Thursday, July 30, 2009

How Making Mistakes and Blabbing it to the Universe Improves My Teaching

Alternate title: Messing Stuff Up, Writing It Down

These are my notes for a workshop next week. Comments/additions/criticisms? Please help, oh PLN of mine.

Why Bother?
- Communication tools make widespread collaboration possible where it hasn't been before.
- If you aren't thrilled by the professional development or lesson improvement opportunities offered by your school, you have other options.
- Speaking for myself, being a learner makes me a better teacher. Continue growing, learning, and improving your craft.
- Network with other like-minded professionals.
- The ability to get ideas, and to get feedback about your work, no longer has to be limited to a planning period, an annual conference, or only teachers in your school and district. As a result, your teaching will improve faster.

Why Start a Blog?
I always had a hard time with reflective practice as a private exercise. I was told it was important, but it wasn't rewarding in a way that led me to pursue it regularly. All my writing landed with a dull thud. Publishing those reflections, successes, failures for an audience means my work is broadcast in a community of intelligent professionals who read, use, and comment on my work. The feedback from them is the reward that keeps me doing it. (Update: Read MizT's elaboration on this point.)

You Don't Have to Start Your Own Blog
There are plenty of ways to develop, benefit from, and contribute to a learning network without starting a blog of your own.

Read Blogs - Through the habit of reading other teacher's blogs, you will get ideas and insights in an easily accessible format, delivered to your computer. You can go to individual websites, but using an aggregator like Bloglines or Google Reader is much more convenient. Instead of bookmarking and visiting individual sites, an aggregator collects them all in one place for you. New posts in your subscribed blogs are automatically sent to the aggregator through the magic of RSS (Real Simple Syndication (you don't need to remember that.)) You only have to check the one site, the aggregator, to see if any of the blogs you read have been updated lately. For Google Reader you will need a Google account, then you can click Add a Subscription and type in an address.

If this is all brand new to you, here are a few to get started with (I chose these to represent a spectrum of math ed bloggers out there... through linking from posts that appeal to you, you will find more and more): 360, colleenk, Dan, Elissa, Jackie, Jason, JD, John, Sarah, Sam, Sue, and me.

Comment on Blogs - Don't be afraid to add to the conversation on a blog by commenting. Include your first and last name, unless you are cultivating a pseudonym (see below). If you start a blog later, you will have built a reputation you can use to draw people to read your posts. When it's available, I always check the box for "email me follow-up comments," so I don't have to go back to the post later to read the latest comments.

Twitter - It's more than celebrities and talking cats! Many educators are coming on board, and I'm finding more and more useful links and discussions on there. It can be a good way to get started. Set up an account and describe yourself in a few well-chosen words. If you are looking for ideas about who to follow, start by checking out who I and other math teachers are following. Once you follow someone, they will often follow you back, if they see that you are a teacher. Congrats, you have readers! (Of your tweets. Limited to 140 characters.)

Delicious - Save bookmarks that are available anywhere there's Internet. I use this as the place to save all those links that I want to remember later. Add tags so you can search them easily. It also has a social component, whereby you can follow people and see what they are saving.

How to Start a Blog
, Considerations, and Potential Pitfalls
There are gazillions of articles about the technical aspects. Spend some time googling and reading articles. I use Blogger and like it fine. Lots of people like Wordpress.

Decide why you want to start a blog. To share your great lessons? To comment on education policy? To relate funny stories about your day? To post pictures of your lunch? It's good for a blog to have a focus. If you don't want to write original content and just want to share links or pictures, consider another solution like Twitter, Tumblr, Flickr, or Delicious.

If you and some friends all want to start, consider a group-authored blog (example). You will immediately have each other as readers and commenters.

Decide whether you want to post with your real name or anonymously/pseudonymously. The decision to use my real name was a personal one and works best for me. Plenty of awesome blogs are written by teachers who would rather not identify themselves. If privacy concerns are keeping you from starting a blog, consider a nom de plume. Either way, I advise against publishing anything you wouldn't want a student, parent, or administrator to read.

Have several ideas for posts before you start. When you begin, you will want to update at least once a week. Otherwise people will lose interest and you won't generate a following.

When you write a new post, don't publish it right away. Several commenters made this suggestion, and it's a good one. Instead of "Publish", the blogging software should let you "Save as Draft." No matter how much you like your post, you will think of a crucial edit 5 minutes later. You will realize that the way you stated something could be taken the wrong way. You will think of more elegant phrasing. Of course, you wouldn't want blogging to put you in a bad light, or give you a reputation for being unprofessional. Write the first draft and let it marinate for 24 hours before publishing.

Stick with it. It will take time to generate a following. You can get readers faster by leaving comments on other blogs (and including the URL of yours,) linking to your new posts on Twitter, or submitting a post to a blog carnival.

It's generally considered bad form, not to mention lawsuit-inducing, to post identifiable pictures or videos of students' faces. If you want to do this, you should get guardians' consent in writing.

Further Reading/Watching


This post wants to convince you of the value of educational blogging.

In this TED talk, Seth Godin says we all have the potential to "change everything" by leading people just waiting to be led. Not specifically about education, but relevant.

This episode of Ze Frank talks about the meaning of creativity, and what it takes to go from 0 to 1.

This post at the Fischbowl describes the value of a Personal Learning Network for both teachers and students.

Darren has his students blogging to expand the walls of his classroom.

Sitmo is a relatively easy way to include mathematical equations in blog posts.

Be Brave

A new math teacher blogger - hooray! I met Jesse at a conference this summer and I have to say, the girl gets it. Aside from being a fantastic teacher, she has the power to make a room full of cranky math teachers feel positive, enthusiastic, and united. And, she dresses cooler than anyone I know. I'm looking forward to good things from her blog, which promises love, beauty, and hope for the future of math education. Check her out.

Math Be Brave

Thursday, July 23, 2009

A Lesson Plan Using a Virtual Manipulative

This post at dy/dan got me thinking about this thing from Utah State's Library of Virtual Manipulatives.


Pretty cool, right? A way to play with volume that avoids water fights. Love it. I used this in a remedial geometry class several years ago. It was fun for the kids for about five minutes. We merely used it to poke at the edges of our intuition. I didn't really know how to exploit it.

It raises a compelling question for teachers: there are some really good digital resources out there, but how do you best use them in a classroom to enhance learning? I'd like to use it this year when I teach Geometry, but I need to write an effective lesson around it.

The barest outline of a plan:

1. Playtime. Let kids slide the height thing and push the buttons, or be teacherbot and do what they instruct me to do. Solicit guesses for heights. Have kids verbalize why they think their guess is correct. Test to see how close they are.

2. Start talking about how you would calculate the new height. Go back to universal problem solving techniques that you should be hitting over and over again. What is the given information? What do you want to find? What stays the same? Encourage/coach them to do this with the rectangular prisms. They should be able to find numerical solutions easily. Develop and write on the board an equation involving equal volumes with an unknown height and solve it. Test to see if it works in the virtual manipulative. Have them calculate a few more.

3. Go through the same procedure with cylinders, then cones. It's going to look different depending on if they already know formulas, what age the kids are, what level, etc.

It wants for structure. I could develop a worksheet and break out the laptops. I'm not a huge fan of many worksheets, because I think they shift the focus from the problem-at-hand to "guess what to write in the blank." (I'm also not a fan of the laptops.) I could try to keep it as a large group discussion, but that could easily turn into me talking to 2-3 kids while everyone else zones out.

What would you do with this?

Wednesday, July 15, 2009

Math around the House

There are any number of reasons parents are motivated to supplement the math their children are getting at school. They want to slow the loss of understanding and skills over a long summer. They are concerned about the school's wholesale adoption of Everyday Math. They are concerned about the school's wholesale adoption of Saxon. They suspect the fourth grade teacher is not a great math teacher. Their child is either ready for more than, or not ready for, the grade-level expectations at school. All of these motivations are entirely reasonable.

Ideally I think parents should make understanding organic to daily occurrences. If they treat math like spinach (we have to get through your multiplication flash cards before you can have fun, because it's good for you) their child will grow to resent it. Gaining real understanding of logic, structure, measurement, relationships, and numbers, done well, should be a creative, joyful process.

These are some things I've noticed while puttering around the house. I hope they are helpful. For all of these ideas, I would:
  1. Know at least a little about the concept/solution before posing it (I put very broad categories after each one to possibly make research a little easier.)
  2. Respond to the child's curiosity - don't force her to do anything.
  3. Don't try to turn everything into a textbook math problem. It's ok to start with undefined terms and not enough information. Learning how to ask clarifying questions is part of learning how to solve problems.
  4. It's ok to start with too-complicated a problem. Learning how to pose a simpler problem is a part of learning how to solve problems.
  5. Don't be afraid to leave questions unanswered for another day - give the ideas time to marinate. Cultivate patience with irresolution.
Ideas:

Notice two cylinders side by side and wonder aloud which uses more material, and which holds more. (Canisters for oatmeal, tennis balls, and Pringles come to mind.) Follow up: roll up a 8.5 x 11 piece of copier paper both the tall way and the short way. Wonder which way holds more. (Volume/surface area)

Do you frequent a particular ice cream place? I bet they offer well-defined options for ice cream flavors and toppings. Wonder how many possible different sundaes you could order. (Or the related questions, such as how long would it take you to eat every possible sundae, if you had one a week?) If the initial problem is too complicated, solve a simpler one. (Combinatorics)

Does your family ever clink glasses at the dinner table? Next time you do that, wonder how many clinks. (They don't have to be clinks. Do they smooch all their relatives at family gatherings? High five them?) If you only have 4 people, this is easy and boring, but if you can get them to wondering at the pattern for 5 people, 6 people... (Combinatorics)

When you are cutting a cake, or pancakes, wonder how you can get the most pieces out of the fewest cuts. (Quadratic relationships)

While traveling, set them to figuring out "How much longer?", using the data from highway mileage signs and the speedometer. (Distance/Rate/Time)

If you are playing a game with two dice, wonder what outcome is most likely. What implications does that have in the game? (Probability/sample space)

"I need 1 and 3/4 cups of butter. Can you get them for me?" When she does this successfully, talk about how she divided by a fraction to arrive at 3 and 1/2 sticks. Draw a picture, write it out with symbols. Notice how weird it is that a division can yield a result larger than the thing you were dividing. Be on the lookout, together, of other examples around the house where one might divide by a fraction. (Division/fractions) (Thanks for this one, Jackie.)

Find number-y fun in your child's favorite sport. These examples are from baseball because I know more than nothing about it: How many outs in a perfect game? Minimum/maximum at-bats in a scoreless game? (Multiplication/division)

Take advantage of anything a child asks about. Sometimes they will hear an older friend or sibling refer to something exotic: prime numbers, or square roots, and wonder about it. I have seen parents give a definition and not exploit the opportunity! Don't stop at "A prime number is only divisible by 1 and itself." Say something tantalizing like, "I wonder if we could find all the prime numbers between 1 and 100? That seems impossible!"

And finally, I can't recommend highly enough a collaborative math circle (as opposed to the type geared toward training for competitions.) If I had kids, I'd be googling "my city math circle" to see what's out there, and starting one up if it didn't already exist.

I'd love to hear about other things you and your kids have come up with! Happy math-ing!

Tuesday, July 14, 2009

Nine

...is the number of separate residences to which I have moved some of these. Thinking about moving them again makes me tired. Most of them are going to Salvation Army today.