I've printed up my class lists. (40 students in each of my two sections of Beginning Algebra, plus 10 on each waiting list. When I taught in Michigan, our cap was 30. If California weren't in a financial crisis, I'd want smaller classes to be my union's highest priority.) I've reworked my syllabus, and thought long and hard about how to grade in a way that works well for the students' learning. For the first week, I've sought out activities for reviewing pre-algebra concepts (fractions integers, distributing, order of operations), always thinking about how to turn their notions of math around.
I'm planning to teach without reference to the required textbook, and I wanted the students to know that before the term started, so they could choose to buy a different textbook. The required text costs well over $100, and used copies will go fast, probably for over $70. They can buy older editions for under $10 online. My students are struggling financially, and knowing this ahead of time will be a blessing for them.
So I got my classlist, pulled all the emails together, put them in the bcc field (so students email addresses wouldn't be seen by other students without their consent), and sent an email welcoming them to my class, giving them the textbook scoop, and telling them about my philosophy of teaching and learning math.
I've already gotten back about 5 emails from students, thanking me, and saying things like this:
I want to say that I like ur approach toward math and it makes me feel better about taking this class. I've always struggled with it therefore it was the class I didn't look forward to, but I am looking forward to changing that perspective so thankyu.
That email I sent last week might make a huge difference in the attitude people bring to class, which might make my life a lot easier.
There was a bit of tech-trouble. I wrote the letter a few weeks ago, with lots of links to online resources, and blog posts of mine. When I sent it to my own college account, I saw that the links looked terrible. (They had changed from the usual underline form to showing the whole url.)
I thought I could solve that by sending from gmail. I didn't want to send from my mathanthologyeditor address, so I created a new gmail account using my name. Sending a message from a new account to 40 addresses, all in the bcc field, alerted gmail's spam prevention system. It didn't go to any of the addresses, and I got 40 separate messages from gmail support, explaining why. I wrote to support, but they never wrote back. I ended up sending a short message from my college account, and putting the longer letter on a wiki I'd made for the class. Here's what I wrote them.
Now I'm trying to come up with a list of reminders for me while I'm up front. Over the past twenty years, I've gotten real good at colorful, concise min-lectures on the topics they struggle with. Now I'm trying to get away from giving them answers - I want to create a 'community of disciplined inquiry' (Schoenfeld) - and I know how hard it will be to change my ways. I don't have much so far, but I'll include it here. Can you all help me add to this list? I'll keep it on my desk while I'm teaching, to remind me of what I'm trying to do differently.
Reminders to Me
Wait time! (Mean < 1 second. Minstrell waited 9 seconds!)
Question to me? Redirect. “What do others think?” or (call on someone) “X, what do you think?”
Mistake? [Don't correct or explain what they've got wrong!] Ask what the implications are. (But ask this of ‘right answers’ too.)
Acknowledgments:
“Thanks for contributing.”
"Ok, so... (repeat the idea)"
“Hmm, where should we go from here?”
Posts
Perhaps the first response to a question shouldn't be a redirect to someone else but to see what insights the original question poser had. I think it's rarely the case that someone has absolutely no idea how to approach a problem, and being able to express various levels of confidence in information is important. (i.e. statements such as "I think X is true" or "in most cases, it seems that X is true" are what differentiate people who give useful advice from people who just make blatant statements about truths and falsehoods)
ReplyDeleteFor instance, if someone asks if irreducible pythagorean triples always have an odd number as the hypotenuse, he or she has almost always done at least some explorative work already.
Wow. I just read the maths autobiography you gave to your students. You're fearless. It's made me reflect on how i start out with new learners.
ReplyDeleteI respond to all students' ideas or answers with one word: "Perfect!" I follow it up with "Any comments?" directed to the rest of the class. In short, I am not the one who decides if an idea is good or bad or if an answer is right or wrong. That job I leave to the students.
ReplyDeleteJan Nordgreen
Way to duck and jab and come up with that wiki letter solution. Maybe you should change the name to Tech Mama Writes.
ReplyDeleteReduce the amount of times you ask a question directly to the class and expect someone to answer back. It's very intimidating to the shy folks or those who feel overwhelmed by math; no one wants to look stupid. Maybe a way to avoid this is to have them discuss the question in groups and then ask the groups what their answer was. Much less frightening. Good luck!
ReplyDeleteThanks, Hao, I think you're right. I'll fix that.
ReplyDeleteThanks, Vicky. There's one fearless bit that wasn't supposed to be there. A good friend pointed it out to me by email, and I've deleted it. (I had used a copy of the autobiography that was on my blog, where I was choosing full disclosure.) If the rest seems fearless, I guess that's just how I am. (I have lots of fears, but I think I worry about different things than many people. And it's important to me not to let fears make my choices.)
Thanks, Jan, I'll include that! (Perfect!)
Thanks, for the compliment, Kate. Luckily I had that wiki set up a long time ago, when I first started thinking about communicating online with this class. But really, technology still scares me. I have a web page for the book, but no way can I design it be be exciting, appealing, easy to navigate, etc. And there is so much tech stuff I want to learn but have no patience for yet.
When I read your thought, Chris, I was totally with you. But then I was thinking about my desire to know what the quiet ones are thinking. I have a system where students can pass if I call on them and they really don't want to answer. I hope that helps the shy ones. I use pairs and groups a lot for big questions, but for little ones (what step would you take next here?), I often call on people.
Well, all I know is I really, really, really, really don't like it when a teacher picks me out to answer a question or asks the group a question. Hypothetical questions are much better, or when the teacher asks a question and expands on it. But when they ask a question, and just look around expectantly...ugh. Buzzkill. I'll talk to the person next to me all day about it before I'll want to answer a question a teacher asks. Makes you look like a suck-up.
ReplyDeleteHi Chris, Umm, I teach college, not high school. Does that make any difference?
ReplyDeleteI'm glad you're letting me know how strongly you feel. I'll remember it, and think about whether there's another way to do it.
I'm back to thinking about what Hao wrote, as I try to incorporate it into my quickie cheat sheet.
ReplyDelete>Perhaps the first response to a question shouldn't be a redirect to someone else but to see what insights the original question poser had.
I agree, and am trying to think in specific terms now. Sometimes a student says "I don't get it." I'm already in the habit of saying, "What do you get?" And getting that student to walk me through the steps. When we get to the sticking point, I've always tried to give a clear and colorful explanation of that point, with reasons why being prominent.
I could ask another student, but I've done that and it often muddies the water. Hmm... My concern that students get clear explanations has in the past trumped my concern that they contribute the math. This is something I'll want to stay aware of this year.
I'm planning to teach without reference to the required textbook... They can buy older editions for under $10 online.
ReplyDeleteyay sue.
everybody else: more of this please.
the entity formerly known as vlorbik.
I'm late to this party, and you're certainly already teaching...
ReplyDeleteStory (as example)
2x - 1 = 10 (solve for x) Relative beginners.
Kid offers x - 1 = 5 hmmm
I'm not throwing that back to the class without straight-jacketing the responses. Watch, and then I'll explain.
"Does anyone know what Katy's first step was?"
"divided," or "divided by 2"
"Most of you added 1 first" (show hands or get nods) "But it is possible..."
(acknowledging the value in an incorrect contribution, and correcting it. Most commonly the instructor needs to supply the lens... kids will want to follow a standard order, standard steps.)
I find this comes up quite often, that a horrible answer comes along with a different approach, or a little insight. Could the approach have worked? Does it have any value?
And in the discussion, or in my discourse, I will pull out what was valuable or original or interesting, and clearly point to what is wrong.
And just redirecting would leave the kids to correct (and they will identify the non-standard algorithm and the wrong answer, and often stop right there).
And I find this happens a lot.
Jonathan jd2718
Jonathan, that's a lovely example. Yes, I make sure I acknowledge the kernel of goodness in 'wrong answers', and I'll continue to do so. This outline is to help me "be less helpful", but I won't let it straightjacket me.
ReplyDeleteThis method of trying not to say what's right and wrong paid off today, I think. Perhaps I'll write a new post about it.