A class I was in a few evenings ago mentioned the MTBos (Math Twitter Blogosphere), and I decided to try to participate in this project. I'm in my tenth year of teaching, having done a number of other things prior. Currently the greatest portion of my limited recreational time is spent trying to learn salsa dancing. Living in New York, I'm learning New York, or On 2, style.
The thing that makes my math class unique in my school, a large, comprehensive urban high school, is that I regularly incorporate technology in my lessons, not as an afterthought, or a rare, special activity, but as an integral part of the whole. I think my lessons exemplify the Common Core Math Practice #5 of using appropriate tools judiciously.
Saturday, October 12, 2013
Reading and Mathematics
I openly admit that I love reading, both fiction and non-fiction. Many people think that, as a mathematics teacher, I must despise language arts. Perhaps this is due to their own insecurities regarding math and sciences, but it is far from the case with me.
One of my favorite writers is Mark Twain. It occurred to me that he has some sage advice for math students in his essay "Fenimore Cooper's Literary Offenses." In particular, among the rules of "art" which he accuses Cooper of breaking are the following:
" ... the author shall:
12. Say what he is proposing to say, not merely come near it.
13. Use the right word, not its second cousin.
14. Eschew surplusage.
15. Not omit necessary details.
16. Avoid slovenliness of form.
17. Use good grammar.
18. Employ a simple and straightforward style ... "
I think these seven rules also apply to the execution of mathematics.
If you care to read the entire essay, you can find one online source here.
One of my favorite writers is Mark Twain. It occurred to me that he has some sage advice for math students in his essay "Fenimore Cooper's Literary Offenses." In particular, among the rules of "art" which he accuses Cooper of breaking are the following:
" ... the author shall:
12. Say what he is proposing to say, not merely come near it.
13. Use the right word, not its second cousin.
14. Eschew surplusage.
15. Not omit necessary details.
16. Avoid slovenliness of form.
17. Use good grammar.
18. Employ a simple and straightforward style ... "
I think these seven rules also apply to the execution of mathematics.
If you care to read the entire essay, you can find one online source here.
Sunday, October 6, 2013
Assistance in Taking Notes
I was covering what I thought was review material in Geometry class. We're on the section where they learn basic concepts of formal logic, preparatory to doing geometric proofs. I asked a question that I KNOW I had covered the previous day (about modus ponens, the law of detachment, one of the most basic logical arguments), and I was met by blank stares.
"What?" I asked. "We just did this yesterday! Turn in your notebooks to yesterday." Notebook pages turned, the students were obviously searching for some hint of the answer, but no answers were forthcoming. I began to wonder if I had only imagined teaching this topic. I went from student to student looking at notebooks. There was no sign any had ever seen the structure, "p implies q. p. therefore q." I took a quick glance at my previous day's lesson plan and saw that I, at least, intended to cover that. Yet, still, notebook after notebook had no hint of that core idea.
Finally, I found a student who had written it down, using the symbols correctly (as I thought I had written it on the board). I was happy for indication that I am not delusional.
But my real takeaway is a reminder of how weak many of my students are at taking notes. I need to be much more overt in telling them when I've written a key concept, and I need to give them time to get those key concepts transferred to their notes.
"What?" I asked. "We just did this yesterday! Turn in your notebooks to yesterday." Notebook pages turned, the students were obviously searching for some hint of the answer, but no answers were forthcoming. I began to wonder if I had only imagined teaching this topic. I went from student to student looking at notebooks. There was no sign any had ever seen the structure, "p implies q. p. therefore q." I took a quick glance at my previous day's lesson plan and saw that I, at least, intended to cover that. Yet, still, notebook after notebook had no hint of that core idea.
Finally, I found a student who had written it down, using the symbols correctly (as I thought I had written it on the board). I was happy for indication that I am not delusional.
But my real takeaway is a reminder of how weak many of my students are at taking notes. I need to be much more overt in telling them when I've written a key concept, and I need to give them time to get those key concepts transferred to their notes.
Friday, October 4, 2013
Interactive classroom
On September 28 I was fortunate enough to participate in a pilot of a workshop entitled Building a (Virtual) Learning Community: Social Media with purpose for teacher-learners. The workshop was hosted at the Westminster School in Atlanta, and facilitated by educator Jill Gough @jgough. I had wanted to write this post the evening of the 28th, while impressions were fresh in my mind and I waited for my flight at ATL, but my battery died, Instead, I'm writing a week later.
Following school on Friday September 27, I headed to LaGuardia and flew to Atlanta. Saturday morning I made my way to the school for the daylong workshop. I have some transportation stories, but that isn't the focus of this post. Should you see me in person, and be curious, feel free to ask me to tell you.
First off -- omg what beautiful facilities! Gorgeous grounds, attractive architecture, and well-kept grounds. Our group was in the middle school building. The classroom was a double room that could be subdivided with a partition made up of whiteboard panels. Each "half room" by itself would have been larger than my high school room with 32 desks crammed in.
I arrived a bit late (see my reference to transportation issues, above) and things had already started. Jill was running things. The rest of the participants were other T3 instructors #t3learns and consultants, many of whom I knew from various conferences and events, mostly that annual T3 International conference. The morning topic centered on twitter, and how it might be used with classes and teachers. I don't think classroom use is particularly relevant to me -- my school does not allow students to carry cell phones or similar mobile communication devices. With my population, I think that's a good thing.
One of the uses that was intriguing was the idea of crowdsourcing conference notes. By sharing tweets at a conference with others, I can get a taste of what may have been happening in sessions I couldn't attend. By sharing our twitter handle on our conference name tags, it could be easy to get feedback from people. The key is to find an appropriate hashtag to filter through the, often loud, background hum of twitter. I think that will always be a limiting factor for me. More on that later.
The other major topic covered was blogging. I've been trying to blog lately, having been encouraged by a friend to record impressions of some of the things going on around me. I think reflection is a good thing, and writing a blog, even if some entries never get published, is a good way to formally reflect in a concrete way. That's something that one of my professors at Lehman College, Serigne Gningue strongly suggested I do many years ago. At the time I just said I don't have time, and he pulled out notebooks to show me how he made time almost daily to write at least a paragraph of reflections.
So, here it is, a week later. I'm not at the point that Dr. Gningue suggested, of writing every day. I do find that the software at blogger makes it easy to start a draft with a few thoughts, and save. I've only published four items since I began this blog in September. That's okay by me. I don't feel the need to publish. I have several other items in draft mode. Some I hope to come back and complete (as this one which I began a week ago). Others, maybe will remain as seeds of ideas, only for me.
As for twitter, for a few days after the workshop I was paying more attention to it. But it doesn't seem such an efficient medium for me. I like seeing the daily math puzzles from MAA, and I like the occasional updates from MfA. I like getting music updates from WFUV. I like hearing from friends who post a few things now and again. But, looking at my twitter feed more often also made me realize how much I dislike the tweeters who feel the need to tweet dozens and dozens of times a day. I realized that there was one person in particular who I was simply ignoring -- tweet overload had made me filter him away. Once I realized I was doing that, I also went in and unfollowed him.
So that's the idea I'm trying to understand about twitter and me. I think it's the same way I view conversation from people. I think silence can be a good thing. And so can talking. But I'm trying to understand where my balancing point is.
Following school on Friday September 27, I headed to LaGuardia and flew to Atlanta. Saturday morning I made my way to the school for the daylong workshop. I have some transportation stories, but that isn't the focus of this post. Should you see me in person, and be curious, feel free to ask me to tell you.
First off -- omg what beautiful facilities! Gorgeous grounds, attractive architecture, and well-kept grounds. Our group was in the middle school building. The classroom was a double room that could be subdivided with a partition made up of whiteboard panels. Each "half room" by itself would have been larger than my high school room with 32 desks crammed in.
I arrived a bit late (see my reference to transportation issues, above) and things had already started. Jill was running things. The rest of the participants were other T3 instructors #t3learns and consultants, many of whom I knew from various conferences and events, mostly that annual T3 International conference. The morning topic centered on twitter, and how it might be used with classes and teachers. I don't think classroom use is particularly relevant to me -- my school does not allow students to carry cell phones or similar mobile communication devices. With my population, I think that's a good thing.
One of the uses that was intriguing was the idea of crowdsourcing conference notes. By sharing tweets at a conference with others, I can get a taste of what may have been happening in sessions I couldn't attend. By sharing our twitter handle on our conference name tags, it could be easy to get feedback from people. The key is to find an appropriate hashtag to filter through the, often loud, background hum of twitter. I think that will always be a limiting factor for me. More on that later.
The other major topic covered was blogging. I've been trying to blog lately, having been encouraged by a friend to record impressions of some of the things going on around me. I think reflection is a good thing, and writing a blog, even if some entries never get published, is a good way to formally reflect in a concrete way. That's something that one of my professors at Lehman College, Serigne Gningue strongly suggested I do many years ago. At the time I just said I don't have time, and he pulled out notebooks to show me how he made time almost daily to write at least a paragraph of reflections.
So, here it is, a week later. I'm not at the point that Dr. Gningue suggested, of writing every day. I do find that the software at blogger makes it easy to start a draft with a few thoughts, and save. I've only published four items since I began this blog in September. That's okay by me. I don't feel the need to publish. I have several other items in draft mode. Some I hope to come back and complete (as this one which I began a week ago). Others, maybe will remain as seeds of ideas, only for me.
As for twitter, for a few days after the workshop I was paying more attention to it. But it doesn't seem such an efficient medium for me. I like seeing the daily math puzzles from MAA, and I like the occasional updates from MfA. I like getting music updates from WFUV. I like hearing from friends who post a few things now and again. But, looking at my twitter feed more often also made me realize how much I dislike the tweeters who feel the need to tweet dozens and dozens of times a day. I realized that there was one person in particular who I was simply ignoring -- tweet overload had made me filter him away. Once I realized I was doing that, I also went in and unfollowed him.
So that's the idea I'm trying to understand about twitter and me. I think it's the same way I view conversation from people. I think silence can be a good thing. And so can talking. But I'm trying to understand where my balancing point is.
Wednesday, October 2, 2013
Conditionals in the News
For a unit on logic, isolate the conditional in each paragraph by identifying hypothesis (p) and conclusion (q). Then write the converse, inverse, and contrapositive of each.
Mr. Obama, in the interview, said he must resist the Republican demands this time because a precedent is at stake. “If we get in the habit where a few folks, an extremist wing of one party, whether it’s Democrat or Republican, are allowed to extort concessions based on a threat of undermining the full faith and credit of the United States, then any president who comes after me — not just me — will find themselves unable to govern effectively,” he said.
Obama Sets Conditions for Talks: Pass Funding and Raise Debt Ceiling, New York Times online edition, 10/2/2013
Mr. Levison said he set up Lavabit to make it impossible for outsiders, whether governments or hackers, to spy on users’ communications. He followed the government’s own secure coding guidelines, based on the N.S.A.’s technical guidance, and engineered his systems so as not to log user communications. That way, even if he received a subpoena for a user’s communications, he would not be able to gain access to them. For added measure, he gave customers the option to pay extra to encrypt their e-mail and passwords.
Snowden’s E-Mail Service, in a Legal Tug of War, New York Times online edition, 10/2/2013
If one combines the segment that wants a more liberal approach to health care reform with those who approve of the law, a plurality of Americans view health care change favorably.
Closer Look at Polls Finds Views of Health Law a Bit Less Negative, New York Times online edition, 10/1/2013
Though he has faced seven years of Republican attempts to frustrate his agenda at every turn, this latest fight, which he believes could have been stopped if the party’s leaders had only stood up to their more junior members, has convinced him that he has no viable Republican partners on either side of the Capitol.
Reid Pushing Tough Strategy in Showdown With G.O.P., New York Times online edition, 10/2/2013
“He is not going to let this crisis make us give away something that is part of what we believe in,” said Senator Patty Murray, Democrat of Washington, and a member of Mr. Reid’s leadership team. “He feels passionately that if we allow our country to be run by hostage-taking — ‘I feel passionately about an issue, and I’m going to shut down the government unless I get my way’ — it is bad for today, it’s bad for tomorrow, it’s bad for democracy.”
Reid Pushing Tough Strategy in Showdown With G.O.P., New York Times online edition, 10/2/2013
Mr. Obama, in the interview, said he must resist the Republican demands this time because a precedent is at stake. “If we get in the habit where a few folks, an extremist wing of one party, whether it’s Democrat or Republican, are allowed to extort concessions based on a threat of undermining the full faith and credit of the United States, then any president who comes after me — not just me — will find themselves unable to govern effectively,” he said.
Obama Sets Conditions for Talks: Pass Funding and Raise Debt Ceiling, New York Times online edition, 10/2/2013
Mr. Levison said he set up Lavabit to make it impossible for outsiders, whether governments or hackers, to spy on users’ communications. He followed the government’s own secure coding guidelines, based on the N.S.A.’s technical guidance, and engineered his systems so as not to log user communications. That way, even if he received a subpoena for a user’s communications, he would not be able to gain access to them. For added measure, he gave customers the option to pay extra to encrypt their e-mail and passwords.
Snowden’s E-Mail Service, in a Legal Tug of War, New York Times online edition, 10/2/2013
If one combines the segment that wants a more liberal approach to health care reform with those who approve of the law, a plurality of Americans view health care change favorably.
Closer Look at Polls Finds Views of Health Law a Bit Less Negative, New York Times online edition, 10/1/2013
Though he has faced seven years of Republican attempts to frustrate his agenda at every turn, this latest fight, which he believes could have been stopped if the party’s leaders had only stood up to their more junior members, has convinced him that he has no viable Republican partners on either side of the Capitol.
Reid Pushing Tough Strategy in Showdown With G.O.P., New York Times online edition, 10/2/2013
“He is not going to let this crisis make us give away something that is part of what we believe in,” said Senator Patty Murray, Democrat of Washington, and a member of Mr. Reid’s leadership team. “He feels passionately that if we allow our country to be run by hostage-taking — ‘I feel passionately about an issue, and I’m going to shut down the government unless I get my way’ — it is bad for today, it’s bad for tomorrow, it’s bad for democracy.”
Reid Pushing Tough Strategy in Showdown With G.O.P., New York Times online edition, 10/2/2013
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