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...
Friday, October 24, 2014
Sunday, October 19, 2014
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.
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.
Sunday, October 5, 2014
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.
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.
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