Education ∪ Math ∪ Technology

Month: January 2010 (page 3 of 3)

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.

Application to the Google Teacher’s Academy for Administrators

So last weekend I finished my application to the GTA for Administrators.  My major reason for wanting to go to this conference is networking and for some more ideas on how to best use Google’s services. In any case, the application process itself was actually kind of fun, and I’m pleased with the results of my work with the 1 minute video which you can see below.

Now I understand that Google has created this academy for entirely financial reasons, as has pretty much every major player in the educational software business.  Basically, if you hook the policy makers, you are more likely to see your services spread all of which are built to support either their search services or their premium products.  I’m okay with that if what you produce is really worth using, it’s better than vending machines and bake sales.

Update:  Unfortunately my application was rejected.  Still I’m happy to have applied, it was totally worth the reflection I had to go through.

Connecting with other people

In the past 3 days, I’ve had 3 different people contact me and ask me if I want to participate in a study.  One is a Ph.D. student about to finish her doctorate, another is an IT director for a school district, and the last is a business student who wants some information about a product his group is hoping to build with teachers in mind.  Each of these messages was personally addressed to me and cited either my online activities as a reason for the contact, or my interest in technology.

I suppose that my willingness to blog about what I am doing and share my resources has made me easy to find.  Perhaps anyone who is blogging and a strong online presence is going to be found in this way.  Anyway it has made me think about an online presence and its value.

The past week my wife has been in Mexico with my son, and every day we’ve been video chatting via Skype.  It’s amazing how powerful this experience is, and how happy I am that I am able to connect with both of them and see their faces.  It makes a difference.  Now I know that video conferencing with loved ones abroad is nothing new, but I’m including it as an example of how people are connecting today.

Another example.  A friend of mine is looking for work, he contacted me through Facebook and asked if I had any contacts.  Turns out, I do, and I shared them with him.  My friend is 9 hours away via timezones, this kind of interaction is very difficult to do via telephone but it worked really smoothly via the inbox and wall of Facebook.

I’ve heard it said that our reliance on technology for connecting with people has reduced the amount of face to face interactions we have.  They are probably right.  It has dramatically improved our ability to connect in so many other ways though, I think a bit of a loss in F2F time is worth the ability for me to see my son via Skype in Mexico, or for 3 professionals to connect with another professional and ask for his support in their personal projects.  

Update:

Here’s a TED video that describes a similar issue.

Removing the option to remove clothing in the Hippo Viewer for OpenSimulator

The OpenSimulator is great, but unfortunately it was written for adults in mind.  One of the options available all over the place is "Take Off" which basically means to take off the given item of clothing.  This means if install this program as is on your school’s servers, you just installed something which allows students to view porn on the school’s computers.  Ouch!

Fortunately there is a solution.  The Hippo viewer uses a series of XML files to create it’s menus.  If you go into ‘C:\Program Files\Hippo_OpenSim_Viewer\skins\default\xui’ (or a similar location based on where you installed the program and what operating system you are using) you can find the XML files which define the menus.  Simply go through them (use find "Take Off" in your text editor) you can safely remove all of the options for removing clothing from every menu. Whew, lots of work, and easy to mess up, but at least it works.

Before you make any changes, make a backup of your installation (just make a copy of the whole program with extra files somewhere else on your computer, like in your ‘My Documents’ folder).  Basically to get this to work you have to find the folder ‘default’ in C:\Program Files\Hippo_OpenSim_Viewer\skins and replace it with the contents of this zip file.  You also want to delete the ‘Silver’ folder from the skins directory so the students can’t switch to a theme with the buttons we don’t want.  Note that if you upgrade this program, you’ll have to repeat these steps.

It’s not foolproof, but it seems to be very stable and I have happily tested that the buttons and menu items which let users remove their clothing are now gone.

 

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.

An overview of Google reader

Here is a brief overview of Google reader.  If you aren’t sure what a reader is, or what it is for, you should really watch this Common Craft on RSS in plain English first.

Link:  
 

Screen-shot:

 

Summary:
Google Reader is an application which lets you pull information to you rather than searching for information on the web.  Blogs, newspaper, even Twitter, publish links called feeds which you can use to subscribe to their services and they will push information to you.


Purpose: 
This application is a way of reading information online using syndication.  It’s much like having online newspapers delivered to you, rather than searching for the newspapers in the shop.

How this can be used for professional networking:  
First you search for blogs written by teachers.  One easy source is to go to http://edublogawards.com/ and subscribe to all of the nominees of the blogs.

How this can be used in the classroom
:
Students can also search for and find blogs and other feeds to follow.  On a regular basis they will be pushed information.  As well, students can subscribe to each other’s blogs and have a single place to read all of the comments and posts from their peers. A classroom could have subscriptions to a number of sources, and you could share the posts with the class as a current events section or something similar.

Advantages of this application

It’s easy to use, it has a number of straight forward features, such as the useful ‘recommendations’ which are other feeds that Google thinks you should subscribe to, based on what you have already found.  It is also nice because it has a single sign on with other Google applications, and finally, there are nice applications for mobile browsers, so you can get your feeds on the go. Finally, Google reader also works when you are offline using Google Gears, which means that you can download your feeds when you have a connection and then read them when you are offline.

Disadvantages of this application
:
This application has no serious disadvantages that I can think of, except that finding the subscriptions in the first place can be a tricky.  I find the interface fairly easy to use, but I could imagine it could be a bit daunting for someone who is just getting started.

Similar tools: (if applicable) 

 
 

 

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.