Live and Learn

In a nutshell... The change to two groups - one faster - didn't work.

As I alluded to in my last post, I have a range of math abilities in each of my precalculus classes. I have 2-3 students who could easily be successful in an advanced calculus class this year alongside students who would be better served by a normal precalculus class. (Groups in-between could include an advanced precalculus class and a normal calculus class.)

The idea was to see if I couldn't serve two groups' needs in one class, and I discovered that it just didn't work. I found that, within a 40-minute class, there wasn't enough time for me to be available for both, and I felt that my attempt to split time (quite unevenly) resulted in less quality time with both.

Live and learn.

Things have settled down quite a bit this semester, however. I've discovered that homework of 6 problems/night is close to ideal for my students and the time we have, and, thanks to some construction changes that took place over our break, I now have plenty of chalkboard space on which to display problems. The students know that they'll be presenting every other day, so they come to class prepared to get started.



Quite a learning process for me. I'm lucky to have such great students.

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.

Feedback Matters

Via Scott MacClintic's weekly blog, Pelican Ponderings (http://smacclintic.edublogs.org), I came across this 2012 piece by Grant Wiggins - http://inservice.ascd.org/less-teaching-and-more-feedback/#.VLleImBWNSM.twitter.

As he states, "You don't need any 'teaching.' You only need a good feedback system."

This has been resonating me recently as I've utilized Wikipedia, Khan Academy, and the like to further explore math topics. Students today have SO many resources at their disposal that the role of the teacher can no longer be that of "dispenser of knowledge." After all, the knowledge is available to anyone at any time.

My purpose, as I see it, in a discussion-based classroom is to provide immediate feedback (hopefully in the form of good follow-up questions) and to enable feedback to be provided by others, as applicable, so that learning takes place. Try. Get feedback. Question. Get more feedback. Fail. Get feedback. This isn't easy, but it's necessary.

Interestingly, I experienced some frustration with an online class recently due exactly to the lack of this - timely, focused feedback. I wanted to talk and discuss what I was thinking and all that was available was asynchronous communication. I found this frustrating.

Immediate, applicable feedback is the foundation of a discussion-based classroom, and it's necessary for learning to take place.

Effective Instruction

In a recent blog update, Grant Wiggins (through whom I learned of Phillips Exeter's Harkness Method) shared the results of a large UCLA study that found a lack of creativity in classroom teaching. A few excerpts:

- Students ''scarcely ever speculate on meanings'' or discuss ''alternative interpretations.''

- a ''sameness'' of instruction, with teachers doing virtually all the talking ... on the average, only seven of 150 minutes of instruction in the course of a school day involved teachers' responses to individual students. Feedback and guidance to help students understand and correct their mistakes were often ''almost nonexistent.''

- for most students school is a place in which to listen, to respond occasionally when called on, to read short sections of texbooks and write short responses to questions on quizzes. Students rarely, the study found, read or wrote anything of some length. Most of the time, they listened or worked alone.

A few days ago, I finished the book "Building a Better Teacher," one of the highly-rated reads from 2014. A few excerpts:

- It was crucial, for instance, to make sure that students did not talk just to (the teacher), but to the entire class.

- Watching (them) teach, (the teacher) had grasped the importance of getting her students to talk.

- "How do you know that?" "What do other people think about that?"

- The key to moving a discussion forward was to listen to students' questions, figure out what they needed to understand, and construct a response to pull them there.

- moving from the usual ask-tell ping-pong to something looser. "Facilitating."

As I read these, I thought about what I'm trying to do in my classroom. I want a discussion-based, facilitated classroom, with the student at the center, in charge of her/his learning. I will readily say that I (will most definitely always) have a lot of learning to do, but I am finding that the Harkness Method is proving to be a very effective way to provide high-quality instruction.

Who's Doing The Learning? (Therefore, Who Should Be Doing the Work?)

Like many teachers, my first years of teaching were exhausting! It's a tough profession, and I could see why it had such high, within-the-first-five-years, drop-out rate.

At the beginning of, I believe, my third year, I enrolled in a Fred Jones professional development course (Positive Classroom Management). He has a number of "Fredisms" to describe education and the bedrock of his system, one of which is really resonating with me this year - 

"There is no reason a teacher should work him/herself to death while the students sit back and watch. Effective teachers work the students to death while they sit back and watch."

Now, in no way am I advocating anyone "working to death;" however, think about it. I know the math, they don't. They're doing the learning, so they are the ones who should be doing the work (and getting tired :-). This year, teaching via the Harkness Method, this is exactly what is happening.

In my classroom, students are:

1) solving math problems (sometimes struggling)

2) presenting their solutions on the board

3) sometimes leading the discussions (made more difficult due to English being their second language)

4) answering my questions (and other students') as to how to do something

In other words, they are often the ones doing the doing; I'm the one "sitting back and watching." Learning requires involvement, the crux of the Harkness Method. In my classroom, the students are involved each and every day.

Is my job "easy?" No way. I'm constantly engaged/focused during class to understand all their different methods. (I'm learning the math so much more deeply.) As I mentioned in my last post, I'm having to relearn my profession, to ask high quality questions instead of providing immediate answers (and I have a long way to go). My job is different, focused so much more on their learning, and, given my experience with the Harkness Method thus far, I wouldn't have it any other way.

Questions. It's All About the Questions

The basis of a discussion-based classroom, is, of course, discussion. This requires good questions in two areas: 1) questions to be solved and 2) questions to be asked to complement, facilitate, and address difficulties.

After three months of using Phillips Exeter's math materials, I will readily admit that I am quite impressed with the level, the depth, of their questions. The vast majority of what I read when it comes to improving our math education is the need for more problem solving, more discovery learning, a greater focus on the richness of mathematics as a whole. Exeter's materials do all of these. I'm so appreciating questions that don't have whole number solutions (why do textbooks insist on always have "perfect" answers?), that spiral through topics, that lead students to derive formulas, and that often require knowing more than one mathematical idea to solve. This is, after all, what mathematics is like in the real world.

(I read somewhere that it took the Exeter faculty eight years to create their textbook! I'm humbled by such an effort.)

So, I have good questions to be solved. Now, as the teacher/guide/facilitator, the issue is asking good questions. This is definitely an area in which I need work. I'm so used to wanting to answer questions to keep things moving that I'm not nearly as good at what's really important - asking questions to guide in decision making, further challenge, or deepen learning. Students need to think and I need to help make that happen.

Area 1, good. Area 2, in process.

The Importance of Talking

I walked back to my apartment with a student last week, discussing with her the TOEFL (Test of English as a Foreign Language) exam. For foreign students, the TOEFL is #1 priority for getting into US universities, as "good" scores are required before the application is even considered.

I asked her, "What can I do in math class to help you get ready for TOEFL?" Her response was not quite what I expected. I knew that having them present problems, as required in a discussion-based classroom, was important, as were my efforts to correct their English. What I didn't realize was the importance of my speaking.

Harkness/Discussed-based classrooms put a premium on student speaking, and I can certainly see how important this is, in any learning situation. However, second-language learners also need to hear the language spoken properly to pick up on the many nuances, particularly in English. My efforts to get them to speak and listen to one another are certainly worthwhile; however, my situation is unique in that they need to hear me a fair amount, also.

The goal remains the same - do what is the best for your students. So, while their discussion (primarily through presentation) remains at the top of the list, my speaking has moved up the list to further help them in an area of need.

Interestingly, in using Exeter's math materials, for which I don't have the answers, my presentations are often prefaced with, "Now remember, I don't have the answers. So you may well need to correct me as you know how I make mistakes." Correcting my mistakes, or challenging my methods (and often showing me another, usually easier, way), is equally valuable. Just because I'm speaking doesn't mean they're not thinking and learning.

To Answer, or Not To Answer

Something struck me over these past couple of weeks - How much answering of questions should I be doing prior to the discussion?

Like many/most (all?) teachers, I've told my students that I'm here for them, that I'm available for questions. "Don't understand something? Ask." As I've said, I can't see inside their heads (and, even if I could, I can't read Chinese! :-D).

However, what I've found myself doing is helping them to answer homework/discussion questions BEFORE the discussion. Eager to capitalize on their interest in the problem and their willingness to come to me to seek assistance, I'm only too happy to help, often leading them to the answer. This is, after all, what I've always done with homework since it was always about practicing something that had been taught.

But, this is a different way of teaching. Learning through problem-solving and the ensuing discussion. How much should I be involved BEFORE both the individual attempts at the problem and the class in which the problem is discussed?

My sense is that, in some (many?) cases, I'm doing too much. Word/Meaning clarification? Yes. (English is, after all, their second language.) Ask questions to help them clarify their thinking? Yes. Lead them to the answer, my answer? No, at least not nearly as much as I've done.

My background as a teacher has always been "dispenser of knowledge." Leading students to the knowledge - through questioning - is so much more difficult.

Step back and allow the struggle to take place. THAT'S when the real learning happens.

Asking Questions

I've yet to fully crack the how-to-get-students-to-ask-when-they-don't-understand nut.

What I really like about a discussion-based (Harkness, Socratic) classroom is students talking and sharing. It's well-documented that real understanding is demonstrated when you can teach someone else, and the discussion-based method approaches this ideal far better than most.

That said, some students simply won't ask questions when they don't understand something, despite:

1) my emphasizing daily that mistakes are welcome and how we learn

2) my making mistakes and letting everyone know that I made a mistake

3) my asking questions when I don't understand something

4) thanking each student who asks a question

5) thanking each student who shares a mistake

6) providing (or attempting to provide) a classroom environment in which everyone is supportive

The struggle I have is between this being OK and how frustrated I feel when a quiz/test grade is low, as I want all of my students to succeed. I mean, part of learning is learning how and when to seek assistance. And part of learning, a BIG part, is failing.

On the plus side, no one is able to remain silent in my class. Each day, at least four students stand in front of the class and speak/present and I rotate through all of the students. But, how to get questions when something's not understood...

Learning the Language of Mathematics

My Chinese tutor (I'm taking Chinese lessons) spoke recently about the sequence of learning a new language - you first listen, then learn to speak, then read, and finally write. (I recall quite clearly this being the case with my niece.) Each builds upon the former.

In the Chinese education system, dominated by teacher lecture and next to no student involvement or interaction, the emphasis is on the latter two building blocks, reading and writing, at the expense of the first two building blocks, listening and speaking. According to her (and the students I asked about this), this results in a very surface level of understanding, one that more quickly disappears once out of school.

(I've had students come up to me who have taken 10+ years of English and tell me that speaking with me is the first time they engaged in an English conversation!)

As many of us know, math is very much like a language - there are unique symbols and either unique words or words that have mathematical meanings. Given this, it's very important that students are engaged in parts one and two of language acquisition - listening and speaking.

I wish I had a nickel for every time a student said to me, "I know what it means but I can't explain it." If you can't explain it, you don't know what it means. If you don't know what it means, chances are pretty good you won't remember it.

Listening and speaking are the foundation of the Harkness Method. Students are required to listen to one another and to present their solutions orally (and, in my case, in writing on the board). This is taking some getting used to (my not speaking), but it has become very clear how important it is for their learning.

Oh The Things You Can Learn

Easily one of my favorite things about teaching is learning from the students.

Prior to taking this position in China, I spent 5+ years tutoring SAT math. I used the College Board's "Big, Blue Book" which meant that I saw each problem (particularly those in the first three tests) many times.

What amazed me was the variety of ways that students solved the same problem. Here I was, the teacher ("I know how to do this, and this is the way"), learning different ways to solve the same problem, in some cases, from the 100th student. To say this thrilled me is an understatement. I so enjoyed being taught a new way that I wrote the student's name next to the problem so that I could reference her/him in the future.

(One student commented, "Really? I made the book?!")

The crux of the Harkness Method is students sharing their solutions. Combine this with several ways to solve a particular problem and learning something new is almost guaranteed. This has happened numerous times in the first four weeks (The Exeter materials are SO rich. I read somewhere that their problem sets were 8 years in the making.), and it brings a smile to my face each time.

A couple of notes:

1) I've gone back to one group in each of my classes. (Remember, my largest class size is 13.) I wanted to hear more and focus more and wasn't able to do this with two groups, particularly given English being their second language.

2) My chalkboard is divided into four panels, so I'm starting off the class picking four students to display the first four problems. This is giving me the opportunity to speak with the other students individually, checking homework and answering questions.

Harkness Good... or Bad

As you know, this is my first experience with the Harkness Method. As is usual for me with such things, I research and tweak, reach out and learn. In my experience, things are usually far more grey than black or white.

With regards to Harkness Math, I came across the following two articles, both speaking to Harkness Math at Exeter:

Harkness - Cons/Negative

Harkness - Pros/Positive

As I've said, I'm quite impressed with the methodology; however, as one who has read the book "Quiet," I can certainly identify with the "Cons" article author. How do you effectively involve extroverts and introverts so that all are able to maximize their learning?

No matter the methodology, one of the struggles I've always found is getting students to ask questions when something is not clear, or not understood. I'm trying so hard to welcome (and appreciate) mistakes, but that doesn't mean that there's an increased willingness to make them publicly. The quiet students can easily slip under the radar and that's frustrating.

The basics of the Harkness Method for math, as I currently understand them, are:

1) working with math at a deeper, more applicable level.

2) owning the struggle

3) recognizing that, more often than not, learning comes from making mistakes

4) presenting your efforts in a coherent way

All of these things are VERY valuable, and the Harkness Method emphasizes all of them. What's important for the teacher is to keep the instruction on topic and to step in when necessary to answer questions, thus meeting the needs of those students looking for a bit more structure and direction than that provided only by the discussion. It's a fine line to walk.

Students (and the Teacher!) Learning From Students

I had a wonderful experience on Wednesday.

The PreCalculus question had to do with whether or not a larger area was possible. One group (each class has two groups made up of either 6 or 7 students each) disagreed as to the answer and I watched as an animated discussion took place, going back and forth with drawings on the chalkboard, IN ENGLISH! It was math, it was in English, it was problem-solving, it was learning from one another.

It was wonderful.

One of the things I love most about teaching is learning from the students. (During my five plus years of SAT math prep, I was always learning new ways to solve the same problem. It was just awesome.) In my case here in China, teaching at one of the best schools in this "medium-size" city of 10-12 million, I have some very bright students (especially true in a STEM subject). Allowing them to discuss ways of solving problems offers a FAR richer learning opportunity than I could ever do as "sage on the stage."

I read somewhere that teaching is listening (to which I'll add and asking good questions); learning is talking. Thus, if my job is to teach, my job is to listen and ask questions. This is difficult for me; it doesn't fit the standard definition of "teaching" as I know it. That said, the standard definition of teaching (I talk, you listen) is rapidly being shown to be ineffective, as learners need to talk, struggle, and make mistakes.

The Harkness Method has taken me out of my comfort zone (and I have a long way to go), but it has, so far, been SO rewarding. Seeing students learning from one another through discussion is incredibly satisfying.

A couple of notes:

1) Following in the footsteps of Johnothon Sauer, I took my two PreCalculus classes of 12 and 13 students and broke them into two groups each. I wanted more opportunity for discussion, which he was also looking for when he experimented and found that groups of 6-8 were pretty ideal. (This is particularly true in my situation with students for whom English is not their first language.)

2) In my classes, discussion will make up 10% of their grade. I'm not sure how'd I handle this in a class in the US (English speakers), but I wanted to emphasize the importance of speaking as a big goal for us is to develop their English.

3) I created a "Discussion Log" and each group has a Leader who keeps track of the presenter and who speaks (asks a question or presents another method) for each problem.

4) So far, we're going through one Exeter math page every two days. I'm hopeful that I'll be able to speed this up a bit as the English and presentation skills improve; however, I'm also teaching technology (using the TI-84 calculator) - brand new to these students - so that will take some time as well. Time well spent.

To Harkness or Not to Harkness. To Harkness.

A roller-coaster week.

On Tuesday (we didn't have school on Monday)...

1) I was asked, "When are we going to start using the textbook" (which they purchased).

2) I was struggling to equate the textbook topics with those in the Exeter materials.

3) I was, quite frankly, struggling to solve some of the initial problems in the Math 3 materials. (For example, it's been some time since I've done anything with vectors.)

4) I was wondering how I was going to complete a required curriculum map using Exeter's discovery and spiraling methodology.

5) I questioned how I was going to get through the questions in a timely fashion using Harkness/discussion given the language issues, particularly in the Algebra 2 class.

My first time teaching since 2006 (I've been tutoring high school math and SAT and ACT math for the past 5+ years) and I was going to take on high school math (most of my teaching experience is in middle school math), teaching in another country, and an entirely new way of doing things!?! It was all too much. Time to simplify. Follow the book.

For the next day-and-a-half, my gut ate at me. I wasn't here, I hadn't gotten back into teaching, to do things the same. I wanted to incorporate a curriculum of problem-solving and critical thinking. I wanted the students to think, make mistakes, struggle, grow. The students need to talk, not me. A comment I had read regarding Harkness - "Teaching is listening, talking is learning" - just kept resonating with me.

So... To Harkness.

Decisions I've Made:

1) Two groups of 6-7 students each in my PreCalculus classes. Johnothon Sauer talked about how he felt 6-8 was an optimal size as it allows for more discussion opportunities. To improve their English - a primary goal - these students need to talk.

2) A discussion leader for each group with a sheet to track who presents each question, who contributes to the discussion, and whether or not everyone understands the question.

3) A guidelines sheet (modeled after the one I got from Johnothon) for the discussion leader, the presenter, and the participants. Talking/Discussing is new to them - they certainly don't do it in their Chinese classes - so these guidelines will help.

4) Trust the Exeter materials. There's simply no way Exeter's Math 3 materials (for PreCalculus) aren't plenty robust for any required curriculum. I'll record the main ideas of the questions as the topics I'm covering.

5) Quit worrying about "Am I getting through a textbook or an as-of-yet defined curriculum?" I want to teach depth and problem-solving. The greatest thing I can do for these students is develop their critical thinking skills and hone their English skills and vocabulary. (They do, after all, hope to attend US universities.) And, let's not forget, they're getting curriculum coverage in their Chinese math classes.

What would I tell my best friend if he were in the same situation? Take the risk. You know what the right thing to do is, you care, so follow your gut.

I have a lot of learning to do, but I'm looking forward to the challenge.

Week One - What Have I Gotten Myself Into?

First things first, as I embark on this adventure (implementing the Harkness Method in my PreCalculus and Algebra 2 classes here in Wuhan, China), I have to thank Phillips Exeter, Johnothon Sauer, and Glenn Waddell. I'm humbled by all three.


Phillips Exeter - Pioneering a discussion/problem-solving method of teaching, creating all of the materials, and exporting their expertise via their website (http://www.exeter.edu/academics/72_6539.aspx) and summer institutes. Incredible!

Johnothon Sauer - Blogging/sharing his experiences, and materials, with implementing this in his public school classes via his blog (http://harknessforthirty.blogspot.com), teacher website (http://www.edline.net/pages/Mason_High_School/Classes/1415_2431_1_1), and email. Thank you!

Glenn Waddell - Blogging/sharing his experiences via his blog (http://blog.mrwaddell.net) and email. Thank you, as well!
Like those above (and others, I'm sure), I'm acutely interested in honing my "teaching math" craft and more than willing to assist those in doing the same. This blog serves as an opportunity to do both.

Background on my situation:

As the math teacher (Algebra II and PreCalculus), my situation is rather unique as the students will be taking two math classes each day - their usual Chinese class and mine. Given that their Chinese math class is traditional (40+ students/class, lecture-driven, very little student/teacher in-class interaction), my goal is to provide a problem-solving, student-driven math class. Internet searches on how best to do this (more fully than I’ve done in the past) led me to the Harkness Method.


I’m the high school math teacher at St. Mary’s Wuhan No. 2 School (http://www.smschool.us/page.cfm?p=561). Our international school is a partnership between Knowledge Link (http://kleducation.org/KnowledgeLink/index.php), St. Mary’s School in Medford OR, and Wuhan No. 2 High School. My school (and, currently, six others) was developed to provide a creative, critical-thinking education, in English, to area students interested in pursuing studies at both China and U.S. colleges and universities.

My classes are enviably small - two PreCalculus classes of 12 and 13, and one Algebra 2 class of 6. (Some recruitment struggles this past summer.) The main difficulty will be generating discussion as the culture generally teaches the students to not speak in class. Throw in the second language of English (not to mention the language of math) and a fear of making mistakes and this method will prove to be both challenging and necessary for future success for those students pursuing college in the USA (the goal for most of them).

From what I’m learning, their math skills are already strong and/or developed/developing in their Chinese classes. What they need from me is discussion/English skills and creative/critical//problem-solving skills. Thus, I’m far less focused on covering some pre-defined, US curriculum than I am on getting them to think, challenge, discuss, make mistakes, etc. Exeter’s materials and the Harkness method really seems to fit the bill.

Week One:

Delightful students (discipline won't be a problem)

Lots of silence; too much talking by me (will I be able to out-wait them?)

An intense need for all of the students to SPEAK UP (this will be a challenge)

Wide range of English ability ("What is an 'estimate'?")

Introducing a template for solving each problem (thanks, Johnothon!)

No Harkness Table so desks currently arranged in an oval

Limited chalkboard space

Smartboard and worksheet projector (use projector for student problem display?)

Working to align Exeter materials to my classes

How am I going to grade? (discussion and HW completion need to factor in somehow)

The Harkness Method is brand new to me and them, so we'll all be learning and growing this year. I have to focus my efforts on getting them to talk (loudly!) in class, discussing and learning from one another. This will be a challenge. That said, teaching via the Harkness Method is pretty much exactly what they need if they are going to be successful in future US math classes.