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.
Sunday, September 28, 2014
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.
Sunday, September 14, 2014
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.
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.
Sunday, September 7, 2014
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.
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.
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