Education ∪ Math ∪ Technology

Month: April 2011 (page 2 of 3)

Math teachers learning about multimedia

During the Digital Learning conference this year, I ran a workshop on "Multimedia in the Mathematics Classroom" (warning large file) which was a huge hit. I started by giving a presenting giving answers to why one would want to use multimedia in math, what does it look like, and what tools I use to actually construct the multimedia with students.

I started the second part of the workshop and gave the participants a chance to escape if they did not feel like participating. I handed out Flip cameras, and gave the very lose instructions, "Create a math video word problem." Some people left the session right away, but about 20 people stayed and worked on videos, while I circulated around the room and helped trouble-shoot.

Here are three of the videos created by the participants in about 40 minutes. A fourth video was created by another group but due to technical issues, we just shared it during the session.

(Note: If you are in one of these videos, and uncomfortable being shared online, let me know via the contact form, and I’ll take down the video.)


What has changed?

In "A School Master for a Great City", Angelo Patri writes:

I realised then that the child must move and not sit still : that he must make mistakes and not merely repeat perfect forms: that he must be himself and not a miniature reproduction of the teacher. The sacredness of the child’s individuality must be the moving passion of the teacher.

Angelo could be writing this material today, in response to the current education reform movement. He’s not, he wrote this in 1917 in response to what was his reform movement in education during his time. Alec Couros recommended that I read this book, making the observation at the time that education never seems to get anywhere because each generation forgets the lessons of the previous generation. We keep going through cycles of reform based on "traditional methods" and reform based on "progressive methods."

Angelo Patri was attempting to reform his own practices, and struggled under one principal, but then worked for another principal who was much more progressive, and gave him this advice:

You must not think too much of arithmetic, and rules and dates and examinations, for these are not teaching; the children don’t grow because of them. They grow because of their contact with you, the best that you know and feel.

Why won’t we heed this advice, given nearly a hundred years ago? What makes us repeat the mistakes of the past over and over again? As Einstein said, "Insanity: doing the same thing over and over again, and expecting different results."


Edcamp Vancouver – “The Best Professional Development of My Life”

When I heard Gino Bondi (@gmbondi) and Tammy Dewar (@teachingtammy) indicate that they thought Edcamp Vancouver was the best professional development session they’ve attended, and the most engaged they’ve been in a professional development session, I knew we had hit a homerun.

I think the key to our success came from three areas. First, participants felt they had complete ownership of the professional development process today, second, the group of people we brought together was amazing, and third, the format of the presentations were exactly like the conversations we were hoping would develop.

Ownership is key because it helps participants feel motivated to attend the session, and be more willing to set aside their fear of the unknown. There is some risk in attending a professional development session like Edcamp, because the participatory nature means that some of your ideas about how education works might be challenged. At a minimum, you can only set aside your fear and be open to learning in such an environment if you feel like you have chosen your path.

Attendees had ownership of their experience at Edcamp Vancouver in a couple of ways. Most importantly, they chose whether or not they attended the conference at all. I heard many times during the day, "No one forced us to come today. We came because we chose to come." As I mentioned half-jokingly in our session on professional development, "I’m not going to grade you, and I’m not going to record your participation for your teacher certification." The second and important piece of ownership attendees had was the ability to choose which sessions they attended.

We also had an amazing group of people attend today. Stephen Hurley (@stephen_hurley) travelled from Ontario, Ron King (@mthman) travelled from Washington State, and Tom Schimmer (@tomschimmer) came from Penticton, BC. We had people from all over the Greater Vancouver area, which in itself is interesting because of the limited opportunities to cross-pollinate ideas between districts in British Columbia (most professional development is organized either at the school or district level). People who attended were passionate about education, and interested in both sharing what they know, and learning from each other.

The presentation format itself was I think the most important reason our unconference worked. Here’s a diagram to try and explain the primary difference between a traditional conference, and an unconference.

We limited the opening presentation to 15 to 20 minutes, and then we had a facilitated discussion between participants for the remainder of the session time. Every session I went to had deep conversations, had people who brought up points of contention and disagreement (respectively) and had many, many people participate in the discussion. Every session  I went to went overtime because people weren’t yet ready to finish their discussions.

At the end of the day, the feedback we got from people was positive. Although we had some small issues that came up during the day, nothing failed completely, we were able to work around every problem that came up. I’ll never use a random number generator to hand out prizes again, for example. We’ll find a faster way to choose prizes for participants. 

So success today, and we’ll see what happens to the Edcamp model for professional development in British Columbia, but my gut instinct is, it’s here to stay.

The Case Against 21st Century Schools

Paul W Bennett, a former Headmaster of the Halifax Grammar school, and director of Schoolhouse Consulting, has a pretty serious critique of 21st century learning. You can read his argument here.

It’s pretty clear that Mr. Bennett has done very little research on the topic of 21st century learning and is lumping all activities and people who do these activities into the same group. I’ve responded to his critique (which has to be moderated and so will not show up on his article any time soon) and will share my critique of his critique here:

Your chief complaints with the push toward 21st century learning seem to be with:

1.  The assumption that more technology is necessarily a good thing in education.

2.  That our education system is discarding that from its heritage which is good.

I am going to agree with you on the first of these complaints. There is lots of technology being pushed in schools which has no business being there.  More technology does definitely not mean better teaching or learning is going on. To ignore technology completely in schools though is foolish. Pencils, paper, overheard projectors, photocopiers, all of these were once outlandish and new fangled technologies that eventually got adopted by schools. Computers are nothing new in this respect.

On the second complaint though, we disagree intensely. Heritage is never a good enough reason to keep a system intact. Our current education system was designed after the Prussian model of strict conformity and indoctrination of the working class to accept their lot in life, to be industrialized workers in a factory.

Where are the factories that we need to prepare our populace for? They are almost all gone, sent overseas. The vast majority of our populace will not work at jobs which require the kind of numbing of self that the industrialized age required. Instead, they will likely work at jobs which require them to use their creative abilities and ability to collaborate with each other.

Why are you fixated on teaching content over skills? Some content is incredibly useful, and needs to be in place to give context to the world. However, much content is radically transforming. How many planets are there orbiting our sun now? What elements are necessary for the formation of life? Both of the answers to these questions have changed in the last 3 years, but most sources of content still contain the incorrect answers 9 and "carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur" to the previous question.

If you do not have the ability to learn and process new information yourself (ie. you have the SKILL of learning new things independently) then you will never keep up with the changes that occur naturally (and more frequently) in our knowledge base.

Furthermore, I would like to point out that these three issues: "soft student-centred pedagogy, classroom info-tainment, and nurturing the self-esteem of students" are not necessarily all nicely packaged up together as you suggest, and to assume that they are necessarily intertwined is illogical.

I would like to make it clear that you do not speak for all independent educators. We have been teaching the International Baccalaureate PYP, MYP, and DP for a few years now in our small independent school, which are all based on "soft" student centred approach to education, and have a history of 40 years behind them. Oh, and they are favoured by most Canadian Universities, as they produce kids who are successful at university.

In many ways, Mr. Bennett’s critique is quite insulting, as he somehow assumes that we are all marching quite blindly forward without consideration to the path we are on. He also makes the very strange assumption that a historical adherence to what we did in the past in education is better than looking at making changes in education to keep current with a very rapidly changing world. If we continued to teach like the "good old days" then we’d still be beating kids with wooden paddles and chanting out multiplication tables in unison, to help prepare our kids for the drudgery of the factories.


Make electrical circuits… out of play dough

This is an awesome idea, and I’m going to try it with my son. It certainly makes making complicated circuits much easier, and much safer. As an added bonus, you also get to easily talk about how topology (mathematics of shapes) affects a circuit (or doesn’t affect it).

Most livable city

We had Daanish Ali, the producer of the video below, come to our school and share his film with us (embedded below). I strongly recommend that if you live in an urban centre, you should watch this video. While it talks about water issues in the downtown East Side of Vancouver, I’m sure that similar issues exist in every major city in the world.

It is a great starting place for a discussion about urban water use, and very accessible for your students. Our kids finished watching the video and had some great questions.

Most Livable City from Pull Focus Films on Vimeo.

Free tools for math education

Here are some tools which I’ve either used (or explored) for mathematics education. They aren’t all open source, but they are all extremely useful, and they are all free to use (free as in free beer, some of them are also free as in free speech).



Geogebra image

This program lets you explore algebra and geometry, much like it’s proprietary cousin, Geometer’s Sketchpad. Having used both, I actually prefer Geogebra because I find it to be more flexible and easier to use. It will run on many different platforms including Windows, Mac, Linux, Android, and iOS.


Mathematics Visualization Toolkit

MVT screenshot

The Mathematics Visualization Toolkit is exactly that, a program which lets you visualize mathematics. You can use it to build complex visualizations, or you can use the visualizations which are already included (which are awesome by themselves). You can either use the web start version of the toolkit, or download an offline installer. 



Scratch screen-shot

Scratch is an excellent program for learning programming but also mathematics like variables, sequences, Cartesian coordinates, and other useful mathematical concepts. Developed at MIT, it is a free download and includes a strong user community to seek help, and see what else can be done with the program.



Netlogo screen-shot

Netlogo is “a multi-agent programming modelling environment” (According to the Netlogo website). It comes with hundreds of models for all areas of science and mathematics preprogrammed. It is a free download and will work on any computer which has Java 5 or later installed.




Audacity is an open source audio editor and recorder. One example use in mathematics is to record a bouncing ball, and use the visual data from audacities recording to turn this into a graph of bounce versus time between bounces. You can also use it so students can record 60 second podcasts explaining some aspect of mathematics.




Calculize is a free (currently) web app which lets students perform mathematical computations using a reasonably simple programming language. 


Wolfram Alpha 

Wolfram Alpha 

Wolfram Alpha is a computational engine built on top of the Mathematica architecture. It is amazingly powerful, and turns some homework assignments into a breeze. Recommendation: change your homework assignments, or do away with them all together.



Desmos screenshot

This is a free online graphing calculator. It emulates a lot of the functionality of a typical graphing calculator but with a much easier to follow user interface and without much of the non-graphing functionality of a graphing calculator. It is easy to create graphs, and then share those graphs with other people. It is also currently in development, so it is still improving over time with new features being added every couple of months.




This Logo emulator lets students play with the classic programming environment Logo, built for kids by Seymour Papert and his colleagues at MIT, all online. It requires Java, but should run on most computers (sorry, no iPads…).


Google Earth

Google Earth

Google Earth is free (but proprietary) software that allows students to explore the world in 3d. One could use it for GIS applications, or even to explore the relationship between our 2d mapping system (longitude/latitude) and 3d space.


Google Sketchup 

Google Sketchup

Google Sketchup (another free, but proprietary program) that allows students to create highly complex (or very simple, if they prefer) models. I’ve used it to have students construct their “ideal” school, and then from this model, they calculate the cost to build their school. 




Screenr is a free (for up to 5 minute recordings) screen-casting (think record your screen as a video) software. Some possible uses of it are for students to use it to create video tutorials, record their process of solving a problem, or create their own video word problems. Another alternative for screen-casting is Jing, but it publishes to a format which is harder to share in the free version.




Endlos is an open source fractal generator which I’ve found runs very fast. It runs in Java, so it should run on any computer capable of supporting Java. The ability to experiment with, and explore fractals is a very interesting thing for students to do, but very tedious to do by hand…


The Number Race 

The Number Race

The Number Race is an open source program intended to help students who have dyscalculia develop their number sense. It has many levels of difficulty, and runs in Java, which means it should run on a wide variety of computers.


Code Cogs equation editor

Code Cogs online equation editor

This free to use online equation editor could be a nice way for students (and teachers potentially) to construct equation images for use in a website.




Eigenmath is an open source program for symbolic manipulation in math. It runs either in Windows or on a Mac. Some examples of what it can do are shown above.


Peanut math programs

Peanut Math programs

These 9 free programs cover a wide range of different types of mathematics. Above is the popular statistics calculation and visualization program included in the package.




Yacas (Yet Another Computer Algebra System) is a command line program which allows for the symbolic manipulation and calculation of mathematical expressions. One thing I like about it is that it calculated 600! in a fraction of a second, so it is very fast (an aside, ever wondered what 6000! factorial is?)


Free CAS programs


Update: Just found an open source implementation of LOGO (as described in Seymour Papert’s Mindstorms) here:


Other free programs which I have used either for constructing mathematical diagrams/simulations or with students in some way include:

The Gimp, Programmer’s Notepad, Flex Builder (free with an education license), Open Simulator, VLC PLayer,
Wolfram Demonstrations (requires a free browser plugin), and Project Euler.

You might find these programs as useful alternatives to the “free apps” which “help” students memorize formulas & algorithms. For an enormous list of other free programs see this helpful list.


What other free programs for mathematics education do you use with or for your students?

How to build an apathetic student body

Here are some of the ways you can ensure your student body is apathetic.

  1. Ignore student voices in important decisions in your schools.
  2. Put up work on the walls students have done for teachers instead of student messages.
  3. Ask for input from students, but make the process nearly impossible or highly exclusive.
  4. Decide that some students have a voice (perhaps because they have a good GPA) but that others don’t.
  5. Blame the students (or their parents) when they are having difficulty learning your course material.
  6. Require students to learn stuff about which they have either no, or limited, choices.

If you watch the video below from TEDxToronto, you’ll see that these very practices are at play in our political spectrum as well.

Space in the classroom

I watched this video a while ago (recommend watching it, it’s amazing) and was amazed at how you could find spaces in the home where each word was learned. Today I wondered, what would a similar analysis of our classrooms show?

Could you do an analysis to find out where ideas were first learned? Would it vary from classroom to classroom? Could you tell the difference between a classroom based on social constructivism, and another based on behaviourism? How much does the use of our space matter in learning? Would you even be able to assess the learning of a concept in some classrooms using video analysis? 

This is just a thought experiment. I don’t have any answers to the questions I’ve posed, but I am curious…

Exploring algebraic complexity

Here is an idea I am exploring.

I’d like some feedback on this idea. If anyone can point me at research already done in this area, that would be appreciated. My objective is to use this to justify the use of technology in mathematics as a way of reducing algorithmic complexity so that deeper concepts can be more readily understood.