A Teachers Dream

So I had an amazing day with my classes. I thought I would share and talk about why it is great.

So I my AP classes were fantastic. My first section surprised me with the different ways they could solve the problem. Then the next section I was shocked that the group with that was working on the same problem came up with another way. Then the third section of AP Calc came up with the same ways of solving it, but within the group of three each person in the group solved it in a different way and shared their methods with each other. That is what I wanted my math class to be about was approaching and explaining the problem in different ways. Then having students to share those methods with each other. I then encouraged them to compare those methods. I felt that in China since they had been taught to memorize formulas and were taught to each solve the problem the same way that they had trouble seeing it in other ways. I did my best to encourage, highlight, and show different ways. Thinking about it now my Chinese students often wanted to see algebraic proof of theorems or problems and did not value the graph or table explanation. Also when we practiced for the AP test they could easily solve the multiple choice problems that required using equations, but often struggled with problems that tested their knowledge of graphs and tables. It might have been because they were used to working with equations. In AP Calculus it is vitally important that you can work with graph, tables, equations, and words because the test will test you in those four ways. I think that is a good skill for a mathematician and what can make the AP test difficult. A mathematician should be able to relate the equation and its graph together. They should be able to use the vocab and explain it in words. They should be able to think critically and think in different ways. So I was so happy that my students were so opening, willing, and able to solve it in different ways. It also means that they will do well being able to think in the four ways on the AP test. I told them and reminded them that you should solve them in multiple ways because the AP test will test you in multiple ways. So the problem that got solved the most ways was a limit problem as x goes to infinity. It was solved using a graph, table, algebra and end behavior model, limit properties and end behavior model, limit properties and algebra, and the l'hopital tule. The l'hopital rule was used by a student who has already studied a little Calculus. So in total for the day that would be six different ways to solve the problem. It was fantastic feeling since I dreamed of being a math teacher since I was in 8th grade. I was planning and dreaming of what type of math teacher I would be from 8th or 9th grade. I started dreaming about how my class would involve students solving the method in different methods, sharing those methods, and then comparing those methods. I wanted their voice or way of mathematical thinking to be valued in my classroom. I think it is now and so I am so happy. My 8th grade self or 9th grade self and espcially the version of me that was working in grad school for a Masters in teaching would be proud of me and the classroom environment I created today.

Also all of my AP classes were good about asking really interesting and good questions. Some of them were specific and good questions about the AP test or what it requires. Then one student in my last section which was the last class of the day made me really think about how or why some people say a limit is equally to infinity or does not exist. He asked good questions and we had a good discussion about a very interesting limit problem. You had to find the limit as x goes to infinity to find the horizontal asymptotes. So I encouraged them to look at the graph. So he said that as x goes towards negative infinity the function goes towards negative infinity. It had no sort of horizontal asymptote in that direction. So the limit was equal to negative infinity, but you can't say that y = -infinity is a horizontal asymptote. That makes no sense, so I wonder if that is why some people often say if a limit is equal to positive or negative infinity that it does not exist since it can mean that the horizontal asymptote does not exist. This function was e to the negative x over x which does happen to have a horizontal asymptote since the limit as x goes to positive infinity is equal to zero. So I was impressed that me and a student could have such a thoughtful discussion of complicated calculus concept.

My Honors Calculus went well as well. At one point we had a little down time and talked about geeky math songs and poems. One of my students told me I should check out a poem by Harry Baker called 59 which focused on prime numbers. I said that I loved number theory and things about properties of numbers so I promised I would check it out. They also each individually presented a problem. All of the students were eager to present and all the presentations were fantastic even some that were given by students who had weaker English.

Now also mixed in with all this Calculus was my algebra II class. This class is made up with students with lower English. Some of them have strong math skills, but lack the English. At first it was hard to get them to speak English, to participate, and engage them. I was also was reminded that international students don't often take notes or know how to take notes. So after the first few days of teaching I realized that I had to support their English more than I expected and find ways to build some classroom behaviors around notes and homework. It is also a big gear switch from teaching Calculus. I think I have learned to love the gear switch, but sometimes it can be jarring. Today I got a new student which I found out about only a few minutes before the class and the first half of the class I was being observed by the head ESL teacher. I asked for her to observe my class because I wanted her feedback to see what else I could do to support their English in math. They ended up being super talkative and participated a lot. I think I smoothly handled incorporating the new student as best as I could on the fly. We worked on translating from English to math and word problems. We didn't get through as much as I wanted since the kids were talking so much. We goofed around and got sidetracked some, but I was kind of happy about since they were using their English. I think I was able to get them back on track well which made me happy that I could manage the classroom behavior. It was a great lesson on supporting the English in word problems and a great introduction in how to do approach or break down a word problem. I might put up the examples and materials I used later.

I personally think that I enjoy and am teaching so well because I am working with international students. I think that because I work with international students that since my students come from various countries they bring a varying perspective of math and diverse ideas about math. I have learned about how tangent was written differently in Russian (tangent = tg and cotangent = ctg). I also learned different symbols for slope through the years. We use m for slope which refers to the slope of a mountain or in French montagne. However in China I saw my students use k for slope and a Vietnamese student told me that they use a for slope. They said on the placement test we gave that he struggled with some questions because in Vietnam they used different symbols for the terms or concepts. I thought the test we gave got the heart of the understanding of their math and did not test their understanding of English, but when he told me that I reconsidered how I saw the test. I guess it just shows it is hard to write a test that is not culturally biased. I also think that when I teach international students and ESL students specifically it forces me to think about how to support their English and be creative in how I present the material. I have always wanted to make math and my teaching creative, innovative, and interesting. So I think because I have to consider my student's English understanding and their cultural differences it forces me to be creative about my teaching which is what I always dreamed of. I can not express succinctly how much I love and benefit from teaching international students.

I will end this post about how my teaching day ended. My student left saying that I should always be this energetic about class. I hope I can be and I hope I can use this day to keep me energized and fuel me when I am down.