Math Reform (or: An Essay in Mathpoetry)

In the spirit of Harry Hess' revolutionary 1962 paper (An Essay in Geopoetry) that set the basis for Plate Tectonic theory and shook the foundations of Geology to its roots but provided no firm evidence or research to support its points, I am titling this blog post "An Essay in Mathpoetry." I doubt it will shake the foundations of teaching mathematics to its roots, but having been a HS math teacher for 15 years prior to becoming a tech facilitator, I have observed lots of changes in math curriculum, and witnessed (and participated) in lots of facets of the 'math wars' over curriculum, technology, calculators and pedagogy, and I have an idea...but I have no research or firm evidence other than my own experience to back my opinion. But then again, that's the perk of having your own blog. :-)

Despite striving to be a modern educator, using collaborative tools and exploring ways for the kids to lead the learning, my math classrooms were very traditional. I often was the 'sage on the stage', guiding instruction with examples and lectures, my teaching notes were meticulous and I carefully scaffolded problems until the kids could see the patterns and could use the underlying mathematical principles in more and more complex situations. The kids were often in rows, isolated with their thoughts and deeply immersed in solving problems, collaborating when necessary, but responsible for their own work. Although I tried, when appropriate, to provide 'real world' examples for the math we were learning, it was always challenging,  limited in scope and a little forced. I always felt a little guilty about this, as the literature and lunch table conversation was about 'using real-world examples' and 'making it authentic', however the mental world my students and I occupied was already rich with ideas and concepts, and I almost never had students who claimed they felt that they missed something by not being given examples of how completing the square would be useful in their lives, or what the role of imaginary numbers would be once they graduated college. I found that, just as a chess player can get immersed in a challenging game with a fair opponent into a state of 'flow' as described by Mihalyi Csikszentmihalyi, my students did not need concrete examples and real life applications to become immersed in the process: increments of success with ever-increasing complexity was enough to draw them in. The beauty was in being able to crack the shell of a complex math problem, use the correct mathematical tools to break it down, and express the solution in the most efficient and standardized form. It didn't matter that the problem was a purely theoretical construct, with numbers and structure rather than apples and pears, and the answer was not expressed in terms of 'how much land should Farmer Brown plant'. The process was as meaningful, and as meaningless, as trying to checkmate your opponents King. And just as challenging and open-ended. And satisfying.

This disconnect between teaching ideology and my pedagogy grew with the release of ever more powerful calculators. As calculators evolved beyond 'number crunching machines' into having more advanced features like a Solver, graphing ability, symbolic notation and CAS operations, more and more, kids could get the 'right' answer by inputting the problem and hitting a button, entirely circumventing the underlying processes. And just as having a cheat code to a game diametrically changes the game experience, having these technical tools drove a change in pedagogy. Math teachers starting using  sensor devices to generate acceleration data, temperature probes to gather data from which to derive logistic curves (using a plotter and solver), and the growing challenge became less about how to scaffold problems of growing complexity, but how to run classroom experiments that had dependable results so students could extract the mathematical concepts, but were authentic enough that they were meaningful. In short, 'good' math classrooms began to look a lot like good science classrooms.

I'm not opposed to this: authenticity is a wonderful thing, and many (even most) students require this to internalize their learning. Many students comment on how they never really understood Calculus until they took Physics and had to use it. Or never understood Geometry until they took a surveying class and had to apply it. Applied concepts are essential, for many. However, science teachers are already quite good at running good science classrooms, and a lot of Theoretical math is being lost in the process, and we may have thrown out a bit of the baby with the bathwater.

Some students actually thrive more on Theoretical Math, rather than Applied math, and many teachers are quite adept at teaching Theoretical Concepts. There is a legitimate debate about what is 'mathematical thought'...I attended a presentation from a renowned math teacher from Philips Exeter Academy who showed us some problems using 'clock arithmetic'. He concluded that the kids were learning to think in a different base and modulo, and that this was a great example of extracting 'mathematical thought' in a physical activity. I challenged him, asking why learning to crack a 5th degree polynomial by hand to find all the precise roots, real and imaginary, by using Descartes' Rule of Signs and the Fundamental Theorem of Algebra, was not 'mathematical thought'. His response was that it was no longer necessary or useful to do that, as the calculator could find all roots and express them, even irrational ones. My point was that the kernel of the activity was not the solutions, but in the process involved in figuring out how to find them using purely mental tools.

Our world still needs theoretical mathematicians; people who like to solve incredibly complex abstract mathematical problems and who do not require any basis in the physical world. This is the underpinning of Encryption, Cosmology and a host of other disciplines. As many have said: mathematics is not necessarily applied mathematics. And HS science teachers already have a conceptually rich environment to use applied mathematics; why should math teachers try to compete with or replicate this?

My proposal is that HS math and science curriculums should differ in ideology. Science classes should teach the amount of applied math needed to understand the physical scientific concepts in their courses, and all kids should be required to take an abundance of these classes. This will develop a group of citizens who not only understand basic scientific principles, but also have enough mathematical skill to participate in intelligent debate, and who see math as a useful and important skillset for existing in the modern world. Science/math courses should use calculators, computers and all sorts of technologies to assist with helping kids find actual, practical and usable solutions and to be able to represent and interpret situations and results.

Math departments, on the other hand, would be smaller and focus on Theoretical or Pure math. Those students who enjoy finding solutions to abstract problems, with an early emphasis on solving problems by hand, could take these courses as electives, taught by teachers who prefer to teach this content. The non-calculator based coursework would establish a firm understanding of the concepts underpinning the procedures, and students could be encouraged to delve into deeper theoretical questions about patterns and theories. And being released from having to offer these courses to ALL students would free up the curriculum for those who truly thrive on teaching and learning this material.

Anyway, I'd love to set up a program that did this; put the 'real world' math and the abundant math tech tools (calculators, etc) in the hands of the science teachers, and let those who liked to play with numbers and patterns immerse themselves in Pure math. They could still use technologies, of course; sharing findings online, recording their efforts and sharing ideas and suggestions via blogs, voice thread, youtube, and online programs etc. Calculators and other devices would be available once the students felt that they had a good understanding of the concepts and principles, but the consistent technologies would primarily be about sharing and communicating, rather than generating solutions or data and trying to extract the (sometimes quite sublime) underlying mathematics.

ADE application

So my application is in the eMail for the Apple Distinguished Educator class of 2013. I applied two years ago and was rejected: a major component of the applications process is to submit a 2-minute video about a topic that changes yearly. The topic in 2011 was 'How do I use Apple technologies in my profession" and in truth, it was a crap video. I was seized up with writer's block until the last second, then I threw something together and it showed. It was pretty much just a talking head rambling on about using technology remotely....not impressive at all.

This year, I put much more thought into it, and the question was much more manageable: "How do I use creativity to transform the learning environment?" I mean, that's practically my job description!

I decided to focus on three things: the SDLT, my Experimental Classroom, and StuCon2012. All are innovative, self-created and were effective in supporting the technology mission of the school. I wanted to include some other stuff, like the cool jury-rigged document camera I made once, and to talk about the websites and protocols I have developed here at HKIS for different purposes, but the video can only be two minutes long. As it was, I had to 'layer' the message with images and voiceover, plus a popup window and a scrollbar.

Lots going on; check it out and tell me what you think.

Catching up

It's been awhile since I've blogged and a few things are running through my head. So there are going to be several blog posts in a row; I want to unload some of my thoughts before they fade.

First: An update on the Gr 9 Blogs
OK, so I have been able to troubleshoot the issue of getting every Gr 9 student to create a blog (using blogger), to link their blog to their myDragonNet profile, to set their security settings so that they would not accept comments (for now) and to make their blogs visible to the world to see, but only if they had the URL.

The challenge has recently been to be able to verify that these settings are correct. I had a big meeting with all the HR teachers and gave THEM the task of checking this with their kids, but unfortunately (and not unexpectedly), the HR teacher's skills are all over the map, so they are not really reliable editors. My newest idea is to have the members of my SDLT go to each homeroom and check settings, etc, then bundle the blogs and send the link to me.

For those who do not know what a 'bundle' is, it's a great feature of Google.reader that they finally got fixed a few months ago. After you subscribe to a bunch of blogs and drag them into a shared folder, you can right-click on that folder, select 'create a bundle' and it gives you a link you can send around. The recipient gets the link, clicks on it, and it installs the complete folder into their Google.reader account. It's a tremendous way to share the blogs. Unfortunately, google.reader does not allow you to make subfolders, so you cannot bundle all these HR bundles into one, but at least you don't have to subscribe to 180 Freshmen blogs at once. In the future, I'll see about putting all these bundles on a webpage and uploading that, so people don't even have to get them in an email.

This thing about the teachers' skills being all over the map is huge. Learning to use technology is a huge process; I do it full time, and I feel like I've just scratched the surface. For my colleagues who teach content area full time, the additional (and uninvited) burden of having to infuse tech tools is really a challenge. A tech colleague put it very well: it's the difference between a 'trip' and a 'journey'. People on a trip just want to get to the end destination, and success is measured by merely completing the task. People on a journey are more interested in what happens along the way; success is measured by the different things encountered and the experiences. Using tech in teaching can be either: to those for whom it is a trip...they just want to get the task done the quickest way possible and get back to their other responsibilities. To those for whom it is a journey...each tech-related task is a learning ground for new experiences and tools, and they don't mind the time spent exploring settings, troubleshooting, etc. They actively link new tools with old, modify tasks to accommodate new skills, and are always learning. I think a major component of the job of a Tech Facilitator is to help teachers become more interested in the journey, and less on completing the trip.

Next post: musings on Math curriculum.

Checking and changing security settings

Here is a video that shows you how to:

• Make the blogs hidden from search engines, and
• Block comments until further notice.

(the video may not show on iPads: it uses Flash)

Blog security

This is the second post to parents about the Gr 9 blogs.

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Blogs work best when they have readership, however it is reasonable to be cautious about letting students broadcast ideas out in an unsupervised fashion.  Although they are already prolific users of social media, we do not expect our students to inherently understand the appropriate boundaries for these blogs, as they are very different than their typical informal social online presence; these are ‘professional’ sites and should reflect maturity and presence of mind. This is quite different from their ‘informal’ digital presence that they have in Facebook and other social media sites, where they use informal symbolic notation (phonetic spellings like ‘ur’ instead of ‘your’, etc) and post humorous and quick comments.  It is quite reasonable to assume that they have little, or no, experience maintaining a professional online presence, so these blogs provide a wonderful opportunity to help them develop this skill.

 They have all created profiles in ‘Blogger’, a simple and user-friendly blogging platform that is contained in the suite of tools provided to HKIS by our google.apps account (along with gmail, google calendar, google sites and several others). The shared platform means we can standardize instruction on how to use them and how to change and control settings. Ultimately, however, control over the settings is in the hands of the student, so it is important that adults regularly check to see that they are properly set.

Currently, as the students begin their creative process, we have asked them to make their blog settings such that no one can comment, and the URL address of the blog is hidden from search engines. As a result, the only people who can see their blog is someone to whom the URL is given directly. As of now, their blog address is stored in their user profile in myDragonNet, so only people with access to that password-protected site can find their site. Parents are welcome, and encouraged, to ask their sons or daughters for their blog addresses: these are meant to be showcases of their growth and achievement, and you can give them feedback on their posts and the appearance of their blogs.

Over the first year, once the blog has enough content to have a ‘tone’, we will instruct students on how to open their comment settings so others can provide feedback in a ‘moderated’ fashion. This means the author will still retain full control of what is seen; they can reject and not publish any inappropriate or non-constructive comments; hence the content of their blog is still entirely under their control. Likewise, at any point, if a post or title of a post is deemed inappropriate, the student can edit and change past posts, and even hide posts until they have reworked them into a form that they are proud to publish.

Blogging is a tremendously common social platform with people all over the world participating. As with virtually all school blogs, our own have a specific purpose: to document growth of understanding of the SLRs. At all times, important stakeholders will have the ability to see the growing content, while the student learns appropriate digital behavior. The author retains full control of their content, even posted comments, and can edit and ‘rework’ their content over time and as skills improve. Teachers, counselors, administrators and parents can all watch these products unfold during the students’ time at HKIS, and the author is welcome to share their blog with relatives and friends, as they choose. Parents are welcome and encouraged to subscribe to their child’s blog and discuss them together. Once there is a good record of posts that show the development of the student, they may choose to share them with summer employers, colleges or anyone else to whom they want to have see their development as a student at HKIS.

Next post: Setting up a google reader account so you can subscribe to your child’s blog.

Commmunication

Keeping parents and other stakeholders informed of the process is crucial. This is the text of the first of about 6 parent communications I will be sending home over the next 5-6 weeks.

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This year, all Freshmen students have staked out a blog space where they will be guided through reflecting on their growing understanding of the SLRs during their time at HKIS. With our rich technological environment and 1:1 laptop program, we have all the right tools in our grasp to make this an authentic and valuable digital learning experience where the students can reflect upon and record their own growth over four years, with guidance, oversight and instruction.

A ‘blog’ (contraction of ‘web log’) is merely a digital presence; an online website where an author posts entries in reverse chronological order (newest on top) about some topic. Blogs can host a wealth of digital content; movies, photos, hyperlinks, embedded documents, and serve many purposes.

• Interest blogs, where authors share their hobbies, like fashion, technology, movies or travel;
• Information blogs, with info on family gatherings, concerts, etc or documenting an event;
• Expert blogs, where the author provides guidance and resources for others with a similar interest. Many teachers post ideas for lessons via blogs of this type;
• Collaborative blogs, where groups of individuals collaborate and enhance their communication channels;
• Reflective blogs, where authors post their thoughts on a topic for an intended audience.

The main thing that all these types of blogs have in common is that the posts are done by individuals in a digital space, with the hopes that they will hold the interest of readers.

The student blogs are of the Reflective type. Over the course of this year, the counselors are teaching the students about the SLRs and their relevance to the HKIS learning experience. As these are transcendent ideas that exist across all courses and activities, they are not usually directly taught within a subject area, yet they are important to the HKIS learning experience. The blogs ensure that the students are mindful of their existence and reflective on their growing understanding. As they make reflective posts once or twice a month over the next few years, they will generate an historical record of their own developing understanding of the SLRs, and as a result can see and share evidence of their own growing maturity as thinkers and learners.

As a digital learning tool, blogs offer some tremendous opportunities, and accordingly schools worldwide are leveraging them. Students improve their literacy skills, learn appropriate online behaviors, improve their skills with using technology, develop a learning partnership with their family, school and friends, and generate a record of content and growth that is relevant and important. As students ‘grow’ their blog with more posts and take increasing pride in their production, they can also generate an audience of readers from among their friends and family, who can provide important feedback and validation for the student’s reflections. This is a truly authentic learning experience being developed under the watchful eyes of their counselors, homeroom teachers, peers and parents.

Next week: More on blog security, and how to check your child’s settings to ensure that you are comfortable with who does, and does not, have access.

Going Blog, part 4

So now we have successfully had all 187 Freshmen create blogs. The next step is to start getting the different audiences and mentors involved at a pace that is manageable for them, engenders their support and gives them a role, but also keeps them all in alignment with information, goals and objectives.

Since the HR teachers will be important mentors, I am working with them this week. Their role will be especially important in the realm of helping the kids make good value choices with how they present themselves publicly, how they cultivate their tone, and how they respond to others, I am helping all sixteen HR teachers create google.reader accounts, subscribe to their kids' blogs, and sometime in the next few days, to check that all the blogs have the following:
     -appropriate blog names
     -appropriate post titles
     -correct privacy and security settings (more on this)
     -appropriate URLs
     -the student is posting under an appropriate name.

The great news is that google has finally fixed the bundling problem in Reader! It's been around for years, but now it works: with two clicks, the teachers can share the entire class set of blogs with everyone else's reader page.

The security thing came up from a couple of parents. Some are less comfortable with their child's blog being accessible to the general public, so they found the setting to make the blog only readable to those who are invited. This solution has several problems.

First: by closing down visibility, no one can see the blog! Blogger only allows a single account to be a member of 100 blogs, so there is no way all 800 HS kids can have their blogs closed by default and still list me or the HS Admin as members.

Second: It's a solution to a problem that might not be as extensive as the parents' believe. There is no evidence of stalkers ever finding kids via monitored school blogs. Instead, data shows that overwhelmingly, situations that arise are in connection to a relative or someone who already knows the child. or through unsupervised social network sites. However, we want to help educate the parents as we accommodate their concerns, so it's important that the HR teachers are involved in the discussion.

Our solution is to have the kids of any concerned parents change their blog visibility settings so it is hidden from search engines. The steps are very easy: just go to the settings and look next to "privacy". This is analogous to having a house with the door unlocked, but the house is hidden in the woods. The blogs are 'open' (unlocked), but hidden. This way, parents can send the URL to relatives and friends who can read the blog, but search engines will not find it.

Of course, search spiders are clever, and this method is not 100% foolproof (what is?), but for now it provides an excellent level of control and assurance for anyone concerned.

We have, of course, discovered a new bug. When the teachers subscribe to this blog, they also see an old cached post from a different blog one of the ETS techs and I were working on a few weeks back! It's not even part of this blog...but somehow it is linked when to subscribing to this one. If anyone reading this (from among my hordes of followers) subscribes and sees this, let me know: the top post (Doesn't matter) should not be there. I'll let you know what I discover.