Year: 2012 (page 12 of 14)

March 20, 2012 / 9 Comments

We need social media etiquette

We need to develop social media etiquette. Some of the conversations I have seen on Twitter have been out of control rhetoric, other tweets have just contributed to the noise, and benefitted no one. During our discussion on how to make Twitter more accessible to new people, I tweeted some "rules" that if all followed, Twitter would be a lot more accessible and usable for everyone.

Of course, these rules are just my interpretation of what should be useful, and probably need to be reworked. Also, the idea for this comes from the email charter, which I strongly recommend you make an effort to implement for yourself.

The network is capable of only so much information. Don’t overload the network.
Be kind to each other, and assume that tweet did not convey the message intended.
Links are a way of sharing extra information in a conversation. Use them sparingly.
When you see a question asked, answer it, even if your answer is to redirect the questioner to another source of information.
The purpose of the social media is not to gain influence, it’s to communicate ideas. Don’t forget the social in social media!
Where reasonable, give attribution to ideas that you find & your sources of information.
Take some time to think about what you are tweeting. Is this contributing to the conversation?
It’s okay to disagree with someone, but do it respectfully. Don’t tweet what you wouldn’t say to someone’s face.
Be safe. Stop before you click on a link & think, does this link have a context which makes sense?
Stop making lists of the "best people" to follow on Twitter. This is completely subjective & exclusionary.

There are other "rules of Twitter etiquette" out there. Here is a page for Twitter etiquette that @jlubinsky found and here’s another article on Twitter etiquette shared by @PivotLearning. There are also other useful resources on social media etiquette here, here, and here, as shared by @erringreg

How would you edit this list? Is it necessary?

March 18, 2012 / 3 Comments

Intuition and research

There are a number of things which have been discovered over the years through research which are not entirely intuitive. In fact, many of the results that have been discovered are down-right odd.

If you pay people to perform simple, routine tasks, in general the more you pay the person, the better they perform. Oddly enough, if those tasks require even a bit of cognitive effort, extra pay reduces performance. What!? How does this apply to education? Well, first it seems that it would drive a nail into the coffin that we should give teachers merit pay (as opposed to just paying all teachers more) for improved student performance. It also suggests that other rewards, which are commonly used in education, may have the opposite of the intended effect; they may reduce performance.
If you tell children how to play with a toy, they are less likely to perform irrelevant actions with that toy; but they are also less likely to do anything novel with it, or discover anything beyond what you told them about the toy. One would think that if one knew how to use a toy effectively, you’d have a base of knowledge necessary to expand upon and to make new discoveries. It turns out; sometimes even a little bit of knowledge is too much.
In a pivotal study done in the 1980s, researcher Jean Lave sought to find out how successfully people applied math in their everyday lives. Her surprising answer is that people actually use mathematics reasonably reliably, at nearly 98% accuracy in the supermarket, for example. What is somewhat shocking is that when the very same people were given a pencil and paper test on the very same skills they had successfully solved in the supermarket, the percentage they got right dropped to 59%. The conclusion Jean Lave had was that the subjects were using strategies in the supermarket that they had developed themselves, but fell back into the strategies they had learned in school for the test.
What do you think would happen if you didn’t teach arithmetic at all to students? In a highly unethical study done in the 1930s, a group of students was given no arithmetic instruction at all until 6th grade. Instead, the students spent this time discussing things that came up in their lives, and some practice in measuring and counting. In 6th grade, the students were taught arithmetic. At the end of the 6th grade, this group of students (who came from the poorest parts of the district) exceeded their peers from the other schools in solving story problems, and had caught up in arithmetic. In other words, not teaching math for 5 years (and spending this time reasoning through discussion instead) improved their mathematical reasoning skills.
A longer work week does not necessarily lead to more productive employees. In fact, most often it reduces overall employee productivity. 40 hours a week seems about optimal (for maximizing productivity, if not morale). What are the implications of this research on education? Should we be looking at less time in school (or at least doing "work" like activities for students) rather than more?

What these studies show is that our intuitive sense of what may be true is often not true, or at least can be shown to be not true under certain circumstances. We must then shy away from relying entirely on our intution, especially when examining large-scale educational practices. We must do a better job in education in funding and supporting effective research in our schools. We also need to be less reactionary when it comes to approaches that don’t fit into our personal perspective on how certain things should be taught, and focus more on dialogue and research to satisfy our reactions.

March 16, 2012 / 8 Comments

Rethinking the standard school schedule

Race to Nowhere

I just read an interesting article on the Salon about how long work weeks produce lower quality work, and that it seems that about 40 hours a week is when the maximum productivity occurs. Of course if this applies to workers, then it presumably (or a similar number) applies to students as well.

So an obvious question is, how many hours are students in school?

In our school, students start school at 8:30am and are at school until 3:30pm with an hour for lunch. This means that they "work" about 6 hours each day*. If they have 2 hours of other "work" to do each day, then they would be working a productive 40 hour work. If they are working more than this, then their productivity drops and one would expect reduced gains for additional time worked, and tremendous drops in productivity after a few weeks of increased work load. What is often forgotten in these types of calculations though is all of the other work students do outside of school.

When students spend time doing adult-type work, like an after school job, or they participate in after school sports, or tutoring, or another school, they are adding onto the total amount of work they have done in a week. The most important work that they do, of course, is learning. This analogy between the 40 hour work week, and how many hours students "work’ at learning has an important caveat; 40 hours may be way too much "work" for students, especially younger ones.

You may notice at your own school that students productivity drops after a few weeks in school. In fact, I can remember this effect quite clearly as we talk about it nearly every year. According to the article, people can sustain slightly greater amount of effort for small periods of time, but each week of extended effort has an additional toll on productivity. So by this logic, the drop-off in student output that educators frequently notice may be due to the over-extension students have been through during the previous weeks.

A potential solution, proposed by a colleague of mine, is to take the month of August (or July) and expect students to come to school during this month, for 4 days a week. This would produce 16 – 18 additional days per year of school, which could be used to offset 16 – 18 long weekends during the rest of the school year. Students would have the same amount of over all time spent in school, but it would be more balanced through-out the year.

There is some support from parents for a change like this in education. The parents behind Race to Nowhere know about this issue intimately. They have been pushing for a shorter week for students for ages. Further, by reducing the length of the summer, students who do not participate in learning activities in the summer would be less likely to experience the ‘summer-time drop.’ Unfortunately, students who normally spend their summers doing highly engaging learning activities would lose some of this time. On the other hand, they would gain many more long weekends during which they could choose to enrich and extend themselves.

There are some organizations which are calling for an extended school day. Kipp Schools are a famous example of a school system where students spend much more time in school. The attempts from these organizations to extend the school day are misguided, at least if you believe the research on productivity versus hours worked. There is some research showing that the increased school year and increased school days at KIPP schools improve student results, but that research has been recently contested because KIPP schools tend to be more selective in their enrollment than the neighbouring schools.

We have to be careful to keep separate ‘seat time’ from productive learning time. Students who are more alert, more productive, and more engaged in what they are doing will learn more. Simply being in school longer, or working longer at school work, will not ensure that students learn more. We need to remember that the same principles that apply to our own well-being apply to students as well. There are philosophical reasons to be opposed to excessive amounts of work for students, it seems that there may also be some research to support these claims.

March 14, 2012 / 5 Comments

Copyright for Canadian Educators

I’ve created a brief presentation on copyright which simplifies (perhaps too much?) copyright for teachers. Please give me some feedback on this presentation before I use it with my colleagues. Note: These tips on copyright only apply to Canadian educators as copyright rules are specific to each country. For example, Canada has no "fair use" provision.

Update: This presentation needs to be updated with the recent changes to Canadian Copyright law. See Copyright Matters! for more accurate information.

March 13, 2012 / 0 Comments

Articles I’ve written on Math Education

Here is a list of some of the articles I’ve written on Math Education

On Mathematics education reform:

On the use of technology in mathematics education:

How does technology affect us?

I’m presenting this morning to our 5th grade students on technology. My objective is to get them thinking about how we define technology, and how in some cases, technology defines us.

February 23, 2012 / 5 Comments

Let them solve the problem

Arts week poster

When I came in this morning to school, the poster in the photo above had fallen down. I noticed it, and thought to myself, "I should fix that." I went and dropped off my stuff, and when I came back to the poster, one of our students was standing there staring at the poster. He said to me, "It looks like the poster came undone here," and he pointed to a spot on the back of the poster. "I’m going to fix it," he said.

"Do you need any help?" I responded.

"Nah, I can do it. Thanks anyway," he said.

Later that morning, the student said "It’s a bit crooked, but it’s up." "It doesn’t matter if it’s a bit crooked," I replied, "The most important thing is that it’s up."

I could have stepped in and solved this problem for my student, but then he wouldn’t have learned how to solve it himself. "Be less helpful," says Dan Meyer of the math class, but of course the same is true all over the place in education. The objective isn’t to show students how to solve problems, our objective is for students to learn how to solve problems. Sometimes our role is to stand back and let students solve problems for themselves. Will they always come back with the "perfect" solution? Probably not, but they will have learned more in the process.

Update:

Sign fallen down again

So it turns out the solution the student tried didn’t work. When I talked to him, he pointed out the flaw in his solution, and suggested a solution. In other words, the problem he solved gave him feedback directly as to whether or not his solution worked.

February 22, 2012 / 0 Comments

Exploring matrices

I introduced matrices to my students last week. Together, we worked out the algebra necessary to find the inverse of a 2 by 2 matrix, and developed the idea of the determinant of the matrix. The algebra was hard for my students, and we focused on looking for patterns. I showed students how a matrix can be applied to solving simultaneous equations, so they understood that there is some context for matrices. Next week, I intend to show some of the applications of matrices to game theory, and have students explore the consequences of this application.

Today, I talked about the inverse of a 3 by 3 matrix, which was easily found on a calculator. However, for good or for ill, students are expected to know how to find 3 by 3 matrix inverses "by hand" in preparation for their IB Math SL exam. So we needed a way to understand how the inverse of a 3 by 3 matrix is formed. I showed students that one can construct 2 by 2 matrices within the 3 by 3 matrix, and that the determinants of these 2 by 2 matrices "magically" appear in the inverse of the 3 by 3 matrix. The proof of this (for 11th grade students) is hard.

So instead of going through the proof, I decided that students should explore the relationships between the positions of the 2 by 2 embedded matrices, and where their determinants appear in the 3 by 3 matrix. I don’t myself have an intuitive sense of exactly where these determinants will show up, but I know there is a pattern, and that my students will find it.

What was fascinating to me is the different ways students represented the notation necessary to show these patterns.

Examples of student notation. Click to enlarge.

Each student came up with their own notation to represent the patterns they were finding. They realized (some of them with some guidance) that it was pretty critical to include the location of the 2 by 2 matrix in their notation, to make it easier to find patterns. The actual notation they use doesn’t matter to me, as if they do continue with matrices, they’ll learn the appropriate notation later. What was critical for me was that they could come to some understanding of how to find the inverse of a 3 by 3 matrix.

What I found most interesting about this activity is that there is room for exploration in learning matrices, which suggests to me that it is very likely that any mathematical topic has some opportunity for exploration.

February 21, 2012 / 13 Comments

What is the purpose of social media?

I’ve begun to question the use of social media. I am finding Twitter to still be a valuable tool for connecting with other educators, but over the past couple of years, I have noticed that the #edchat channel has become more and more cluttered with advertisements and links, and there appears to be less discussion occurring.

When Clifford Stoll suggested that computers had no place in education, he said:

“Every voice can be heard cheaply and instantly. The result? Every voice is heard. The cacophany more closely resembles citizens band radio, complete with handles, harrasment, and anonymous threats. When most everyone shouts, few listen.”

To be clear, I don’t agree with Clifford Stoll’s assessment of the use of computers in schools. Computers can be powerful tools for education. Are they always used for the most productive purposes? Definitely not, but they have that potential, provided we (as educational technology enthusiasts) provide appropriate support and guidance, and that the teachers using the technology are thoughtful in its use. However, Stoll’s observation that there is an awful lot of noise in the Internet is totally true.

Neil Postman had the following to say of our information age:

But what started out as a liberating stream has turned into a deluge of chaos. If I may take my own country as an example, here is what we are faced with: In America, there are 260,000 billboards; 11,520 newspapers; 11,556 periodicals; 27,000 video outlets for renting tapes; 362 million TV sets; and over 400 million radios. There are 40,000 new book titles published every year (300,000 world-wide) and every day in America 41 million photographs are taken, and just for the record, over 60 billion pieces of advertising junk mail come into our mail boxes every year. Everything from telegraphy and photography in the 19th century to the silicon chip in the twentieth has amplified the din of information, until matters have reached such proportions today that for the average person, information no longer has any relation to the solution of problems.

When we post endless links after each other in Twitter (in what seems to be an effort to increase our own online profile?) and forget the social aspect of social media, we contribute to the noise. I can remember going through a phase myself where I was using scheduled tweets so that I could be posting all day and night, and fortunately, it did not take me too long to see the error of my ways; I too was contributing to the noise of the Internet.

While the regular #edchat discussion was happening today, I noticed that the stream was littered with off-topic links, mostly by well meaning people looking for some exposure for their product, service, or exciting news from their part of the world. These posts are inevitable as we want to share what we are doing, but we also need to remind ourselves of purpose of social media; it’s not about attention, it’s about communication and collaboration.

There is some room for sharing resources and links, but we need to be mindful of what the ratio of noise to conversation is at, and limit ourselves to sharing only that which is most valuable, and ideally share it outside of times people are using a particular hashtag to have a discussion. Obviously a link can extend the conversation, and where possible, we should post links which extend or challenge our thinking. We need to post a few less links, and have more discussion.

Howard Rheingold says, “If we decided that community came first, how would we use our tools differently?” The purpose of social media is to connect to other people. Let’s remember that when we post, please.

February 20, 2012 / 3 Comments

Taking advantage of the mobile nature of a mobile device

An iPhone (or any other smart phone / tablet) is a mobile computing device. Applications that are designed for a mobile computing device should take advantage of the mobile nature of the device. Too many educational (cr)apps are designed simply as better flash card systems. They rarely take advantage of the most important affordances of the mobile devices they are on, and are easily replicated without using the technology.

Not only can you take pictures and videos of the world wherever you are able to travel, with a little bit of hardware, you can turn your iPhone into a mobile microscope, allowing you to view the microscopic world, which combines the mobile nature of the smart phone with its computing power. Your GPS in the iPhone allows you to participate in Geocaching.

Have an idea on the go? Use your smart phone to record a note about the idea, or a create a podcast on the fly. You can use the Internet capability of your smart phone to collaboratively keep track of data (or anecdotal observations) when out in the field. Heading out bird watching? Keep track of your GPS, a photo of the bird, and any other anecdotal evidence you need with that one device in your pocket.

The point is, try and find the educational uses of Smart phones which actually take full advantage of the capabilities of the phone, rather than limiting kids to using the phone as an extremely small computer screen.