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.
Friday, November 21, 2014
Friday, November 7, 2014
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.
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.
Friday, October 24, 2014
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...
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...
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.
Sunday, September 28, 2014
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.
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.
Saturday, September 20, 2014
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.
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.
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