Showing posts with label xkcd. Show all posts
Showing posts with label xkcd. Show all posts

Saturday, August 20, 2011

Gradual Release of Responsibility

xkcd: 894
How is it possible that I haven't blogged about this? The Gradual Release of Responsibility has been one of the key ideas to help me improve my teaching. It hails from literacy education, but applies to any kind of learning, and has helped me understand why some people's best learning stories are what they are.  It's also very useful at the beginning of the semester/school year as I'm planning a course.

This is the first visualization I saw of this, from Margaret Mooney.  Fisher and Frey are also strongly associated with this idea, and their Google book preview is extensive. I was introduced to this by Dave Coffey (of course) and he has a very nice explanation on his blog.  Rather than repeat what he wrote, I'll share what it means to me.  Sometimes it's a framework for a single class period, sometimes for an entire course, depending on the scope of the objective.


When I first became a believer in active learning, thanks to the reading provided by Sue Feeley when I was prepping my first math for teachers class, I became very extreme about never telling the students anything. I was proud to hear students pass on asking me questions and work further for themselves. On student evaluations, I took their comments about frustration as statements that this kind of learning was new to them. And I do think that's partially true. But one day when a student said, "why are you asking him, you know he won't answer..." it sounded more like I was denying my students support they needed. I realized that their telling me they were frustrated was because they were frustrated. (Crazy, I know.) And humans can't learn when they are frustrated.

What was missing was demonstration. I had stopped equipping my students for tasks because I equated it with telling. What the literacy education reading let me in on was the idea of a think aloud. Authentically sharing your thinking. But the key for me was the idea that while you're doing this, the students are active observers. You let them know what to watch for and debrief them on what they saw in your demonstration.  They are still active! But they may need demonstrations on how to be observers. Early on in a class you might hear me say things like, "Oh. I hoped you'd notice how I..." Or just share my own observations. This is particularly relevant in math ed classes, but I use the idea and technique in content classes, too.  Hopefully the  demonstrations decrease in frequency and duration during a course.

The next phase for me I typically am too quick with, I think. Whole class work where I solicit ideas and suggestions from the class. It's a bit close to my novice teaching style for comfort, so I think I under use it.  You can often gauge in a demonstration when students want more responsibility, or when you've seen some developing use of your objective process.  The positive reason I skip more quickly to whole class-students lead-I support is because I want students to have the experience of trying without knowing how. If they can get used to that feeling of 'maybe I could...' it will make them so much stronger as problem-solvers. You can also do this phase in groups with active support from you, and I think this is easier with heterogenous groups.

This just makes so much sense to me as a structure, I sometimes feel guilty for having to be shown it. Of course I want my students to be independent, and of course they need to see and experience what I'm asking them to learn and of course there is an inbetween.  Gradual Release also helps me keep focused on those big goals that I want the most, the problem solving and communication. It helps me with instruction because I better know what kind of responses are available for where I assess a student to be.  A few classes have gotten to the point where they knew this for themselves; "could we get a demonstration of this?" That's an awesome place to be.








Monday, June 28, 2010

A time problem

Wrote this problem for my spring final and fell a little too in love with it.  Has some fun algebra behind it.
Jane glanced up at the clock and noticed that when the second hand was on the 12, the three clock hands divided up the clock into a right, acute and obtuse angle.  What time was it:
  • 3:30, 
  • 5: 43, 
  • 1:22, 
  • 9:15, 
  • more than one possibility or 
  • none of those  
Remember the hour hand moves during the hour.
When grading, many students ignored the idea of the hour hand moving in between, so I evaluated based on their assumptions.  In general on the test, I was trying to create the possibility of seeing some problem solving, where they could demonstrate understanding of ideas without necessarily having to get a right answer.  It was partially successful.

As I was trying to write the problem, I posed myself this question: 
If it is y o'clock and x minutes past the hour, what is the angle formed by the clock hands?
If you're considering either, I'd love to hear what you think in the comments.  How do you evaluate the first?  In the second, would you expect the equation to be linear?  Why?

Cartoon from xkcd, of course.



Some of the exam problems were pretty open-ended, like:
1.    Find an L-shaped figure with an area of 84 sq.cm and a perimeter of 44 cm.  Is there more than one?
2.    What kind of triangles can be made by connecting vertices on a regular octagon?  Specify the side-angle type.  Did you find all of the types? 
And some were more closed, but hopefully with multiple ways to do them.
5.    Sort the quadrilaterals into two overlapping Venn diagram circles: one for rotational symmetry, one for reflectional symmetry.  Quadrilaterals that don’t fit either should go outside.
6.    A Hershey’s chocolate bar is 43 g.  A kiss is 4.56g.  You remember that 1 pound is 454g and 1 pound is 16 oz.  How many ounces is a Hershey bar?  A Hershey kiss?  How many kisses in a bar?  (Make a joke if you want.)
Nobody made a joke.  How many kisses in a bar?  Come on!

Sunday, August 16, 2009

More Math Correlates to Higher Income

The blog where I saw the study referenced: Free Exchange at the Economist.

The study the blog is citing: Joshua Goodman

The cartoon that teaches correlation:


(XKCD is occasionally profane, almost always funny, and frequently geeky. Clicking the cartoon leads to the site.)