The Reflective Educator

Education ∪ Math ∪ Technology

Tag: mathematics (page 4 of 4)

November 16, 2008 / 2 Comments

Using a class blog effectively

Something I have been doing for the past three years now is using a blog with my classroom.  I have developed my practices with the blog over time and so far here are some of the things I have been doing with it.

The first thing for which I used my blog was to distribute information to the students, and provide announcements for the class.  Some of the things I might announce would be dates of upcoming tests, due dates for assignments, and upcoming topics.  I also used the blog originally as a way to provide links for resources, intended to be used in class.  This way students would not have to type in any lengthy URLs and could just click to get straight to the online resource.  Occasionally I would also upload a file to our class blog and expect the students to be able to download it for access.

Now that I have been using a blog with my classroom for a few years, I have found some more sophisticated ways of using it, which I want to discuss here.

One immediate change I made was to transfer the load of publishing to the blog with my students.  In the first year that I tried this, what happened was that one of my classes, an advanced grade 10 math class, posted daily summaries of what happened in class to the math blog.  This responsibility rotated around the class and when each student had posted their blog, they chose the next person.

This worked reasonably well, since occasionally students would come to class with questions they had discovered when reading the blog.  They would also occasionally comment on each other’s summaries and I hope that most of the students read each other’s posts.

The next step I took was logical, having tested out blogging with a class, I decided to try it with all of my classes.  I actually took the time to install the blogging software myself, hosted on my school’s server, so that I would have greater control over the process.  I wanted to be able to easily administrate the students’ accounts and be able to assist them with common problems, like forgetting their passwords.  I also made sure that posting to the blog was a part of the students’ grades, given its growing importance.

As soon as I did this, it became clear to me that not all of my students were reading the blog on a regular basis.  So this year I implemented another change, students would be marked on their full participation in the classroom blogging.  Not only would they be rotating through responsibility for creating summaries of that day’s class, they would have to post comments on the summaries for other student’s summaries.  This way I could guarantee that students were at least reading each other summaries.  The comments students have produced have mostly been really appropriate and high quality.

When I added the commenting on each other’s posts, something fascinating happened.  The quality of the blog summaries improved.  Students were aware that I grade the quality of the blog, but that I use a pretty forgiving rubric.  If students complete their summary, and it makes sense, they get full marks for participation.  What has obviously driven the improvement in their posts has been the awareness that their peers are reading them.

I think a second driving factor in the improvement in the quality of the posts has been a bit of competition, particularly among the stronger mathematics students.  They are basically competing to see who can create the best post.

Some of the posts, especially recently have been exceptional.  Students have become more comfortable with the format and are incorporating humor and more media into their posts.  Graphs and properly formated equations have almost become an expectation for their posts.

The ways students have been creating the graphs and equations have been quite creative.  Some students find images from other websites online, and use these instead.  Some students take the time to create their images instead using programs like Microsoft Paint, Adobe Photoshop, and Geogebra.  For the creation of the equations, most students have been using my built in Equation parser (which means learning a little bit of Latex).  The equations shown in the pictures here are actually created in Microsoft Word, and then exported to pictures using a lengthy process.

I’m not sure what the next step is.  I know I need to collect some information.  At some point near the end of the semester, I plan on collecting some anonymous data from the students to try and answer the following questions.

  • How long, on average, does it take you to create a summary?
  • How often do you check the blog to see if any new summaries are up?
  • Do you read the summaries from any of the other classes?
  • Have you felt any of the comments have been too critical?

In summary, blogging with your students as a class can be an effective way to increase their retention of your material.  They may end up learning some of the material from their peers because of the differences in how it is explained.  Your students will also end up having to view your classroom material in a different format, so it will activate a different part of their brain, and so some students will benefit from this experience (think Howard Gartner’s multiple intelligences).  Your students will also be likely to learn some valuable technical skills from the experience.  Finally, your students may just enjoy the experience, which will make them enjoy (and remember) your class for a bit longer.

November 15, 2008 / 2 Comments

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 www.sitmo.com.  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.

November 14, 2008 / 0 Comments

What can I do to help my child learn mathematics?

Update: It’s amazing how much my thinking has changed since I wrote this post. I literally cringed as I read the part about homework & test scores.

One of the most common questions I am asked by parents during parent teacher conferences is, what can I do to help my child learn mathematics?  There are a variety of answers I can give to this question.

The very first thing you can do is have a positive attitude about mathematics.  Almost anyone I meet who does not use mathematics for their career tells me how hard they found it, or how much they dislike mathematics.  Your positive attitude about mathematics will rub off on your child and will help encourage them to keep trying.

Show an interest in what your child is learning.  Find out what they will be learning this year in mathematics and keep track of where they are at.  There are certain topics that everyone finds more difficult, make sure your child has the help they need for those topics.  If you move from one school to another, this information will help your son or daughter adjust to their new mathematics class.

From an early age, encourage your child to think about puzzles and problems.  Having an active imagination and a willingness to think carefully are two huge assets when doing mathematics.  Many times students struggle with mathematics because they do not know how to persevere.

Work with your child on their homework whenever possible.  This does not mean do their homework, it means help them finish it.  There is a clear relationship between finishing their homework and your child’s scores on classroom tests and assignments.

Make sure your child has their addition and multiplication tables memorized.  This can be very difficult for some children, but it is one of the few things that really should be learned by repetition.  Not having to use their calculator for every single calculation will speed up how quickly your child can work, which will lead to improved test scores.

Keep in touch with the person who teaches your child mathematics.  Make sure you are communicating with them often so that you are aware of your child’s progress in mathematics.  Strong communication between parents and teachers helps improve students’ progress.

Most of mathematics is interrelated.  There are connections between different topics which can sometimes be missed by students.  If you send your child to Kumon math, or something similar, you should be aware that these connections are not taught in these types of classes.  This time would be much better spent having your child work with a private tutor in mathematics.

Be realistic in your expectations.  Not every person is a mathematician, and therefore not every child will be a mathematician, but all children can experience success in math class with sufficient support.  Give encouragement when your child improves rather than discouraging them when they do poorly.  Set reasonable goals for your child to achieve and give rewards for their achievement.  An expression used often in North America is “you catch more flies with honey than with vinegar” which basically means that rewards are more effective than punishments.

If you follow these guidelines, your child should have a rewarding experience in mathematics.  Remember that the goal of a mathematics class is to encourage analytical thinking and problem solving skills.  If at the end of your child’s school career they are a critical thinker, and are willing to tackle challenging problems, then you have done a good job.

November 14, 2008 / 0 Comments

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

 

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