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.