Education ∪ Math ∪ Technology

Tag: projects (page 1 of 1)

Moderating external projects

For the past three years, I’ve been an official IB Assistant Examiner.  This means that each May (or November, but I usually don’t sign up for the November sessions, too busy), I get sent a whole bunch of external exams or projects, and I have to grade the assignments.  The money isn’t great, it’s a huge amount of work, but I see it as really valuable.

I had just received yet another package this morning, which one of the administrative staff gave to me, so I felt obligated to explain to her about my role as an assistant examiner for the IB.  Her response was "Wow, that’s cool, it must really give you some perspective into your own students’ work."  

This really is true, I love being able to see what other schools do.  I can’t share it directly with my peers for confidentiality reasons, but certainly I share the principles behind how student work is arranged, and what the expectations are around the world.  I’ve now observed a few dozen different school’s work, which means that I have a few dozen perspectives on what it means to produce a student project.  The best part is, almost all of these projects are based on the same small set of projects, so I can actually control for type of project.

I highly recommend moderating other school’s work, the perspective you gain is totally worth it, even if the money is not.

Using Google Docs when teaching mathematics

Google has a lot of cool tools they have been working on recently, and I enjoy trying them out.  Once in a while they come up with a tool you can use in your classroom right away.

One of the tools we are using in my classroom right now is Google Docs.  This is an online document collaboration tool which allows people from anywhere, using most modern browsers to upload, edit, and share documents online.  It supports many different formats, and you can export the document and download it at the end if you finish working on it.

I have been using it as a place for my students to share their workload.  I created 12 Google Documents, 1 for each of 12 groups in 2 different classes.  I then collected the email addresses of my students and assigned them to groups of 3.  I went through each of the 12 documents and used the ‘Share’ feature of Google docs to allow the students to collaborate on the each document as well.

One caveat I discovered is that if the student’s email address is not a Google mail account, they need to verify their account.  Unfortunately this verification process takes about an hour of real time, presumably as Google syncs up the account verification across their many, many servers.  There are two solutions to this.  The first is to make sure you have the students do the account verification a day before you actually want them to use the documents.  The second solution is to have the students sign up for Google mail accounts first, and then send them invitations to their groups.

To be honest, mathematics as a subject is not especially suited for online collaboration.  This is because the creation of equations can be a bit tricky for the uninitiated.  There are a number of solutions for creating professional equations online, which all have their benefits and drawbacks.

The first and easiest solution for the students is to use Microsoft Word and create their equations in Equation Editor (or if you can afford it the far superior Mathtype).  The only problem here is that the kids think they can copy and paste the equations into their documents, which of course doesn’t work.  The second problem is that if you ‘Import’ a document (another feature of Google Docs), your equations don’t make it.  Ugh.  The work around for me was to have the students take screen-shots of their equations in Word, and then crop the screen-shots in an image editor program (like Microsoft Paint).  I’m not normally a huge fan of Microsoft programs, but their Equation editor really is one of the best tools for easily creating equations I’ve seen.

The second solution is to use one of the online services offered to use the Latex document format and an elaborate system to convert the Tex documents produced into equations.  The one I like best right now is offered by  You basically create the Latex, which is made easier using the editor above, and you can immediately preview the results.  Underneath the preview image there is a link, which the students can right-click and ‘copy link location’.  Once they have the link to the image, they go back to the ‘Insert => Image’ offered by Google Docs and paste the link into the textfield provided.  I have been teaching my high school students some Latex and they have picked up the simple things pretty quickly.

Formating the text otherwise in the editor is relatively straight forward, it feels similar to how you format text in most word processing programs, which maybe a few less options.  What’s brilliant about this system is that each student can be editing exactly the same document online at the same time!  You can also be sitting at your desk with all of the documents open and see the students editing the document.  This means a little bit less concern about students messing around while accessing the internet, which is always a huge problem in a 1 to 1 computer set up.

The other handy feature is the ‘View revisions’ tool which allows you to see what changes have occurred to the document over time.  I use this to see who added what to their projects and to make sure that each student contributes at least approximately equal amounts to their projects.

When the students are done working on their document, you can just go and look at it online and grade it.  No need to print out the document, but if you feel the need you can download it in your format of choice and then print it out.  They have a print directly feature as well, but I have found the output varies greatly depending on your browser.

Deciding what kinds of projects are appropriate for this kind of collaboration can be a bit tricky.  I am currently using it for my students to produce sample projects for their International Baccalaureate (IB) Mathematical Studies course so they have a bit more practice before they have to do the real thing.  What you decide to use it for is up to you, but note that some of the problems (like inserting equations or graphs) don’t happen in other subject areas, so this technique might be even more useful in an English class, for example.

Helping students produce effective high quality projects

As secondary mathematics becomes more and more about how you find the solution to a problem and less about what the correct answer is to a problem, it becomes easier to justify assessing students using a project.

One immediate advantage of doing projects in high school mathematics is that students learn valuable job related skills, such as formatting documents properly, technical writing, and communication skills.  It is arguable that these skills are more important than the actual mathematics content we teach.

So now it becomes a question of helping students produce high quality projects that are worth your time to grade.  We as professionals need to come up with some strategies for helping our students through these projects, because if done correctly, they can be far more difficult than our most challenging topics in mathematics.

First, when assigning the project, it is helpful if you have taken the time to do it yourself.  Make sure that whatever work you are planning on giving the kids has a clear solution, and that the students in your class are capable of finding it.  This does not mean that your project can’t be open-ended, but students need to have some measure of success when working on the project.  I have made the mistake in the past of assigning a project which was much too difficult for my 10th grade students to do, and regretting it in the end.  No real learning comes from doing a project which is beyond your talent to complete.

The next thing to consider when assigning the project is the clarity of your instructions.  The first few projects you assign should be pretty doable by the students by following your instructions verbatim.  Give the students a formalized structure to follow.  It is a good idea to even give the students a template to follow.  This does not mean a ‘fill in the blanks’ style assignment, but more like giving them the following structure.

Sample project structure

You also need to give the students the same assessment criteria you will be using to grade their projects before they start working on them.  A rubric is a handy way to grade a project, so give the students a copy of the rubric you will use.  Take the time to go through the rubric, and if the project is one you have done before you might even be able to show some examples from a previous year.

Now you need to set aside at least a couple of lessons during class for the students to work on their projects.  Once the students have started on their projects and have some work, they will want to finish the projects.  They will come to you and ask for more help, but you have to give them enough time to get ‘hooked’ into the project.  Sometimes what I will do is have students collect data on some phenomena in groups, and then they work on the calculations, conclusion and evaluation of their projects individually.

Give the students enough time to finish the projects before expecting them back.  You can have a project that takes the students three weeks to finish, if you provide daily reminders of the tasks that need to be completed.  You may also want to set goals for the students to reach and remind them what stage of the project they should be at in order to complete it on time.

If the students turn in work, and it is not as high quality as you would like, take the time to analyze the work as a class.  Maybe photocopy some of the best and worst work, making sure to obscure who’s work it is (retype it if you have to) and hand it out to the students.  Discuss with the students what worked and what did not.  Let the students redo their assignment if they have to and turn it back in.  Remember that your objective is to have the student capable of producing a high quality piece of work.

Once you have done a few projects, they become easier.  The first few projects I did were nightmares to supervise, and what the students turned in ended up not being very good.  After 7 years of having students do multiple projects a year in mathematics, I now have high expectations for what the students will produce and how to help them achieve this level of work.

Here are some specific ideas you can use in your classroom for projects and the topic from mathematics they cover.

Functions and Logos – function transformations

Aunt Dot – arithmetic and geometric sequences

Threes and Ones – number patterns