Education ∪ Math ∪ Technology

Month: August 2011 (page 2 of 4)

Ineffective professional development

I tweeted out the following yesterday during the #edchat discussion. So far 72 people have retweeted it (4 more since I took that screen-shot).

Ineffective professional development


Every teacher is very likely to have been part of ineffective professional development at some point in their career, either as the organizer, the presenter, or the recipient of the professional development. Bad professional development, while fortunately not the norm, is very common.

I’ve been in professional development sessions were totally inappropriate for me as a math teacher, and sessions where I already knew everything that was being presented. I’ve presented sessions where I had participants literally falling asleep (although not recently!) and I’ve fallen asleep (nearly) in a presentation. I attended virtually the same algebra tiles session at least 3 times while working in NYC.

There are a few reasons I can think of why this happens.

  • The professional development content is inappropriate for teachers because it is not at related to their practice.
  • There is either expertise or a lack of expertise assumed of the participants by the presenter when presenting, which means the presentation is not developmentally appropriate.
  • The style of the professional development doesn’t meet the teachers’ learning needs.
  • The teachers have been coerced or forced into the professional development.
  • The presenter does not develop a positive relationship with the teachers.
  • There is little opportunity to interact with the material and discuss the ideas being presented.
  • There is little to no follow up after the session.
  • Much professional development lacks feedback for the teachers as to whether they have learned anything.
  • The teachers in the session have personal problems or concerns which interfere with their ability to learn during the professional development.

(Do these reasons remind you of the reasons why students sometimes struggle with school?)

What can we do to ensure that we develop and participate in meaningful professional development? What can we do to convert professional development into professional learning?

Math in the real world: Roller coasters

This is another post in a series I’m doing on math in the real world.


When my son and I were on the roller coaster, I was again in awe about how quickly even a small roller coaster like this travels, and how it doesn’t drive right off the tracks.

Roller coasters have to be constructed fairly carefully, and follow some mathematical rules in their construction. They need to first be concerned about how to make the roller coaster safe. They need to calculate exactly how fast it will travel through the loops and turns, and how much of an angle they will need to prevent the roller coaster from taking a dive during those turns. They need to watch out that they don’t cause the participants of the roller coaster to pass out during a turn as they experience additional forces on their bodies!

The various costs associated with a roller coaster need to be calculated as well. There’s the cost to build, maintain, and operate the roller coaster. There’s an additional cost to pay for insurance for the roller coaster, which means an actuary needs to examine the probability of a problem occurring for any given roller coaster. The operator of the roller coaster needs to determine, given the cost to operate the roller coaster, etc… what they should charge to make a return on their investment, and attempt to maximize their profits.

While you could use a roller coaster simulator to explore some of this math, it’s a lot more fun to experience it in person…

Google’s Pierre de Fermat Doodle

 Google Doodle

Pierre de Fermat was a mathematician in the 17th century who often doodled and wrote down mathematical ideas in the margins of his notebooks. Once he wrote down the theorem that bears his name, Fermat’s Last Theorem, shown in the Google Doodle above.

The doodle itself has a flaw I wish to point out. You see, Fermat never wrote down his theorem on a chalkboard. He couldn’t have since a chalkboard wasn’t invented until about 200 years after he had his insight and wrote down his theorem. He wrote his theorem in a notebook.

The reason a chalkboard is depicted in the doodle is that mathematics today is seen as an activity done on a chalkboard, probably by a professor or a teacher, and not something that students do.

I’d like to change that.

Edcamps happening in Canada next school year

 So far we have the following Edcamps planned in Canada for next year.

If you know of another Edcamp happening in Canada let me know. If you want to plan an Edcamp yourself, I recommend reading Mary Beth Hertz’s excellent description of what an Edcamp is, and how to plan it here. All you really need to plan an Edcamp is a small team of dedicated professionals, and someone willing to provide some space.

Share what you do on the first day of school

Heidi Siwak and I were chatting, and she pointed out that, quite often, beginning teachers don’t know what the first day of school looks like. When I did my teaching degree, we talked about the rituals teachers use on the first day of school, but never got to see them actually practices. By the time we observed any classrooms, the rituals and procedures of the classroom had been firmly established.

I suggested that we should all share what do on the first day of school and then provide these resources to new teachers. There are a number of ways we can share these ideas.

  • We can blog about how we start school on the first day.
  • We can video tape ourselves during our first day (please edit it down to 5 minutes) and share it.
  • You can just list ideas of how to start the first day of school on Twitter.
  • You can share your ideas in any other ways you want.

To share links to these first day of school resources on Twitter, Heidi has suggested we use the hashtag #newteacher1styear. I’d also recommend cross-posting your resources to #ntchat and #edchat.

Update: In discussion on Twitter, Jana Scott Linday thought of expanding this project to the first year. Lisa Dabbs is setting up has set up a YouTube account to host the videos, and we will be continuing discussions on how we can share ideas for the first year of teaching.

If someone has already started a similar project, please let me know… 


Calculators vs the Abacus

Michael Doyle, a science teacher, has posted a critique of calculator use in math class on his blog.

My response:

See this is interesting, because I have a strong number sense and I never grew up with an abacus.

I did spend hours and hours playing with numbers with my calculator. I would add/subtract/multiply/divide them and look for patterns. I was able to look for patterns into big, big numbers, because the speed at which I could calculate wasn’t limited by the tool I was using.

What’s missing from current instruction is actual time using the calculator to play around and construct one’s own notion of numbers. Just like you want kids "doing science" they don’t get enough time "doing math." The calculations are not the math, anymore than the list of content expected by your state curriculum in science is the science.

There is not enough time spent ensuring kids understand concepts, and too much time kids "cover a broad curriculum."

The issue is not the technology being used to do the calculations, as the abacus is a visual & kinesthetic tool, while the same holds true of the calculator (you do have to press the buttons after all). The issue is that students do not get enough time in math do more than memorize rote facts, and almost never get exploration time.



How should we change teacher education programs?



I’m looking for feedback on the document started below. What recommendations would you make to change teacher education programs?



Put some thoughts together on the implications of the technological literacy of students arriving at our schools for both teacher education and professional practice.  What do our teacher education programs need to do to prepare teachers to teach kids who arrive at school knowing how to make movies?  What new thinking do we need about how we educate teachers in preparation for certification and how teachers currently holding certificates need to direct their life-long learning?

What is already being done?

5 out of 9 of the colleges in British Columbia have an optional educational technology course already as of January 2010. See this spreadsheet for details. No colleges require educational technology be learned by teachers, although some colleges do at least require some use of technology by teachers.


Two main ideas:

1. Teach teachers how to use specific technologies

  • Teachers arrive with very different skill levels themselves.
  • Schools have different levels of access to technology, so student teachers may not be able to use it during their practicum.
  • Teachers should learn enough about technology that they can teach themselves future skills.
  • Teachers should use technology to connect themselves with other educators.
  • Teachers should understand & know some of the research behind different types of media and their effect on learning.

2. Teach teachers why they would want to use technology in the classroom

  • Teachers should know how to evaluate educational technologies
  • Teachers should understand philosophy of educational technology
  • Teachers should know some of the history of educational technology



As with any other skill in teacher education programs, the use of technology by teacher candidates varies greatly.

A variety of different technologies should be included as access to any given technology may be limited at schools. Some schools limit access by policy intended to safeguard children and/or monitor teachers. Other schools have limited access because of budgetary concerns. Either way, teachers may not have full access to their preferred choice of technology, so they should know enough technology that they can use it flexibly.

Given the importance of technology in today’s world, teachers should understand the purposes of educational technology, and how to incorporate it into their classroom practice. Relatively simple processes, like the SECTIONS framework (Bates and Poole, 2003, see this PDF for an example implementation), can be used to evaluate new technologies and decide on their utility in a classroom setting.

Educational technology, just like other technologies, is rapidly changing, following the trend of the exponential change in technology as per Moore’s Law. This means that, in order for teachers (and by extension schools) to remain current, teachers must be able to learn new technologies and make decisions about whether they will be useful. Teacher education programs must prepare teachers not just to use today’s technology, but how to learn the technology of

Further, technology exists today that is freely available and easy to use, which allows teachers to connect with each other like never before. Social media has the potential to break down the walls of the classroom and provide teachers with the opportunity to share their practice widely.  Teachers should learn how to use social media as it is not only a way for them to keep current in their practice, it is also a way for the already existing excellent practices in education to spread. Just as it is the expectation that doctors will keep themselves current by connecting with other medical professionals in the field, so too should educators.

Educators need to learn how to share their ideas openly. For example, the use of Creative Commons licensing, should be wide-spread in our profession so that, while attribution remains similarly important, we can ground the existing sharing of materials in a supportive legal framework.

However, without knowing the history of educational technology, teachers are more likely to fall into the same pitfalls as others before them. It is easy to use technology in a classroom and have a room full of students who are actively engaged in pseudo-learning rather than real learning. Technology used only for the purpose of engaging or entertaining students is not a good use of technology, nor an example of good teaching practices.

It is important that the use of educational technology be grounded in good pedagogy. Teachers need a deep understanding of constructivism before they can use technology effectively as a constructivist tool for learning. Teachers need to understand that just being exposed to an idea does not mean that students will learn it, and the same is true of technology. The use of multimedia in classrooms has traditionally been to deliver content (or to entertain students) and teachers should recognize the power of multimedia to enhance the understanding of students, but also the danger in changing one ineffective practice (lecture) into another ineffective practice (video lecture).

Teachers should learn about how to facilitate the student use of technology so that students, who are often exposed to the language and vocabulary of technology at an early age, are able to actively use technology rather than just be passive recipients of the teacher’s use of technology.

Specific Recommendations

  1. Teacher education programs need to include a history, philosophy, and practical use of educational technology course.
  2. Educational technology learning at teacher colleges should be grounded in research, pedagogy, and use current technologies.
  3. The technology should be taught to teachers in the same ways we would like teachers to teach.
  4. Professional development should be available continuously to teachers so they can keep their knowledge current.



What are some good in-classroom techniques for being a more effective K-12 teacher?

José Romão created a document from a thread on Quora, in an effort to generate more thoughts on how one can become a good teacher. We are planning on getting as many ideas as we can, extending the ideas in more detail, and either creating a short "this is how you can become a better teacher" book or presentation.

Add some of your ideas here on how you think people can be more effective classroom teachers.

Password Strength

I’m using the following xkcd comic to help the teachers at my school with their password selection.

Password strength


There is also a very useful script, created by Steve Gibson, available to test how long it would take a brute force attack to figure out your password with a computer. While I don’t recommend entering any actual passwords you intend to use into an password strength checker (there aren’t that many websites out there, so an hacker could easily steal the passwords you enter into their "password" checker and try them all over the place, thanks to @drdouggreen for the reminder), this can be an excellent way to experiment with different types of passwords.

I also recommend reading this post I wrote about how to change your password for every service you use, without having to memorize a new password for each of them.

As suggested above, we’ve spent many years training people to use complicated passwords which are actually not all that secure, when instead, you can use a longer, much easier to remember, password that is much more secure.