1:1 Environment – Where the Old Impossible is the New Easy

Geometry homework tonight was:

At home or school, take three pictures of objects that fit the following descriptions 

1) not a polygon

2) polygon with 3-5 sides

3) polygon with 6+ sides

Upload them to a Google Drive folder shared with everyone in the class and rename the image with the name of the polygon shown

It took me under five minutes to set up the tech side of this assignment (including collecting Gmail addresses with a Google Form during class and sharing the folder), and perhaps another five minutes to explain to students what they needed to do.  

The end result:  a folder full of real pictures (some good, others not, but none of them provided by me) that we are going to (hopefully) have a good discussion about tomorrow.

Last year, I wouldn’t have been able to do this without a lot of hassle, and two years ago, it wouldn’t even have crossed my mind to try it.  Say what you will, but mobile technology is a game changer.


Mistakes are Great

Earlier in January, I wrote about the Collaborative Exam Review that my pre-calculus classes (a total of 43 students) wrote using a variety of tools from Google Drive.  Today was exam day, so the project is done, and have decided that what I liked best about is was that it was their responsibility and it wasn’t perfect.

In preparing the review, students had to take responsibility for knowing what they needed to know (so they needed to become experts on their topic) and they had to take responsibility for knowing it well enough to explain it coherently (via their solution image) to others.

Even so, kids made mistakes.  However, because of the culture of responsibility for the material that already existed in this review, the mistakes actually made the comments and discussion on the review problems/solutions that I required in the week leading up to the exam even better.  Students evaluated peer solutions and, when they had questions or found mistakes, used Google Drive’s commenting features to offer constructive criticisms or additions to the material was already there.  Lots of different students started getting in on the discussions, going back and forth about what was right and what was wrong.  At the end of the day, I think this helped them demonstrate their mastery of the material better than simply completing a review packet.  After all, you can’t tell someone else they did something wrong if you don’t know how to do it yourself!

A New Take on Midyear Exam Review

Margaret teaches the highest level of Algebra 1 at our school, and I teach Pre-Calculus at the same level.  At the beginning of December, we both had conversations with our classes that began something like this:

I am not going to give you a review packet for your first semester exam…

**anxious/borderline angry looks exchanged around the classroom**

…instead, we’re going to do something better!  You’re going to write the exam review yourselves.

Wait, what, you’re asking?  Last spring before finals, Margaret and I decided that we were done with giving our upper level students an exam review packet or problem set and spending a couple of days in class going over it, as we had done in the past.  So, we decided to try something new, and we thought it was valuable enough that we both decided to try it again for the midyear exam that is coming up in a couple of weeks.  This year, iPads are making the workflow much easier for all involved.  

This is what the process looks like:

1)  We created a skeleton Google Doc with an outline of the topics to be covered on the exam.  We intentionally broke the topics up into a number of subsections equal to the number of students we each have.   We shared this document with our students specifically so that we could hold them accountable for their work via the revision history.

2)  On the day we introduced the project, students accessed the document via the Drive App on their iPads and claimed the topic they wanted.  Then, we gave them a day in class to work on researching their topic (going through notes, the text, old quizzes and tests, etc). and draft 2-4 questions that would help classmates review the topic.  We required that at least one question be conceptual and one question be computational.  

3)  Students entered their questions into the original Google Doc.  They used the built in equation editor to enter any equations.  If they wanted to use a graph or other image, they drew it in Notabilty or graphed it on Desmos on their iPad, took a screen shot, uploaded the screenshot to Drive, and then inserted the image into the review doc.  The limitations of the Drive app were such that most students did this step on the web-based version of Google Drive on a regular computer.

4)  Margaret and I reviewed the questions, made comments, and students used our comments to edit their questions into final versions.

Here’s a copy of my pre-calc review in its almost finalized version.  In order to write these questions, students needed to figure out what they need to know about a topic AND come up with questions whose solutions demonstrate that information.  This forced them to think a bit outside of the box, especially for some of the conceptual questions.  I think its so much better than completing a review packet!

5)  Once questions were finalized, students created solutions to each of their problems in Notability on their iPads.  These solutions are supposed to include a worked out solution to the problem with step by step explanations.  Students uploaded a screenshot of each solution to Google Drive and submitted a link to the image to me via a Google Form.

Directions for Creating a Solution

6)  Once all solutions were submitted, I made the response spreadsheet available to all students.  Each entry in the spreadsheet includes a verbal description of the topic, the number of the associated review problem, and a link to a solution.  When students are studying, they can go to this spreadsheet, find a topic they want to know more about, and then see a comprehensive explanation by one of their classmates.

7)  Once all the solutions are in, students are required to evaluate each other’s work, use the commenting feature on Google Images to share their evaluation.  The owner of each solution is then responsible for replying to the comment with an answer to a question or a resolution for an error.

Commenting Guidelines

This whole endeavor is still very much in the work in progress stage.  Stay tuned for a follow up post after exams about how we thought it went, how our students thought it went, and what we would do differently next time!

Teach them to fish

Two weeks ago, I had my pre-calculus students do an investigation about the characteristics of the graphs of power functions using the Desmos iPad app, which I wrote about in an earlier post.

Last Tuesday, they had a quiz that included the content of that investigation, and on Monday night, I was surprised and delighted to find an email from one of those 11th graders with the screen shot below attached and a question that said something to the effect of,

“I’ve been drawing all these graphs to practice and I’m a little unsure of why the graphs shown have this shape. Is it this reason?”


Possibly one of the best emails I’ve gotten lately because this boy was using a tool he had for a helpful purpose that I didn’t suggest. And you know what? That student got full points on the quiz.

QR Code Scavenger Hunt

Test review days.  You can’t live with them, you can’t live without them.

In an effort to make a recent geometry test review day a little more interesting, I decided to try an idea I had heard from another teacher:  making a QR code scavenger hunt.  I was really pleased with the way it went.  Here is what I did:

1.  I created a set of 10 geometry problems and made each one a separate Google drawing (most of them had diagrams).

2.  I used a free online QR code generator to generate a QR code for each question.  I printed out these QR codes and posted them in semi-sneaky locations around the school library.

QR Code 7 hiding on the side of a bookshelf

3.  I paired up my class and created a Google form that

a) sent each pair to a different starting question

b) for each question, told the student where to look for the QR code

c) once they found the QR code, they scanned it and got the question.  Then, they had to input their answer into the Google form.  If they got it right, it told them where to look for the next code.  If they got it wrong, it told them to try again until they got it right.  The questions looped around until each pair had answered every question.

Things that I liked

1) It got the class up and moving.  I read an article a while back about how students need to move more during class, and I’ve been trying to think of ways to make that happen.

2. It fostered good team work.  One student was responsible for managing the form, the other for managing the QR scanner, and I saw a lot of conversations about answering the questions.

3. It left room for surprises.  I put one QR code on the inside of a wide window sill, and when my students started the scavenger hunt, a girl had sat down in the window to read with her back to QR code.  One pair found it eventually and tipped the rest off, but it definitely added a little twist to the morning!

I would definitely do that again.

And you can’t beat the colors!

Margaret’s love for Desmos is fully endorsed by the other half of this blog!

If you aren’t convinced, here’s some additional classroom action:

Yesterday in pre-calc, my students did an investigation about power functions.  They graphed groups of these functions and made generalizations about their characteristics.

Here’s what a group of power functions looks like on a graphing calculator:


Here’s what the same group of power functions looks like graphed on Desmos:


Which one makes it easier to tell that all the functions in this group are symmetric about the y-axis?  A picture is worth a thousand words.

The Downside of Digital Textbooks

This year, my Algebra 1 students have digital textbooks, and my Pre-Calc and Geometry students have hardback textbooks.  Back in September, I wrote a post about how I didn’t think it made sense for my Algebra students to use their iPads as notebooks like I was planning have my other students do.  My reasoning was that they needed to be able to work on problems from the book at the same time that they are looking at their textbooks, and I was worried that this much multi-tasking was going to be a recipe for disaster.  

A couple of months into the school year, I don’t regret that decision, but I regret that I had to make it because my Algebra 1 students need to spend a significant amount of time using their powerful mobile devices to view Algebra problems that they then work out in their notebooks.  This is not very different at all from what my classes did with a hardback book last year.  

On the flip side, I just posted about how my geometry students were able to use their iPads to collect and pool some data last week, and they have also used them to access Google Earth, find pictures of things on the internet to add to their digital notes, draw better, more colorful pictures, and more. They rarely touch a piece of paper.

Next year, these geometry students will have digital textbooks, and I’m not sure if this is going to mean that I am going to ask them to switch back to paper for notes and homework.  I don’t want to.  I am being prompted to try activities this year that I don’t think I would have tried if I had this class working in notebooks and binders.  I am at the point where I would rather have no textbook than a digital textbook.

Why?  I wasn’t exactly sure until I read a post on Dan Meyer’s blog called The Digital Networked Textbook:  Is it any different? about a month ago which said everything I had been thinking.

Meyer contends that digital textbooks aren’t different enough from their paper cousins, and I agree with him.  I think this is because that their main function is still to be a vehicle for content.  They are not a work space or, ideally, a collaborative work space.  Because they are just vehicles for content delivery, I think digital textbooks actually limit the power of the mobile devices being used to view them because students have to use the mobile to look at something, not to do something.

If my geometry students had been able to enter that data they collected last week into their digital textbook, see the data entered by their classmates (and maybe people in other geometry classes?), and then use that to draw conclusions and do other work (all in the
“book”, THAT would be different, and THAT would be worthwhile.  

Until then, I can write my own geometry problems, and I don’t mind the extra work if it means my students can use their devices to actually do something instead of just looking at slightly more interactive textbook pages.