f (x) = 3x, x < 5
7, x > 5
f (1) = ?
This is a piecewise linear function. Since 1 < 5, f (1) = 3(1) = 3. So it's three -- and today is the third.
I haven't really gone into functions yet with my eighth graders (the F strand), but earlier this week, the Illinois State STEM project gives function notation in its tables. A more logical version of this question once I reach standard F1 would be:
f (x) = 3x
f (1) = ?
Today I give all classes a 50-point quiz based on this week's material. For the eighth graders, this means the first quiz on algebraic concepts. Standard EE7a is on solving equations that may have one, none, or infinitely many solutions -- and the way it's written in the Illinois State text, this standard is almost indistinguishable from EE7b, on multi-step equations.
Going from geometry to algebra is, of course, a tough transition for any student. But I also have a little concern with the way the standards are presented in the Illinois State traditional text. Although this applies to the eighth grade text, the following is best illustrated by a sixth grade example.
This week the sixth graders covered NS1, on division of fractions. So now you might ask, what happened to addition, subtraction, or multiplication of fractions? Well, these aren't mentioned in the sixth grade standards because they are fifth grade standards. And so the sixth grade text begins the Number Sense strand with a lesson on dividing fractions.
But let's compare this to other texts -- not necessarily even pre-Core texts, but traditional texts other than the Illinois State text. There would be a chapter on fractions -- and in this chapter, students review how to add, subtract, and multiply fractions before the new topic, division, begins.
Likewise, other eighth grade texts might give simple one- and two-step equations before jumping into indeterminate or multi-step equations. But one- and two-step equations are considered a seventh (or even sixth) grade standard, and so they don't appear in the eighth grade text. And as I'm bound to follow the Illinois State text, I must jump into these harder equations.
Despite this, one girl manages to earn a perfect score on the quiz. On the other end of the spectrum, two students earn the lowest score on both last week's test and this week's quiz, and I'm deeply concerned with their progress. Let me describe what happened today with those two girls.
It all begins before the quiz. You see, Illinois State provides an Intervention Focus Tutorial with some review questions -- another part of the Illinois State curriculum I've been neglecting until now. I find it a good idea to have the students answer these on whiteboards. Lately I've been working on ways to improve my classroom management, and one way is to foster competition among groups, or "teams," of students. Of course, this leads straight into group points and the "Who Am I?"/Conjectures game.
Last month I wrote some conflicting information regarding this game -- which, as you may recall, was a favorite of mine as a sub. It turns out that the game works better when introducing a lesson than as a review -- in the latter case, the smarter, louder students end up dominating the game. I didn't necessarily plan on playing my game today, but it follows naturally from the whiteboard review and team point concept.
But another factor to consider is my Bruin Corps member. The college student who works in my room on Mondays, Wednesdays, and Fridays ends up sitting with one of the groups (consisting of the two who fail the test). Note that she is an environmental science major, not a math major -- and so she may have been tricked by some of the multi-step equations. The girls in her group ask me for help -- but then I can't help them. This is because the other groups think that this group is getting an unfair advantage in the team points competition -- they already have a Bruin Corps member assisting them, and then I, the teacher, am about to help them on top of that!
Again, this reveals a flaw in my game as review for a quiz or test -- giving students the help they need to pass the quiz looks like unfairly aiding them in the game for points. My support staff member helps the group of the girl who goes on to earn the top score on the quiz. I end up helping another group -- normally I wouldn't, but I want to neutralize the advantages two other groups have with extra adult help. The group I assist contains the new girl who transferred in from another school.
Notice that it's the girls who seem to be driven by the competition more than the guys -- normally we'd expect it to be the other way around. Indeed, one group of boys (who I know are competitive on the basketball court during P.E. and breaks) seems completely uninterested in solving the equations faster than the girls. They are delighted when I announce a non-speed question -- while the girls are disappointed that the next question is not a race.
I haven't said much about seventh grade yet. Standard EE1 in this class, at least in the Illinois State text, seems to cover a hodgepodge of topics -- identifying whether an expression is linear or not, using the distributive property to simplify and factor linear expressions, and filling in values of y for given values of x in a linear equation. Here is my song for music break, to help this class out:
LINEAR OR NOT
Exponent on the variable?
It's not linear!
Multiply two variables?
It's not linear!
Variable on the bottom?
It's not linear!
Everything else?
It's linear!
Despite the mixture of topics and seventh grade having less time during the week due to the new Wednesday schedule, this class earns the highest quiz scores among the three grades.
By the way, yesterday, a Thursday, was supposed to be "learning centers," but of course it wasn't since I still need to know how to set them up. I've seen the fifth grade teacher do centers in her classroom -- and I know this because she often hosts the Wednesday Common Planning meetings and I see what's posted on her wall. Well, she tells me that she can help set up the centers in my room for next week. She says that she might do so on Monday -- that's right, coding Monday.
But she tells me that instead of having centers on Thursdays only, it may be a good idea to have them even on Wednesdays, with one of the centers being the traditional lesson. As I continue to struggle with classroom management and getting the students to be quiet all at once, perhaps it's better just to give up that idea and only teach to a small group of students at a time. (Sorry, traditionalists -- this means that I can never become a "sage on the stage.")
Well, we'll see what happens next week.
Despite this, one girl manages to earn a perfect score on the quiz. On the other end of the spectrum, two students earn the lowest score on both last week's test and this week's quiz, and I'm deeply concerned with their progress. Let me describe what happened today with those two girls.
It all begins before the quiz. You see, Illinois State provides an Intervention Focus Tutorial with some review questions -- another part of the Illinois State curriculum I've been neglecting until now. I find it a good idea to have the students answer these on whiteboards. Lately I've been working on ways to improve my classroom management, and one way is to foster competition among groups, or "teams," of students. Of course, this leads straight into group points and the "Who Am I?"/Conjectures game.
Last month I wrote some conflicting information regarding this game -- which, as you may recall, was a favorite of mine as a sub. It turns out that the game works better when introducing a lesson than as a review -- in the latter case, the smarter, louder students end up dominating the game. I didn't necessarily plan on playing my game today, but it follows naturally from the whiteboard review and team point concept.
But another factor to consider is my Bruin Corps member. The college student who works in my room on Mondays, Wednesdays, and Fridays ends up sitting with one of the groups (consisting of the two who fail the test). Note that she is an environmental science major, not a math major -- and so she may have been tricked by some of the multi-step equations. The girls in her group ask me for help -- but then I can't help them. This is because the other groups think that this group is getting an unfair advantage in the team points competition -- they already have a Bruin Corps member assisting them, and then I, the teacher, am about to help them on top of that!
Again, this reveals a flaw in my game as review for a quiz or test -- giving students the help they need to pass the quiz looks like unfairly aiding them in the game for points. My support staff member helps the group of the girl who goes on to earn the top score on the quiz. I end up helping another group -- normally I wouldn't, but I want to neutralize the advantages two other groups have with extra adult help. The group I assist contains the new girl who transferred in from another school.
Notice that it's the girls who seem to be driven by the competition more than the guys -- normally we'd expect it to be the other way around. Indeed, one group of boys (who I know are competitive on the basketball court during P.E. and breaks) seems completely uninterested in solving the equations faster than the girls. They are delighted when I announce a non-speed question -- while the girls are disappointed that the next question is not a race.
I haven't said much about seventh grade yet. Standard EE1 in this class, at least in the Illinois State text, seems to cover a hodgepodge of topics -- identifying whether an expression is linear or not, using the distributive property to simplify and factor linear expressions, and filling in values of y for given values of x in a linear equation. Here is my song for music break, to help this class out:
LINEAR OR NOT
Exponent on the variable?
It's not linear!
Multiply two variables?
It's not linear!
Variable on the bottom?
It's not linear!
Everything else?
It's linear!
Despite the mixture of topics and seventh grade having less time during the week due to the new Wednesday schedule, this class earns the highest quiz scores among the three grades.
By the way, yesterday, a Thursday, was supposed to be "learning centers," but of course it wasn't since I still need to know how to set them up. I've seen the fifth grade teacher do centers in her classroom -- and I know this because she often hosts the Wednesday Common Planning meetings and I see what's posted on her wall. Well, she tells me that she can help set up the centers in my room for next week. She says that she might do so on Monday -- that's right, coding Monday.
But she tells me that instead of having centers on Thursdays only, it may be a good idea to have them even on Wednesdays, with one of the centers being the traditional lesson. As I continue to struggle with classroom management and getting the students to be quiet all at once, perhaps it's better just to give up that idea and only teach to a small group of students at a time. (Sorry, traditionalists -- this means that I can never become a "sage on the stage.")
Well, we'll see what happens next week.
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