Education ∪ Math ∪ Technology

Tag: education (page 12 of 13)

Idea for alternate school structure – School without a daily bell schedule

So I was just walking up the steps and had an idea.  What would a school without a restrictive bell schedule look like?  I was wondering about this because I remember so many times this year having students working along in a great groove on one of my projects, and then suddenly time is up and the students all have to move to another room!  This is very frustrating, especially if another 10 minutes means they could finish their train of thought.

So what would it take to make this work?

First, teachers would need to have daily small group planning time built into their schedules, probably every morning.  They would need to plan how the schedule was going to unfold that day and to review on a daily basis the progress of the students.  Technology could be used to help keep track of where students are at so that teachers don’t have to push around gigantic piles of paper. Update: Or as John Holt suggests, we could trust students more and give at least some of them more ownership over this process.

Next, the curriculum would have to be broken down, not into subject areas (except for review possibly for external certification) but by project.  Each project would have to have the traditional subjects integrated into it, with percentages (and specific skills or content areas) for how much the project counts towards each subject.  Students would have individualized education plans because the teachers would have the time to construct plans for each student. Update: Again, this would be easier if at least some of the students, or all of them at some stage, had more control over what they were learning, and when.

Assessment would be standards based assessment.  Partially this is because it is a bit easier to assess a bunch of students who may be at difference places in your curriculum using standards, and partially because I believe that standards based assessment works better than norm referenced assessment.  Finally another argument for standards based assessment is that students should move through standards, rather than through grades.

Another thing that might be possible to remove in such a school is the barriers that we construct between students of different ages.  Clubs quite often have students working together with very different skill levels and ages, and quite a large number of school clubs work quite well.  So it’s not impossible for students of even very different ages to work efficiently together.  As well, it might be that students of different ages are working on very similar projects or even the same project (being assessed differently because the standards might be different for each student).  So what I envision is a school without grade levels and maybe with a very different layout or structure.

Perhaps this school is architecturally different as well.  Students would need some private space to work (maybe in multilevel groups so that older students have the responsibility to check on the younger student’s progress and model appropriate behaviour?), many small group sized rooms, and some wide open places as well.  The small work spaces could be offshoots of the general meeting areas which are in turn offshoots of a larger wide open space.

Every student should have to do some physical activity each day.  Physical education is SO important for children, their bodies are built to move.  It would be one of the core classes in a school like this instead of an aside that is government mandated.

What else do you think this school needs?  Are there any schools which are actually like this?

Update: Of course, I’ve made some pretty broad assumptions in the original version of this piece – one of which is that every student should learn exactly the same thing. While I do believe that a liberal education (in which one learns about a wide variety of things) is important, there are many, many different ways to achieve that outcome.

Authentic learning experiences

This year I have really tried to step up the process of bringing the real world into my mathematics class.  A major focus has been on using technology appropriately as a tool to help solve real life problems.

Here are some examples:

 

Distance formula:  Finding an optimal (or near optimal) solution to the Traveling Salesman problem for a small number of cities.  

Basically here the students were given the assignment of choosing 6 or 7 cities fairly near each other on a Google map and finding the x and y coordinates of each city, then using the distance formula to determine the distances between the cities.  Once they had this information, they were to try and figure out a shortest path, or at least something very close to the shortest path, and then justify their solution.

 

Linear graphs & Piecewise functions:  Compare 4 or 5 difference cell phone plans.

Students should take a few cell phone plans and compare the plans, including the cost for text messages (which may include similar graphs), the cost for extras, start up costs, etc…  I found the students end up needing to create piecewise functions in order to represent a cell phone plan which has a fixed rate until the minutes are used up at which point the customer has to pay extra for each minute.

 

Shape and Space: Design a new school building.

Here I showed the students the new lot our school is in the process of purchasing and our project is to design a building for that spot, and calculate how much their building design will cost (within the nearest $1000).  It involves finding area, volumes, perimeters, scales, perspective, etc… We are using Google Sketchup for the designs but I am now trying to work out how to import the students designs into a virtual world (like OpenSim) so we can have each student group lead walk-arounds of their building.

 

Polynomials:  Determine how many operations multiplying a 100 digit number times a 100 digit number takes.

Students are learning about computational complexity theory by analyzing the number of steps it takes to multiply numbers together.  They record each step in the operation and increase the size of the numbers of each time and re-record their results.  They then compare the different number of steps in each operation and try to come up with a formula, so that they can answer the 100 digit times 100 digit question.  Our object: Figure out why our TI calculators can’t do this operation.  It turns out that the formula itself is a polynomial, and their substitutions to check their various formulas count as a lot of practice substituting into polynomials, which was a perfect fit for our curriculum.

 

Quadratic functions:  Create an lower powered air cannon and use it to fire potatoes a few meters.

Here the students are attempting to use quadratic math to try and analyze their cannon, then the objective is to try and hit a target with a single shot later.  The cannons should be very low powered for obvious safety reasons, capable of firing a potato (or Tennis ball) a few metres at most.  There is also a slight tie-in to Social Studies where my students will be studying cannons in their unit on medieval warfare.

 

Bearings and Angles: Set up an orienteering course in your field or local park.

Students attempt to navigate a course through a park and pick up clues at each station, which they use to figure out a problem.  Students have to be able to recognize the scale on the graph, navigate using bearings, and measure angles accurately.  Also lots of fun, we did this in Regents park for a couple of years in a row.

 

Integration: Calculate the area (or volume in a 3d integration class) of an actual 2d or 3d model.

Basically you have the students pick an object which they then find the functions (by placing the object electronically in a coordinate system) which represent the edge of the object, then place the object in a coordinate system and calculate area of the object using integration.

 

Percentages: Find out how much your perfect set of "gear" (clothing) costs when it is on sale and has tax added.

Students take a catalog and calculate how much it will cost for them to buy their perfect set of clothing.  They can buy as many items as they want (with their imaginary money) but have to keep track of both the individual costs and the total cost of their clothing.  You can also throw some curve balls at them, like if they buy more than a certain amount, they get  discount, etc…

 

If you have any other examples of real life math being used in a project based learning context, please let me know.  I’m always interested in other ideas, especially for the more challenging areas of mathematics.  I’ll add more ideas here as I remember them.

OpenSimulator and the possibilities for Education

So I downloaded OpenSimulator, which in case you didn’t know, let’s you build virtual 3d worlds, much like Second Life.  You can view these virtual worlds using the open source Hippo Viewer, which basically acts as a way to view the data in 3D from an OpenSimulator server.

Installation is relatively straight forward if you follow this tutorial or just download the installers from the sites above.  I had to play around with some of the configuration settings, which involves some Googling and a willingness to open up a file and make some small changes.  It wasn’t too hard, but it’s considered Alpha software so you get what you paid for in this respect.  It took me about 45 minutes or so to get it set up and running once I had it downloaded.

Here’s a brief video example of what it looks like:

So having installed this, some ideas immediately sprang into my head as to how it could be used.

  1. Students could learn about perspective (in Art or Math) by building 3D models and examining what the view of the models look like from different camera directions.
  2. If you set up a multiuser version (known as a Grid) instead of the standalone version, students can edit terrain together.  They could rebuild a historical landmark together in Social Studies, or view existing models by importing them into the server.
  3. Students can edit the basic 3D shapes and learn about transformations of objects.
  4. The entire world is built on a 3D coordinate system so as students build their world, they will learn about mapping in 3D Cartesian coordinates.
  5. Students could learn about architectural design
  6. There is a plugin for Scratch which lets students create scripts to control animations in the Hippo Viewer (which unfortunately I can’t find anymore).

The first advantage I can see to using this system over Second Life (which admittedly is much easier to install) is that you can control exactly who uses the system.  It can be your class, a student, each student is on their own server, whatever, but you have complete control.  The second advantage I see is that it is much cheaper to build and create things, rather than having to spend money on land in your virtual world.

A disadvantage I see is that the server which runs a world for a classroom of students is going to have to be pretty decent.  This could definitely be a problem for schools which don’t have their own infrastructure.  On my own computer the server runs absolutely fine with multiple other programs open, but I have 4G of RAM and only 1 person using the server (me).  I’m not sure exactly how much memory each client uses when they connect, but I can imagine it’s not small.

Anyway, this is definitely something to consider.  I may use it when we look at perspective, but I’ll have to see if I can install (and run) the standalone version of the program on one of the school’s desktop computers successfully…

Update:  Oh and one classroom management thing. You might want to create a rule about the clothing of the avatars as I have yet to figure out how to disable their removal by the students…although see this post about removing the problem all together.

OPML file for the 2009 Edublog awards

A few weeks ago the final results of the 2009 Edublog awards were announced.  I looked around for an OPML file, which is basically a way to import and export RSS feeds from your feed reader.  Long story short, much searching, no file found.

So I took the page that Edublogs published with all of the nominations, wrote a script in PHP to parse the page and find the links to the individually nominated blogs, and then extracted the RSS feed for each page.  Finally I used an online service to generate the OPML file, since I didn’t want to manually add each feed.  I tested the import in Google reader, and over 340 blog feeds were successfully added.  Pretty cool.  During the process a few blogs were lost, and I removed the Twitter feeds.

Anyway, here is the OPML file (I’ll get a better version up soon, the last one had a few wikis and Ning activity feeds, not as useful), which you can download and import into your reader.  I recommend not attempting to actually follow ALL of these blogs, but you could spend an afternoon and filter the list to what you actually find useful.  Caution: You will end up with THOUSANDS of unread posts so be prepared for some sifting afterwards.  I’m currently in the middle of going through each of my subscriptions and scanning the blog posts to make sure they are interesting/useful.  I’ve noticed a fair number of feeds of Wikis, which to me is pretty useless if you aren’t involved in creating the wiki.  Stay tuned, and I’ll export my final OPML file and share it here.

Perhaps someone could export definitions for each of the categories of blogs created by Edublogs?

Update: The trimmed version of the OPML file, suitable for an ed tech junkie with an interest in Math or Science education. Just save it to your computer, then import it into your feed reader.  Be warned, I follow A LOT of blogs.

The value of homework

So I was at a dinner party last night, and was the only high school teacher in a room of university students and academics.  It was quite an enjoyable night, and I got to reconnect with a bunch of old friends.

Of course as a teacher, eventually the subject of what I do for a living comes up.  It’s pretty clear that everyone has an opinion of good and bad teaching. I made the declaration at one point that I no longer assign typical math homework.

Actually it’s true, I haven’t assigned a problem set from the textbook this entire school year.  This is a conscious decision, not me just being forgetful and a real reason behind based on research.  I do assign other types of homework occasionally.

I read something in the summer that changed my perspective on homework.  It was about the value of feedback when learning. I don’t remember the exact title of the article, it was in my course readings.  In any case, what the authors of the study discovered is that the length of time between when you make a mistake and when you get feedback on that mistake makes a huge difference in whether or not you remember either the correct material or the incorrect material.  

If you make a mistake and get feedback within a few minutes, chances are pretty good you’ll remember the feedback rather than the mistake.  As time goes on, the probability you remember the mistake instead of the feedback increases.  If it takes more than a day or so to get feedback on your mistake, chances are pretty good you’ll make the mistake again and forget the corrective feedback you received.

The implications of this in assigning student homework is pretty easy to see.  If I assign to be done Monday night, and some of my diligent but struggling learners do the homework that night, then I see the students on Wednesday, chances are pretty good that there’s very little I can do to correct the misunderstandings of the students for that assignment.

So I’ve stopped assigning homework which doesn’t give immediate feedback.  I’ve discovered dozens of websites which offer free online quizzes which are marked immediately and display the correct answer for the students.  Assistment.org is especially good, it gives hints on how to solve the problem as they go wrong and keeps track of how many hints each student makes.

There are other types of homework you can assign.  Anything which forces the students into a state of active engagement with their material is good.  This could mean internet research and summarization, gathering curriculum resources, creation of online tutorials, extended project based work, etc…  The analogy here is, what types of things do you do as preparation for school?  These types of tasks are also appropriate for the students to do.

Do what your students want to do

So something I’ve noticed recently is that my classes have been going really smoothly.  Actually, every class now I have nearly no classroom management problems and every students is engaged for nearly the entire class on their work.  I don’t think I’m doing anything tricky, I’m just doing what the students want to do.

Imagine this box represents all of the possible learning activities you could do in a classroom.

Rectangle

Now imagine that you draw a circle inside the box to represent all of the activities your students want to do.  Note: Diagram not to scale.

Rectangle with one circle

Now we draw a circle which represents the portion of the possible educational activities you want to do and which are relevant for the topic area you are facilitating or teaching.

Rectangle with overlapping circles

All you do is choose a learning activity for class which occurs in the intersection of the two circles shown in red.  In my experience this includes any activity in which all of the following three criterion is met:

  1. The students get to create something or interact with the material more deeply.
  2. The students see the point of the activity.
  3. The students are engaged at a higher level on the pyramid of learning.

Some examples of activities which qualify include, but are not limited to:

  • Students tutoring each other
  • Creating video tutorials or podcast tutorials
  • Projects based on the real world applications of what you are teaching
  • Student led interviews with professionals in the field
  • Student generated quizzes, worksheets, tests, etc…
  • and more….

What I’ve also noticed over time is that the intersection gets a bit larger as the students see a trend: they are doing fun, relevant and engaging activities all the time.  They will tend to more willing to do other activities because they spend most of the time in your class engaged, so they will jump in and focus on activities which they may have otherwise enjoyed less in a non-interactive class.

Using Google docs for student report cards.

Here’s the basic idea.  I create 31 identical (one for each of our 11th and 12 grade students) Google Documents using a agreed upon template.  The teachers have access to edit the documents, and add their grades.  Our IB diploma coordinator adds comments to the documents, and then we download the documents as PDF files, ready to be emailed to the parents.  We could do this entirely electronically, but we are also going to print a copy to mail to the parents for their records.

The trickiest part is making sure that the documents that are formed will look good when converted to a PDF.  I suggest using a very simple structure of the documents, in this case less is more.

Our document has our school logo at the top, a space for a generic comment about our program, a simple 2 column table to report grades in subjects, space for a more specific comment about the student’s performance, and then space for our IB coordinator to sign the report, which he’ll only be able to do once it’s printed.

See what it looks like as a PDF here:

View sample as PDF

Creating a WiiMote interactive white board at my school for under $50.

So someone sent me a link to the video below and I decided to act upon it.  I thought I would link my resources I find for this project here, and keep you all up to date on how it is working.

The immediate attraction for this project was the idea of being able to create an interactive white board for what looks like close to $50.  Our school currently has three Smartboards at the Upper school and three Smartboards at the lower school and three times that many classrooms at each building.  This means that only 1 out 3 lessons is taught using a Smartboard at best, and teachers tend not to use the Smartboards.  Part of the problem here is the Smartboard technology is not immediately obvious how to use, and part of it is because of training, but access to a Smartboard is a big problem for most teachers.

First I had to do some research into the controllers themselves which are necessary, which are basically a Nintendo WiiMote and a Bluetooth receiver on your laptop.  According to Amazon the WiiMote costs about $35 and the Bluetooth receiver costs about $4.   You might also want a cheap tripod to mount the Wiimote onto, that should cost another $15 or so and is useful but optional (my tripod cost me 9 dollars) since in the video below you can see Johnny mounts the Wiimote directly on top of the LCD projector.  You also need an LED pen, which you can apparently build for about 5 dollars or purchase online.  Total cost so far is 44 dollars or if you are lucky and find a cheap tripod (like I did), 53 dollars.

As for turning the Wiimote into an interactive white board, Johnny Lee (the inventor of this process) has instructions up on his website.  He has also created a community forum where you can post questions, and if it is like most online communities I know, get answers to your questions.

Johnny Lee has also presented at TED, so you know there are some very smart people who love (and have tested) his idea.  What I really love is the demonstration of the VR system he has designed using pretty much the same hardware with some different software.

Here’s a good video showing a pressure sensitive pen, which will make writing much easier.  The brand name of the pen casing is called Tide-to-go pressure tip pen.  Yes, as in Tide the laundry detergent company.

Social software comparison

Facebook My Space
Location of terms http://www.facebook.com/terms.php?ref=pf http://www.myspace.com/index.cfm?fuseaction=misc.terms
Who “owns” materials posted by members? Members own material but give right to use it forever for no fee. Members own material but give right to use it forever for no fee.
For what purposes can these materials be used? Any purposes. Any purposes.
Would using each site be appropriate with your students? No, for a couple of reasons. First, the students will end up having to create profiles on this website, something which their parents may have forbidden. Second, it is too difficult to keep our group content private, since the license agreement of the content lets them use it for whatever they want. No, for a couple of reasons. First, the students will end up having to create profiles on this website, something which their parents may have forbidden. Second, it is too difficult to keep our group content private, since the license agreement of the content lets them use it for whatever they want.
In your opinion, how well are the privacy interests of members represented? Facebook has an exxcellent privacy policy, which they detail at: http://www.facebook.com/policy.php The most important part of this policy is that profiles can be set to private. My Space has a seriously improved privacy policy available at: http://www.myspace.com/index.cfm?fuseaction=misc.privacy
They have the same conditions as Facebook and private profiles, but are famous for the number of times they have been hacked and user information compromised.
Bebo Twitter
Who “owns” materials posted by members? Members own material but give right to use it forever for no fee. Members own material but give right to use it forever for no fee. Also, the terms and conditions describe a procedure with which to make a claim for copyright infringement.
For what purposes can these materials be used? Any purposes. Not listed.
Would using each site be appropriate with your students? No, for a couple of reasons. First, the students will end up having to create profiles on this website, something which their parents may have forbidden. Second, it is too difficult to keep our group content private, since the license agreement of the Bebo content lets them use it for whatever they want. Yes, because Twitter is fine with anonymous accounts, they do not require one to fill in your name. A friend of mine has used it successfully with younger students, where he signed up all of the students for accounts using pseudonyms like “risstudent1” and had control over the accounts.
In your opinion, how well are the privacy interests of members represented? Excellent privacy agreement available at http://www.bebo.com/Privacy2.jsp. Key points are the ability to set any part of your profile private, and can end membership at any time. Twitter has a well spelled out privacy policy, available at http://twitter.com/privacy.
It seems very comprehensive and also allows for users to set their updates and profile as private.

What did you discover?

As I expected, most of these social networking sites have terms of service which are designed to protect themselves and their younger clientele. A high school aged student who knew something about being careful online would be safe using any of these services, simply because they are designed at their heart to allow their users to choose what information they show. However students with less acumen may choose a poor setting for the privacy of their account, and end up giving near strangers too much information.

What surprised you?

I was a bit surprised to find that all of the language for the first three sites (Facebook, My Space, and Bebo) was exactly the same when it came to user generated content. The words “non-exclusive, fully-paid, royalty-free, sublicensable” were used by all three of the first sites. It seemed to me that they were all using some boiler-plate legal text. Maybe they all used the same law firm?

How would this inform your own participation in these social network sites?

I would be a little bit more likely to use these sites, but I have used at least the first two somewhat extensively and see little educational value in them. Too easy for students to wander off in the wrong direction. The only use I could see would be to subscribe all my students who were using Facebook (for example) to a group and then send them information via group emails. Pretty sure it would be more useful to set up my own system, and suspect the parents of my students would prefer that as well.

What are the implications for education?

The terms of service for these websites seem favourable for use in education, but I would be hesitant to do so. The only big reason I can see for using these particular websites is that they are frequently trafficked by our students. An reasonable analogy is that using a social networking website to connect with your students is like standing on a street corner preaching lessons to your students as they walk by or sit on their front steps. I just don’t think this is necessary, and really students deserve a break from school once in a while. I teach in the International Baccalaureate, and these students are so busy, they hardly get two moments to breathe, let alone have their personal online space invaded by school.

In terms of privacy, these websites do well, at least according to their privacy agreements. Most of these sites are aware that many of their customers are teenagers and that many countries have enacted laws to protect youngsters online. These websites need to comply with these laws, and so must have safe-guards in place. However, many of these safe-guards appear to be off by default, and this requires teenagers to be savvy users to turn them on so I think many teenagers are not properly protected. Hence, we should seriously consider whether or not is appropriate for schools to be advertising the use of these social networking sites.

Philosophy of Educational Technology

In my teaching, I infuse technology through-out my lessons.  Although I have a deep interest in technology going back as far as I can remember, I hope I am using technology purposefully and appropriately.  It is important to me that technology not just be a fancy add-on, but that it should be a tool with which to help students understand the world.

The purpose of using educational technology is to enhance pedagogy and enable students to learn.  We have many tools we use as educators, and different types of technology are included in this toolset.   The major benefit of using technology is that it can greatly expand the variety of types of lessons students can participate in.

In my experience students learn best by doing, rather than by watching.  As much as possible, I try to have students work as participants in a collaborative guided investigation, rather than relying on direct instruction.  William Glasser once famously said "We learn, …50% of what we see and hear, …80% of what we discuss and 95% of what we teach," modifying Edgar Dale "Cone of Learning." (Dale, 1969)  Hence, in my classroom I try and have the students do, discuss, or teach the material they are learning.  This style of instruction is aided by the powerful technological tools of today.

My strongest values in education are compassion for students, open-mindedness about what they are capable, and recognizing their differences.  Educational technology allows me to be more compassionate, in that I can differentiate a lesson better, understand my students through their work, and provide more opportunities for student voice.  One of the ways I provide this voice is using multimedia presentations and integrated technologies as summative of the students’ understanding.   These types of activities assist students in remembering what we have learned.

I have recently begun to move away from lecturing to students and have this experimented much more with student led research.  For example in my science 8 class each pair of students is researching one of the body’s systems, and presenting their work in the form of a website.  Other students will be responsible for reading this material, then summarizing it in a short audio podcast.  This way I will be attempting to improve the retention of the material, and moving ownership of the learning process to the students.

My personal theory is based a lot on Ausubel’s assimilation learning theory (Novak, 2007)which suggests that knowledge is retained and more useful when it comes from meaningful learning experiences rather than rote learning.  I try very hard not to rely on rote learning in my teaching for I know how quickly students forget the material once they no longer need it.  I also know that if you excite students about a subject, they will put tremendous effort into learning it, which greatly improves their retention.  One of the areas I have made the most change is recognizing that teaching specific content is less important than teaching the skills necessary to learn and retrieve that content.

References:

Novak, J.D. (2007). Ausubel’s assimilation learning theory. In Custom course materials ETEC 512. Vancouver, BC: University of British Columbia, Bookstore. (Reprinted from Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations, pp. 49-78, 1998, Mahwah, NJ: Earlbaum).

Dale, E. (1969) Audiovisual Methods in Teaching – Third Edition, Published by Holt, Rinehart and Winston, record retrieved from Eric database on October 18th, 2009