Education ∪ Math ∪ Technology

Month: September 2010 (page 1 of 3)

A bunch of Math games

@joe_bower said he was looking for some decent math games online and couldn’t find any. I remembered that I used to make math games all the time so I fired off a bunch of links back. I decided it was worth gathering all those links into one spot. Who knows, maybe some of these old games are useful.

Good for teaching about perspective: Labyrinth

Gives students a feel for how fraction operations work: Fractions operations

Practice operations and solve a number puzzle: Countdown

See how simple rules result in much complexity: John Conway’s Game of Life

Practice factoring numbers & remember prime numbers: Factors!

Just a fun spaceship game (similar to Asteroids): Spaceship game

Useful for recognizing some similar fractions: Horse Races

Really just algebra practice & puzzle solving: Algebra puzzle

More of the same type as practice as above but quadratic algebra: Quadratic algebra puzzle

Look at patterns when moving rings: Towers of Hanoi

Try a variation of the classic logo programming language: Logo Programming



A Day in the Life of a Student

You wake up in the morning earlier than you want to. You try and struggle to stay asleep but your parents come into your private space and nag you constantly until you get up. Wearily you get up and get dressed in your school approved clothing.  If you still have time you munch down some food and then you grab your extremely heavy backpack and head to school.

On the way to school you are teased by some of your "friends." You’d mention it to an adult but nothing ever happens so why bother. When you arrive at school you place some of your belongings in a tiny cubicle that doesn’t quite hold everything and smells faintly of that lunch you managed to pack last week but forgot in your locker over the weekend. Jostling through the over crowded and identical hallways you make your way to your first class of the day.

Fortunately you had time last night to finish some of that boring homework you assigned so you get it out of your book and prepare to share it with your teacher. Unfortunately you’ve forgotten that this teacher never actually looks at the homework and gives you any feedback about it so back into your book it goes. You are actually enjoying your class discussion when all of a sudden a loud bell goes off and you have to rush to your next class. It’s too bad because you feel like you were finally understanding some of the reasons why World War II happened.

In your next class you hardly have any time to think because you are spending your whole class frantically trying to keep up with the enormous amount of inane stuff you are being asked to write down. Right at the end of the class the teacher finally pauses to ask if anyone has questions but before you can ask why Hamlet did all those mean things you have to wait through three people before you ask questions about when the homework is due. Bell goes again and off you trudge to your next class.

In your math class your teacher patiently goes through solving quadratic equations but never explains WHY you want to solve quadratic equations. She’s good at explaining this stuff but a bit out of touch with your needs. You try and do her homework because you know math is important but it seems like the stuff that is on the test is different than the homework. You’d love to be able to ask questions but you feel too intimidated and stupid to do so.

Next you get to have lunch. You head down to the cafeteria where they are serving slightly warm pizza AGAIN. You sit around on a table and chat with your friends for a while. You’d like to go and play a game of football outside but there’s no one to supervise you so you are stuck inside. It’s even a beautiful sunny day outside so you are pretty frustrated.

After lunch you have your final class of the day which is usually your favourite but today you have a sub. He hands out a bunch of worksheets and reads instructions off of a piece of paper in his hands. He apologizes but says he knows nothing about computers and so they have to remain off. He’s not, in his own words, "licensed to teach about computers."

At the end of the class you pick up your stuff and go home. You’d like to hang out with your friends but there’s really no place for you to do that now that the school instituted their new "go home if you aren’t supervised" policy. Instead you play a little bit of Farmville to relax and then take a look at your homework. Your parents come home late and ask what you did today and you say "nothing" because really that’s the truth. You had to make your own food for dinner which unfortunately consists of an over cooked microwaveable dinner because that’s all you’ve ever had the time to learn how to make.

None of it seems very interesting but you manage to get through it while IMing with your friends, watching an old rerun of The Big Bang theory. When you are finally done you work on some of your own projects you’ve been thinking about but too tired you give up and go to sleep. You know the next day will be the same as today and you wonder why you bother to go to school.

Why mass teacher evaluation systems are flawed

There are lots of enormous flaws at the root of the current effort to evaluate teachers across the US. We could talk about how each teacher serves a much different population, or how the resources which are provided to each teacher are different because of the wealth of their educational community, or how a poor administrator can influence teacher evaluations, but there is a deeper flaw, one based on a more mathematical argument.

Imagine we ranked all of the teachers according to how much material they covered (which is essentially what grading them using standardized assessment scores from their students do), much like the current SAT system ranks students, and then graphed how many teachers were at each rank.  The graph would look very much like the following.

Normal Distribution - Credit: Wikipedia

This is called the normal distribution in statistics. The function written at the top doesn’t matter very much. What matters is that μ is the mean (average) of the distribution and σ is what is known the standard deviation (read this explanation if you are confused). μ is measure of where the center of the data is, and σ measures how spread out the data is.

A couple of important facts to know about this graph is that about 68% of the teachers will be within one standard deviation of the mean and that just over 95% of teachers will be within two standard deviations of the mean. This means that the vast majority of teachers will be ranked near the middle of the graph. Teachers within one standard deviation of the mean could be considered average, and teachers ranked below two standard deviations of the mean would be in the bottom 2.3% of the teaching profession. These are the people that typical reform efforts like to target and were recently "exposed" in the LA Times value-added assessment project.

Now let’s suppose we managed to improve the education system in the US a whole bunch. In fact we manage to improve it so that instead of each student learning one years worth of material in a year, they learn two years worth of material! Wow! Good for us! What would happen to the picture above then?

Well it turns out nothing would happen at all. The reason is because the picture above represents a relative ranking between teachers and there will always be teachers who rank lower than other teachers. No matter how much we improve education, the picture above will always remain the same, with one exception. If every teacher was ranked equally, then the picture above would look more like a very thin bar sitting above the mean. I don’t think that will ever happen though and it would certainly be a pretty boring education system. Imagine if students never had a favourite teacher; who would want to join the profession then?

The other point to bring up is that if we supposed that the teachers at the mean of the distribution teach what we call a "year’s worth of material" then as we improved teacher quality and this mean rose, then so would what we defined to be a "year’s worth of material." We’d always be stuck bemoaning the fact that there are teachers who can somehow only cover half a year’s worth of material and other teachers who can cover two year’s worth of material. The amount of material to cover would just rise.

The flaw is that the more material we try to cover each year, the less room there would be for the individuality and creativity which is so important to the teaching profession and to education in general. I’d like to see a slightly different way of assessing teachers. Let’s assess teachers based on their professional relationships with each other, based on the rapport they develop with students, on how willing they are to share their expertise, on the quality of the research they have done, and a host of other factors which cannot be measured by a test, or conveniently broken down into a normal distribution.

Let’s assess each teacher individually.


Participate, don’t reparticipate

I have to tell you a pet peeve of mine. It’s people who retweet all day long and never add anything of their own thoughts to my Twitter stream. I use this fun tool called Twit Cleaner and it happily allows me to find all of the people who only have retweets in their stream and unfollow them.

For those of you who don’t use Twitter the basic analogy is this. A retweeter is someone who demonstrates none of their own ideas but keeps repeating the ideas of the people around them. You can’t have a conversation with them because they don’t respond and you have no idea what they really think.

Please add your own thoughts to the stream. Create a blog and link to your entries, join the EduPLN and post resources there, or just start chatting away on Twitter with other people (or even yourself!) but please don’t post into my stream with your constant retweet spam. A retweet in my opinion counts as a thumbs-up to a great idea so the occasionally retweet is okay. Retweeting something which you really feel should reach a wider audience is fine too. Retweeting something to get your tweet count up? Pretty lame; you know who you are.



A different way to do parent-teacher interviews

We started a different way to do parent teacher interviews this year and upon reflection, I love it. Let me describe last year. We started with a very brief introduction to our DP and MYP programs, then sent the parents around on a wild night where they rushed through every single teacher in their schedule and got to hear our quick introduction to what our course is and then sent them off on their way without a single one of us getting to chat at all.

This year we did something totally different. We spent half an hour in the first session with the advisors and really went through a lot of detail about general expectations of the school. We took the time to listen to the parents’ concerns and questions. Next each teacher joined into groups based on their main specialty and the parents got the opportunity to walk around the school. I ended up in the Math and Science teacher room with some of my colleagues and we waited around. Parents then moved from room to room and chose which teachers they wanted to chat with. None of the conversations were terribly private so we discussed generalities and arranged appointments for more private conversations when we felt they were necessary.

Parents didn’t feel like they were rushed and teachers didn’t feel like they needed to give parents information that the parents could have just as easily read. The whole evening felt a lot more like a real opportunity to mix and mingle with parents, while still providing parents with the choice to visit specific teachers. It worked.

In a few weeks we are going to host our student led conferences for our MYP students. Right after those conferences we’ll send home letters to the parents where teachers will specifically request interviews with parents that we feel like we need to see. In other words, we’ll never have to sit down and have an unnecessary conversation with a parent in a typical parent-teacher interview night. 


How can you use sound in your classroom?

Here are some ideas for using sound in your classroom to help your students understand concepts through another of their senses.

In Math:

There’s a fun experiment you can do with students where you bounce a ball and they watch the ball bouncing and try and measure the height of the ball as it reaches the tops of its bounce. Graph the number of the bounce versus the height of the bounce and you have an example of exponential decay. Unfortunately the results you get from students tend to look like straight lines because of the enormous potential for error in measurement.

Here’s another way to collect the data. Set up a sound recorder in your classroom. I used my iPhone but a laptop with a Mic would work. Ideally anything that can record sound in a digital format should work. Now turn on the recorder and bounce the ball close enough to the recorder that it can pick up the sound of the ball bouncing but not so close it gets damaged. Stop the recording when the ball stops bouncing. Now you open up the audio recording with an audio editor, like Audacity for example, and take a look at the recorded audio. 

Audacity editing

(listen to the sound of this ball bouncing here)

You can see from the image above that the bounces are really obvious in the recording. If you click on each bounce Audacity happily reports it’s time position in the recording to a very high level of accuracy, and to determine the amount of time between bounces, you can just subtract the time positions of any two adjacent bounces. Graph the number of the bounce versus the time until the next bounce and you’ll still get a nice exponential decay function which was the whole point of the original experiment but now your experimental error is much smaller.

In English:

Want to provide all of your students with feedback about their essays but didn’t feel like you have the time? Annoyed that all they do is check the actual grade instead of your valuable feedback?

Why not record your feedback in audio instead of writing it down? You can talk much faster than you can write and you can put the numerical grade (if you feel like you need it) into the recording itself so your students will listen to your feedback to find out what their grade. You’ll be making your feedback more useful and faster to create.

In Moodle there is a plugin which is very useful for this called Nanogong. It allows you to embed audio recordings in any of the text fields which means you can add an audio recording when you are providing feedback for your student’s online assignments.

If you have students who struggle with the written word, have them speak aloud their ideas and record the audio. They can then transcribe what they have spoken and use it in their writing. There are some useful programs for doing the transcriptions, like the Dragon Speaking Naturally app for the iPhone. They could also call a Google Voice number and leave a voice message which will be transcribed for them. In both cases there will be lots of editing work to do after they have the audio transcribed.

In a Second Language:

Besides the obvious, listening to lots of the language in many different contexts (music, radio, talk shows, etc…) have your students record themselves speaking sentences and then listen to what they sound like. Have them compare the words they are saying to what the words should sound like. Rinse and repeat. Students can then practice their pronunciation on their own without as much direct feedback from the teacher.

It also worth noting here that an actual conversation with someone in that second language is possible (and probably more desirable) through programs like Skype. Check out Around the World with 80 schools as a good place to get started connecting your classroom to the rest of the world. You may also want to see the iEARN project for global connections.

In the Humanities:

You could have students listen to a historical speech. For example you could have students listen to the actual audio from Martin Luther King Jr’s famous "I have a Dream" speech. Students might recognize that when they listen to the entire speech that his message is slightly different than the version which is highly abridged. Have students create their own "historical" speeches that might have been from different famous figures from through out history or alternatively have kids act out historical figures in a podcast play.

Have students listen to folk music from around the world through the Folkways website. They could then take their own folk music and create their own recordings and share them with their peers. Through this medium they can learn part of what the differences are between people from around the world, but more importantly our similarities.

In Science:

Here’s an idea: have students record notes played on one of their musical instruments. Try and record every note from middle A to an octave higher. View the recorded notes in a tool known as an oscilloscope (try this Oscilloscope you can use on your Windows computer). Now students can actually measure the frequency of the sounds they are listening too and see a relationship between the music they like to listen to and play and that stuff about waves you were trying to teach them.

Want to teach students about the Doppler effect? How about a demonstration using a portable sound recorder, someone running around (with the recorder) and a loud sound maker of some sort, ideally something that makes a sustained pitch. Students will be able to hear the difference in the sounds as the person passes by the sound maker. This might be even better down with a video recording of the person moving timed to match the audio recording taken by the person.


Although most of these ideas involve some technology, I think that you can see that many of them can be replicated fairly easily. Want to give your students feedback about their essay? Talk to them in private. Want to connect your students to speakers of the second language they are learning? Invite them to your classroom. The point is to try and connect your students to what they are learning and to try and engage more of their senses.

Post your positive experiences about school here

NBC has a new section of their Education Nation website asking people to their negative experiences about schooling. This lacks journalistic integrity in my opinion. The typical person when faced with a bunch of negative stories will assume that there are many other negative stories just like the above. The effect of this collection of negative stories by NBC will be to demonize teachers and school administrators and portray all schools as failing when in fact most educators work extremely hard and the majority of schools are successful.

So I ask you to stand up to the NBC manipulation of the public and share your positive stories about school. Things you know would not have happened without the assistance of a kind teacher, or an excellent administrator. Share your stories of schools where the kids are excited to learn and where you have seen good things happen.

I’ll start the ball rolling.

I went to a medium sized public middle school in Courtenay, BC. One of the things that school had was an excellent arts and drama program. I was lucky enough to be part of the musical theatre course. All through my schooling I learned about how to perform in front of crowds, how to be part of a theatrical team, and how to project self-confidence. Without this training, I would not have the self-confidence that I do today, in fact I probably wouldn’t have become a teacher.

What’s your positive story?

What’s missing?

Bill Gates thinks that a video with a nameless person showing math concepts is the future of education. He’s wrong. Here’s why.

In that video there is something missing. Some major feature of learning that is completely missing from all 1800 of the videos up on the Khan Academy website.

Do you know what it is? Of course you do!

Kids! None of the videos has kids asking questions about what is happening in the video. You can pause the video, fast forward it, rewind it to re-watch the video, but you can’t ask it any questions. The ability to ask questions is a critical part of the learning process.

You can still use these videos as part of your classroom because your students can pause the video, bring you over, and say "hunh?" They can ask questions. Until the student can ask questions of the video, it will never replace a classroom teacher; the best it can do is support good instruction.

Differentiating in Math Class Using Online Videos

I told my colleagues about the Khan Academy last week. They thought the idea of being able to access all these resources was incredibly cool.

One of them today built his entire lesson around the Khan Academy videos. You see he has a class with a very wide range of abilities. Some of the students know nothing about exponents, some of them know a tonne already. So he found all of the Khan Academy videos that related to the rules of exponents, organized them in order of difficulty and content area, then shared his list with his students through Moodle. The idea is that the kids get to start with the curriculum that they need rather than the curriculum which comes first in the book. It’s a great way to turn one teacher into 15.

When the students finish their video and feel that they have absorbed enough information, they were instructed to come back to my colleague and ask any questions they had and find out what problems from the text would be best for them to do. Here’s where my colleague discovered a flaw. After about 15 minutes, which is the length of one video, he suddenly had 22 8th graders asking him for problems. Wooops. Now he’s setting up the problem exercises in advance. It will blow his mind when I show him that he can use something like to automatically give the students feedback on their problems as well…

Observations about the Pre-Internet generation

I’ve noticed some things about a few people I know in the Pre-Internet generation. Just sharing my thoughts here and wondering how we can help them. Note that these generalizations don’t apply to everyone in this generation, but almost never apply at all to anyone outside of it.

  • They often double click when they should single click
  • They single click when they should double click
  • They drag stuff around by accident because they forget to release the mouse before they move it again
  • They don’t scan the entire screen and look for instructions so they often have to repeat entering information on a form
  • They don’t keep track of multiple windows or tabs very easily
  • Each program looks completely different to them, they haven’t learned the commonalities of their programs
  • They find technology frustrating and slow, to them it is hardly ever reliable
  • They want to hide their lack of knowledge of technology
  • They generally don’t know the language of technology, icons, arrows, and other common notation is lost on them

Does this remind you of anyone you know? How can we help them? I can imagine it must be very frustrating to be in a technology rich world and not know how to use a lot of it, especially when it seems like every week there is something new you have to add to your repertoire of skills.