Education ∪ Math ∪ Technology

Tag: teaching (page 1 of 2)

I will miss you

Yesterday was my last day working with students as a classroom teacher, at least for the foreseeable future. Next Tuesday is my last day of work in my current school, and on Wednesday I will be flying to New York to start a new job.

I will miss hearing piano music drifting into my office as I work.
I will miss people asking me questions about all sorts of things.
I will miss the sound of students working and playing.
I will miss wandering around our quirky but lovable buildings.
I will miss standing on the street corner to make sure kids are safe.
I will miss our kids.
I will miss calling a group of people who are in no way “mine”, “my” kids.
I will miss discussing the big (and small) ideas with students.
I will miss random treats in the staff room.
I will miss grateful letters from parents and students.
I will miss grad pranks and graduation dinners.
I will miss taking kids on field trips to see exciting things.
I will miss heart-felt discussions about life with a group of people that has hardly lived any of their own life yet.
I will miss seeing an aha moment when someone gets it.
I will miss watching a group of kids grow and mature.
I will miss the bustle of a class working on a project that has meaning to them.
I will miss being surprised by what students can do.
I will miss my friends.

Massively collaborative educational research

The book Wikinomics has really got me thinking about how collaboration happens in our society.  One of the area where I think massive collaboration would be really useful, but where it is underutilized is in the area of educational research.  Imagine the power of collaboration that we could have if hundreds of educators collaborated to run a research study.  I’ve written about this before, but I have a new perspective since reading Tapscott and Williams.

Let’s look  at some of the benefits of being involved in such an undertaking.

First, each educator would have their name attached to a valuable piece of educational research.  So much research in education is done with tiny sample sizes that tend to invalidate the purpose of the research.  A large sample size does not guarantee that the research is valid, it still needs to be done with care, but it does tend to reduce things like selection bias, small sample size effect, etc…

Second, we could do research on a wide variety of different socioeconomic backgrounds, different parts of the world, and be able to analyze our data from many different perspectives.  We might even have enough data to spawn multiple educational research papers on our chosen topic.  We could release our data under a Creative Commons license, and let other educators remix and look at the date in different ways.

Finally, the amount of work each educator would have to do would be a lot less.  Designing a study, collecting data, researching sources, analyzing data, and writing an educational research paper are all time-consuming tasks.  Dividing up these tasks over a larger group, even with the additional overhead of maintaining coherence in the research, would greatly reduce how much work each educator would have to do.

If you are interested in participating in such a research study, please sign up at this form.  There is no specific topic or agenda set yet, just an initial examining of the interest from the educational community.


Research based teaching

I’d like to be a research based teacher.  This means, if research comes out which is compelling and reliable and which suggests that an alternate approach to what I do will work better, then I’ll experiment and try that out.  If research tells us that people learn in a certain way, then I’ll need to look at my practices and adjust them correspondingly.

Here’s an example of one change I’ve made recently because of research I read.  The research is a meta-study of the relationship between the time between a learner makes a mistake and when they receive feedback on their mistake.  If there is more than a very small amount of time between making a mistake and getting feedback on that mistake, interference between the mistake and the feedback is likely to occur and the feedback may not be what is remembered, instead the mistake may be remembered.  "Teachers who want their quizzes to help students learn should try to arrange conditions so that students receive feedback as quickly as possible after they answer quiz questions." Kulik & Kulik, 1988

I don’t assign homework anymore of a quiz or exercise nature which doesn’t provide immediate feedback.  So this entire year, I haven’t assigned a single exercise from the textbook.  I still provide a textbook in case the students want to study, or practice with their tutor or parents, but we only use it during class-time.  During class I can roam the classroom and provide feedback when students are making mistakes, and I can make sure students are checking their answers with the back of the book on a regular basis. If I want students to practice assignments at home, they get an online self-correcting quiz.  Fortunately for me, all of my students have internet access at home.

One problem with this approach is that so much good educational research is locked up in the vaults of proprietary publishers and difficult to access. I am lucky and can access much of this material through my university, but I can imagine that this could be a major stumbling block for most teachers, and of course schools can’t afford to pay for the expensive subscriptions to all of the educational journals out there.  Just having access to the database to search through the journals is difficult.

We need to, as a profession, come up with a solution to this.  Either money has to be spent ensuring that teachers have access to the best educational research out there, or teachers need to become better researchers themselves.

What would you tell a new teacher?

I had the opportunity to have a new teacher hang out in one of my classes today.  We had about a 20 minute discussion afterward where she asked some questions and I got to share a couple of resources.  She is being trained to teach Math and Science so we have a lot of overlap in our specialties.

First we talked about instructional strategies.  I mentioned that I don’t assign exercises from the textbook anymore, I haven’t all year.  I read brain based research which talked about how important immediate feedback (related meta-study) is in the learning process and realized that there was no effective way to have an exercise from the textbook tell my student what they are doing wrong, it just doesn’t work.  If I give any repetitive exercises at all, they are online quizzes hosted at either (if I want to create the quiz myself) or (if I want the students to have more open ended questions and more feedback).

I also mentioned that I focus on including real life examples of everything I teach.  In other words, every unit has at least one (usually many) examples of ways this math is used, or could be used.  I’ve got a bunch of examples up here, more to follow later.  The idea is obvious to me, connect what you are doing in class to what the students will be doing outside of your class, or at least to things they are interested in outside of class.

I talked about my strategy during my first years as a teacher.  My first year I focussed on surviving, I started my career in inner city Brooklyn so this was a necessary survival strategy.  My second year I started experimenting.  Every week I used a different instructional strategy.  In my third year I tried a new thing two or three times a week.  Every year I’ve been teaching I’ve created all of my lesson plans from scratch every day for every lesson.  It has forced me to reflect on my teaching and I think it has helped me to keep improving my practice.

She asked for some website resources and I gave her the ones I mentioned above, and she said that it was SO difficult to find resources in today’s age because there are so many resources to choose from.  The ranking algorithm of Google is good, but not perfect and doesn’t always help find the best resource for you.  So I pointed out Twitter.

I said that Twitter is like having however many people who are your followers acting to do some of your research for you.  Ask question, get an answer.  See a question, give an answer.  Follow 1000 people who Tweet regularly, multiply your productivity 1000x in terms of searching for resources and information, assuming you follow the right people.

What would you share with a new teacher?

More advice from Twitter PLN:

penphoe @davidwees re: new teachers, "5% lesson content, 95% dealing with people"

sharon_elin @davidwees I’d tell new tchr "Put bureacracy aside; it’s all about you & the kids." Relationship 1st, w/you as curiosity coach (not peer).

Philip_Cummings @davidwees Dear New Teacher – Develop a PLN & pick a really good mentor.

acmcdonaldgp RT @davidwees: I would tell a new teacher: Build GREAT, appropriate relationships and never take away hope!

rrodgers @davidwees Be adaptable and process-focused, and he end results will take care of themselves.

amichetti @davidwees I would say that the most important thing to remember is to be flexible!

misterlamb @davidwees "Teaching is your job, it’s not your life." Advice from my co-op from student teaching. Make time for yourself.

TSherwood @davidwees That it’s OK to cry. There will be more smiles than tears. 




Introduction to Technology in the classroom course

We are having a discussion in one of our classes, ETEC 533 (Technology in the Mathematics and Science classes) where we are all talking about how little support we’ve received over the years in our use of technology.  We’ve all come from different education programs, but a common thread is that these programs usually have courses about how to use typical technologies, like Word or Powerpoint, etc… but no courses on the integration of technology into education.  All of us complained that we have almost no professional development time devoted to the use of technology in our classes.

So I took a look at the course schedule for my Alma Mater, UBC, and I discovered that there isn’t a single EDUC course which mentions the use of technology at all in their quick descriptions.  I did notice that the standardized time-tables seem to include 2 cohorts which talk about how to teach technology or computer related classes but there seem to be no elective technology courses at UBC.

I thought this is such a shame, because I know that technology is integrated into the teaching practice of so many professors on campus at UBC that the Education faculty should at least provide a survey course in the use of technology in education.  I’m sure such a course would be very popular.

Anyway I had some thoughts on how such a course should be run, and I thought that I might as well share them.  This is still a work in progress, so I’d appreciate any feedback or suggestions anyone has.

The course would run something like:

Use of Technology in Education

Course Description:

This course is intended to be an introduction to how technology is used in classes today.  It will help prepare students for the changing future where it is likely that technology will become a part of nearly every classroom.  Students will complete this course with a better understanding of how to use and implement technology within their own classrooms.

Course plan:
Unit 1 – Historical use of technology in a classroom (1 week)

Unit 2 – How is technology used at <insert university here>? (1 week)

Unit 3 – Arguments for and against technology use (2 weeks)

Unit 4 – Ways to use technology in your classroom (3 weeks)

Unit 5 – Keeping on top of new technology, habits for life (1 week)

What kinds of mathematics SHOULD we be teaching in schools anyway?

I was surfing around when I found a really interesting post by Steve Yegge.  He makes the point:

I’m guessing the list was designed to prepare students for science and engineering professions. The math courses they teach in and high school don’t help ready you for a career in programming, and the simple fact is that the number of programming jobs is rapidly outpacing the demand for all other engineering roles. – Steve

He then proceeds to describe some processes for learning mathematics on your own from the perspective of a computer programmer, which are worth reading about since pretty much anyone with an analytical mind and some experience in mathematics could follow a similar approach quite successfully.

This one point I think needs a bit more in depth discussion though.  Are we teaching the right types of mathematics in high school?  Are there any topics which might better prepare our students for careers outside of school?

First let’s look at career opportunities, focussing on jobs which are growing the fastest.  I’ll compile a list here, see my references at the end for sources of this information.

If we look at the list of the 30 professions with the largest employment growth, as an absolute growth rather than a percentage growth we see can pretty much separate them into two basic categories: those which require specialized training in a university, and those which do not. 

The professions in the first category, according to this list, are registered nurses, postsecondary teachers, elementary school teachers, computer software engineers, accountants and auditors, management analysts, network systems and data communications analysts.  The professions in the second category include things like carpenters, security guards, home health aides, etc…

We can also look at the current job statistics, where we see that professional, service, administrative support positions are by far the most common occupations for people to have today.

So the obvious question becomes, what types of mathematics do you need to be successful at these jobs?

1.  Statistics

Everyone needs to know statistics.  We use it all over the place because our society has become driven by data.  We collect it, we sort it, we analyze and we use statistics to make all sorts of arguments as a result.  Not understanding some pretty complex ideas in statistics is a serious hindrance in many areas.

2.  Probability

In order to be able to make intelligent decisions, people need to understand that the outcomes of those decisions are all based in probabilities.  Decisions about what medication to give, etc.. are based on the probability that a given treatment will be successful so understanding probability helps care-givers make better decisions.

3.  Number theory

Having a good grasp of what is going on in the various computer algorithms out there isn’t a bad thing, and courses in number theory could help out a lot of people.  It might be hard to justify this mathematics for the typical profession, but for the computer related professions, number theory is almost vital to being able to do their jobs properly.  So some more advanced number theory should be part of the higher level mathematics courses at high school and a basic introduction to number theory should continue to be included for everyone.

4.  Algebra

We still need to teach algebra and everything related to it.  We should also include more linear algebra in school in the more advanced mathematics classes, as a deeper understanding of linear algebra is crucial to many computer related positions.  As well, linear algebra is useful for almost all of the engineering fields and sciences, which is why universities typically include an introduction to linear algebra in those programs.

5.  Geometry

A little bit of geometry is a good thing so let’s keep a small amount of important geometry.  However we are still hammering our kids with geometric proofs from 2 thousand years ago that have almost no relevance in the work-place.  Proving something true is good for developing analytical reasoning but let’s do that in number theory instead.  Let’s leave the chords and tangents to a circle for a university level course instead.

What’s important in these statistics is that of the technical jobs, we no longer see engineering (except possibly computer engineering) prominently placed, which was one of the professions for which the US originally developed the current mathematics programs.  Computer related fields have surpassed the design and engineering fields which suggests that more mathematics which is useful for computer scientists should be taught in school.

Curriculum needs to be chosen that reflects the trends in the workplace, rather than on an ad-hoc basis, or because we have always taught it.  If the US, and countries whose education systems emulate the US, are to be more successful in a global market, our high school students need to be better prepared for the real world.  Every day we are inundated with statistics and a typical member of society needs to understand these better, in order to make more informed choices.  It is our school’s job to supply this curriculum, and it is our job as educators to implement it.

US Department of Labour


My analysis of two different video case studies on the use of technology in a classroom

These two case studies refer to videos I have watched as part of my Masters course, ETEC 533 and the copyright on the videos is unclear, so I am unable to show them here.

Learning Environment 6 with Teacher G (Post-secondary Applied Science)

This case study is about the use of a “clicker” or instant feedback device in a post-secondary applied science classroom.  The basic idea is, students have a remote clicker which they use to wirelessly transmit their answer on a multiple choice question presented at the front of the class.
The first thing I noticed about this video was that the instructor’s approach to teaching and what kind of information he was collecting seemed to be similar to what a secondary teacher might want to collect.  In other words, the position of the instructor in a post-secondary institution was less important than the fact he is an instructor.  This suggests to me that his experience with the “clickers” might be applicable to where I teach, in a secondary school.

The second thing I noticed is that what he likes about the clickers is the apparent engagement it creates among the students and how this could be useful.  However this has to be taken with a grain of salt, since as one of the students put it “Everyone else is just using PowerPoint or overhead projectors, so this is much more interesting”.  So the WOW! Factor might be critical here and we might be seeing a skew in our results.

The clicker technology though has the advantage of immediate feedback, not only for the students, but more importantly for the instructor.  Once you know whether or not everyone gets an idea, you can move on.  It seems to me that the clickers only allow for multiple choice responses, so this could be a bit of a disadvantage because it can be quite difficult to frame a multiple-choice question so that all types of learners are able to process the question and apply their knowledge to it.

There is another newer technology this reminds me of, where you create polls on a website, and students send in their responses via text message, and you can view all of the responses live on the website.  Very similar to the clicker technology, but might be more useful in a distributed learning environment.

The benefit of this technology is obviously the immediate feedback it gives the students.  A major drawback is the cost, both in terms of time setting up the multiple choice questions during the class to which the students respond and the cost of purchases enough remote clickers for every student.

Learning Environment 7 with Teacher E (Science, Elementary Preservice Teacher Education)

This case study is about using stop-motion animation to help teach physics concepts.  The basic idea here is, create an animation for the students to help them understand a concept in science.  An example would be, showing the animals in a food-chain actually eating each other in an animation, instead of using a simple picture with arrows pointing between the animals.

First reaction is that it must take an enormous amount of time to create the stop-motion animation.  This reaction was born out by the responses of the participants, nearly all of whom complained about how much time the animations took to create.

My second reaction was that I couldn’t hear the interviewer’s questions in most cases, so it was difficult to follow along the various videos for this case study.

One of the participants mentions that the stop-motion animation allows a teacher to present their instruction in a medium that the students of today, immersed as they are in digital media, can understand and appreciate more deeply.  By using the same digital media to present an idea, it is more likely to be understood.

Another participant used the students to help create the backdrop and pieces used in the stop-motion animation which he suggested help the students be even more engaged in the process, since it was their work they were seeing.  The same group suggested using a narrative as a way of helping students follow the process along more easily.

The instructor’s main point about the exercise was that the use of technology should be integrated into all of the courses a student takes, rather than as a stand-alone course.  He also mentions that if a textbook is “good enough” for learning a particular concept, then the use of technology to present the same concept should be carefully examined. 

A benefit of this technology is clearly the enhanced student engagement by the use of media.  A serious disadvantage is the amount of time taken to go through the process, whether it is classroom time with students or preparation time for the teacher outside of class.

Further questions

How much do these two different technologies cost to implement?

How much time does it take to learn how to use the technology?

How much time does it take to prepare the use of technology for the classroom?

Are there other cheaper alternatives that can be used within a classroom with similar effects?

Communication Online with Students Outside of Class

Once you’ve started working with creating and managing online resources for your students, it becomes natural that the ways the students communicate with you is going to change a little bit.  Here are some guidelines for ways you can communicate with your students, and some ways to protect yourself while doing so.

Last night a student of mine asked me a question while I was online through Google chat.  I didn’t mind answering it, and so we had a quick 5 minute discussion about her project.  This saved me a bunch of time the following day, because I didn’t need to repeat the same conversation with everyone else, I just posted the relevant information to my classroom Math blog and then all of the students had access to it.

Google chat has a very handy safety feature for teachers, it automatically records your chat history, which you have access from your Google mail account.  This means that you can easily protect yourself from any accusations of misconduct which might occur.  This process is very similar to a student calling you on your phone and so the same principles apply.  If you don’t want a student trying to contact you via Google chat, don’t give out your gmail address.

You can also communicate quite effectively with students via email.  This has the advantage of allowing multiple students to receive responses, being able to record your conversations for later, and finally being able to send responses when it is convenient for you.  I hate it when students come up to me immediately after a class and ask a bunch of detailed questions because I almost always need to go to the bathroom, or prepare for another course, or get a snack.  These are the times when being able to send an email later is very handy.

Google mail has two neat features that make email with students a bit easier to manage.  The first is that you can apply a label to any email message sent or received between you and a student, which is a handy way of finding messages from students in specific classes.  The other feature I like is called filtering, which can allow you to perform automatic actions on emails that you receive depending on the sender, the contents of the email, etc…  One of the things I like to do is automatically label student emails by class when I receive them.

Finally, never delete emails between you and a student.  They are proof that you have been trying to help the student, which can be useful for administrative reasons I won’t go into here.  You can keep them to help yourself remember what types of questions ask about particular topics.  Finally your record helps protect you from potential problems later.

An interesting and relatively new way to communicate with students is through a website called  This website basically acts as a place where you can post a quick (140 characters maximum) message to the world, and anyone who is "following" you gets a copy of the message.  Since you can forward messages sent to you to your cell phone, it allows you to receive messages from an online source quickly and easily to your mobile phone.  This can be an easy way to set up a one-way broadcast system between you and each of your students in a particular class.  As long as you don’t "follow" your students’ messages, you won’t get any messages from your students that you don’t want.

Emails and chats are good for 1 on 1 or 1 on a few types of communications, but by far the best tool I have used for communication with my students is my classroom blog, described in another post.  Basically, I post information, worksheets, assignments to my mathematics blog, and students can all come read it on their own time.  The information is totally public and always available to look at later.  I also have students do daily summaries of what happened in class, which means I have a record of all of my lessons.  Students are free to post comments, which gives me some idea of what the class understood, and what they had difficulty.  For some reason I find my students are a bit more honest when responding on the blog, or rather less likely to remain silent about difficulties.  In fact, I’ve enacted policy changes because of legitimate complaints students have brought up through the blog, so it has acted as a tool to empower students as well.

These are 4 ways you can communicate online with your face to face students on a day to day basis.  Although we all don’t want our professional life to creep into our personal life too much, we also want to make sure that we help our students learn effective modes of communication, and that they have the help they need to handle those difficult projects we seem to be throwing at them endlessly these days.  Stay tuned for a future article about how to use for communicating with up to 20 students simultaneously for free.


Ways to use Geogebra in a mathematics classroom

There are a lot of good open source programs out there, but not many of them have direct application to a mathematics classroom the way Geogebra does.  Geogebra is a software package for creating and manipulating geometric objects.  It also allows for graphing of funcitons and manipulating the functions in all sorts of interesting ways.  It runs on the Java framework, which means if you have Java installed on your computer, you can run Geogebra, which makes it any Java enabled operating system.  This means the very same program will run on Windows, Mac, Linux or Solaris, although the installer is different for each operating system.

If you are planning on using the program with your students, it is nice to know that they can install the program for free, and that it is very likely to work on their computer.  The only caveat is that you need to make sure the students have the right version of Java installed if they have any problems as this can sometimes be an issue.

Geogebra has all of the standard Geometry software functions.  You can add lines, circles, ellipses and all other sorts of geometric functions to the document.  You can also make one object a dependent of another object which means that changes in the original object propagate to its dependent objects.  So in other words, if a you draw a line segment which depends on the location of point A and point B, changing either point A or point B modifies the line segment.

There are 2 cool things I like about Geogebra.  The first is that you can export your working file as a dynamic worksheet on a web page, which means you can easily make what you are working on web ready.  The second feature which I use all of the time is the ability to export my current file as a picture in PNG (and a few others) format.  This allows me to use Geogebra to create graphs for inclusion in my online posts, something my students and I use Geogebra for all the time.

Geogebra also has an input textfield, which means that every command you can use the interface to enter, you can also type in.  Some commands are done much more easily through the input textfield, things like entering y = x^2 + 3x which uses the nature notation to graph a function.  Entering Function[x^2, 0, 2] graphs the function over the domain from 0 to 2 for x.  Very handy.

Using Geogebra with your classroom is an affordable way to bring high quality geometry software to your classroom at an extremely affordable price (its free!!).  I’ve only scratched the surface of what Geogebra is capable of doing, I suggest you try it out yourself.  Maybe when I have time I’ll create some tutorials on using it.


Resource sharing between teachers.

As part of my Masters degree, I have created a venture pitch for a project I am working on called  Our assignment was to create a pitch as if we are the CEO of an organization which is looking for venture capital.  We are essentially creating our own start up idea, and then learning how to create a pitch to market our idea.

The process has been quite fun, although I have found myself wading through problems editing the video, and getting the quality of the video high enough to make it worth watching.  I tried unsuccessfully many times to convert it into FLV format to reduce the size of the file a bit, but found the quality degraded too much to make it worthwhile.  So I gave up, and settled on both embedding the file within a page, and providing a link to download the file as an AVI.  Hopefully everyone can figure out a way to watch the pitch.  Unfortunately this means the file size is sitting just under 50 MB which is pretty large.  I’m not going to want to host this myself for too long…

The idea of my pitch is to introduce how organization of information has evolved over time and to place Pedagogle as a logical step in that process.  As I go through the pitch I introduce some benefits of Pedagogle, but am mostly focussing on the organizational benefits as I see those as the most important reasons why a teacher might want to use this resource.

On the page where my venture pitch begins, I describe some other reasons for using my service, including the fact that other people will use it which improves the pool of available resources and that your resources are automatically backed up for you, reducing the likelihood of computer malfunction costing you hundreds of hours of work.

Anyway, check out the pitch and the site, and let’s see if we can make a difference in the lives of educators.