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.