Mid-Year Thoughts

After a long Spring Festival break, second semester begins on Monday. Thus far, it has been quite an adventure, both teaching in China and teaching in a Harkness/discussion-based format. Time to reflect:

1) I've definitely become quite a fan of the Harkness Method of teaching. It is student-centered, problem-centered, and understanding-centered which I absolutely love. In addition, it really brings forth the different ways math problems can be solved, which deepens learning.

My experience immediately prior to coming to China was as an SAT (and ACT) math tutor and what I found was that students didn't really know how to problem solve and didn't have a good grasp on the concepts they were working with. This leads me to my second thought...

2) The Exeter materials are pretty amazing. I've written previously that they were 8 years in the making and you can tell. The problems are so rich, the spiraling is impressive, and the concept development is really well thought out. I'm humbled that they've done all this work and made it available for free.

3) The teacher's role as facilitator/guide is quite different from that of "sage on the stage," and mastering it will take some time. As I've mentioned, I need to get better at asking questions: questions to clarity, questions to draw out, questions to expand upon. No doubt, this is part of the art of teaching.

4) Allowing for different ways of solving problems means you, as the teacher, really need to know your stuff and be paying attention. Things are definitely easier when "there's only one way, the way I taught you;" however, this is, to me, incredibly anti-student and anti-learning. Suffice it to say that I've learned A LOT thus far this year and I have relished all of it.

5) It's difficult having an extended discussion in a second language. I applaud what my students are doing (taking classes in English), but I've come to realize that I need to temper my expectations as to  discussions. They are presenting in English and asking questions of me in English; however, sometimes, when other students have questions, I let them switch to Chinese. There's no shortage of discussion, questions or answers, when they speak in their native language.

Decided to make a few changes for this semester, principally dividing the students (precalculus) into a "faster" group and a "normal" group. One thing Exeter does is have their incoming students take placement tests, and I can see why - some students can simply fly, while others need more time. Curious to see how this is going to work.

Student Thoughts on Harkness

Our first term ended last week. As I look to make some changes after Spring Festival (Chinese New Year), I asked students to provide me with some feedback as to how the class has been thus far.

A couple of background comments:

1) Our (international) classes are MUCH smaller than typical Chinese classes. My largest class size is 13, most of the Chinese classes have between 40 and 50 students. My students are therefore having a very different experience to begin with.

2) As one who is taking Chinese lessons, I'm amazed at how tiring it is trying to think and speak in another language. My students have generally had around 8-10 years of English; however, I remain humbled by their ability to take 6 high school classes each day in English.

First Question: "How has the math class been for you thus far? Are you enjoying it?"

• I really like this way of learning math.
• Good. Fine. OK. No I'm not, I hate writing things down.
• I think most of the things are OK. And the way that students present the questions on the blackboard is good. I am enjoying studying the math. I think I can understand most of the problems very well.
• Good. I enjoy the math class because I learn things little by little.
• Not that enjoy. Some of the questions that (are) in the last (recent) pages are kind of complicated. I hate complicated questions.
• I think it's kind of hard for me, and I got (have) to spend much more time than others to solve the math problems in English.
• I think it's pretty good. I really enjoy it. The questions we (have) done were not too hard.
• I like the method. I feel better and more comfortable to speak in front of people.
• I enjoy it. Some problems are hard for me and I can't figure it out by myself. But listening to others explanation is pleasant to me.
• I think the math class is really good. I like the method we used that (for) learning new knowledge through new question(s). I enjoy it.
• It's good. It's exciting.
• Yes, I enjoy this class. I practice my English in this class. I had a good time in the math class.
• I think I feel good about it now. Maybe I feel a little bit uncomfortable at the beginning of the semester, but I gradually felt much better.
• I like math class. Everyone has opportunities to show their method during the class. I learnt (learned) many different ways to solve same questions. And also, when I did question on blackboard, other people could check my answers.
• I enjoy this class because was can participate in the class. We share the ways we solve the problems and discuss. It's helpful.
• I enjoy the math class so far. The teacher gives plenty of time for me to practice both solving problems and speaking English. I learn some mathematical terms during the class so that I will demonstrate more accurately next time.
• I like the way of our math class. I enjoy it because everyone can share different opinions in the class and we have more chance to practice our spoken English.
• I'm not that enjoying the math class because I'm not good at math all the time. I think it's hard for me to improve my math skill.
• Great. I am enjoying the discussion because this process let me know more way to solve questions and fix my mistakes.
• Good. I enjoyed it.  I like to see using different ways to solve problems because sometimes others' way is quicker and easier than mine. And we have the chance to correct our quizzes, that's so helpful for us to learn.
• I think it is very good. I enjoy it because I think we have different kinds of questions for a day, so it is not very boring to do homework.
• Great! I really enjoy it. I love different ways doing the problems and people showing their own ways.
• Yes, as discuss questions together, we know more methods.
• Yes, I enjoy this class because in this class I feel very free. I can discuss with class and I can find lots of different answers. That's great.

Second Question: Would you like to see anything done differently? If so, what?

• I wish I can do more difficult problem.
• I prefer more geometry questions. (My note: comment from precalculus student.)
• I don't really want to do solve many problems. I actually want to study the book. (My note: they purchased a textbook. I've using Phillip Exeter's "book" instead.)
• To be honest, sometimes I did not listen to the discussion. Maybe the discussion time could be shorter. In this case, we can learn more things. I always do my homework during the discussion, except there is something important.
• I hope that next semester, we could do new question that teach us new math such as (logs). I don't want to do many easy questions again and again. I want the same amount of homework but it could be harder.
• I think the math class now is good.
• I like the present condition.
• I don't know why don't we use our textbook instead of so many paper. Maybe we could use textbook next semester. (My note: The Exeter materials have been copied onto paper for each student. I'm putting it all together in a "book" for next semester as all the paper is a bit of a pain.)
• Yes. More questions with graphs and less words.
• I think it is fine now.
• Everything is great.
• I would like to see something different.
• I have one suggestion. For problems like exponents and simplification, we can just go over the answers, and leave much for other problems, like parametric equation. I don't study this in my Chinese math class, so it's new to me. You can introduce the math skill to me starting with some easy problems not based on the problem we have on the paper. That will help me understand the parametric equation more deeply and clearly.
• More and harder problems on geometry; less problems on three-dimensional. (My note: from a precalculus student)
• I think the math class we have now is pretty good.
• Yes, I'd like to have more geometric questions because graph is more interesting that words.
• I think the Harkness Method is great.
• Yes, I would like to see more geometry questions. (My note: from a precalculus student)
• No, it's good.
• It is good now.
• I'd like to have more time to do homework in the class, because we have much homework and TOEFL class. So we are a little busy. That is why I want more time to do homework at class. If we find the homework we don't know, we can ask questions in time.

In general, a lot of positive comments and some good suggestions. I'll be making some changes for sure.