You Can Dance If You Want To, You Can Leave Your Friends Behind...

So here I am, updating my Math blog, even after MAED 314A has finished. I decided that I will keep this updated for some time. This is about my professional growth as a math educator, so why not keep it fresh?

Today, I went to my practicum school to visit my sponsor teachers and hang out in the class. According to my sponsor teacher, I picked a good day.

Sponsor: "So, Paul, did you bring comfortable shoes and comfortable clothes?"

Me: " Uhh, yeah. Why?"

Sponsor: "Because today, in class, we're gonna dance. Didn't you see it in the curriculum?"

She really had me going for a moment. I was pausing to think about how dancing could possibly make its way into a math class, with the exception of some form of interpretive dance (like the short movie we saw in MAED 314A class). Once I figured out what the dance moves were, I thought the idea was brilliant! The "dancing" had four moves, all based on the orientation of polynomial functions on the Cartesian plane.

For odd degree polynomials with positive leading coefficients the dance move was this...
....O
.._|_/
/.. |
..../\
because the function is plotted (from left to right) from quadrant III to quadrant I.

For odd degree polynomials with negative leading coefficients the dance move was this...
....O
\_|_
....|.. \
.../\

For even degree polynomials with positive leading coefficients the dance move was this...
.....O
.\_|_/
.....|
..../\

For even degree polynomials with negative leading coefficients the dance move was this...
.....O
..._|_
./.. |.. \
...../\

The purpose of all of this was to get students to recognize what the general shape of the polynomial is before hitting the [Graph] button on their graphing calculators, so that they know whether what they see on their screens is truly representative of what they should expect to see. All in all, I thought this was a great activity, but only if the students are willing to try it out. This might not work right away with me, unless the students feel comfortable enough with me to act a little foolish. But hey, it's in the name of education!

Unit Plan: Circle Geometry (Principles of Mathematics 11)

http://docs.google.com/Doc?docid=0AXSOUnLC8EogZGc2cDZid25fNDljbXZwZjRkNw&hl=en

Here's the link for my unit plan on Circle Geometry in Principles of Mathematics 11.

Member of the Math (of Least) Resistance

Susan guided our minds in class today to the beautiful coast of some foreign land. I decided to recreate myself as Jacob, the 21 year-old chemistry student (how original!) who, because of the army, was unable to complete his studies. I pined at the loss of my chemical acuity due to inactivity. Remaining unemployed on the coast, I found myself just wasting the days away. That was the case until that fateful night when I was awakened to the harsh knocking on my door. I was brought out to the field in the cloak of night and told that my services were enlisted by a small faction of rebels seeking to overthrow the current army regime. Their request: work with several other math-oriented locals to solve problems vital to the rebel alliance's work. We (Jacobi, Ruth, Alma, Doran, Captain and I) gathered in the cave (also known as the underside of two desks) to discuss two problems: one involving scouting for enemy camps with possible traitors in our midst and one involving distribution of rations. With only a dim candlelight in the cave, we had to work together and solve the math problem.

This has to be one of the most memorable math curriculum/methods lessons I have had so far. The incorporation of drama into getting students to solve simple yet practical problems was excellent. It appealed to my sense of a need for something interesting and it appealed to my sense of getting math done. We worked together on simple problems and it was fun. Overall, I thought it was great. I just hope that I can learn to adapt this method to suit my science courses, as well. (It would be great if I could try this!)

Assignment 3: Math Project (Tessellations, Part 1)

Our group (Erwin, Gigi and Stanley) worked on the Islamic Tiling project. I chose the tiling pattern that consisted of ninja-star-looking units. (This was my first impression of the pattern.) Using a more sophisticated description, the unit cell that I identified had the general shape of an equilateral triangle, with the edges composed of a sine-like curve (1 period). There was an empty space in this unit cell, which contained a Star-of-David-like hexagram. Individually, I was not able to re-create the unit cell--err, pattern. (Forgive me: I keep calling it a unit cell because the chemist in me keeps popping out and remembering first-year chemistry and molecular stacking patterns.) Using straightedge and compass, I created a (more-or-less) similar curvy triangle. The part which gave me the most trouble was creating the empty hexagram with only those two implements. Gigi tried to help me with it and she may have figured it out. (The diagram is on one of the three pages of work.) I did not get through the entire project, but that was the point, wasn't it? To give it a try.

In terms of evaluating the benefits of this project, I think this project caters to the student's artistic flare and mathematical prowess. The first part (drawing the pattern, describing the pattern in words) appeals to those people inclined towards art, not requiring any math skills (except trying to keep things in proportion). The second part (recreating the repeat shape with straightedge and compass, making minor modifications) caters to the mathematician. It requires visual analysis of the shape to look for patterns that can be recreated using the geometry knowledge that students have thus far. Teaching analytical skills will be helpful not just in math but in so many other areas of life. One weakness of the project is that it could be overwhelming for students who cannot see the pattern that can be recreated with the two simple instruments. Tessellations are covered in the Math 8 IRP. Some of these might be difficult. (I will admit: I got a bit frustrated that I could not recreate the hexagram in the middle.) Of course, this problem could be alleviated by choosing simple tiling patterns for the students. I would not modify this too much, but I would pre-select some not-so-challenging tiling patterns or at least have two sets of patterns (medium and hard). One constraint of using this project in my classroom would be time. I might not know how long to prolong this project or how many class sessions to allocate for in-class work. Overall, I could see this being used in my class to get their creative juices flowing.

Liouville Problem, Two-Columned Approach

Together with Gigi and Stanley, we chose to attempt the Liouville problem in the "Thinking Mathematically" book by John Mason, Leone Burton and Kaye Stacey, found on page 179. Here are my thoughts on the problem and my approach. (You will note that in the right column, I wrote "What do I do now?" a lot because it was not clear to me what the question was asking.)

Memorable Moment From My Short Practicum

One of the most memorable moments of my short practicum occurred during my Principles of Math 11 class, on my first full day of teaching. My faculty advisor was present for my first class. After teaching my first class, a review of linear inequalities for the Honours Math group, I was pretty content with what I had planned. Granted, I needed to work on my habits of staying only in one place during the lesson and having my back to the students while writing on the board, but overall I was quite pleased. The next block began and my faculty advisor left and my sponsor teacher was observing me. That's where everything went downhill. I took up homework problems that were considered difficult by the students and during the explanation, I stumbled on my words at several points. I had not looked at that particular question beforehand so I was doing the problem for the first time on the board. I messed up and made mistakes on 3 occasions. This left me wondering, "Why am I here? Do I still want to teach?"

Luckily, things improved for the third block and by that time, I reassured myself and realized that what I needed to do was learn from my mistake and move forward.

Short Practicum Update

Even in the midst of all my lesson planning and UBC assignments that need to be one, I wanted to write a little something about my short practicum so that I do not forget about it. I have been working at St. Thomas Aquinas in North Vancouver for the past week, and it has been a teaching eye-opener. The whole secondary school dynamic is something that I had forgotten about, being almost 6 years out of that environment. My sponsor teachers (2) and faculty advisor have been tremendously helpful in guiding me to be a more effective teacher.

I taught my first lessons today: three Principles of Math 11 classes. I learned some things about my teaching style.

1. No matter how much I try the questions out, I'm bound to forget a negative sign when writing on the whiteboard.
   
2. No matter how well laid-out my lesson plan may be, things will get off-track and I will be racing to finish everything.
3. Timing. Nothing more needs to be said about it.

I hope that I take all my advisors' words to heart and really change my teaching habits. If not for my sake, then for my students' sakes.