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# The Earth at your Fingertips

When I taught geometry for the first time two years ago, I used some screenshots of Google maps to help my students visualize the angles formed when a pair of lines are cut by a transversal.  After a year on the geometry bench, I’m back in the game this year with a completely new set of resources that calls for a new playbook.

Here’s what we did in class today:

1)  At the board, I did a quick introduction to the vocabulary we’ll be working with:  transversal, the names for the different pairs of angles formed, etc.

2)  Then, I had everyone open up Google Earth on their iPads and we visited the area around our school (it’s so fun to fly in from out of space) and hunted for pairs of lines and transversals.  Once we found some, we practiced naming different pairs of angles formed.

3)  Finally, students found their houses and searched for examples of pairs of lines and transversals nearby.  One by one, each student mirrored their iPad using my Apple TV, ed us their house (I think most people were more excited by this part…) and their example.

I think the really good part of this activity was the fact that it wasn’t just me using Google Earth, which is what would have had to happen if we weren’t in a 1:1 environment.  Everyone had the chance to look for their own example which was more engaging, and the class got to see more examples and practice the new vocabulary in many different contexts.

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# Their Work: More Interesting than Mine

Since Margaret was singing the praises of the killer combination of Apple TV and homework done on iPads earlier today, I thought I’d chime in.

I always struggle with how to review homework in pre-calc.  It’s easy for another student to share their answer with the class, but its usually more complicated than “x = 5,” and I really don’t think its that helpful for the rest of the class to hear the answer unless they can see it. When a student wants to talk about a problem they got wrong, what I have been doing is either projecting my solution or having a student project their correct solution to give us a visual for discussion, which was okay.

What I’m finding I like better is getting a student (or a couple of students) to project their entire assignment while we discuss the answers.  That way, we always have something to look at while we’re talking, because its hard to talk about math problems without seeing them, and, even if the student go something wrong, they can fix it in real time with my/the class’s input.  I think it’s really valuable for the rest of the class to see both the mistakes and the fixes.   I’m going to try this set up for going over homework more often.

# Geometry Proofs: So Many Ways!

I teach Geometry.  My students struggle with the idea that there are lots of different ways to prove something.  What they really hate is that there isn’t one right answer.  I on the other hand get the most frustrated when a student is looking at a proof I have projected saying,  “I did something different … am I wrong?”

Prior to our 1:1 iPad environment, I would have said, “well let me come take a look” or “how about you write it on the board and we’ll look at it?” Oh the time I wasted waiting for kids to write on the board … oh the time I wasted looking at one kid’s work while the rest of the class stared off into the distance.

Enter Apple TV and students doing their homework in Notability on their iPads. Now I say, “could you mirror your iPad and we’ll look at your proof together as a class?”  Within seconds, the whole class is looking at an alternative method of proving something.  Sometimes  it’s right.  Sometimes it needs to be tweaked.  Other times, it’s way off.  But regardless, we get to look at several different proofs for each problem and still have class time left to do something else!

When my students are working on a particularly difficult topic, I like to know if they’re on the right track.  If I don’t get questions via email or see students in my room the next morning, I begin class without knowing where my students stand with yesterday’s material.  This isn’t exactly ideal.  (I realize I could scrap the idea of homework, but that’s not where I’m headed.)

Instead, I have my students enter the answers to their homework problems into a Google Form.  They’re not submitting all of their work, so it doesn’t take much for me to scan through their answers and quickly get an idea of whether each student is on the right track.

I tried this for the first time last week when my trigonometry students.  I created a Google Form asking for identifying information (first and last name, email address, and class period) and answers to each of the five homework questions.  Since my students do their homework in Notability on their iPads, it was easy for them to quickly enter their answers and submit the form when the were finished with their homework:

I checked in on the responses a few times, emailed students who seemed to be way off track and offered some hints based on which problems were wrong.

I sent emails to students in lines 1 and 3 when I noticed their answers were incorrect.

Then, before class, I used Flubaroo, a script in Google Forms, to “grade” the homework and email students their grade (out of 5) as well as the answer key.  Below is the summary of the grades.  [Note: I did not use this grade, but rather, I gave full credit to students for completing the assignment.]

Instead of starting class by asking what questions my students had, I was able to target the one question that  most students struggled with.  Another nice thing about using forms to collect homework responses is the ability to project all of the responses at the beginning of the class period.  When I ask an open-ended question, I like for my students to see all of the different responses and discuss which ones are better explanations.  Thank you Google!

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# Low Tech Success

Margaret and I are lucky to teach in a school where we have access to a lot of technology and are encouraged to use it as much as we can, especially in new ways. The 1:1 initiative this year has meant we are finding new ways for students to organize, share, create, and collaborate using their devices. These are valuable 21st century skills, but so is being able to have a productive, face-to-face conversation!  I was reminded of this yesterday during my geometry class.

Before school, I drew several pairs of complementary and supplementary angles on plain white paper with red and purple Sharpies and taped them up all over my room, some adjacent to their partners and others across the room from their partners (and behind a trash can).

The class’s task: find all the angles, pair them up (I had numbered the pairs) and decide why some are red and others are purple.

Tables rather than desks provide an ideal workspace

Watching my students do this was fascinating. At first, they worked alone while finding the angles, and then some started laying out their bounty on one table while others laid them out on another, but they soon realized everyone needed to be at one table. Suddenly, my whole class was standing around one of my tables (a time I’m glad I don’t have desks) having ONE CONVERSATION. After a little puzzling and disagreement, they figured out that the pairs of red angles all added up to 180 degrees, while the purple pairs added up to 90 degrees!

This experience reminded me of how important it is for my students to be able work with others through every step of a problem solving process. Devices can be a vital part of that process, but several of the skills students need to develop to be successful 21st century citizens can be honed while stepping out from behind the screen.  A good reminder as I finish out the week.