Monday, April 27, 2015

WODB - Online Class

I was asked by my colleague, Grace Twietmeyer, to guest lecture for her online Geometry class.  I immediately said yes because I never say no to more Geometry!  Grace's parameters for what I would teach were wide open.  She said it didn't have to be a whole lesson, it could be GeoGebra, it could be short, it could be about any 2nd semester Geometry topic, etc.  When I started to think about doing this lesson, I was stumped was because I didn't know how to engage online students.  I couldn't have a dialog with them and I couldn't see their faces for reactions to the lesson.  Engagement goes far beyond a teacher posing a question and a student answering. I was so lost for an idea that I almost backed out of my commitment.  That's when I found Which One Doesn't Belong and I knew it was a perfect way to engage students online.
I made a short (2:40 min.) video.  My hook was an introduction from Sesame Street with the song "Which one of these is not like the other."  Then I gave an example that I got from a blog post by Jennifer Wilson.  I wanted to give a quick example of how you could actually start coming up with reasons for why each one doesn't belong.  
I posed two questions to students.  One was a right triangle example where each student had to write a discussion post giving a reason for why each box could be left out of the set.  The second challenge I posed was an incomplete set.  This was an idea I found from Mary Bourassa.  I wanted students to draw a picture that could both be the shape that doesn't belong and also completes each other set.

Students did a pretty good job of coming up with a reason for why each box could not belong.  Some misconceptions that students had
with this question was that a few students picked one box that didn't belong, instead of giving a reason for each box.  Their explanation for the one box was good.  They were able to defend their answer which was cool.  One student actually solved for x in each box so he didn't really understand the idea of comparing and contrasting the boxes.  I think it would be cool for this class to get to do WODB again to improve upon their comparisons of all of the boxes.
I thought they did a great job with the incomplete set.  They all gave different answers.  One of my favorite things about WODB
is that the questions are open-ended, providing an opportunity for different correct answers.  I think this is particularly good for an online class when students are posting answers to a discussion board.  They can see each other's answers if they need a little guidance, but they are still challenged to come up with something different.  
After one day of this lesson being posted, Grace and I got some great feedback.  A parent posted on Twitter that her daughter had a great experience with the WODB lesson.  And the director of digital learning was engaged too. 

I felt like the students were engaged with this lesson.  They put some thought into the activity and had creative answers for the incomplete sets.  Here's what they came up with for the 4th box:

I think a future challenge for this class, or another online class could be to come up with their own WODB then have each other give reasons why each box doesn't belong in a discussion post.  
I made this video on my home computer with slow internet, so it's not perfect and kind of glitchy.  Since I got great feedback on Twitter and from students, I thought I'd go ahead and share.  Feel free to take it, use it and make it better!

Saturday, April 18, 2015

GeoGebra Project

I've done this GeoGebra project in my Geometry class for the quadrilaterals unit the past few years and it's been really fun.  The project is to make the following quadrilaterals on GeoGebra:  Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid and Isosceles Trapezoid.  Here's a link with the assignment and rubric:  Project.  We go to the lab 3 times to complete this project.  Most students finish within the 3 period allotted time, but some work on it outside of class.  I always make it due the day of the test because I believe that working on the project helps them study.
We do a lot of GeoGebra throughout the school year, but I've found that students need some guidance with what tools will be helpful to make these shapes.  The first thing I have students do when we get to the computer lab is this tutorial.  By going through this GeoGebrabook to practice making parallel lines, measuring, perpendicular bisectors, and reflections, it give students an idea of what they'll be doing to make quadrilaterals.  In fact I often see students referencing the tutorial throughout the project.  It's also convenient when a student asks a question like "how do I measure an angle inside the quadrilateral instead of outside?" to be able to direct them to the tutorial instead of reteaching the measuring tool.
I lay out some guidelines for what students should be accomplishing each day we're in the lab (Day 1: parallelogram, Day 2:  rhombus, rectangle and square, Day 3: trapezoid, isosceles trapezoid and kite).  We talk about Math Practice Standard 1:  Make sense of problems and persevere in solving them.  This is a challenging project.  Students don't have much guidance or direction for how to make these quadrilaterals.  The whole point of the project is that they figure it out.  Because students are figuring out the project and deciding which tools work and don't work, figuring out the parallelogram takes longer than the rest of the shapes.  On the 2nd day I post a youtube video for how to make a parallelogram.  If students spent one whole period trying a parallelogram and still can't get it, I want to give them some directions so that they have a foundation to complete the rest of the shapes.  I also want to be cautious about students getting to frustrated and giving up.  After they've made the parallelogram, they get a lot more confident about the rest of the shapes.  About half way through the 2nd day when students are struggling with the rhombus, I give a hint.  I suggest that students try building their shape from the inside out. Start with the diagonals and build the 4 sides after (or start with 2 sides, then do the diagonals, then finish the shape).
I know that some students go home and look up how to create these shapes online.  I'm ok with that.  If they're looking it up, they're still learning how to create these shapes, and they're still responsible for making them on their own.  In the past I've added a test question "Give step-by-step directions for how to make a parallelogram."  This shows me who understood the tools and how to use them to make a quadrilateral vs. who copied steps from an online source.  Students often ask if they can make a square with the regular polygon tool.  I say yes.  They've found a tool that makes the problem easier, but they still have to measure and show me all of the properties of a square.
Another helpful idea is to give students examples of a shape the looks like a parallelogram but is not a parallelogram and one that is a parallelogram.  I show the example of what isn't a parallelogram and we use the rubric to see how a student would be graded who didn't meet all of the requirements.  Students use these links throughout the project as a guideline to make sure they're fulfilling all of the requirements of the project.
One idea I've thought about, but not incorporated yet, is adding a creative element to the assignment.  One year I had a student paste random pictures (Justin Bieber, a lawn mower, a goat, etc) into each of her shapes.  It was fun and funny to grade.
My favorite thing about the project is hearing students teach each other how to create each shape.  They are very proud of accomplishing the project and are more than willing to share their expertise with their peers.
Do you use GeoGebra with quadrilaterals?  In what ways have you found the software to add value to this unit?