Scaffolding & Storing Teaching Materials

As I was searching for "teaching polar coordinates" materials from an NCTM workshop I attended a while ago, I came across a packet that described scaffolding. I liked their 4 tier process they layed out:

1. I teach, you watch
2. I teach, you help
3. You do, I help
4. You do, I watch

I got me thinking about how I've been teaching lately, and about how different uses of these 4 steps work for different populations of students. I think lately my philosophy is more "2", then practice based on "4" with help if I see they need it. I teach preAP and AP classes that are supposed to be for students willing to try things on their own, but realistically has a whole range of abilities. I internally balk at running through all 4 steps because it makes me think of them learning math by seeing, "oh, this is THE method/way of doing things. I will memorize this technique and parrot it back when tested".

I want them to think for themselves. But then another part of me says, "well, they have to learn the basic skills first, and THEN you can throw in some harder thinking problems". And then a 3rd part of me is inundated with comments of "hard homework" and "you didn't teach us how to do THOSE types of problems". I, apparently, need to have more time to think through each lesson and map out my strategy of presenting concepts then mixing the types of problems effectively .... maybe with some warning about various problems and hints (?) and admonitions to actually put forth some effort on the more challenging ones.

Anyhow. Then that got me to thinking about how I store my teaching materials, and how my plan has evolved since I started teaching. I use those large plastic tubs (with tons of hanging files to store papers). I have 4 tubs currently: one for precalculus, 2 for calculus, and 1 I just started for algebra 1.

My hanging file folders used to be: "chapter 1", "chapter 2", .... because I shortsightedly thought I'd ALWAYS be teaching out of the same book and the same school and the same topic. Then I think I moved to large groups of topics in each hanging folder. I'd have to paw through all the papers each year when the time came to teach concepts. Then, for some reason, I moved to "first 6 weeks", "2nd 6 weeks", ... (what was I thinking). Maybe I was a masochist or liked to take tons of time to sift through the whole pile every time I had to teach something.

I finally wised up (at least it's working MUCH better for me) and added manila folders inside each large hanging folder, and the manila folders have concept titles: "vectors", "triangle area", "graphing lines". I've also used large sticky notes attached to lessons to make my reflections about how a topic went after I taught it the current time and possible suggestions for the future teaching of it. MUCH more convenient and time-saving for me.

Fresh Starts

One thing I love about teaching high school is that you're forced to start every day fresh no matter what happened yesterday with the kids. Last semester I had a rash of cheating and some student crying and bad behavior and the usual drama of day-to-day high school life. Teachers usually don't have the luxury of banning the students from our vision/life/class, so we have to make the best of the situation.

This is good because it forces me to see beyond black and white to the gray: "cheating student = bad person" vs. "cheating student = bad decision and potentially a person that has other great qualities".

Today was another such day. I have a student in BC Calculus whom I had (ooh pompous-sounding "whom") in precalculus last year. He's a football player, smart as a whip, lazy as a cuss, funny as all get out. He struggled 2nd 6 weeks because of various life things and football things and laziness things, and didn't pass, but has since made up some grades and keeps coming to class and plugging away. Anyway, this morning (he's my aid in another class ... so that I can force him to spend 1.5 hours on his calculus homework) he looked to be in a foul mood, and he was texting and I was "put away your cell phone" in a grumpy voice. We didn't talk much the rest of the period as I was teaching vectors in precalculus.

Later on in calculus he comes in and asks how my day had been so far, and I mentioned that it was not good at all, and he commiserated with how crappy his day was and recalled this morning and how he almost lost it with me because of the "cell phone incident", but he thought better of it. Anyway, we had a good "grown up" discussion about horrible days and various other things.

These are the fun parts of teaching.

Mish Mash

As someone else has probably said before, when your mind is consumed with how bad things are at work (crazy decisions from "above", bullying of new teachers called "mentoring", being tested ad infinitum, ...), you have less to give your students (reflecting about the lesson, making sure in a positive way every kid is doing okay, developing new ways to teach concepts). This is the position I find myself in.

It's a never-ending loop in my mind about what I'd really like to say to so and so, what should be done in regards to being a successful math department, how you could make kids succeed. Copy room conversations with other math teachers revolve around the nightmare of this year and what/where they/we will do/be next year. Already 2 teachers have quit midyear. More are planning to leave at the end of the year. I'm sad and frustrated.

On a positive note, I've read some quotes lately that resonate with me, that I find myself referring to repeatedly:

When dealing with yourself, use your head.
When dealing with others, use your heart.

People first, paper second.

Great people talk about ideas. Average people talk about events. Small people talk about others.

And from my phenomenal teacher friend from the northeast when dealing with bad situations: Here is where you grow a little.

Accumulation Functions (Calculus)

I'm so excited. I think I found a more effective way (for me) to explain a certain part of Accumulation Functions in calculus. These are functions defined by

f(x) = integral (from some number to x) of r(t) dt

where r(t) is a graph. The graph can be (say) from -4 to 8 and the lower bound of f(x) could be 1, so: f(x) = integral (from 1 to x) r(t) dt.

Anyway, if r(t) is ABOVE the x-axis to the right of 1, then f(x) is accumulating "things" and getting larger, and if r(t) is BELOW the x-axis to the right of 1, then f(x) is losing "things" and getting smaller.

Well, everything is "reversed" in this example if you pick an x value to the left of 1. Say, f(-2) = integral (from 1 to -2) r(t) dt. Then if the graph is ABOVE the x-axis, between -2 and 1, then this defined f(x) is getting smaller.

This always confused the kids, and I hadn't a effective way to explain it. This year I tried: Suppose you took a movie of how f(x) is changing from start to finish on the SHOWN graph (regardless of the lower bound of your integral), so in this case, the movie would run from -4 to 8.

Now if f(x) = integral (from 1 to x) r(t) dt, you start this movie at "1" and show it either forward (for x>1) or backward (for x<1) and you see what is happening to f(x). This seemed to make sense to them, since ABOVE the graph r(t) means you're accumulating, and so if you show the movie "backwards", then you're doing the opposite.

Anyway, it looks kind of confusing written out here, but it was a small joy of my day to see their looks of comprehension.

I asked for it...

It was good to be back with the students today. I ignored the administrative silliness and just concentrated on the kids. My new mantra this semester will be asking myself, "what's best for my students at this time?"

For example, today what was best for my students was to not go to a department meeting that was slated for 30 minutes, but that I heard lasted (not surprisingly as it always does) 1 hour. It was also a meeting that sounded not purposeful. It was also a meeting scheduled after we'd proposedly spent 3 hours in a math meeting the day before during our "work day". Anyway. Today it was best for my kids (and my sanity) to skip the meeting during my one planning period and to concentrate on thinking through the best way to teach the next 2 lessons of this day.

One funny thing happened in class. I was going over calculus problems with my kids, and I was modeling the stream-of-thought way I work through the problem and how I ask myself questions about what is needed or what is to be done at each step.

I said to my students, "you could do this. Just pretend you have a little Ms. Cookie on your shoulders asking you these questions while you're working through a problem." And I put my thumb and forefinger together to mimic a small me and put my fingers near my shoulder. Then out of the corner of my eye I see one funny kid swat his shoulder to get rid of the nuisance.

Happy New Year

I have no idea how reasonable an idea this is, but what the heck. I was looking through my "teaching closet" at home and realized I had all these teaching books that are just sitting there gathering dust. I culled through the ones I wanted to keep and found many I'd be willing to share with someone who may get more use out of them.

I'll mail any of them to you on a first come first serve basis on the following condition. You will send a check to me made out to the charity of your choice for whatever amount you think is reasonable, and I'll pass the check along when I get it and mail you the book. If you're interested, please send me e-mail at math_mambo@yahoo.com indicating which book(s) you want. We can continue the conversation there. I also have favorite charities in town I'm willing to suggest (food banks and "safe places" and such).

Here's the list in "pulled out of the closet" order:

"The Passionate Teacher", Robert L. Fried
"Ordinary Children, Extraordinary Teachers", Marva Collins
"Among SchoolChildren", Tracy Kidder
"Small Victories", Samuel G. Freedman
"Escalante", Jay Mathews
"Why I Teach", Esther Wright
"36 Children", Herbert Kohl
"The Classroom Crucible", Edward Pauly
"Mentors, Masters and Mrs. MacGregor", Jane Bluestein
"Hot Tips for Teachers", Harrison and Spuler
"Teaching and the Art of Successful Classroom Management", Harvey Kraut
"Nothing's Impossible", Lorraine Monroe
"Growing Minds", Herbert Kohl
"In Code", Sarah Flannery
"Ed School Follies", Rita Kramer
"Positive Discipline: A Teacher's A-Z Guide", Nelsen, Duffy, Escobar, Ortolano, Owen-Sohocki
"Improving Schools from Within", Roland Barth
"Positive Discipline in the Classroom", Nelsen, Lott, Glenn
"Teaching Matters", Whitaker & Whitaker
"The Teacher's Almanac", Patricia Woodward

Holy Cow! What a book hog.