but this is most likely because I actually give the sixth graders a Dren Quiz, while I give my seventh graders a general quiz.
This gives the sixth graders more time for construction, but there's still one problem. Recall that on Dren Quizzes, any grade less than a "A" (or 45 out of 50) is a failing grade. One of my sixth graders is upset when she finds out that she has failed the Dren Quiz. Her problem is that she continued to write 10 times 10 as 110, and this question appears five times. I say that six mistakes is failing -- and her sixth mistake is when she writes 10 times 5 as 5. She tells me that she makes this error because she feels under pressure by the other students, who want her to hurry up so that they can begin the mousetrap cars! She begs me to let her retake the Dren Quiz right away -- but unfortunately, my policy is that she will retake her 10's Dren Quiz in three weeks, when the other students move on to the 2's Dren Quiz. Anyway, there might still be a problem with giving Dren Quizzes on project days.
It might have been possible to let all three grades build mousetrap cars simultaneously. Originally, I saw the three boxes of mousetrap cars and thought that each box contained one car, which is why I had my smallest class, the eighth graders, work on them first. But each box actually contained enough material for six cars! I probably should have opened one of the boxes on Monday night, but I hadn't because, again, I'd thought there was only one car in the box and I didn't want to lose any pieces by opening the box.
Instead, I opened all three boxes during the eighth grade class -- and because of this, many of the tiny washers and other pieces got lost. We contacted Illinois State, who told us that it was OK to have the eighth graders take their cars apart so that the younger students could rebuild them. This would mean that the best strategy would have been to have just one class build them first. But again, if I'd opened only one box in each grade, the parts might not have gotten lost -- meaning that I could have had all three grades work at the same time after all.
In the end, I'm trying to figure out what to do about next week. Next week, the eighth graders are scheduled to have a Dren Quiz, the seventh graders a test, and the sixth graders a general quiz. But after seeing the eighth graders struggle, I now wonder whether it's best just to scrap the whole idea of staggering the tests and just assess all three grades at the same time -- especially through the first four Learning Modules of the Illinois State text, which is the same for all three grades.
Of course, this means that I will have changed my mind yet again -- which can only confuse the readers of this blog. But I am a teacher, and so my priority is helping students learn. Given a choice between frustrating my blog readers and frustrating my students, I will always choose to frustrate my blog readers. And so if I write something (such as an assessment schedule) and I see that my students learn better when I do something else, I will contradict what I write on the blog and do what appears to be best for my students.
Happy Admission Day and Labor Day! My next post will be on, Tuesday, September 6th.
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