I taught three classes:

Math Art with Computers (First Year Seminar)
Power Algebra
What Is Math

This semester I became very comfortable with all the students in all my three classes and my students felt comfortable with me.  One reason for this was that I started interviewing individually each student for 30 minutes periods from the start of the semester and developed personal learning/teaching situations with the students.   I was not only teaching them but they were also teaching me.  The interviews took a long time and so I changed my work habits and started spending most of the day in my office (while in previous years I spent many hours at home).  I learned more than ever before about the hardships that students experience here during the first semester.  We as teacher have little idea what they are going through.  Since students live in small rooms in the dorms they influence each other.  There is a lot of drinking and general discontent  that effects every one.   I was looking for ways to help.  I found that in general students who come to college feel quite isolated and in order to feel more comfortable they go to parties and try to conform to what they believe will help them feel "belong".   It is a kind of a  "social survival mechanism".  In order to help my students overcome this obstacle to learning and living happily, I created a class atmosphere where they became comfortable with each other and some of them stated to form small support groups and feel better and better about themselves realizing that they are really not alone and that they could actually help other students also.

For the first time in my life I was teaching without fear.  In past years I strived to reach this stage and tried all kind of techniques, for example preparing the classes very carefully, but it never worked.  Now I know why it did not work.  There was always some hidden assumption in the mind that things will not work right and since the mind is such a powerful instrument this self fulfilling prophecy was manifested in the physical dimension.  What a relief it was to find this semester that this assumption was gone  and all the remained was a playful nature of creativity and adventure in teaching.

Another aspect that I added this semester was meditation and active visualization, in particular in my 4:00 pm "What Is Math Class".  Students come to this class quite tired after a long day of activities and here they need to sit on their butts for another long hour and get bored.  No meaningful learning could happen that way.  So I adjusted my plans to fit students needs and I felt that everyone benefited from this.  In this particular class that consists mainly of Seniors and Juniors who needed to fulfill a Math requirement we also showed the movie "What the Bleep Do We Know" ( see http://www.whatthebleep.com/) that effected our thinking in this class.  The video is about the connection between Science and Spirituality and tries to demonstrate the inner and inter connectedness of all things.  I used to tell the students the sentence "The Neurons in the Brain just like to fire.  They do not know the difference between Music Math or Art".  Thus we learn something by "doing It"  by "Having Fun with It" and we create our own meaning of what we learn.   One of the major events that this class sponsored was the Math Day on November 5th, 2005.   It was also part of the 50th years celebration of the school of H&S at Ithaca College.  My other two classes participated also but most of the math exhibits were done by this class.  A few hundreds children from the Ithaca area came to the event and other teachers (Pat Woodworth and John Barr) participated also.  Some of the pictures from the event can be viewed in: http://www.ithaca.edu/dani/programs/MathDay_Fall_05/pictures

In my other two classes, Math Art (a first year seminar class) and Power Algebra I tried to teach the concept of a function in a meaningful way.  I think that students do not really understand what a function is simply because they had no reason to use and work with functions except by answering test problems.  So in both classes I devised questions and "doing problems" where students had natural needs to use functions to achieve certain tasks.  I used the computer language SeeLogo to achieve this goal.  In both classes I use the exploration approach whence I have a general idea as to what I want to teach but am open to changes in the actual classroom situation.

In both classes I introduced the students to short computer programs that I wrote and asked them different questions about the program that create well defined visual effects that can be tested.  Students can tell themselves if they answered the question correctly by observing the visual effects.  In the Math Art class the emphasis was on programs that produce dynamic art (pictures that change with time and are fun to watch) while in the power algebra the scenario was more "dry".
Example:  Define a function that will turn a fractal from having 2 fold symmetry (2 babies in the jargon of the class) to 3-fold symmetry.

In the Power Algebra class I asked the students among other things to write a program that flies a red space ship from the point A(0,0) to the point B(100,100) but after a certain time units shoots a blue satellite ship in the direction of the tangent line of the function.  By answering this question students learned about the idea of the derivative without having to understand the formal definition but rather use the idea to solve a practical problem (flying the blue ship in the direction of the tangent line)

One of the requirements for all the classes is to write a class web page for the class where every student will have a link to their own web page in which they will express what they learned in the course.  During final we plan to watch the web page and share what we have learned (including this page) and individual testing will happen all through the final week by individual 30 minute interviews and a paper that each student is asked to write.  This is the first semester in which I am asking all the students to do this and I am writing this page as an example for them.
 

For years I wanted to do more for children who are getting hurt learning Math in schools and to bring the beauty of Math of Math and Love for Math to young minds.  This semester I started an experiment that proved to be successful. I contacted local school and the home schooling community and arranged a situation where young kids (grades 1-5 in general) would come to Ithaca college once a week and Ithaca College students would teach them Math.  The first student teachers came from my own classes but later other students joined in and now we have about 10 Ithaca College students voluntarily teaching about 10 young children.  By teaching and interacting with the children the IC students are not only teaching them but also learning Math themselves.  For example, one of the children, a 5th grader from South Hill School who actually loves math and is good at it said that he wants to learn the multiplication table really well.  This lead the college students to develop lesson that explore patterns intuitively.  For example, he discovered that pattern:
4*4=3*5+1, 5*5=4*6+1, 6*6=5*7+1, 7*7=6*8 + 1. etc.  Later another student shared some memory rhyms that young students like:  For example:
"6 and 7 went to heaven on a bike made for (4) two (2).  6*7=42"
"6 and 8 went on a date, and didn't get back until four (4) past eight (8).  6*8=48"
I think that this "school within school" has a future and other teachers may try it also.  It really brings a new dimension to education that is missing from traditional schooling and is a 1-1 relationship between a student and teacher that allows for flexibility, creativity and improvisation.   With the support of a colleague I brought the idea of creating a Math Learning Center in the department that will serve the larger community (including the college) to learn math in a meaningful and fun way and the department supported it.  Now a few of us are starting to work out the details.

Another inner calling that I had was related to the quality of food at Ithaca College.  I believe that the quality of food does effect the well being of students and that in addition to the quality of the ingredients that go into the food, the  main ingredient is the Love and Care in  which the food is being prepared.  Mark Darling shared his idea of having three meals this Fall semester were students will eat healthy and wholesome food.  The First Year Seminar students will be in charge of the first meal, the Students for Sustainability will take charge of the second and the International students will be responsible for the third.  From all the three events only the third one was really successful  (the other two did not get much publicity and support and the the food was not very good) and this is because of the consistent care and involvement of the staff from the Office of International Students.  Students helped prepare the food, there was beautiful music and some students even started to dance.  from what I have seen, the food habits of students and the work habits of people in the dining services are deeply ingrained but I believe that eventually with consistent effort things will change.  I envision a situation the dining situation at I.C is wholesome and healthy, that occasionally there are groups of musicians and maybe others who perform while students are eating food which is served with care and is organic and wholesome and where the dining experience becomes part of the general learning and growing of students here at Ithaca College but this year it was just a modest start.  I think that one of the main places where we can improve as a community is the collaboration and communication between Res. Life, Dining Services and other non academic parts of the college and the academic side.  We are one community and we have one goal: To educate and help young people learn and grow and I think we need to work on improving ourselves with respect to this goal.

Another experiment that I started this semester was to try and give up one of our two cars.  After the Katrina Hurricane struck New Orleans and the gas prices jumped up I felt that this is a good thing to do and since then I almost did not use the car.  I ride the bike and bus and do combinations since the bus has a bike rack.  It became such a wonderful experience and effected other areas in my life too (I am not buying "things" any more)

Another meaningful experience I had this semester was my visit to Croatia and connecting with the Holocaust experiences that my family went through.  It was very healing for me.  I documented the experience in a web page in: www.ithaca.edu/dani/croatia