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Archive for the ‘philosophy’ Category

Virtual Conference: July 3 – July 31

12 Jun

The community of math teachers that read and write blogs is an amazing resource.  We share lesson plans, techniques, philosophies, exams, and project ideas.  I’ve organized a “conference” to focus more specifically on the soft skills we need to be effective teachers.  Not the killer worksheets, or the progressive grading systems, but on the skills of raising children.  This conference is a great opportunity for us to share the way we bring out the shy kids in our classes, handle teasing, build confidence, create opportunities for leadership, and acknowledge the beauty and significance of the blossoming lives for which we are responsible.  I hope you’ll join us by making your own presentation and placing yourself in the schedule below.

The conference has five scheduled “speakers,” who will each be presenting on a Saturday in July.  Here’s the lineup:

July 3: Dan Meyer

July 10: Kate Nowak

July 17: Riley Lark

July 24: Sam Shah

July 31: Shawn Cornally

[Update 6/12 1:00 PM - for clarity: the "speakers" will not be speaking, but writing posts on their blogs under the title "Virtual Conference on Soft Skills."] 

These speakers are enthusiastic bloggers with five pretty distinct styles and focuses.  We’ll have different takes on what it means to have and use soft skills in our classrooms, we’ll share different specific techniques (successful or not) you can use, and I hope you’ll find them useful.  Pre-register now for zero dollars!

But the real opportunity here is for you to add your own presentation to this lineup.  Write your own article under the title “Virtual Conference on Soft Skills,” and I will link to it from the convention center between the links for the scheduled presenters above.  If you already have a blog and haven’t taken the time to share things like this, this is your chance to get started.  If you do not already have a blog and are interested in starting one, go ahead and start it!  If you don’t want to start a blog, but do have something interesting to share in the conference, write me an email at riley@larkolicio.us and I’ll post your article on this blog under your name.  Especially for new bloggers, this conference will be an excellent way to get attention for your writing so you can start getting feedback on your ideas.

Interested, but can’t think of what you might write about?  Here are some ideas.

  • A presenter could write about specific strategies for:
  • Engaging the small group of kids who didn’t buy your first shot at the lesson even though the rest of the class is atwitter
  • Encouraging questioning in class
  • Helping kids with dyslexia, dyscalculia
  • Addressing disrespect when you see it in your classroom
  • Promoting a supportive community in your classroom
  • Making it easier for students to speak up with answers and information
  • Helping kids feel like they “like math” or “are good at math”
  • Helping students manage big assignments or prepare for big tests
  • Giving students a sense of pride in their mathematical accomplishments
  • Acknowledging student contributions without sounding trite
  • Giving students feedback about their social contributions to a class
  • Dealing with a lesson when 29 students get it and are ready to move on but 1 is totally lost
  • Helping students feel ownership of the curriculum, assessment, or some other aspect of the class
  • Handling cheating or plagiarism or other lying
  • Ending teasing and hurtful sarcasm in your classroom
  • Helping kids having a bad day
  • Helping students who are currently failing your class and have given up
  • Managing senioritis
  • Demanding high standards of students without making them feel consistently substandard
  • Figuring out what’s going on with a student who’s always depressed, always tired, always nervous, etc
  • Getting some fun into your classroom
  • Helping your students bond as a group
  • Getting some exercise into your classroom
  • Teaching students how to help others constructively
  • Helping the student who is in Algebra 2 instead of prealgebra, which would be more appropriate
  • Showing kids that you care about them as individuals
  • Recovering from conflicts with students or between students
  • …and so many more skills we need to raise children.

 

If you have a favorite technique, a favorite lesson, a favorite class norm, a favorite mediation strategy that focuses on something that would fit into the list above, please share it in this conference!  If you would share experiences that didn’t go well, that would be helpful too.

We don’t have a lot of time to develop ourselves as teachers.  Articles with specific suggestions that are easy to deploy will be the most helpful immediately, while articles with general philosophies will be harder to incorporate in our classrooms but can help change the way we look at our roles. 

I hope you’ll contribute and follow along as the conference progresses.  Please email me if you’re thinking about presenting but aren’t sure whether you’re qualified or have anything interesting to say (a common doubt), and I can help you figure it out!

Update 6/12 @ 2 PM: This “Virtual Conference” will not necessarily have any actual speaking at it. It is a conference in that many people will write and confer about soft skills, but it will not be in real time (unless an ambitious blogger wants to arrange that in a smaller way – I will be happy to advertise for you!). Once someone has written a post about soft skills, they will be added to the schedule on the “Convention Center” page. That is what I call “presenting.”

This conference is a lot of people writing about the same subject within the same timeframe, organized in a single index.

 
14 Comments

Posted in Virtual Conference: Soft Skills, holistic ed, philosophy

 

In Which Riley Admits To and Eventually Embraces Being Sappy

19 May

Our most important job is as a role model for children.  Our students spend a huge percentage of their lives with us and our colleagues – they’re not only learning math, right?  They’re learning how to speak to people, how to treat people, how to hold others responsible and be responsible to others, manners… they are learning everything.  And yet the professional development I go to focuses only on the math, and the tests my kids take focus only on the math, and the grades I give are only on the math, and it is so easy to forget that there is so much more going on here and that it is so much more important than the math.

Other people are doing better work than me in their treatment of SBG, math curriculum, interactive, thought-provoking lessons, etc, and I’m so glad of that.  My skills in these areas have soared enormously this year from reading your great blogs (see list on the sidebar).  Thank you!

What I don’t see as much of is the explicit focus on how to help our students become better people.  Even on my blog, where every other post seems to be about how to empower students constructively, I often steer away from the topic, and you (on statistical average) don’t read as much when I do write it!  Here’s why: it’s intractable, it’s easy to be wrong, we have other stuff to do, and we’re not explicitly held accountable for our social curriculum.  But it’s the point.  Teaching our students about community and society is the whole point!

I was prodded in to seeing this imbalance in emphasis just last week, actually, when I was thinking about how to make my blog more popular (#okIadmitit).  I have to tell you that when I noticed nobody (small exaggeration) reads my homey-values posts and that everyone (big exaggeration) reads my technical posts I was disheartened.  I thought no one was interested in the really important part of school!

Then I realized all the reasons that these core values are so much harder to handle than concrete techniques.  And then! @samjshah, @jybuell, @monk51295, and @mctownsley wrote and said that they thought these are important ideas!  I am surprised by how affected I was by these tweets – a mixture of “They really do like me!” and “oh, of course people care about the really important part of school!  We’re all so bogged down that we just don’t have a lot of time to focus on it!”

After all, we all focus on community, responsibility, and respect in some way.  None of us lets students swear and insult each other, or flip their desks upside down, or paint on the walls.  We all teach kids how to be members of society automatically, by being good members of society ourselves.  When we write a good lesson plan, more often than not it is good because it empowers students and helps them interact in a good way.  I just want to focus on social skills and norms specifically. I want to improve in this dimension the same way I’ve been improving in assessment and feedback, lesson plans, and classroom management!  Do I just miss these sessions at NCTM, or is there a whole strand about “Personal Responsibility and Other Social Skills in the Classroom?”

With this new realization I feel more free to spend a large part of my writing time on the social values of teaching.  I’ve organized a page about it: http://larkolicio.us/blog/?page_id=412.  Don’t get me wrong: I’m still a huge dork and will be posting geogebra applets, and I’m still passionate about math curriculum and will be posting lesson plans.  As we move in to summer I will be writing more sparsely, and more specifically about camp (as education).  But I will no longer feel that no one wants to hear about my hippier (certainly not hipper) side.

Thanks for reading, you guys.  This blog is living up to its name for me.

PS: You know what profession has great professional development opportunities?  The camp director profession.  I run a summer camp (still accepting campers 9-13!) and so I get to go to conferences that focus on these important skills instead of the random skills like factoring that we deem vital for our future mathematicians (or whatever).  Like a quarter of the sessions are fun games you can teach to kids to build skill xyz.  You should go to an ACA conference even if you have never been to summer camp.

 
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Posted in holistic ed, philosophy

 

How to Teach Curiosity

07 May

There are ways that I have found to boost and encourage curiosity in my classroom.  Some of my techniques you can try tomorrow; others rely on a basic classroom culture that takes a long time and careful planning to build.  I’ll touch on the easy ones first.

Easy Ways to Teach Curiosity

Labels

When you see it, name it.  The label is more important than praise.  Here’s some psychology for you that I learned from an actual psychologist: people adopt the labels that they hear applied to themselves.  As a person of authority, if you say to someone, “nice question!  More evidence that you’re a curious person!” (or whatever version of this feels natural to you), he will actually start to actively think of himself as curious.  If two persons of authority give him that label he will almost certainly assimilate the label into his self image.

It was hard for me to believe in the power of this technique at first.  How could such a small thing change the basic nature of another human?  An alternative example helped me believe: what if you called a student “stupid” or “bad at math” once a week or once a month?  Such a student would start to think of himself as stupid and bad at math.  For some reason that’s easier to believe in than positive labels, but why should it be?  I’ve been intentionally using specific, positive labels for about a year (and I mean I throw them out all the time) and the results are tangible.

It’s mind control and it’s manipulative, but… whatever.  I say go for it. Please only do it if it’s true.  Uncle Ben, right?  Please do not tell a student who asked a boring question that he is curious – you’ll water down your power and give the kid delusions about himself.  And specificity reigns here: please say “this shows that you’re curious because you asked about xyz even though it’s not obviously related,” not “that question shows curiosity” and certainly not “that was a curious question!” ;)  Try not to say “great question” without saying why it was a great question.  Evidence that makes your claim believable is vital to the success of this technique, but it doesn’t have to be a lot of evidence.

Games and Secrets

Make your review into a treasure hunt that takes you around the building or the room.  Tell a story without telling the ending.  Make a show of explaining a theorem or puzzle quietly to one student or a group of students and then audibly say “don’t tell anyone else.”  This is more incitement of curiosity than teaching of curiosity, but it can complement your other techniques well.

Harder Ways to Teach Curiosity

Modeling

This is also psychology: people do what they see other people doing.  If you can spare a few minutes of your lesson to be interested in a tangential question in a way that includes the students, you can show that curiosity is a norm in your class.  This is hard because not every class period offers up an interesting side-note, and even if it does, you have to be careful not to interfere with your plan so much that learning is affected too much.  Before and after class are a good time to try to be interested in what your students are up to and what they’re learning that interests them.  Even your most bored student has something that they’re learning at the moment (bike tricks, knitting, texting, a videogame).  Hopefully it’s not something totally passive.

Finding Interesting Problems

I’m sorry for even including this.  It’s really hard.  Check out Dan Meyer’s WCYDWT, Shawn Cornally’s “How I Teach Calculus: a Comedy,” Kate Nowak’s and Sam Shah’s whole blogs, etc.

Make Students Responsible for Their Own Learning

Shawn Cornally writes, “I then have them construct a grant out of their group’s best/most interest­ing question.”  Students who are responsible for choosing an idea based on how interesting it is must evaluate how interesting ideas are.  This is the beginning of curiosity.  Students who are responsible for writing about an interesting idea in an interesting way must become interested in the idea and find ways to study it.  This is full-fledged curiosity in a way that “Complete items 1-4″ will never teach.  I achieve this effect in my classes by involving students in their own assessment, which is a little bit easier than involving them so deeply in the curriculum itself (but also less effective, I’m sure).  However you do it, increasing responsibility will also teach independence and curiosity.

I mean, what is curiosity besides a feeling of confident independence?

 
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Posted in holistic ed, philosophy

 

Tweeting Your Own Horn

05 May

I grew up a privileged kid.  Not private-boarding-school privileged, but certainly computer-in-my-room, internet-access privileged.  I learned most of what I know about programming and the internet in my spare time.  I helped create and run the very-successful Uniball, a huge learning experience for me: I dealt with hundreds of players in my leagues and on the chat service, dealt with technical issues, and even supplied and hosted a game server, all for free (1500 hours and 18,000 lines of code).  I made free game frameworks, free time-card applications, ray-tracers.  I contributed to an open-source physics simulation engine.  My interests shifted towards education and I started contributing for free to the blogosphere, writing this blog, leaving comments on the blogs of others, and now tweeting (follow @rileylark).

I’ve done all of this for no money; the experience and the learning has been its own reward (and I got a job at Microsoft for my Uniball work).  In this community of free contributions, doing anything to make money is frowned upon, actually.  There’s a pressure not to be making money and not to be looking for the most followers, etc.  Your work should speak for itself, and your learning and fun should be the only reward!

Well, I have an announcement to make.  Next year I will be drastically reducing my hours at school in order to write software to better support teachers in the switch to and maintenance and improvement of standards-based grading.  My steady yearly income will drop to something like $10,000, which is, as they say, not enough.  I’m betting a year of my life on the software I plan to create.

Developing great software is hard, but I can do it – I have tons of practice, both professionally, academically, and as a hobby.  What I don’t have practice with is intentional networking.  About 180 people follow this blog (thanks!  I’m glad you like it!), but I’m going to need more exposure than that if I’m going to support myself on my own handiwork – I know what your budgets look like.

Now, finally, the point: the last 15 years of internet social experience are telling me not to publicize.  Don’t add “Tweet this post” buttons to your posts, and don’t put ads on your pages!  Looking forward to a profession based on the internet, though, shows me that I have a lot to learn about marketing and revenue.  So, I’m adding these things to my blog as experiments.  If you think they’re trashy, please let me know.  If you don’t notice them, please let me know.  If you like tweeting about stuff when you’re given a little box, please let me know!

I’d love to hear from you in the comments.  What place does marketing have in our blogging community?  What about money?  How do you feel about tweeting your own horn?

 
13 Comments

Posted in Uncategorized, philosophy

 

A Probability Discussion

05 May

There’s a major problem with probability: it doesn’t work very well.  For example, common knowledge tells me that in a fair coin toss I have 50% odds of flipping heads and 50% odds of flipping tails.  But flip a coin once and you’ll either get 100% tails or 100% heads.

Now, I get it.  I mean, don’t worry.  After many flips, blah blah blah.  We can study a fair coin toss for two weeks, counting total possibilities, various games, expected values, special orders with surprising probabilities, etc, but none of this helps me guess the next flip at all.  Even in the next six flips there’s a depressingly low chance of getting three heads and three tails.  We certainly can’t rely on it happening in our math class while we try to convince people of what “50% likely” means!

I believe in probability, but it is indemonstrable.  Once you do something, it 100% happened despite its 50% (or 5%) odds.  The challenge for us, then, is to reconcile these seemingly-disparate pieces of evidence.

I chose to let the students have a 30-minute discussion about the issue and I brought several props.  My goal was to get the students to seriously consider their beliefs about probability – to be wary before they were confident.  By the end of this conversation, I want some students to doubt that heads and tails are equally likely.

I started the conversation by showing them this quarter, through which I have inserted a piece of paper:

After the requisite jokes about how hard it was to get that piece of paper through the quarter, I asked, “What are the odds of flipping tails?”

“50%,” one student immediately asserted.  The other students all agreed (I was surprised that they all agreed).  Experimentally, we showed that the odds are not even – there was a strong correlation between the side that starts up on your thumb and the side that lands up on the table, apparently because the paper drastically reduced the coin’s tendency to flip at all.  It sort of parachuted down instead of flipping and rolling.  One of the students tried cutting the paper (which started as a clean square) to see if she could affect the odds.  The students’ assumptions were incomplete and wrong, which is one of my favorite ways of getting them interested.

Then I asked another set of questions, this time with a plain coin and no paper:

“When I hold this coin way above the table with tails facing up and drop it, what are the odds that tails will land up?”

50%, Riley, [obviously | I think | assuming it bounces].

“Ok… when I hold this coin one inch above the table with tails facing up, what are the odds that tails will land up?”

100%, Riley, it won’t even flip.

But at two inches, the coin bounced a bit, and at three inches it was hard to tell what was going to happen.  ”At what height does it become 50%, class?”

They got my point.  If we can tell what is going to happen after an inch, why can’t we tell what is going to happen in a foot?  Philosophical questions abound here, right?  And they started to doubt themselves about everything.  They started to see that there’s no way to test the probability with perfect accuracy.  They started to see that you might be able to rig a coin flip to turn out the same every time.  They started to see the effects of human bias in selection games (I had a deck of cards too).

By the end of this discussion, my students were using phrases like “assuming that there is enough complexity” and “assuming that no one is cheating” and “assuming that the sides are equally heavy.”  They saw the assumptions that go into a statement like “heads and tails are equally likely,” and saw that we can’t rely on that information in all cases.  I sacrificed 30 minutes of class during which they could have practiced permutations and combinations, but I hope that their increased savvy about statistics will pay off.

 
5 Comments

Posted in Lessons, creativity, philosophy

 

How to Teach Respect

29 Apr

It is the rare adult that intentionally uses strategies to explicitly show respect to others.  Our students are learning a lot of things, not just math, and respect has to be one of them.

Last week I wrote about how to teach responsibility.  The quick version: give and expect responsibility.  This week, respect.  The quick version: give and expect respect!

In both cases, it’s harder than it seems, which is my best excuse for writing pages and pages about it.  This post will focus on tangible ways to increase the level of respect in your classroom right now.  I write as a teacher of high school students at a private boarding school and as a director of a summer camp with 25 staff and 150 campers – two places where respect is vital to my mission.  I do not work at a school with a single student who would cuss me out in the middle of class, though I have been called some names and broken up a (singular) fight in the last five years.

Easy Ways to Give Respect

  • Please say “please” when you ask someone to do something, and thank them after they do it. I direct a summer camp and this is almost a mantra I try to repeat with the counselors.  We make little kids do say “please,” right?  As adults, we sort of forget to do it, or understand that we’re all comrades and forgo the explicit “please” to… save time?  Anyway, saying “please” and “thank you” is probably the easiest way to show your respect for someone.  ”Take your homework out” becomes “Please take your homework out,” an expectant pause while they do it, and then “Thank you.”
  • Say “Thank you” when you’re thankful for something.  For extra power, name explicitly that for which you’re thankful.  ”Thanks for being prompt, everyone” or “thanks for getting so into this material, guys, it makes my job really fun!”  This has the top-secret side-effect of making it easier to give negative feedback when you need to do that.
  • Let them know how you’re feeling. You have to trust them before you can do this one, but once you do, it really shows them that, uh, you trust them.  ”When you guys get into discussing a concept so thoroughly it makes my job fun because the concepts are my favorite part!”  If they understand that you have favorite parts, bad days, pet peeves, and personal triumphs (“I’m really proud of this lesson plan”), they will all but have to respect you.  You trust them and you are a person and you are telling them all the ways you are trying to help them.  How could anyone resist?

Already, with this easy stuff, you are implicitly creating and reinforcing a culture of respect.  There’s deeper respect than adding a few words to your diction, though.

Hard Ways to Give Respect

  • Make the schedule of your class clear, and stick to it. If you say you’ll hand back graded work the next day, please actually do it.  If you say there will be a test every Friday, please be ready to give one every Friday, and if you say your office hours will be at 7:30 on Thursdays, don’t change that at the last minute.  If you do need to change the schedule, please show respect in that as well, by announcing the change as soon as possible ahead of time.  If you change things up all the time, take variable amounts of time to grade work, and are inconsistent with your schedule, please do not expect the students to have their work done when you want it to be, or for them to even show up to class on time!
  • Find ways to make students part of their own assessment. If you can trust a student to be his own judge (in any part), he will see that you respect him and his time.  You’re saying, “hey, I’m getting paid, and you’re required to be here by law.  I think you should have some say in what goes on here.”  If you can find a way to let students guide the class as a whole, that’s even better.  ”You’ll go to jail if you leave (or whatever happens), but while you’re here, I want to do my best to make this interesting and enriching from your point of view.”
  • Tell students what you’re trying to do with the class. Just tell them everything.  This was hard for me in some sort of ego way I can’t describe.
    • Apologize when you waste a student’s time. The obvious corollary is Try Not To Waste Students’ Time, but you’ll fail in that for at least some kids (sorry, I’m a pessimist I guess).  When you do give a stupid assignment or are unprepared for a lesson plan (not that I’ve ever been unprepared!) just apologize for it.
    • State the objectives of your lesson. It’s OK if they know your plan.  Bill Ferriter, a NC county teacher of the year, explains why the pedagogy is good.  But it also just shows your students that you want them involved in the process.  You think they’re smart enough to be in the know.
    • State everything else. “I was hoping you would do xyz.”  ”I never thought of that!”  ”It’s frustrating to me that you won’t focus on this.”  ”Today we’re going to try something that I’m a little worried about” (and then all the reasons you think it’ll be great, of course).

These harder things to do are hard for me because I can’t remember to do them all the time.  Some of them are a lot of work and some of them just don’t occur to me naturally.  Why do the students need to know what’s going to happen – they’re about to find out!  But intentionally striving to express your respect is worth some extra work to me, and, I’m not kidding you guys, I’ve seen these methods improve my classroom and camp culture dramatically.  Please try these out!

Explicitly Appreciate Respect You Receive

All the same reasons, and all the same benefits.  ”I appreciate you letting me know that you’ll have to miss a class next week,” “thanks for getting back to me about this,” “thanks for waiting so patiently while I answered Sarah’s question,” “it was so nice of you to think of this!”

Don’t Accept Disrespect

Frankly, I have much less experience with this than some other teachers at my school.  I don’t know if my methods of fostering respect are just SO GOOD, or that I mostly teach older students, or what, but I don’t get a lot of disrespect directly.  More often one student will disrespect another in some way.  Whether I get it or a student gets it, I address it directly and immediately by saying briefly something like “that was disrespectful, and disrespect has no place in our school.”  I’m serious when I say this.  I’ve got a controlled anger in my voice even for such a small infraction as “shut up” (“shut up” usually gets said exactly once per year in each of my courses).  I ask the students involved to (please) find a respectful way to express whatever they want to communicate.

This is a high priority for me and I will stop a lesson to talk about respect even when we’re a week behind my original schedule (“sorry class, we have to change the schedule because I made unrealistic estimates/you guys aren’t in to it/you guys are so into it”).

I hope you’ll give some of this a try.  I bet all of you think of your students with respect, and I’m sure almost all of you treat your students with respect.  It is the rare adult, though, that intentionally uses strategies to explicitly show respect to others.  Our students are learning a lot of things, not just math, and respect has to be one of them.  Please audit your own communication methods and see if there are any ways you can build more respect into them!

 
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Posted in holistic ed, philosophy

 

How To Teach Responsibility

15 Apr

Graceachen recently wrote a post that got me thinking about ways to teach the “stuff” that is hard to assess accurately and even harder to teach explicitly.  For example, I would like to teach all of my students:

  • Responsibility
  • Respect
  • Curiosity
  • Investigative skills
  • Teamwork skills
  • To be comfortable with a lack of knowledge and with mistakes

But I’m not going to make a standard for each of these things and assign grades, and no section of any one of my lesson plans will start, “here’s one way you can be curious1.”  However, I do teach these things intentionally and I do assess them.  In this post, I write about how to teach responsibility, and about some traps that seem important to avoid.  There are two types of responsibility: the fulfill-your-obligations kind and the take-ownership-of-your-destiny kind.  I’m talking about both.

Find Ways to Give Ownership, and Communicate Them

Give students the answers to their homework

Matt Townsley and grace said that they use homework to teach responsibility.  I do this too and so do many other teachers.  The three of us make sure that students have answer resources available before assignments are due so that they can more easily feel responsible for the quality of their work.  Without answers, if a student does his work incorrectly, the excuse is easy: “I didn’t know how,” or “I guess there’s a mistake.”  With solutions, a student is denied these reasons for poor work.

Tell students, “the solutions to these problems are available to you so that you can make sure you understand; please make sure you understand.”  This communicates that it is their responsibility, that you think they can do it, and that you trust them to do it.

Refer to student work and expertise during class

Please have students create projects that explain or summarize the concepts you’re studying.  When you’re lecturing, or when a student has a question, refer to those projects.  Whomever made that project will be directly responsible for the knowledge being disseminated.  You might also make different groups of students “expert groups” in different areas, and ask those groups specific questions (but please do give them the tools to actually become experts before putting them on the spot).

Again, it’s not always easy to think of telling the students that you’re doing this, but saying “these posters will be used as reference for the rest of the year” will let the kids know that you expect them to make production-quality work.  Actually using them will show them that you expect them to make production-quality work.  ”These posters are going live, kids.”  They won’t mess it up after you’ve articulated (and demonstrated) such high expectations of them.

Use Standards-Based Grading (if you must grade)

Or at least, some grading system as clear.  Please don’t use a grading system that obscures the reasons for your students’ grades (like averaging), because then the focus will shift from the responsibility of the knowledge to the responsibility of the grade.  I think grades should be as invisible as possible.  SBG is the best grading system I’ve seen because it gives the clearest idea about what a student needs to learn to improve his status.

You can only hold a student responsible for his grade after convincing him he can control it, and showing him how the controls work.  If, at any point, he loses that control, you won’t be able to expect anything more out of him.

Model responsibility (visibly)

Let your students see something you’re working on.  Let them in on your process for their class!  Show them all the ways you practice, prepare, and follow up.  Some of my students read my blog (hey guys!) and they see me in their other classes, observing other teachers.  Unique to Scattergood, perhaps: they see me attending required community events, keeping my apartment clean, helping with dinner cleanup when it’s my turn.

Don’t take responsibility away

Don’t grade homework

You shouldn’t grade homework because doing so transfers responsibility in a bad way.  When students have to do homework for their own sake, they are being responsible for their own knowledge and edification.  When you give them a grade, they will change – they will think themselves responsible only for that grade.  Please also tell your students why you are not grading homework – the effect doubles when they know what you’re trying to do.

There are many arguments for grading homework, but I haven’t heard one yet that’s convinced me.  Let’s debate in the comments if you’ve heard one that’s convinced you.

Avoid assigning unnecessary work

No one will feel much passion for work that they consider pointless.  If you really think that Johnny needs to do 30 factoring problems (lots of good arguments for assignments like these), then please explain to Johnny why you think so.  It may take something more convincing than mere explanation.

If a student thinks your whole class is unnecessary work, you have a more fundamental problem on your hands, and you might consider starting there.

Of all of my suggestions, which are all hard to do, I think this is the hardest.  If you’ve got a bunch of kids at different levels, 140 hours, and 140 skills to teach, you may have to give assignments that are not individually tailored to each student’s level – but you can at least tell them that!

Don’t answer questions that your students have the tools to answer

In my experience, I am my students’ favorite resource.  They will ask me a question before they use any other resource, including their notes, their books, or even their own understanding.  If you think that a student should be expected to be able to answer a certain kind of question, expect it of her!  Please do not waste your own effort by completing parts of your student’s lesson for her!  Don’t be too helpful!

None of these are explicit ways of teaching responsibility.  You make them explicit by talking about them, but the real lesson lies in their practice.  The real lesson happens when a student didn’t do some homework and can connect that with the fact that he’s feeling left out in class, or when he doesn’t understand something he’s expected to.  The real lesson happens when his classmates are looking at the crappy poster he made and complaining to him about how inaccurate or incomplete it is, or, better, when his classmates are looking at the awesome poster he made and complimenting him or incorporating it in their own work.  I guess that for my suggestions to work, your classroom culture needs to be set up in a way that allows these feelings to happen, and you need to be on the lookout for them, ready to emphasize them and focus them.

Assessing responsibility is more vague in my mind than teaching it.  I mean, ultimately, if a student passes a class, she’s responsible for that, and if she doesn’t, she’s responsible for that too.  If you get the opportunity to give written feedback to your students, or to have one-on-one meetings with them, make sure to emphasize what you saw working and not working towards the goal of passing.  Any other ideas out there?

This is a fascinating topic to me as a teacher and as a member of society contemplating parenthood.  Expect more, focusing on my other bullet points!

  1. though as I write, I’m pretty sure I’ve said this  during a lesson ↩
 
5 Comments

Posted in holistic ed, philosophy

 

Train a teacher in one week? (!)

29 Mar

I run a summer camp and am charged with training my staff of 25 in one week, immediately before campers arrive.  I can’t tell them everything I know.  What are the most important pieces of being a good teacher?

  • Basic skills
    • Smile
    • Listen
    • Comfort
    • Support
    • Keep them safe
  • Advanced skills
    • Model
    • Challenge
    • Bond
    • Feedback
    • Cooperate
    • Improve
    • Let them be in danger1
  • Basic Knowledge
    • Safety policies
    • Fun activities
    • Hard skills: Cooking, pitching a tent, adjusting a pack (multiplying, dividing, solving a system of equations)
  • Advanced Knowledge
    • Edifying activities
    • Stages of child development
    • The bigger picture of skills: Where’s the best place for a tent?  (Why do we solve systems of equations?)

Anything else?  Look how much summer camp has in common with math ed!

The basic categories are easy enough to teach, but let’s look at some advanced topics in closer detail.  These are the skills we use in math class, too.

Feedback

Praise should be specific and direct.  Criticism should be specific and direct.  All feedback should be timely: “see it, say it,” right?  How do you teach someone else to give good feedback?  We all struggle with giving more and better feedback in our classrooms, and my counselors have as many kids as we do.

Challenge

Kids on a bedrock of support and success will learn best when they’re challenged.  We want them to feel comfortable most of the time, but acknowledge that most learning happens at some stage of discomfort (though we must avoid stages of panic).  How do good teachers move kids out of their comfort zones in a safe way?

Improve

We want our kids to improve themselves, and as their role models we must improve ourselves.  At camp, staff meet with supervisors once per week.  In school, my PLC meets 1 or 3 times per month.  How do you teach someone to improve?

Edifying Activities

At camp we have kickball, right?  And in school we have, for example, properties of exponents.  Both of these can be lead in a basic level 1 way or an advanced level 2 way.  At level 1 we have kicking, running, adding, multiplying.  At level 2 we have working as a team, changing the rules to make the game more fun, understanding why exponents are added, building on previous knowledge, verifying results.  How do you teach someone to build level 2 into their activities?  How do you convince them it’s important?

  1. a safe amount of danger, of course ↩
 
5 Comments

Posted in philosophy

 

Try bringing the problem to virtual reality

25 Feb

One fundamental problem: in Algebra 2 there are few good examples and fewer (zero?) relevant to my students’ daily lives.  The solution, so far, has been elusive;  wrapping a context around the equation being studied or finding a situation that you can help your students explore in a mathematical way are my best attempts so far.

Let me extract what I mean from that jungle of punctuation and parenthesis. My goal is to help my students see how they can superimpose mathematical models upon their reality to help them do stuff.  Unfortunately, at the level of math that I am supposed to be teaching, their skill level with the stuff is actually still too low to be useful in any kind of exploratory way – they know just enough to do what I’m doing and see that it works.  That is, they aren’t going to stumble upon the formulation of a logistic population model by themselves, but if I show them such a model they can understand what it means and how to manipulate it.

If we take this too far, we run in to the problem of being overly specific in our instruction and robbing our students of the chance to be creative or even inquisitive.  When we are talking about volumes of circular cylinders we have to narrow it down for them, and often our only way of doing so is to narrow it down all the way.  ”You see, kids, since V=\pi r^2 h, h = 6.0 cm (or even just 6) and r=2.0 cm, the volume is… I mean, what is the volume, kids?  And why do you all look so bored?”

But what choice do we have?  Real cylinders don’t actually follow this law, when measured by students – they fall somewhere within 5 and 500%, depending on the quality of measuring going on.  Also, measuring real cylinders takes like five hundred hours.  Are you going to let your kids use an entire hour to get the five data points they need to see a quadratic pattern?  Even if you know some of those points will be completely wrong?

Computer models offer us the opportunity to narrow the problem space without narrowing it right down to the nub of the solution.  Without going so far as to say that every math teacher should be able to program a computer (I’ll do that later), I’d like to extol some of the benefits of modeling problems with something like geogebra.

Consider the following geogebra applet, which took me about 10 minutes to cook up (I’m a geogebra whiz, though).  Drag the bottom right corner of the cylinder to change the radius of the cylinder.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now). If you're reading this in an RSS aggregator, try following the link to the actual page.

Here, I can let my kids explore!  There is a confined space that I have carefully constructed for them and within that space there are no rules.  They can do whatever they want.  In this universe I can ask questions like “Can you find a cylinder with a volume of 2000?” or “what happens when you double the radius of a cylinder?”  I can ask them to make a graph of volumes against radii, and they will enjoy doing it (you may have to trust me on this if you haven’t used an interactive program like geogebra with your class yet).

And from this problem space they can actually figure out the formula for a cylinder with a height of 10.  They can try many experiments very quickly, and with satisfying proficiency.  When they make the graph of volume vs. height radius, they will do so with a speed that lets them really enjoy that the shape it makes is a parabola.  And the discussion taking you from cylinders with heights of 10 to cylinders of height 20, to cylinders of height 5, to cylinders of height h will be delighting because they not only know what you are talking about but freaking invented what you are talking about.

I haven’t even talked about the best part yet, you guys.  The purest virtue remains unsung, if you can believe it.  So, here I come with the biggest freaking bell-ringing mallet I can find: the feedback kids get from their computers is absolutely unjudging, unbiased, unhelpful, instant, and 100% correct.  Kids don’t have relationships with their computers.  Kids don’t ask computers for help, and computers mercilessly avoid volunteering any.  There is no “Clever Hans” effect happening with computers.  Kids can try an idea and if they’re wrong their computer shows them so without the slightest hint about why.  So, guess where that why has to come from?

Whew.  More on this later (with more examples, hopefully).


PS: As I was writing this post, one of my students submitted an honors project from last month (due any time in the next month).  Drag the points around.  Do you have any doubt that this student thoroughly understands how to graph an exponential function through two points?  She created this file from scratch.  Double-click a and b to see how she did it.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

PPS: For teachers with students more or less skilled than mine: you can adjust any problem space tighter or looser, right?  If your kids don’t understand graphing or squaring yet, let them vary the height of the cylinder instead of the radius.  If your kids were talking about volumes of cylinders with their parents when they were 8, let them vary the height and the radius at the same time.  The basic benefits remain.

PPPS: Bonus points for anyone who can concisely explain how to make a cylinder like that in geogebra.

 
4 Comments

Posted in geogebra, philosophy, teaching through computers

 

Percentages don’t have the power to express a grade.

08 Feb

The traditional model for grades in a class lacks the flexibility required to reflect what I really think of a student.  When I used weighted categories (e.g. 50% exams, 30% homework, 20% class participation), I found that some of the students passing my class didn’t really seem to deserve it, and some of the students failing my class really should have been passing.  ”Well, adjust your weights,” you say, and that’s a good idea: I made several improvements and was progressively more satisfied with my results.

But.

One test of the 29 I’ll give this semester deals with simplifying exponential expressions.  If a student gets 100% on each test except the exponential simplification test, on which he gets a 0%, his average will be 96.5%, A+, Honors.  He doesn’t have to worry about exponential simplification at all, and he can just move on and never learn it.  I’m not suggesting that this hypothetical kid be made to retake Algebra 2, of course.  I’m suggesting that he be required to learn exponential simplification.

So, in my class, I require that every student earn at least a 3/5 on every single skill that we study.  Then, I require an overall average of 75% on top of that minimum requirement.  Students get some leeway, and they do not need to master every single subject (I understand that there are time constraints involved in my students lives, and that they may not really care about my class).  However, they can’t just do well on a lot of skills and decide they’re not even going to bother with one.  I am not willing to send a kid who can’t simplify exponential expressions at all to the precalc teacher.

The same philosophy can extend to homework.  If you think homework is vital, make it a requirement of passing.  If you don’t think it’s vital, don’t.  Averaging test scores with homework scores is harmful because it dilutes the meaning of your tests and the meaning of your homework.  Averaging mathematically destroys information!

At my school we only have three grades, Pass, No Pass, and Honors.  Each grade has certain clearly stated requirements that I give the students at the beginning of the semester.  I think that a teacher using letter grades could more clearly define what a C was and what an A was by stating the objectives vital for that award than he or she can by trying to come up with a formula to fit every student.  We shouldn’t be afraid to use some criteria that cannot be expressed with percents.

 
5 Comments

Posted in assessment, philosophy

 
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