Psychology of Pricing

I had an epiphany the other day about how much each homework was worth. In our grading program we can assign different weights for different types of things: homework, tests, projects, etc. I have a totally independent category for homework and it was worth 25% of their total grade. Now since this is the only type of object in this category, it doesn't matter what each homework is worth if they're all worth the same: each 2 points, each 100 points, etc. It all comes out in the wash. My homeworks were worth 2 points each, and I deducted points (or partial points) as needed, so you could still earn 100% or 80% or so on on an assignment.

I don't know why the 2 points always worked for me. Maybe I fell prey to the psychology of pricing, too, and subconsciously I thought that tests were where you really showed your stuff, so those were worth 40 or 50 points or what have you, so the homeworks should be worth 2 points.

Anyway, at my new school, all the 9th grade classes have to have the same percentages: 45% homework/classwork and 55% tests/projects. There was some extra wording about deducting 5 points for various homework infractions, and so being new on the block and wanting to at least try things the way everyone else is doing them, I'm deciding this year to have each homework be worth 100 points. Again it shouldn't matter because it's in its own category.

So here was my epiphany. In my old school maybe part of the reason why kids were lacksadaisical about turning in their homework was because, "hey, it's only worth 2 points. no biggie if I don't turn it in." When in reality, it was a big deal because those 0's started to add up. I'm wondering if they would have had a different attitude if I'd assigned each homework 2000 points, just to mess with their minds or to get them to think about how the math all works out.

In other news, how's my new school going? Well, I think all the staff I've encountered have come from a different planet: the planet of graciousness and kindness and hard work. Oh my goodness, I can't tell you how many nice e-mails or cards or words I've gotten from other staff just to welcome me (and other new teachers, I'm sure) and check to see if I'm okay and to see if I have any questions or need anything. I'm so blessed this year. WootWoot.

Creating Your Own Thing

In this crazy week of prepping for the start of school, I've been in a few situations where I keep thinking about the book "Why We Teach", well really about one essay in particular. The teacher described her growing up years and the need for her to find her own voice and opinions. She got to the point where she didn't want to have a discussion with others or listen to other people's opinions on something before she had a chance to digest things and form her own opinion or method of doing something. Otherwise, she felt that she was just going along with the crowd or that her thoughts would either be stifled or not formed or swayed by what others thought.

So I periodically thought about this as I was coming up with a syllabus or a first day activity or how to decorate my room or procedures I want to put into place. Maybe it's not a "la la la la I don't hear you" type of situation where I think "it's my way or the highway, baby", but more of a reminder to think my own thoughts, then gather other opinions, then go back and reflect about how I think things should be done that carry my personality stamp.

Here's one new idea I'm trying, and who knows if it'll work. For the past many years I have taken a picture of each group of students on the 1st day of school and during that 1st class I had them fill out a seating chart AND print their names on a small sticky note. Then that 1st night I go print the pictures, and with double-sided tape I put their sticky notes on their picture. This helps me learn their names, and I also put all the pictures up in the room. They love to look at them at odd times during the semester.

Because I've seen that they SO love to go up and glance at all the pictures and discuss things and point certain things out (ooh, I just realized one reason why ... this helps them also to see who everyone is). Anyway, because of this, I'm going to ask them to bring in a favorite picture of themselves that 1st week (that I'll return to them later), and I'll use the awesome stikki clips to put them up as a border around either the blackboard or a bulletin board.

New Toy

I was recently at training and learned about fun ways to present information such as:

A Movie I Made (I see a side job forming)

I could see it getting old, but it's a nice thing to throw in the mix.

I've also met amazing people at my new school. It's only been open for 2 years, so they're still inventing who they are and what they are capable of doing. They seem genuine and smart and committed. BUT.

Information Overload. I'm totally at the stage of, "I'll never remember to do all this", and "Argh, what if I screw up, and they secretly shake their heads at the mistake they made hiring me", and "Oh My GOD, I'll never be ready come Monday". You know, the usual jitters (and don't forget: they have only HOW MANY copiers? What, no work/eating/microwave room?, etc.)

I'm teaching 4 different preps this year ... well, 3.5 (one is a type of study hall). And I've agreed to be some sort of team leader and occasional yoga instructor. I must be woozy from lack of sleep. Must. Learn. To. Say. No. I practiced a bit today when an afternoon robotics team leader position presented itself: no. Whew! Go me. Baby steps.

Words to Ponder and Chew Over

I recently came across a chart that contained these comparisons, while I was searching various high school websites. (hmmm, the formatting is wonky, but ...)
Comparing Solution Building with Problem Solving
Solution Building vs. Problem Solving

1. "How did you do that?" vs. "Why did you do that?"

2. Focus on the future without the problem vs. Emphasis on past with the problem

3. Solution talk vs. Problem talk

4. Attention on what is working vs. Attention on what is wrong

5. Student is capable. vs. Student is flawed.

6. Teacher skilled at "not knowing." vs. Teacher is "all knowing."

7. If it works, do more of it. vs. Just keep using what you think should work until it, hopefully, does.

8. Change is inevitable. vs. People cannot change.

This resonated with me and it's been popping in and out of my mind for the last few days. If I scan down the list, this past year I could count 5 of the 8 where I was more focused on what was wrong at my school than just rotating my thinking and concentrating on what I could change or fix or be a part of making better.

Ooh, 7 makes me wince because in some of my classes, that's what I did sometimes. Off the top of my head: if students were having continual problems understanding, I would tell myself that I was ALWAYS available after school and they had every opportunity to come to tutoring. Yet every year, there are kids who for a variety of reasons don't come to tutoring and STILL fail to understand various topics. Maybe I need to enhance my toolbox of skills so that more kids understand more topics in class or have different avenues of seeking help other than coming to my tutoring.

Anyway, more stuff to reflect on.

Learned & Reaffirmed Things

After a slew of math workshops all crammed together in one summer, I can generate a list of things I've either learned or relearned from my experiences:

1. Your math text is NOT your curriculum. Not for what you should teach, not for how you should teach, not for why you should teach something.

2. Every workshop seems to have the same set of characters (other than perfect people like me ... cough cough):
- the know-it-all that has to shout out all the answers quickly just to show they know things.
- the on-the-sly-constant texter
- the nary-a-peeper
- the challenged learner that asks TONS of questions
- the I-know-this-&-am-too-cool-to-REALLY-process-what-you're-saying person who will probably be unpleasantly surprised when they have to actually apply this current knowledge next year.

3. I'm set in my ways. Before my 1st out of town workshop, I was stressing, "oh no, I won't have my favorite tea, my vegetarian food, my own bed, ..." waa waa waa. I *mostly* had a change of attitude and used it as an opportunity to try new things ...... mostly.

4. I love my new school-provided laptop. When I was getting homesick, I could stream our local NPR station, and I could Skype my husband, and I could send e-mail and impatiently wait for replies to feel connected to friends.

5. "yelp.com" is a great new asset in my traveling life. I could just type in a city and "thai restaurant" or "breakfast" and get tons of opinions to scroll through to find places to go.

6. "mathforum.org" has a section called "math tools" and you can enter the subject you teach and the topic you're interested in, and it returns a list of resources for you to browse through to use: applets, calculator tasks, worksheets.

Even Better Calculator Trick

We explored a "different ways of payment" problem and learned a new calculator trick to boot. Suppose plan A gives you $20 the 1st day and increases your salary by $1 per day. Suppose plan B gives you $0.01 the 1st day and doubles your salary every day.

Calculator:

{1, 20, 0.01} (to represent 1st day, plan A, plan B)

ENTER

{ANS(1)+1,ANS(2)+1,ANS(3)*2}

ENTER, ENTER, ENTER, ..... to keep seeing current day, plan A, plan B updates.

Nice. And sandwiched between 2 nice pictures of a recent trip.

Ooh Cool Calculator Skill

Today at my math workshop, I learned some new-to-me calculator skills that I believe I'll use this year.

Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:

{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.

Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.

Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:

{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.

Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:

seq(x,x,1,100,1)--> L1

I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.

Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.

preAP math ideas

I'm at a week-long workshop for "experienced" preAP math teachers (for nonTexans, preAP is like an honors course or the higher level math students). After the 1st day, I already have some good ideas on what to do differently next year. In my school district, we have to get re-professionally-developed in preAP techniques every 5 years. At first I was thinking, hmph, I do so much other professional development on my own, this is not needed. Oh contraire. Even though I've taught calculus and precalculus, it is apparently still needed and useful.

Today our instructor did various things using calculus and statistics AP questions as the basis. But. The way he did it was very useful. We worked through a calculus problem. Then we brainstormed on earlier class skills it addresses. He showed concrete ideas on how to modify the problems to address alg, geo, alg2, precal.

But what I really came away with were the LOAD of things I could do with statistics and why it's useful. For example, at the end of the day, he had a sheet with a cm ruler on it, and we all measured our hand span from outer index finger to outer pinkie finger. We got that list in L1 on the calculator. Here are some of the things we did with it besides calculate mean, range, Q1, Q3,...:

1. What if the ruler on the page had a mistake, and we were 2 cm off, so we had to subtract 2 cm from each data point. Without using your calculator, discuss what that would do to the: mean, range, median, ...

2. What if instead of cm, we wanted inches. How would you change data? What would this now do to mean, range, ...

3. What if instead of the largest span we had, that person was replaced with (name some local basketball player who's tall with BIG hand span) ... and we put in a large reasonable number. What would this now do to ....

4. What if for our data of spans that ranged from 16.5 cm to 21.5 cm, someone got a mean of 15 cm. Discuss why this is reasonable or not reasonable.

There were a ton more good ideas. I liked it because it made us think and it would make the kids think and it was in context they could understand and it had them manipulating formulas and thinking about meanings (throughout the day).

Real Life Math (as opposed to the fake kind)

We're going on multiple longer-than-a-week trips this summer, lucky us, and our outside Texas plants are begging for dribbles of water. We decided to put a timer on a drip irrigation system, and then we wouldn't have to worry about coming back to an Adam's Family set of plants.

I was hooking up the 1 gal/hour drippers to each pot, and doing the math. I usually water them every two days with a huge dollop from a pitcher. Hmmm, how many dollops in a gallon? How many minutes every other day to equal a dollop? I guess I'll see if I did my math right when I come back to either a lush plantation or a brown oasis.

Student Teacher Interactions

My 2-week training is over, and now all that's left to do is practice, practice, practice and map out what I'll teach when. It was put on by these folks, and everything was so professional and well-thought-out. I also know from other teachers who teach the curriculum that you are well-supported throughout the year.

For 2 weeks I was in a class with 16 other varied-ability people - lots of time for reflection on how teachers respond to students and how different students handle their learning. Two people had their hands in the air basically the whole time - asking for tons of help and being a little gun-shy of exploring on their own. I'm wondering if there was something non-demeaning the teachers could have done to make them more self-sufficient. Maybe something along the lines of, "I'm confident that you can figure out the answer. Try 3 things first to see what happens and then I'll help you." or "Here's a hint, explore it for 3 minutes and then ask me." Instead, every time they went over to help them on the program, the teachers would take the mouse in their hands and solve the problem. To me that just kept the people helpless.

Another 2 students had already had a lot of exposure to the program, so something that would take me all night of homework to figure out, they finished during class. They weren't rude or bragging about it, but it was clear that was what was happening. But. By the 3rd day of our 2-week workshop, the teachers would frequently make comments such as, "I bet R. has it finished and has improved on it.", or "I bet C. has already figured out how to do that.", etc. As a student, that got annoying to hear. I'm thinking it wasn't helpful to either R. or C. because maybe they felt singled out, and the other students (me included) would feel that much slower. Then I started wondering if I did that in my class. I'd better stop it if I did/do.

Okay, one workshop down, 4 to go. Mwa ha ha ha.

My New Love Affair

Dear Webcam,

I love you. Today we started a "reverse engineering" project (don't ask), and you came through for me by easily allowing instant digital photos needed for our engineering notebook. Contrary to what your lens tells you, this is NOT a gun. It's a tape dispenser that we are to improve in some way. Thus, the inspecting and analyzing and taking apart and sketching and improving and drawing. Because of you, my technical toolbag has grown.

I also like your friend, Skype. We are concurrently working on a virtual project with other students in Ohio, Colorado, and South Carolina. Fancy Schmancy new skills.

I had to tell my husband about us. He now suggested I should reverse engineer the vacuum cleaner that keeps breaking because of SOMEONE'S long hair that keeps tripping up the inner workings. Good luck on that account.

Love,

Me (click click strike a pose)

Core Set of Knowledge

I'm currently at an engineering teaching workshop (ooh, math teacher teaching engineering) with many other teachers from all sorts of disciplines - math, english, science, computer languages, ... and during lunch or breaks or in the course of our training I have had various conversations with many people.

During one conversation, I was talking to a middle-school math teacher who was mentioning that she was helping out her science-teaching friend with one piece of their homework that involved plotting points on the coordinate plane. The other teacher was having trouble with the negative y-axis. During another conversation, I was helping my table partner figure out how to put one dimension from the paper (a radius length) into the computer which demanded a diameter length. I thought she was having trouble reading where the paper number was located on the busy drawing, so I pointed out the radius number, and waited for her to convert it to the diameter length. She blankly stared at me. We finally got her to the point of doubling the length, but I was astounded that she didn't know this basic D=2R fact.

This got me to thinking of what I assumed was basic adult math knowledge regardless of your job. I got on my high horse and was scared of what I was seeing. Then I flipped it around and wondered what science teachers would assume I should know, or what english teachers assumed I should know, etc. Maybe I'm one of those people who cause others to inwardly raise their eyebrows and say, "you don't know THAT?!?!"

I went to dinner with another participant who's a biology teacher and asked her what she thought was an example of what I should know as core science facts. She thought a while and said: what are the functions of different body parts (liver, kidney, pancreas) ... as one of her questions. Eek, eyebrow raising.

Sooooo, hmmm, I assume some math adults should know/retain-from-schooling:
basic circle, square, rectangle facts
plotting points

... so I started that list and then thought: why should they know that (for what purpose)? why did I think they should know that (because I thought those were "easy" to remember and basic)? Maybe it's more of a case of "I'm surprised they don't remember those facts .... like I'd be surprised if they didn't remember how to add, subtract, etc.".

Engineering Education Workshop

On Saturday I went to a free workshop about teaching engineering. It was pretty cool. We got to experiment on how to create "penguin houses" out of various materials for ice-cube-penguins to keep them from melting in 20 minutes of a heat-lamp-induced stay (conduction, convection, radiation) while keeping under a $200 budget. We got to build boats out of aluminum foil to see how many would fit before the boat sank (bouyancy). We got to create lunar landers out of cardboard and straws and index cards and such to land from shoulder height without jarring the astronauts (marshmallows) out of their shuttle (cup). ... and other activities.

It was a fun day and showed me what I DON'T know about engineering, and what I want to explore more about. By the way, our group's penguin house cost $2000 and only preserved 6g out of 10g of ice (whereas others cost less than $200 and preserved anywhere from 8g to 9.1g). Go us. But the presenter did NOT have to make a face when she read our results out loud.

I liked the concepts. Most seemed to assume you were teaching science or had the freedom to use up lots of time to do these things. So now, as a math teacher, I have to see how I can break these lessons up into smaller chunks to wedge into a packed curriculum. I do think the activities were worthwhile, now I have to see how to incorporate them into algebra 1 and geometry.

I did see one geometry connection. When we were making our lunar lander, our accordian shaped index-card "legs" kept flaying out. Then I recalled that triangle shapes are sturdy, so we fashioned some extra supports that used this geometry fact ... of course it didn't prevent our marshmallow astronauts from bouncing boisterously out of the cups to their sure death on the moon.

I did like their continued stressing of the fact that your 1st attempt was not it. As an engineer, you learn from your mistakes and go back to the drawing board to rethink and recreate.

I also liked the talk related to NASA and "Design Squad". There are videos of the DS show you can stream and discuss. It's broken down into chapters (she said), so you can show snippets. NASA has a ton of free resources for teachers. Also, there are video profiles (Pro Files) of engineers (on DS site) that show cool things they do and non-stereotyped people who work as engineers.

Whew! Stuff to think about.

Center of Mass Fun

This is an activity I did with my calculus students post AP exam. We had talked about center of mass, and we calculated it with integrals in a previous class. Then I saw this problem in my new favorite book, so I decided to run with it. I first had the students try to balance one ruler on the desk top with the condition that it should go out as "far as it can".

Then I gave them 2 rulers and said they should line up and for the future tasks, if a ruler is on top of another ruler, it should be farther out than the one below it. So they were to play around and get the whole system to be out as far as it could be.

You can get the total out 9". There's a pattern and a reason, and I'll be mean and not give it away yet because half the fun is figuring it out. Then they got 3 rulers with the same rules.

Do you see the coolness ... almost off the table (you can get 11" with 3 rulers). Then 4 rulers.

Woot! 12.5". And just for fun, 5 rulers:

13.7" off the table edge.

Stating the (not so) Obvious

You know how you go around all the time interacting with a set of people, and you have nice opinions of them in some sense but you never voice these things because in your mind you're thinking, "oh. THEY know that about themselves." Well, it turns out that either they don't, or they're unsure, or they just like to hear other people confirm what they *may* suspect or hope is true.

For example, I have a lovely friend in tap dancing. She's in her late 50's and funny and pretty and vibrant and wise. She's also a teacher (at a different school in a different subject), and she always has some common sense take on school occurrences. I'm forever thinking these things about her. Well, today she was telling me about meeting a gentleman for the first time and how unsure she is about her "package". Holy cow! I had to tell her that she was gorgeous, and he would be thanking his lucky stars when he laid eyes on her. She seemed totally taken aback and did not seem to think this about herself.

Now I'm wondering what other friends I need to pounce on and tell them all the good things I constantly think about them.

Alternate Finals

All year in calculus I told the kids that if they signed up for and took the AP Exam, and if the proctor mentioned that they worked hard and didn't put their heads down or doodle or such, then those students would have an "easier" final exam in my class. Everyone this year took the exam, and I debated what final to give them.

I had a discussion with an AP English teacher whom I respect, and she mentioned that she gives the kids (in the same situation) a college-style text (poem?) to read, and they have to analyze it in some such way. That got me to thinking that even though I want to teach textbook reading skills to my kids, I never seem to get it together to manage such a thing effectively. Then, VOILA, idea. I scanned some books and found a section on probability using calculus. It "looked" like heavy reading from the perspective of a high school kid, but once I plowed through it, I saw that it was very friendly and gave examples and such for the problems I had them do for their final.

I prefaced the final with, "you will be reading such things and learning on your own in college, so this is your chance to practice it. Read through the section, and look carefully at the examples, and do the 6 problems I've circled". They (for the most part) worked hard, and I got a wide range of scores back, and it was enlightening for me.

At the same time, I'm thinking of various precalculus students I have. They scored in the high 90's all semester, and I know that the final would just be an exercise of spewing back stuff to me. So for those kids, I copied some sections of a precalculus book on a topic or 2 that we didn't cover, and did the same thing with them. I did not get to cover induction proofs or binomial theorem this year, and those were my topics of choice. In my mind, I'm thinking of just averaging their semester grades and giving them that for their final exam grade, but I also wanted to challenge them a bit. It was extremely fascinating to see how various students handled it. Some just dove right in and tripped a bit, but with a wee bit of help did fine. Some quietly plugged away without asking any questions, but when I went over to see what they were doing, they were lost. Some were completely flustered at not having a good handle on things. They were so out of their comfort level and had to keep being reassured.

This makes me think that I want to give such a test to the whole class some time periodically, to give them an incentive to truly read a text for understanding. Of course the problem is time, time, time. We'll see.

Wrapping Up the Year and School

Technically I have 4 school days left with children. I teach 5 of 6 classes that have seniors in them, and since seniors are having some finals early, I have NO FINALS ON THE LAST DAY. Woo Hoo. That will give me a huge chunk of time to pack up all my stuff and do "leaving chores".

I have to say that in my 12 years of teaching, this fall counted as my worst ever. This was not kid-related but adult-related, so in January I decided to look for a new school to teach at for next year. I found one, and based on several e-mails and encounters with my soon-to-be coworkers, I think it'll be a great place to work.

That doesn't mean it's not sad leaving a place I've worked at for 6 years, leaving students I've grown to love and would have been teaching calculus to next year, leaving many other teachers that I respect and enjoy being around, leaving a comfort zone of routines that I know, leaving a place where students know me.

And then there's the constant battle of thoughts in my head:
- you're jumping ship when you should have stayed and fought for what's right
- you can't work for people you don't respect
- you're moving to a functional place
- you're deserting the kids
- you'll have better mental health next year and more to share with the kids
- you'll never see these teachers again
- change is good
- change is scary
- will it be weird
- will it be better

Crabby Pants Cookie

Raowr! It's really quite shocking that students would rather text with their friends or chit chat or stare of into space lately than learn super cool math (redundant, obviously). I'm shocked, I tell you. I do have some kids showing snippets of interest and other kids showing tons of interest, and I'm most likely at the end of my patience with this particular class because of year-long behavior of a handful of students.

Cases in point:

One student flitters in and out on attendance, and has missed some classes lately and all of a sudden (1 week before the end of his school year ... seniors take finals early) wants to make up a grade from 6 months ago, and can you please show me what I missed and can you please make copies of it for me and thank you so much.

One student after constantly coming in all year and starting every other class with, "oh miss, I was going to skip today, but I decided to come," has been absent the last 3 classes (one was valid, the other 2 shady). I gave her a zero for the quiz she missed on her shady day. Her current average is now a 25%. She suddenly shows up and has an interest in class and wants to please know what she can do to make up the grade. I question her about the validity of her absence. Oh, I went home sick. Cough cough. Oh, I'll get my mom to write a note. Oh please reteach me EVERYTHING I missed oh and thank you very much.

Two other girls start "maam-ing" me when they know they're getting on my nerves from disruptive behavior. "Yes, maam. No maam."

Deep breaths. They're just kids. They're still pushing buttons and learning how to act. It's spring. Repeat.

On positive notes: various students come up to talk to me after class about what we did and wanted to talk through further thoughts on the matter. Many students mentioned they'll be sad I'm not teaching at this school next year. Handfuls of students stop by periodically and chat about life and such. A student who got pregnant with twins her senior year 3-4 years ago and still managed to graduate now has cute little girls and comes to visit periodically and is going to school to become a nurse. A student I had last year who was so edgy and ADHD and rudely violent in the hallways last year has turned out to be one of my favorite students this year. She's pleasant (still edgy) and interesting and humorous.

A cool fact a student shared with me in calculus today while we talked about breaking the sound barrier: The 1st man-made object to break the sound barrier was ........ the whip. Cool.

Post AP Exam

After the AP Calculus exam every year (of the 4 I've taught it), I've done different things. The first year I did a volumes of cross section project with foam and hot glue and a ton of grief. That was the year I had a screaming match with a student outside of class. The 2nd year I took a break from that and did various other snippets of math topics with mini quizzes. No screaming matches. The 3rd year I revamped the volumes project and tossed in a volumes of revolution project with foam and hot glue and stricter guidelines. That year I had a child sit in class with his pants unzipped and then tell me later that HE WILL DECIDE what is socially acceptable.

This year I'm teaching snippets of advanced calculus to my 2 classes with "easy" quizzes at the end of each class that should be ace-able if they simply pay attention. So far I have one class being good about it, and I've even had one student finally perk up and get out of his morose I-suck-at-math state and pay attention to be able to pass the quiz. The other class was great for one day (when the loud students were gone for other AP exams).

There are students in that 2nd class though that are enjoying things. They come up to me after class to discuss the topics some more.

So far we've "covered" (just given them a taste of) double integrals used for calculating volumes of weirder shapes, surface area calculations, and Gabriel's Horn Paradox. I think I also want to do Fourier Series with my BC class and centers of mass and .... who knows what else. I have a great resource ... the Smith calculus book. It's the THICK blue one, and it has amazing problems and historical snippets and ideas. Anyhow, busy busy busy trying to learn things right before I teach them.

I was also intrigued by the Hubble Telescope news of late, so I assigned my precalculus class an assignment of bringing back 3 facts in their own words about anything to do with "Hubble". I told them that I wanted to learn about it, too, since I didn't know much about it, and I would also do the homework. I told them that we couldn't just exist in our own little bubble of everyday existence. We had to be informed about the world. Then a student said, "we'll bring Hubble into our bubble."

I told them to explore the "what,when,where,who,why, & math" of the situation. Anyway, I went on a particular website, and WOW, the pictures it sent back from space are breath-taking. Can't wait to see what they find out.

Surprising Gap of Knowledge

My teacher friend was having her advisory class address envelopes to their parents the other week to send out invitations to an acadamy picnic. She quickly realized that more than 75% of the class did not know how to do this and was shocked. After she relayed the story to me, I asked my freshman class and my mixed class of juniors and seniors if they knew how to address envelopes. I basically had the same result. We went through a quick lesson. In my freshman algebra class I wondered out loud when I had learned it and why it was useful (because they think they can just text and e-mail their way through life). I told them that it was fun to get letters in the mail, and when I was a kid, I had pen pals in different states. They then wanted to get pen pals with "littler kids" in other math classes. Hmmmmm, I think it's too late in the year, but maybe it's an idea for next year.