The Reflective Educator

Education ∪ Math ∪ Technology

Tag: The Reflective Educator (page 39 of 43)

September 6, 2011 / 0 Comments

Global #edchat tweetup

Here’s the basic idea, which someone (and who that someone is, I’ve forgotten) suggested on Twitter; we should all host local #edchat tweetups, ideally at about the same time. One suggested time period would be during the GlobalEd conference ( dates suggested by @iEARNUSA ) which would mean the tweetups would be scheduled during the week of November 14th through the 18th. These are not the firm dates though as I do not want to interfere in anyway with the GlobalEd conference. It might be better to host these in the week prior to this for example…  See below.

Each local organizer will fill out the form linked below and indicate the date, time, local venue, and geographic location of their tweetup. The local organizer would be responsible for advertising to their local Twitter community, and for keeping some sort of record of the #edchat tweetup. This would encourage more of our network of teachers on Twitter to meet each other. I will also take the information from the form and turn it into a Google map of all of the various tweetups occurring.

As an organizer, you could also:

 

Submit the details of your tweetup here:

https://docs.google.com/spreadsheet/viewform?formkey=dFp1anNxc3RnQkFPZ1NnUXJIN0NRUnc6MQ

 

Update: It looks like it will be too much of a conflict with November 14th through 18th and the Global Ed conference, so I’m moving the dates of the Tweetups to the week of November 21st through November 25th.

September 5, 2011 / 1 Comment

Questions about Edcamp & professional development

If you’ve not heard about Edcamp, I recommend first reading this blog post by Mary Beth Hertz on what Edcamp is. I absolutely think that educator centred professional development, like the Edcamp model, is a necessary part of our future professional practice.

The descriptions of edcamps, according to the foundation statement of the Edcamp foundation is:

  • free
  • non-commercial and with a vendor-free presence
  • hosted by any organization interested in furthering the edcamp mission
  • made up of sessions that are determined on the day of the event
  • events where anyone who attends can be a presenter
  • reliant on the “law of two feet” that encourages participants to find a session that meets their needs

These are all great attributes of the Edcamp model, but I have some questions, and wonder if we can push the Edcamp model to be a more robust replacement for traditional professional development.

  • How can we encourage follow-up and continued conversations after the Edcamp conference day? One common complaint of traditional professional development is that it’s like a drive-through at a fast food restaurant. It tastes great, fills you up, but leaves you hungry for more in a few hours. Traditional one-off professional development is equally ineffective, except when it inspires educators, and makes them want more.
     
  • The traditional presentation style of workshops is itself problematic. How can the edcamp model support a more learner centred model? In a traditional professional development model, the learner is expected to sit and passively absorb knowledge from the presenter, and while the edcamp model addresses this to some degree (in their "law of two feet" & Twitter backchannel chats), under the existing guidelines, an Edcamp could end up looking very much like a more traditional conference. At Edcamp Vancouver, we at least partially addressed this last April by forcing presentations to be limited in length, and opening up more time for a discussion about the presentation.
     
  • How do we address feedback to the learner in the Edcamp model? In the learning process, getting feedback about your own perspective is critical. Discussions are one way to get feedback, but not everyone is comfortable jumping into discussions, but every learner requires some feedback on their learning.

The Edcamp planning commitee for Edcamp Vancouver will be meeting in a couple of weeks, and I plan on bringing these questions to them. If you have suggestions on how we can address these questions using the Edcamp model, I’d love to hear them.

September 4, 2011 / 6 Comments

New York Times article misses the point

Matt Richtel, of the New York Times, has recently written a piece on the use of technology in schools which should be read carefully. He writes:

Since 2005, scores in reading and math have stagnated in Kyrene [emphasis mine], even as statewide scores have risen.

To be sure, test scores can go up or down for many reasons. But to many education experts, something is not adding up — here and across the country. In a nutshell: schools are spending billions on technology, even as they cut budgets and lay off teachers, with little proof that this approach is improving basic learning.

This conundrum calls into question one of the most significant contemporary educational movements. Advocates for giving schools a major technological upgrade — which include powerful educators, Silicon Valley titans and White House appointees — say digital devices let students learn at their own pace, teach skills needed in a modern economy and hold the attention of a generation weaned on gadgets.

He has assumed that the purpose of education is to improve test scores, or at the very least that these are a good measure of learning. He has also generalized about the use of technology in classrooms across the US from two examples; a single school district, and the state of Maine. He is right that many schools are spending money unwisely on unproven technologies, and have not put into place practices to either support these technologies, or examine their effectiveness.

Aviva Dunsiger has written a response to this article based on the results of a direct reading assessment (DRA) she’s done during the course of the year. She doesn’t attribute the phenomenal gains on the DRAs to the use of technology in her classroom, she attributes it to the change in her teaching practices that resulted from the technology being available in her classroom.

This is my reason for promoting the use of technologies in schools. The introduction of computers in the classroom has the ability to be a disruptive force, and transform the pedagogy that is used in the classroom. This doesn’t mean that it will transform pedagogy, it just has the possibility to do so. In 50 years of attempts to change the classroom, nothing has come as close as this current driving force from technology.

In 1993, Seymour Papert wrote,

"Video games teach children what computers are beginning to teach adults–that some forms of learning are fast-paced, immensely compelling, and rewarding. The fact that they are enormously demanding of one’s time and require new ways of thinking remains a small price to pay (and is perhaps even an advantage) to be vaulted into the future. Not surprisingly, by comparison School strikes many young people as slow, boring, and frankly out of touch."

While it is possible to teach in ways which are compelling and rewarding, many schools do not do so. Technology in the classroom can be a lever through which we effect real change in our schools in a positive and fundamental way.

September 3, 2011 / 12 Comments

Questions about the flipped model of instruction

I’ve been reading a lot about the flipped model of classroom instruction, where students watch instructional videos for homework, and then do the practice and problem solving during class time. Here’s a video of the process being explained by Aaron Sams.

 

Some of the questions I have are pretty much the same as the ones posted as responses to the YouTube video so I’ll just quote them:

I’m curious as to what you do with kids who don’t have the internet or a computer at home? I see someone else asked this question below, but I don’t see where that was answered. This seems to be just another way to divide classroom success socioeconomically. ~ Rubyfreckles78 

What if you don’t believe in homework? What if you believe a child’s time outside of school should be their own, to explore the other adventures life has to offer outside the formal academic arena? ~ katiramom 

"What to learn, how to learn it, when to learn it and how to prove to me that they learned it". I can see that the times of learning has changed but is it not still teacher-cetred in this respect? Yes, a different modality – online and video (great!) but what underlying structural changes in terms of power and student-centredness? "We’ve changed the place in which content is delivered". In what ways are the pupils negotiating content? ~ audhilly

This is great, Aaron. Unfortunately, some school districts–like that one I work in–do not allow their teachers to access Youtube. ~ l2spanishteacher

It seems to me that there is no good answer to the first question. Students without parents at home, who are homeless, or who do not have access to technology at home to view these videos are out of luck. They’ll have to stay at school to watch the videos in the library.

As for the question about homework, this to me is the biggest question I have about the flipped model. It assumes that the time kids spend outside of the classroom should be taken up watching videos. In essence, the flipped classroom model assumes that the instructional time schools are given is insufficient for kids to learn the material. Perhaps we there is simply too much content for kids to learn effectively?

The third question is mostly about pedagogy. Should kids learn in a teacher-centred way, or a student-centred way? While our curriculum is bloated and filled with content, it seems impossible to switch to a more constructivist model, particularly in the upper grades. Constructivist teaching methods take more time than more traditional methods of teaching (but hopefully lead to deeper understanding). 

The fourth question is similar to the first question as that both of them are about access. Clearly the solution here is for the school to self-host the videos, but if this becomes a common instructional strategy at your school, the costs incurred to host what could be thousands of videos is enormous. Now we have an issue that the schools with the money to afford the hosting (or at least the policies in place to allow YouTube and other video hosting sites) are a further advantage to the poorer schools.
 

Some more questions I have are:

  • What does this approach look like for someone who is a novice to teaching?

    One of the valuable pieces of feedback a novice teacher gets about their instruction is the questions students ask during class. Students will often share misconceptions they have about whatever is being taught, which helps improve the teacher’s delivery for the next time. While I think an emphasis on lecture based instruction is not the best possible pedagogy, it certainly is an easy place for novice teachers to start during their career. Flipping the classroom could reduce the feedback the teachers get on their instruction, but see my next question.
     

  • How do students ask questions?

    Students need feedback during learning as well. One of the points of practice problems, and of problem based instruction, is to maximize the number of opportunities for feedback during learning for students. Lecture based instruction typically fails in this regard, and so many instructors have switched over to discussion based instruction. The flipped classroom model, without a way for students to actively ask questions, moves instruction back to a purely lecture based format. One way to counteract this a bit would be to provide space for students to ask (& answer) questions underneath the video lecture as comments, but then the job of the teacher will be to moderate and join into these discussions. While students can obviously record the questions they have (which is a useful learning strategy), this requires organizational skills and self-management skills not every student possesses.
     

  • How much time does it take for teachers to make these instructional resources?

    Preparing for classes and assessing students are the two tasks, other than administrative paperwork, that take the most time for teachers during the course of their day. Preparing high quality instructional videos has certainly become much easier for teachers to do, but it is also time-consuming. Sal Khan might be able to create 8 videos a day, but teachers do not have their entire day available to devote to making videos, and would like to produce videos which include images and animations to clarify some concepts. We could rely on the videos from sources like the Khan Academy rather than making our own videos, but we’d need to search for and preview all of the resources we use, which in itself is time-consuming. There is also the additional time spent during our evenings responding to questions students might have about the videos.
     

  • Will class time be used more productively?

    Aaron’s video above shows some great examples of what I think should be happening in more science classes. The students look like they are getting more chances to experiment, and more chances to interact with and actually do science. Is this what happens in every flipped classroom? If students really understand the concepts being taught by the end of a unit, how can we tell if it was the instructional video, or the time spent actively experimenting that made the biggest impact on their learning? One comment I had from a student was that although his teacher assigned videos for homework, he rarely watched them, but made sure to actively participate and learn during class time. He loved the flipped model because "it meant [he] had less homework."
     

Although I have these questions, there are some things which I really like about the flipped model of instruction.

  • It forces teachers to really think about their instructional strategies and the potential questions students might have.

    You can’t create these videos without putting some serious thought about what you will be teaching for that lesson. This particular type of teaching is much more difficult than turning to page 27 in the textbook and selecting some questions for students to do.
     

  • Students can potentially access a variety of different explanations for different concepts from teachers all over the world.

    Not every student has access to a specialist in their subject area. In British Columbia, for example, there are many teachers teaching math outside of their specialty. I can remember tutoring math when I was in grade 11 in the PE teacher’s classroom (who was not a math specialist, or trained to teach math) and frequently helping the teacher understand the math he was "teaching".
     

  • It provides more class time for more student centred instructional strategies.

    This is the best reason to implement the flipped classroom model since many teachers aren’t ready to give up on teacher led instruction. Students need more time processing the concepts to which they are being exposed. If they do this at home, as is unfortunately too typical in many classrooms, they struggle. In the flipped classroom model, that struggle can happen with their peers and an expert facilitator.
     
  • Students can now more easily opt out of rote memorization.

    Richard Feynmann, one of the best physics lecturers of all time, investigated Brazilian science education, which was heavily dominated by memorization, and discovered that almost no one from this system actually understood science. Since students do not learn well from memorizing information, one can conclude that lecturing is not sufficient to produce students who understand concepts at a deep level.

Does anyone have any answers to these questions?

 

August 16, 2011 / 0 Comments

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.

August 4, 2011 / 1 Comment

RSCON3 presentation online

I’m happy to report that the recording from my Reform Symposium presentation on Interactivity and Multimedia in Math is available to be downloaded here. Almost all of the recordings for the other presentations are up as well, which you can access here.

I’ve also uploaded my presentation slides here, so that you can download it and look at it yourself. Finally, if you are interested in further reading from my blog related to my topic, see these two links:

Update: Taking advice from @shamblesguru advice, I’ve converted my presentation, using a screen-casting program, into YouTube format.

 

July 25, 2011 / 3 Comments

The quiet revolution in education

(Clay Shirky: How social media can make history)

While education reformers like Michelle Rhee, Joel Klein, Bill Gates, and others will tell you that education is stuck in the status quo, right underneath their noses there is a quiet revolution occurring in education.

The revolution is happening through social media. Every day thousands of hours are spent by educators, even during the summer, to improve their personal practice through discussion and sharing of resources. Every day more and more educators are joining the fray, choosing to sign up for social media sites (like Twitter) so that they can become part of the conversation on education reform. While the number of educators not yet sharing their ideas dwarfs the number sharing, those that are sharing are vocal about the benefits that they are getting and inviting their colleagues daily to join them.

There are probably 50,000 educators using Twitter alone, and if each of these teachers posts just 1 average length tweet a day, that’s about 500,000 words written each day on education by people in the trenches. If each teacher on Twitter reads just 10 tweets a day, that would mean that more than 5,000,000 words about education are read each day via Twitter (The actual numbers are likely to be much higher than these conservative estimates).

Outside of Twitter, educators are connecting through Classroom 2.0, Future of Education, and literally thousands of other Nings and professional development sites. There are almost certainly thousands upon thousands of conversations between educators, about education, happening on Facebook every day as well.

Educators are doing much in the non-digital world to connect as well. Edcamps and Teachmeets, which are free professional development conferences, have sprung up all over the world. Educators are organizing TEDx conferences, like TEDxUBC, TEDxDenverEd, and TEDxPhillyEd, to name just a few (I attended all three of these).

This is all done outside of the more traditional professional development avenues, and it is having an impact on education. Teachers are flipping their classrooms, engaging in education hackjams, discussing educational practices in massive weekly Edchats, presenting their innovative educational practices with thousands of other educators via online webinars, and much, much more.

Much of this quiet revolution is happening during times when educators would have traditionally been off work, during their summers, their breaks, and at their homes, challenging the idea that educators aren’t willing either to change, or to spend their own time doing it. Educators are not being paid to participate in the opportunities discussed above, nor are they being given much support.

Instead of blaming all of the current problems of education on educators, maybe it’s time to support the thousands of innovative educators out there taking matters into their own hands? None of the accountability systems in place, or being developed, accounts for the incredible professional sharing occurring globally in education today.

The grassroots efforts are a much more effective way to introduce systemic change than top-down efforts ever will be since peer pressure is always stronger than authorative pressure.

July 14, 2011 / 6 Comments

Toolkit model of math instruction

(exec talking to IT person) Apparently our open API is empowering our customers with unprecedented control over their destinies. So please shut it down.

Image credit: Rob Cottingham

I’ve been doing some programming recently for a friend of mine, and while programming I made a realization. Every time I needed to remember how to do a particular algorithm, or use a tool with which I’m less familiar, I look it up online (or I ask someone for help). In fact, I spend a lot of time as a programmer looking up things called APIs and core functions in the programming language I’m using. The basic structure is very solid at this stage, since I’ve been using it over and over again, but there are still lots of things I look up frequently.

I wondered to myself, what would this look like in the mathematics classroom?

It’s not ridiculous to compare programming and mathematics. Programming and mathematics have a tonne in common, in fact much of programming a computer itself is deeply rooted in mathematics. They are both domains of knowledge which allow for high levels of creativity (provided you are given the freedom to be creative) and rely on an ability to construct algorithms and perform computations. Being good at constructing algorithms is useful, but not sufficient, in both domains for creating complexity and solving difficult problems. It takes more than just knowing your stuff to be good at these two areas of knowledge.

What I imagine would happen, were one to follow this model, is that students would have a resource available to them, whenever they needed it, which had very simple and short explanations of each mathematical computation in their toolkit. Whenever they ran into a computation, and forgot how to do it, they could look it up. Perhaps this toolkit (or mathematical API reference) would be in paper form, perhaps it could be in digital form. Whatever it is, it should be easy to search through. In digital form, it should include short (2 minutes ideally) video snippets showing how to do the computations. Perhaps it could even be searchable by entering an example of the computation itself. Students could add to their personal toolkit as they discovered or encountered mathematical techniques that they found useful, which is very similar to the process programmers go through as they build a code library.

Over time as the students used the reference material, the computations that students used often would be things they would naturally memorize. The less frequent computations might be things they looked up a lot. Students could spend more time working on highly engaging and personalized problems or activities, and a bit less time memorizing all of the computations. Most importantly, they would spend a lot more time practicing an important skill, recognizing what type of computation is useful in a given situation, and being able to relearn that computation as needed.

In Keith Devlin’s book, "The Math Instinct" he makes a lot of interesting points about mathematical ability. One thing he points out is that many people use mathematical strategies successfully in life, for example to do their shopping, but almost no one uses the highly efficient "school math" algorithms they learned. The problem is one of transfer of knowledge. People just generally don’t know how to transfer stuff they’ve learned in school to their lives.

The hope is that these types of API references for mathematics would be something so useful, kids would keep them year after year, and potentially use them in their lives. We already give students formula sheets for many exams, this is just one step further.

Note here that I have a premise which I should make explicit. It is not the learning of algorithms or specific computations which is mathematics, it is the learning of how to use these algorithms and apply them to problems in creative ways, and then extend them as necessary which in my mind is what defines mathematics.

June 12, 2011 / 1 Comment

Let’s run a greener ISTE conference

Recycle
(Image credit: auntiep)

Last year at ISTE, I saw a lot of waste, and I feel like we should be able to run a greener conference this year. Here are some recommendations.

First, take advantage of the watering stations.  If you are planning on attending ISTE, bring a water bottle (or two). Make sure to fill up your water bottle rather than using the disposable paper cups, or even worse, plastic water bottles. You need to be hydrated, but you don’t need to be producing extra waste. In fact, you could bring your own utensils and a plate as well, and rinse these off in the bathrooms so that you don’t have to throw away paper or plastic plates.

Next, participants, please avoid vendor hand-outs. You aren’t going to look at them. Use your electronic device, and take pictures, or take notes instead. Take the time to get the contact information on the vendors whose products you are really interested in exploring further, and say no thanks to their brochures. Vendors, please learn about QR codes. Provide short urls to resources which are deep-linked if you must, but don’t be fooled into thinking that your little pieces of paper are useful; they aren’t.

ISTE organizers don’t give every participant a copy of the program guide to look at.  Post maps at strategic places within the venue itself, and your already out-of-date schedule, is up already in electronic form on the ISTE conference website.  This is a technology conference, use the technology effectively! Demonstrate best practices.  There were hundreds of laptops with internet connections set up all over the place; these could have been better utilized. Again, nearly every participant will have a portable electronic device with them. Instead of your newspaper, use a blog on the website with an RSS feed.

Everyone at the conference should put their devices to sleep when not in use. The power output at ISTE will be enormous, and given that in the United States some of this power comes from coal, it behoves those of us involved to be aware of our power use. The ISTE laptops, while useful, should go to sleep, with instructions beside each one available so that people know they can wake them up from hibernation mode and use them. The LCD projectors that nearly every vendor feels like they need to use are expensive in terms of power use. Vendors, your products aren’t more likely to sell because you have a flashy presentation, they  will sell if they are useful.

What are some other things we can do to run a greener conference?

 

April 14, 2011 / 2 Comments

Free tools for math education

Here are some tools which I’ve either used (or explored) for mathematics education. They aren’t all open source, but they are all extremely useful, and they are all free to use (free as in free beer, some of them are also free as in free speech).

 

Geogebra

Geogebra image

This program lets you explore algebra and geometry, much like it’s proprietary cousin, Geometer’s Sketchpad. Having used both, I actually prefer Geogebra because I find it to be more flexible and easier to use. It will run on many different platforms including Windows, Mac, Linux, Android, and iOS.

 

Mathematics Visualization Toolkit

MVT screenshot

The Mathematics Visualization Toolkit is exactly that, a program which lets you visualize mathematics. You can use it to build complex visualizations, or you can use the visualizations which are already included (which are awesome by themselves). You can either use the web start version of the toolkit, or download an offline installer. 

 

Scratch

Scratch screen-shot

Scratch is an excellent program for learning programming but also mathematics like variables, sequences, Cartesian coordinates, and other useful mathematical concepts. Developed at MIT, it is a free download and includes a strong user community to seek help, and see what else can be done with the program.

 

Netlogo

Netlogo screen-shot

Netlogo is “a multi-agent programming modelling environment” (According to the Netlogo website). It comes with hundreds of models for all areas of science and mathematics preprogrammed. It is a free download and will work on any computer which has Java 5 or later installed.

 

Audacity

Audacity

Audacity is an open source audio editor and recorder. One example use in mathematics is to record a bouncing ball, and use the visual data from audacities recording to turn this into a graph of bounce versus time between bounces. You can also use it so students can record 60 second podcasts explaining some aspect of mathematics.

 

Calculize 

Calculize

Calculize is a free (currently) web app which lets students perform mathematical computations using a reasonably simple programming language. 

 

Wolfram Alpha 

Wolfram Alpha 

Wolfram Alpha is a computational engine built on top of the Mathematica architecture. It is amazingly powerful, and turns some homework assignments into a breeze. Recommendation: change your homework assignments, or do away with them all together.

 

Desmos

Desmos screenshot

This is a free online graphing calculator. It emulates a lot of the functionality of a typical graphing calculator but with a much easier to follow user interface and without much of the non-graphing functionality of a graphing calculator. It is easy to create graphs, and then share those graphs with other people. It is also currently in development, so it is still improving over time with new features being added every couple of months.

 

Logo 

Logo

This Logo emulator lets students play with the classic programming environment Logo, built for kids by Seymour Papert and his colleagues at MIT, all online. It requires Java, but should run on most computers (sorry, no iPads…).

 

Google Earth

Google Earth

Google Earth is free (but proprietary) software that allows students to explore the world in 3d. One could use it for GIS applications, or even to explore the relationship between our 2d mapping system (longitude/latitude) and 3d space.

 

Google Sketchup 

Google Sketchup

Google Sketchup (another free, but proprietary program) that allows students to create highly complex (or very simple, if they prefer) models. I’ve used it to have students construct their “ideal” school, and then from this model, they calculate the cost to build their school. 

 

Screenr 

Screenr

Screenr is a free (for up to 5 minute recordings) screen-casting (think record your screen as a video) software. Some possible uses of it are for students to use it to create video tutorials, record their process of solving a problem, or create their own video word problems. Another alternative for screen-casting is Jing, but it publishes to a format which is harder to share in the free version.

 

Endlos 

Endlos

Endlos is an open source fractal generator which I’ve found runs very fast. It runs in Java, so it should run on any computer capable of supporting Java. The ability to experiment with, and explore fractals is a very interesting thing for students to do, but very tedious to do by hand…

 

The Number Race 

The Number Race

The Number Race is an open source program intended to help students who have dyscalculia develop their number sense. It has many levels of difficulty, and runs in Java, which means it should run on a wide variety of computers.

 

Code Cogs equation editor

Code Cogs online equation editor

This free to use online equation editor could be a nice way for students (and teachers potentially) to construct equation images for use in a website.

 

Eigenmath

EigenMath

Eigenmath is an open source program for symbolic manipulation in math. It runs either in Windows or on a Mac. Some examples of what it can do are shown above.

 

Peanut math programs

Peanut Math programs

These 9 free programs cover a wide range of different types of mathematics. Above is the popular statistics calculation and visualization program included in the package.

 

Yacas

YACAS

Yacas (Yet Another Computer Algebra System) is a command line program which allows for the symbolic manipulation and calculation of mathematical expressions. One thing I like about it is that it calculated 600! in a fraction of a second, so it is very fast (an aside, ever wondered what 6000! factorial is?)

 

Free CAS programs

 

Update: Just found an open source implementation of LOGO (as described in Seymour Papert’s Mindstorms) here: http://www.softronix.com/logo.html

 

Other free programs which I have used either for constructing mathematical diagrams/simulations or with students in some way include:

The Gimp, Programmer’s Notepad, Flex Builder (free with an education license), Open Simulator, VLC PLayer,
Wolfram Demonstrations (requires a free browser plugin), and Project Euler.

You might find these programs as useful alternatives to the “free apps” which “help” students memorize formulas & algorithms. For an enormous list of other free programs see this helpful list.

 

What other free programs for mathematics education do you use with or for your students?

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