Education ∪ Math ∪ Technology

Month: July 2011 (page 2 of 3)

Recording Google+ Hangouts

Today, thanks to Aaron Mueller, Dave Zirk, Devin Page, Greg MacCollum, and Skip Via I had a chance to test recording of Google+ Hangouts. I have Camtasia Studio 7, which allows for screen recordings and has the option to record both system audio and the microphone. There are lots of other options out there for recording your screen, many of them free, but I don’t know which of them allows for recording of system sound, which is critical for making this recording work.




Aaron, Dave, and I discussed the Tour de France, and noticed that even in a highly competitive environment like the Tour, people collaborate extensively, at least within their team.

The audio of the recording is fine, except for a few places. The next time I record a Google+ hang out, I’m going to make sure I’m wearing headphones, which should handle the audio issues, which seem to be caused by a slight delay between the microphone being fed by the system speakers, and the system sound itself. However, the small audio glitches aside, Camtasia Studio seems like a highly effective way (if expensive) way to record Google+ hangouts.

If someone knows of a cheaper way to record system audio directly that is as easy to use, I’m all ears. I’d love it if I could find easy ways for students to record Google+ hangouts. I’m not tied to this particular technology itself, but if it works and isn’t too complicated, use it.

(Disclaimer: TechSmith, makers of Camtasia Studio 7, did not pay me for this post. I just like their product.)

Some people actually like mathematics

I just posted this over on Joanne Jacob’s blog in response to some of the comments from her readers.

I recommend reading Keith Devlin’s "The Math Instinct." He makes an interesting argument, which he supports with research, that the math people learn in schools is virtually never used outside of schools, except by a very small percentage of people.

First, he shares research which shows that people have a high rate of accuracy when solving mathematical problems using self-made strategies in such contexts as the supermarket, etc… He then points out that the longer people have been out of school, the MORE successful their strategies are. In other words, remembering the school math strategies for solving problems is a hindrance when trying to solve real life math problems. Further, he points out that only a tiny percentage of people are able to use the school math strategies (which are highly efficient in many ways) to solve problems.

The problem, according to him, is one of an inability to transfer knowledge gained in one domain, and in one style of learning, to another domain in our lives. In other words, knowledge gained about algorithms in schools, regardless of the curriculum used, is too far removed from the actual applications of the math.

So it seems to me that this means that it doesn’t matter if the kids memorize some algorithms as a kid, that this should not be the primary purpose of mathematics education.

Another interesting point to make is that mathematicians, engineers, and other professionals who use mathematics are often not the best at arithmetic, but excel in problem solving and applying math they’ve learned to different contexts. They become a profession that uses mathematics because they are able to use it creatively.

I’m really sick to death of everyone worrying about whether or not kids know how to multiply 6 by 4 and worried that no one seems to be concerned about whether or not kids know WHY we would want to multiply 6 by 4, and HOW this is useful in their actual lives. 

If you don’t think that we have a serious problem with numeracy (the ability to think mathematically and apply mathematics to different contexts), see this map of numeracy levels (including ALL adults aged 16 and older, so like all of you who learned mathematics the old way):

It paints a pretty scary picture of the problems in numeracy across Canada, in one of the best education systems in the world.

Maybe if we spent a lot more time doing engaging mathematics and applying what the kids learn in context, we might actually have a generation of people who USE mathematics, rather than a generation that complains about how awful math was when they grew up, and how horrible they were at it, but then asks their kids to do the same thing they did.

Some people actually LIKE mathematics, believe it or not.

 It’s a bit strong, but so were the comments on her blog.

Second BCed chat coming up July 25th at 7pm

Chris Wejr ( @MrWejr )  and I polled the #BCed chat channel on Twitter and found out that Monday nights work best for most people. So we are going to try to hold either weekly or biweekly chats about education during the year.

We plan on having our first chat on Monday, July 25th at 7pm. There seem to be enough of us still active on the #BCed Twitter channel during the summer time to make a chat worthwhile. Our first topic, as chosen by people who submitted responses to our survey is: "What should personalized learning look like in our schools?"

Please join us, and if you can invite a colleague who is not on Twitter to join in from the sidelines.

Trial, error and the God complex

Tim Harford has some great points here. I recommend watching his video.

"I will admit that [the process of using trial and error to solve problems] is obvious when schools start teaching children problems which don’t have a correct answer, stop giving them lists of questions, every single one of which has an answer, and there’s an authority figure in the corner behind the teacher’s desk who knows all the answers, and if you can’t find the answers, you must be lazy or stupid…When a politician stands up campaigning for elected office saying, ‘I want to fix our health system, I want to fix our education system, I have no idea how to do it. I have half a dozen ideas, we are going to test them out. They’ll probably all fail, then we’ll test some other ideas out, and we’ll find some that work, we’ll build on those, and we’ll get rid of the ones that don’t." ~ Tim Harford

Imagine we used an iterative process to solve the our problems in education. Our current system assumes that there are people who know the best solution already, and that all we need to do is implement it everywhere. Obviously this isn’t true. Our education system is far to complex to be something that any one person can know how to solve, no matter how smart they are. 

Imagine we had a public policy that was designed to promote innovation in education. Imagine people were expected to experiment more, and share their results. Imagine we had the mindset that no one could solve the problems in education alone, and that no single theory is the best theory. Imagine we found actual solutions to the education system, even if we didn’t complete understand the solutions, rather than changing policy on 4 or 8 year election cycles with little positive effect on the system.

That would be refreshing.

Assessment during professional development



Image credit: uconnlibrariesmagic


If you are running a professional development session for teachers, and you recognize that teachers are learners, how are you assessing their learning? Are you embedding formative assessment within your workshop? Are you providing an option for summative assessment of the learning, either at the end of the workshop, or in a follow-up session?

While I don’t think you should be giving grades to teachers for workshops, you do need to provide some way for your participants to receive feedback on what they’ve learned. Feedback in some form while learning is critical. Otherwise, how do you know your participants are learning anything? 

Toolkit model of math instruction

(exec talking to IT person) Apparently our open API is empowering our customers with unprecedented control over their destinies. So please shut it down.

Image credit: Rob Cottingham

I’ve been doing some programming recently for a friend of mine, and while programming I made a realization. Every time I needed to remember how to do a particular algorithm, or use a tool with which I’m less familiar, I look it up online (or I ask someone for help). In fact, I spend a lot of time as a programmer looking up things called APIs and core functions in the programming language I’m using. The basic structure is very solid at this stage, since I’ve been using it over and over again, but there are still lots of things I look up frequently.

I wondered to myself, what would this look like in the mathematics classroom?

It’s not ridiculous to compare programming and mathematics. Programming and mathematics have a tonne in common, in fact much of programming a computer itself is deeply rooted in mathematics. They are both domains of knowledge which allow for high levels of creativity (provided you are given the freedom to be creative) and rely on an ability to construct algorithms and perform computations. Being good at constructing algorithms is useful, but not sufficient, in both domains for creating complexity and solving difficult problems. It takes more than just knowing your stuff to be good at these two areas of knowledge.

What I imagine would happen, were one to follow this model, is that students would have a resource available to them, whenever they needed it, which had very simple and short explanations of each mathematical computation in their toolkit. Whenever they ran into a computation, and forgot how to do it, they could look it up. Perhaps this toolkit (or mathematical API reference) would be in paper form, perhaps it could be in digital form. Whatever it is, it should be easy to search through. In digital form, it should include short (2 minutes ideally) video snippets showing how to do the computations. Perhaps it could even be searchable by entering an example of the computation itself. Students could add to their personal toolkit as they discovered or encountered mathematical techniques that they found useful, which is very similar to the process programmers go through as they build a code library.

Over time as the students used the reference material, the computations that students used often would be things they would naturally memorize. The less frequent computations might be things they looked up a lot. Students could spend more time working on highly engaging and personalized problems or activities, and a bit less time memorizing all of the computations. Most importantly, they would spend a lot more time practicing an important skill, recognizing what type of computation is useful in a given situation, and being able to relearn that computation as needed.

In Keith Devlin’s book, "The Math Instinct" he makes a lot of interesting points about mathematical ability. One thing he points out is that many people use mathematical strategies successfully in life, for example to do their shopping, but almost no one uses the highly efficient "school math" algorithms they learned. The problem is one of transfer of knowledge. People just generally don’t know how to transfer stuff they’ve learned in school to their lives.

The hope is that these types of API references for mathematics would be something so useful, kids would keep them year after year, and potentially use them in their lives. We already give students formula sheets for many exams, this is just one step further.

Note here that I have a premise which I should make explicit. It is not the learning of algorithms or specific computations which is mathematics, it is the learning of how to use these algorithms and apply them to problems in creative ways, and then extend them as necessary which in my mind is what defines mathematics.

New meme: If we taught _____ like we teach math, _____

There is a new meme out there, suggested by @r_w_wright. "If we taught _____ like we teach math, kids would _____."

Here are some examples people have posted so far.

If we taught construction like we teach math, kids would bang nails into boards but never actually build anything. ~ @davidwees

I’ve frequently said similar about statistics: "We show kids the screwdriver, but never show them a screw." ~ @heyprofbow

If we taught driver’s ed like we teach math, students would feel no shame in announcing "I can’t drive" ~ @datadiva

…and as we integrate technology, let’s be sure kids aren’t just banging virtual nails into virtual boards ~ @ChrisHunter36

If we taught English the way we teach Math, students would be able to punctuate a sentence but have no appreciation of literature. ~ @ChrisHunter36

What if we taught math like Umbridge teaches defense against the dark arts? Oh wait, we do. ~ @rjallain

If we taught mathematics the way we taught music, everyone over 11 would have 1:1 tuition outside school… oh wait… ~ @ColinTGraham

If we taught teaching the way we teach math, then most teachers would only teach the way they were taught…oh wait…  ~ @mathhombre

If we taught science the way we teach math, then people would think it’s only for the smart kids…oh wait… ~ @mathhombre

If we taught music the way we teach math, then most people would not be able to play an instrument…oh wait…  ~ @mathhombre..

If we taught videogames… wait, we don’t teach videogames? Why do so many people play? ~ @mathhombre



Want to add your own examples? Add them either here as comments, blog about them, or post them to Twitter with the #ifwetaught hashtag.

If we taught carpentry like we teach math

Your instructor brings you a board. Before you can use the board and play with it yourself, she tells you how to properly line it up on your table. Next, you practice this over and over again with everyone in your class practicing the same number of times regardless of when they master the skill. When you line it up in creative or fun ways, you get scolded, and sometimes even have your board taken away from you. You look around the room and notice that everyone’s boards all look the same.

Finally, after you are considered to have mastered the skill of lining a board up, your instructor takes your board away and gives you a nail. She shows you for 10 minutes all of the various ways you can line up a nail, but never shows you how this relates to the board, or any other possible tools. You want a chance to practice lining up the nail properly, but your instructor says that time is up, and assigns it for homework, and takes away the nail. "You’ll have to find your own nail to do this for homework," she says. You wonder if that is fair for the students who don’t have nails at home.

The next day, your instructor checks to see that all of you have practiced lining up the nail. She then gives you a chance to practice with the nail for a few minutes, before she again takes away the nail and gives you a hammer. You spend some time learning about the history of the hammer, and finally you learn some of the possible uses of the hammer. You ask if you can play with the hammer, but your teacher says, "That’s much too dangerous for you now, you’ll learn more about hammers when you are older, and then you can use them."

You never get a chance to see how the board, the nail, and the hammer relate to each other before the unit finishes. You don’t really understand how to use a board, and you’ve forgotten how a nail works by the time the test is given and so you fail the final assessment. You want a chance to practice some more with these skills your teacher says are "vitally important" but she moves onto another unit.

"Okay class, in our next unit we are going to learn about sanding wood. Everyone take out their boards and practice lining them up again…"

At no point in your learning of carpentry do you ever find out why people might want to use carpentry, how beautiful some works of carpentry look, or how to put it all together and make your own buildings.


You might think that this would be a ridiculous way to teach, but this is exactly how we teach mathematics today. Each unit is separated from one another and the connections between the units, and often the lessons, are virtually never taught. Students almost never have the opportunity to play with mathematics, and never get a chance to use some mathematics once they have mastered it. If we even connect mathematics to the real world, we do it in arbitrary and often nonsensical ways. We teach mathematics as a bunch of discrete tools and not as a holistic study of patterns and our world. In fact, we don’t even really have a consensus as to what mathematics actually is!

It’s no wonder kids usually hate mathematics. They say, "Math makes no sense," and they are right.