This morning as I was looking for images to use in a new math course I'm developing for students in a country I've never visited, I came across the work of a math educator named Ben Chun. Chun seems to be one of those brilliant people who, fortunately for his students and those of us who read his blog, gravitated into teaching. His "Facebook Visualization" in Flickr Creative Commons

... bears an interesting resemblance to the Fibonnaci seqence (from Algeblog9)

... and will fit into my unit on Patterns in math, nature, music, art, and more.

Conceptualising this course has been a bear of a task. Many of the students drop out when they are young teens, and a one-to-one laptop program with individualised learning packages has been instituted as a way to keep them engaged in school work. The students will have no connection to the internet so the wonderful world of online interactives cannot be accessed.The courses have to be completely self-contained and self-managed so if the students go into school only occasionally, they can still be successful.

Interestingly, depriving me of the ability to use what I've spent 5 years becoming good at has forced me to think more deeply about the relationship of curriculum structure to student learning. How do I build in interactivity? What will be its purpose? How can I make math into a 'do with' rather than a 'get through' subject? How can I give the students more choice and control and at the same time ensure they take on the responsibility for ensuring they have the skills needed to meet the requirements of standardised tests? I want them to look forward to opening their laptops to do math. I want them to be interested enough to take on the hard stuff rather than have the course reconfirm that math and staying in school are not for them.

Chun's reflection on the benefits of teaching programming to math students is a nice metaphor for  my underlying big idea:

"School teaches that errors are bad; the last thing one wants to do is pore over them, dwell on them, or think about them. The child is glad to take advantage of the computer’s ability to erase it all without any trace for anyone to see. The debugging philosophy suggests an opposite attitude. Errors benefit us because they lead us to study what happened, to understand what went wrong, and, through understanding, to fix it." (http://goo.gl/Mdqgu)

You can't convince a kid on the verge of dropping off that math is good for him because it will help him get something he wants some day in the future. The work either has to be intrinsically interesting or have a real-world usefulness. One has to get the kids staying with the work and enjoying the results so they have an opportunity to engage in what Chun calls 'computational thinking':

"When we analyze the effects of computation, we take note and measure how data is transformed. We look at how information is processed and what is accomplished by that processing. We can think about what we might do if such computational power wasn’t available. That can also help us start to imagine new things we can strive to accomplish using computation." (http://www.ctillustrated.com/)

Another math educator, David Tall, comes at mathematical thinking in a different way (http://www.lsri.nottingham.ac.uk/mtw/onlinevideos/Tall.html). His writing reminds me that there is also still a place for solid procedural learning in my course. Part of math learning requires that students give up replicating real or natural processes over and over and do the work of commiting facts to memory and coming to recognise relationships automatically.

Most of us don't have to examine and mentally aggregate the parts of a table to know we're looking at table. We've been there and done that enough times that we can instantaneously recognise table-like shapes and objects. Yet many children, especially those who struggle in math, cling to primitive routines such as counting (instead of learning math facts). This makes such processes as long division and calculating fractions into Herculean tasks. If students don't encapulsate mathematical processes into "thinkable objects", all their attention and brain power is sucke up be by the lowest level tasks. These students end up with huge 'no go' mathematical zones that at first slow them down and eventually cripple their ability to enage in the the kind of nimble, flexible thinking needed to use math more powerfully.
 
So today's conclusion is that crystallized intelligence +  fluid intelligence = a more "global capacity to learn" (http://psychology.about.com/od/cognitivepsychology/a/fluid-crystal.htm). People aren't either left or right brained. The 2 hemispheres are in continouous communication with each other giving us our ability to engage in complex behaviour and higher order thinking (http://goo.gl/Qdfm and http://goo.gl/R6GqH).
 
The problem of what will make a good course structure then becomes a sort  of 'chicken vs. egg' problem of where to start. How to keep more students learning more math more successfully comes down to letting the students choose where to begin --i.e. with learning prodedures if that makes them more comfortable or exploring problems and projects if that's what will draw them in. It doesn't really matter where a learner starts in the mathematical landscape, but the couse must also develop the understanding that it's not good enough to just get better at what you already does well or like.

Becoming a powerful thinker involves leveraging what you do well to learn something new or different. In math it means growing and expanding your talents rather than using them as a boundary or circumference to delineate what you will (safe; inside the circle) and won't (too far outside the compfort zone) try. It also means being able to later look back, engage in a little of Chun's computational thinking, and savour how far you've come.

I just finished co-authoring and co-moderating a Moodle Meet on mLearning.

(Click on the heading to see the entire resource collection).

 

Today I was looking back through this blog and came across this passage which was written in 2008. It was part of an interview I gave for the company (Freepath) which generously sponsored my first conference presentation. At the time I'd only had internet and a computer in my house for about 18 months. Yes, I was an edtech late bloomer .....

Question: How do you see social media impacting students in the 21st century? How does it impact teachers and where do you see the intersection? 

My response: Marshall McLuhan created the slogan "Reach out and touch someone" for the Bell system in 1979.   I think he’d be delighted by the way technology has so shaped our lives in the nearly 30 years since his death.

Clearly many students are wrapped up in a web of connections -- whether it’s as simple as passing notes by texting each other or participating in Facebook or Second Life. Contrary to school rules, their phones are always on. We can either fight this or, in the parlance of the 60’s and 70’s, co-opt it. We may not be able to ‘out-tech’ our kids but we can certainly outsmart them and harness their desire to be connected and use it for our own purposes.

Students with their phones out on their desks, accessing the internet and completing tasks using these as a primary learning tool can’t be texting each other under the table.  Students who are using the wealth of the internet as their primary learning resource and who are more engaged in their learning don’t have time in class to manage their Facebook files and keep up with their Tweeting friends.

Regarding how social networking impacts teachers:  I’m of the “Be wary because Big Brother is watching” generation, and I still have a lot of distrust for living so publically, but I will say that finding how willing people “out there” are to make time to help each other completely took me by surprise.

That 2008 reflection of mine sounds so much like many of the comments about the educaional benefits of mobile devices shared by participants during last week's Moodle Meet. Did I have amazing foresight or, as was suggested yesterday during a TLT Friday Live webinar, has education moved into a state of perpetual 'beta' with advances in technology both forcing us to revisit the same challenging questions and giving us the opportunity to experience the same joys of redicaovery over and over?

This week I started out by thinking about David Wiley's challenge to all Change.MOOCers to envision how our personal ideas about change and educational technology might be played out in the world at large. He urges us not to be content to keep our thoughts inside ourselves but to actualise them by dreaming BIGGER and pushing our vision for change out beyond its normal horizons.

Then I came across this oh-so-short but eloquent piece from a Brazilian blogger.

(Link to original -- http://lucidatranslucida.blogspot.com/2011/10/fragments.html)

And I was reminded of a piece I read years and years ago in the weekend supplement of my hometown newspaper. It was an interview with Jean Vanier about L'Arche. Vanier explained how he'd been frustrated by his inability to change society. On the advice of his local priest, he created a home for two mentally challenged people. Through his daily life with them, he came to understand that his desire to be of some use in the world could be realised through simply giving one person (or a few people) a better life. Vanier gave up on being a radical and as a result has become a revolutionary.

So, perhaps the greatest task of new age educators is to confirm/reassure/convince/ each student who comes into our care of the value of his/her own fragment .... of the potential of that fragment to be the missing piece in someone else's bigger picture. Holding back may mean that other person's moment of understanding will be lost. Contribution may result in an exquisite new pattern or trajectory.

I've been working for a while on an application for a position as Educational Technologist in a Canadian university. Because I'm not a perfect-fit glove for the fingers of their job description (I've only used 2 of the 3 specific tech tools they mention and have no higher ed. instructional experience),  I'm crafting a statement of qualifications to try to convince the selection committee to give my application a second look. It needs to convey to them that the experience, skills, and understandings I've developed over a 30 year career as a K-12 teacher and during my recent foray back into the world of higher ed as a student pursuing an M.Sc.in Instructional Media make me uniquely qualified for this position. (I can figure out the hard skills in less than a month. And anyway -- because one of their big 3 programs creates flash-based media that don't work on many mobile devices, they'd be better served by hiring someone who will find them something new and easy-to-manage fast.)

Over the past month I've steeped myself in this campus's teaching and learning literature, created 2 Scoop.its on blended learning, and attended a bunch of webinars in the higher ed world. The latest was yesterday's with Martin Weller on Digital Scholarship. His blog led me to to another Cormier/Siemens course. From there I linked to an interesting  'bark out' in the Cogdog (aka Alan Levine) blog about his getting caught for a gross breach of copyright. Near the end of Levine's article was a paragraph about how hard it is to do a really good mash-up -- to combine ideas and learnings from a number of different sources "into a whole to create a new meaning or structure" (Ask.com).

But wait -- isn't that the definition of SYNTHESIS? And shouldn't a pedagogy of abundance pay special attention to synthesis? And where is synthesis in the updated version of Bloom's Taxonomy?

GONE, THAT'S WHERE!!!

Some educators equate 'creating' with 'synthesizing'. But more and more I'm feeling that, in this age of information abundance, it's short-sighted of us to ignore synthesis as an important higher order cognitive skill in its own right. To assume learners come to courses knowing how filter and blend so much input is to make mental mashing-up into a precarious task.

I agree that the old Bloom needs revising, but perhaps, instead, 'applying' and 'creating' could be subsumed into one new category -- innovating -- which would then leave room for us to restore 'synthesizing' to the critical thinking skills list thereby ensuring learners have lots of chance for practise.

So here I am -- still at my lonely desk -- trying to mashup what I have to offer this university into a package that will fit enough of what they need so they'll invite me for an interview. If I write it well enough the selection committee will be able to give up just enough of their preconceived notion of what an ed tech person should bring with her to this job to give me a kick at the can.

 

I've been clearing out my webmail this morning. I'm in a MOOC, and Moodle Meet, and the MathFutures Google Group, and there is so much material is floating into my inbox that I tend to let it pile up like a log jam and then have to selectively blast out a few holes so I can find critical daily communications amongst the torrent of inputs.

But before I finish my clean-up, I want to address the issue of filtering when it comes to input overload because this idea keeps coming up over and over again for me. It was in an old email I will throw out after today and in a Moodle Meet discussion I read last night. For that Meet, I'm curating the main discussion points and resources that are being shared. I'm just following the discussion so there's no overarching or underlying organizing principle; it's simply a record.

The suggestion was made that perhaps the entries could be arranged to show a better correspondence between teachers' needs and wants and the information bubbling up in the course. But I'm wondering if this might end up helping to perpetuate traditional paradigms by giving them a 21st century face lift (not necessarily a bad thing) and whether leaving the information messy and MOOC-style might encourage people to construct their own processes using the pieces they like. Is filtering helpful when it comes to consolidating best practices or a hindrance to innovative thinking?  I think as long as the amount of information doesn't deter potential readers altogether, then hodge-podge might serve many goals whereas linear only fulfills one.

In late August the video below touched off a similar discussion in the MathFutures forum about what constitutes a good thinker. 

When I first saw that during a cognitive neuroscience course a year before, I so completely missed the gorilla I had to replay it to make sure it wasn't a hoax. I knew part of the problem was my gullibility. Like magicians who use sleight of hand in card tricks, the video makers sucked me in and even reinforced my selective attention with misdirection.One view in the discussion group was that missing the gorilla is a sign of a highly-focused brain. A good thinker is someone who can "dismiss unnecessary inputs". Although I've cultivated that ability, I'm no longer sure it's always a strength.

A long classroom teaching career has taught me that many educators are too quick to dismiss unexpected inputs or inputs that don't seem to fit a pattern as unncecessary. The kid who doesn't work productively in class becomes a trouble-maker who needs to learn to conform. Complaints become inappropriate remarks that are personally motivated instead of information. New technolgies become add-ons that take time away from the important stuff in a curriculum.
   
After a recent workshop on a new math program I stayed beind to listen to the workshop leaders debriefing the day. There was one person in an audience of 20 who'd kept urging them to shorten their traditional 'show and tell' (pushing out of information) and move the learning into more interactive, small groups. The leaders were relieved that she would not be back for Day 2 as her comments were deemed 'unnecessary input'. The proponents of this program have scientifically-produced research to prove that the best results are achieved when people stick to the script. There is no room for creative applications of key ideas. Digressions are politely acknowledged and then just as politely ignored. Workshop groups are doggedly herded along one trail.

I think this way of 'not seeing' goes to the heart of the main shortcoming of their entire program. Although they can ensure all participants will be able to count the number of baskets, the regimentation is turning teachers off so the program isn't getting broad acceptance in the public school system. As a result, huge numbers of kids are missing out on a wonderful learning experience. But the program leaders, armed with their own selective focus, choose not to see that gorilla. The potential to transform the way math is being lost because they're taking this all or nothing approach. Instead of showing people the fundamentals of what makes this program work, they are teaching scripts.
 
So I think we often leap too quickly to the 'unnecessary' brand and remain unaware of potentially important information (i.e. the gorilla) because we get too intent on theone path we see between us and our desired outcome. Sometimes being open and alert to what does not fit can be as (or more) important than just paying attention to what does. That way lies creativity and innovation and best of all - delightful surprise.

Can you watch the gorilla and count the passes at the same time? I haven't tried but I suspect not. Perhaps this means that we should be modeling and teaching how to become more adept at swtiching focus, at seeing issues through different lenses, especially when it comes to educational change. In the words of Mike South (member of the MathFutures discussion group): "In the case of the gorilla problem, you are asked to solve something simple, and the better you are at ignoring distractions, the better you are going to do. I think the brain that sees all the motion on the screen and then goes to 'ignore everything in black' is doing the right thing ... but only if you were right about the nature of problem in the first place." And in retrospect, how often does that really happen?[[posterous-content:pid___0]]

 

I've been watching a video of Doug Belshaw's 2010 presentation about the importance of not taking a one-size-fits-all approach to implementing mobile learning (or any other educational reform for that matter).

Readings:

~George Siemans: Narratives of Coherence (http://ltc.umanitoba.ca/connectivism/?p=61) ~Teaching in Social and Technological Networks (http://www.connectivism.ca/?p=220) ~Constructivist Learning Theory (http://www.exploratorium.edu/IFI/resources/constructivistlearning.html)

For some time I've struggled with constructivism. Surely, I've wondered, there's a lot of knowledge that's just better passed on in the old way -- taught directly by a person who understands it well. Would I want to entrust my body to a surgeon who'd completely constructed his/her own learning? Would I want to buy a house wired by a completely self-taught electrician?

Unfortunately, for some students, when their teaches implement a constructivist model, they abandon the role of instructional leader in the name of giving students responsibility for their own learning. Such teachers laud the value of peer-to-peer sharing and helping, but what they fail to see is that often the stronger students end up shouldeing over instructional role and provide teach their friends who need help. (I suspect that in some constructivist classes, there's plenty of direct instruction going on. It just isn't emanating from the teacher.)

A few days ago, I came across the term 'narrative of coherence'. "Aha," I thought. "Here's the secret that will save me!" I thought it show me the middle ground between traditional delivery and extreme constructivism. I thought I'd find someone else's vision for how to infuse learning experiences with an underlying narrative that would give students' explorations coherence. But when I read the articles (top 2 above) more thoroughly, I realised the phrase was used as a sort of educational pejorative.

'Narrative of coherence', it seems, is a way to describe what traditional teachers do. They work out the setting, plot, characters, and theme and tell the whole story to their students who learn it by listening and studying it over and over until they know it by heart. Reaching the end of a lesson is like coming to the end of a chapter when a bedtime story is being read. Learners develop the habit of waiting until the next lesson to find out what happens next. The problem isn't so much that students don't learn the story (for many do and have), but that they hear only one story with an ending that always comes out the same way.

I firmly believe that well-crafted learning experiences must offer COHERENCE. I grew up as a teacher when 'discovery learning' and 'concept formation' were the progressive ways to teach. We believed back in 1974 that these new models would end the 'learn & forget' cycle (sound familiar???) because learning would become a sequence of 'aha' moments. I remember one day trying to lead a young fellow through the process of discovering how to do long division. I patiently laid out a trail of bread crumbs that have led him to a magical moment of concept formation, but it just bewildered him. Finally he pleaded: "Please, miss, would you just teach me how to 'dibide'? I just want to know how to dibide!!!" So I did it the old way and after a few practice examples, he went away relieved and happy. For me it was a lesson learned.

But perhaps it was one I learned too well. Over the years I became a great educational story-teller, and my kids learned my narratives well, but for many that's where their understanding and questioning began and ended. Job well done, I thought -- but in retrospect it seems like a job only partially done.

So this morning I've been working on a new metaphor -- 'landscape of coherence'. I once read that some mathematicians see a landscape of math. Like a virtual world, for them math has geography that is navigable and can be learned, enjoyed, used, enhanced, changed, and perhaps even destroyed. I think this metaphor may hold some power for educators as well. Perhaps the middle ground I've been seeking between narratives of coherence and radical constructivism is 'landscape of coherence'.

This landscape has important landmarks with some pathways connecting them, but the way a learner moves around in it is determined sometimes by need, sometimes by signposts, and sometimes by interest. Instead of leading students down one garden path or telling them one story, teachers have to make informed decisions about what the critical landmarks are and then ensure the students understand & master those. We then entrust to the students the work of making their own network of meaningful connections. To foster this, we make time for sharing, comparing, crowd sourcing, and reflection (when we contribute our own perspectives as one of many).

When you revisit a learned landscape after a while, it's still familiar because it was extensively and intensively explored. You can revisit old landmarks and retrace old paths, but you'll also appreciate how the big picture has changed with time.

(Video Link: Rotating Earth Animation)

The key then is for the teacher not to refrain from making any decisions, but to give up on trying to teach everything to everybody in case they might needed it sometime -- because it never takes anyway. Our job is to do the much harder work of being selective -- of making better decisions about what the important landmarks are -- and to then ensure our students know how to fulfill their role in this new paradigm.

And so I think I've finally made peace with constructivism. I guess you can teach an old dog new tricks.

I don't think there's any way to be prepared when an educational tsunami comes your way, but it is possible to make sure your ship is water-tight so you can try to stay afloat.

This morning I've been working on my old Big Returns blog -- mostly getting used to the changes the Posterous people have made to how this all works. My feeling is that, in order to boost the social media aspects of blogging, Posterous has given up the absolute simplicity that drew me to them as my first blog site of choice. Like many fast food restaurants which have 'ballooned' their menus to attract more people to their counters and drive-throughs, Posterous has 'complexified' what used to be a very simple set of choices to navigate. It's taken me the better part of the morning to get ready for the real work of the MOOC to begin.

In any case, you can look at my Change.MOOC.ca page to see my initial impressions of the MOOC process, some links, and my goals.

I'm looking for a small team of study buddies to team up to figure out a way to spread the work of filtering the incoming wave of information we're going to have to sort through to keep afloat until the end of this event. Is anyone interested?

 

I was always a student who could do math but had no idea of what people do with it. Because I had a facility for pattern and cue memorization, I could even do math problems like the old classic about two trains hurtling towards each other at breakneck speed. I'd identify the keywords in the problem that would help me figure out what type it was. Then I could match it with an example I'd done before, and more often than not I could solve it correctly.

I realise now that while I was playing my matching game, there may have been other kids in my classes more interested in the story -- imagining the piles of smoking rubble and screams of the injured. They probably wondered how the a knowledge of precisely when the accident was goint to occur would help the doomed passengers meet their horrible fate. (This was way before the era of cell phones -- now at least they could figure out how much time they'd have to connect once more with their loved ones at home.) While there were always students in my classes who wanted to know what the point of the problem was, I was just interested in getting the questions right. Math class was safe for me because it didn't require any imagination.

My brothers, on the other hand, were just enough years behind me that they went to school during the era of 'new math'.

This was a time when the 'discovery method' was the greatest good. In the hands of talented and creative math educators, discovery learning can provide young people the sorts of exciting 'aha' moments which are associated with better math recall and appreciation. But my brothers went to a small elementary school in a suburb of Winnipeg, so it's likely that most of their teachers took on the task of teaching the 'new math' without enough mathematical understanding to see the bigger picture.

As well, when kids at that time came home looking for help with their math homework, many parents found that they didn't even recognise what was being taught. Conventional processes which they felt served them well were gone. If their kids weren't succeeding, they could no longer hep them. Discovery learning, though it held greater potential, became difficult to defend. Many parents and  teachers were relieved when teaching 'the basics' came back into vogue, and I think there has been a general resistance to changing the mathematical model since those days.

That legacy even now makes it easy for school people to put meeting standards ahead of developing true understanding and forces many classroom educators to 'dumb down' their approach in order to keep achievement standards high (as was so aptly illustrated in the video by Dan Meyer). In the eyes of many reformers, this dooms thousands and thousands of students to spend hundreds and hundreds of hours mastering content for which they can see no use.

I believe that Wiggins' and McTighe's (W&McT) Understanding by Design (aka. 'backwards building') model of curriculum development offers a sort of demilitarised zone in the 'math wars', but for us peacemakers there's both good news and bad. The good news is that, contrary to what Conrad Wolfram implies when he says we ought to just turn over the calculation part of math to computers, direct teaching and skills mastery still have an important place in math classrooms. I call W&McT's model: 'hook, line and sinker'. It's sort of like an inside-out sandwich with one layer of bread between two layers of delicious filling. The image that follows came from the Wolfram video, but it works as a way to illustrate backwards design.

The bad news is that coming up with the 'right questions' takes me far more time than developing a lesson and finding the resources. Starting with the end in mind (W&McT) means asking ourselves what students ought to be able to do with their math skills -- and the answer isn't 'solve harder math problems' or 'be better critical thinkers' or 'be successful later in higher level math courses' or 'get a better job'. For take-aways have to be real to the students, we have to do the hard work of coming up with better questions to frame their learning.

"What are the traits of an essential question?

• The question probes a matter of considerable importance.
• The question requires movement beyond understanding and studying - some kind of action or resolve - pointing toward the settlement of a challenge, the making of a choice or the forming of a decision.
• The question cannot be answered by a quick and simple “yes” or “no” answer.
• The question probably endures, shifts and evolves with time and changing conditions - offering a moving target in some respects.
• The question may be unanswerable in the ultimate sense.
• The question may frustrate the researcher, may prove arid rather than fertile and may evade the quest for clarity and understanding.

... It is not the sweep or the grandeur of the question that matters so much as the significance of the issues addressed" (Essential Questions, 2005). Students should feel that the essential questions which overarch their studies are worthy of their time and give meaning to the acquistion of the math skills we educators feel are so important.  

Big ideas in most content areas readily give direction to interesting lines of inquiry and exploration. They are expansive in that they reach out towards the world. They draw students into the content, give them a reason to grapple with the specific skills, and provide a glimpse of how those skills connect to something greater.

Here are some samples --

• From Science: What does it mean to be living? What do living things need to survive? How can we safeguard our environment? Hpw can we organize ideas and events to help us make sense of what we observe? What is our place in the universe? (Science 21, p.3)

• From Social Studies: When is violence justified? Should there be limits on personal freedom? Do we have a responsibility to help others? Are the benefits of progress worth the costs? (Lattimer, 2005)
  

• From Language Arts: How can reading this story help me understand my own life? Where do writers get their ideas? "What makes a 'great' book'? Can fiction reveal truth?" (McTigue, 2010, p.23)

In math curricula, however, "teaching using BIG ideas" is aimed at "concentrating student attention on key concepts and procedures. The linkages and connections between math concepts are made explicit by linking previously learned big ideas to new concepts and problem solving situations. Big Ideas are key math concepts that can be continually used to teach a variety of math skills/processes. They provide referential starting points for students when learning new math concepts/skills and are explicitly modeled by the teacher" (MathVids, n.d.). 

(Image source: Michael Rossiter)

Where in other subjects using essential questions to guide learning can help make students better at using their learning in a meaningful way, in math the big ideas seem only to serve bigger ideas -- in math. And so .. these are what pass for essential questions in math:

• What are prime and composite numbers? What is the relationship between fractions and decimals? How are factors and multiples useful in math? (Essential Questions, n.d.)

I'm not saying these are not important concepts for students to be able to explain and use, but they are hardly the stuff that dreams are made of. I think the secret to translating math skills into enduring understanding is to create a new set of overarching big ideas that will deliver on the promise of bringing essential questions into classroom teaching. As Dan Meyer (2010) says, we have to "bait the hook."  And we have to choose the bait that suits the fish (Olabimpe, 2009).

------------------------

References

A) Math Wars

 Brown, S., Seidelmann, A., & Zimmermann, G. (2006, July 01). In the trenches: Three teacher's perspectives on moving beyond the math wars. Mathematically Sane. Retrieved February 6, 2011, from http://mathematicallysane.com/in-the-trenches-three-teacher%E2%80%99s-perspec...>

Van de Walle, J. A. (2003, April 01). Reform Mathematics vs. The Basics: Understanding the Conflict and Dealing with It » Mathematically Sane. Mathematically Sane. Retrieved February 07, 2011, from http://mathematicallysane.com/reform-mathematics-vs-the-basics/

B) General

Conrad Wolfram: Teaching kids real math with computers | Video on TED.com. (2010, November 15). TED: Ideas worth spreading. Retrieved February1 06, 2011, from http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computer...

Essential Questions. (n.d.). Castle Heights Upper Elementary School. Retrieved February 06, 2011, from http://www.chue.net/EssentialQuestions.html

Essential Questions. (March 2005). The Question Mark, 1(5). Retrieved February 06, 2011, from http://questioning.org/mar05/essential.html

Lattimer, H. (2008, October). Challenging history: essential questions in the social studies classroom | Social Education | Find Articles at BNET. Find Articles at BNET | News Articles, Magazine Back Issues & Reference Articles on All Topics. Retrieved February 06, 2011, from http://findarticles.com/p/articles/mi_hb6541/is_6_72/ai_n31038991/

MathVids. (n.d.). Teach Using BIG Ideas. Florida Center for Instructional Technology. Retrieved February 06, 2011, from http://fcit.usf.edu/mathvids/strategies/tubi.html

McTighe, J. (2010, September 13). An Introduction to Understanding by Design [Pdf]. Retrieved February 06, 2011, from http://www.mtace.org/pirday_sept2010/Intro%20to%20UBD%20Handout.pdf

Olabimpe, O. (2009, April 2). Bait The Hook With What Suit The Fish « Mind Juice. Mind Juice. Retrieved February 06, 2011, from http://mindjuiceplus.wordpress.com/2009/04/02/bait-the-hook-with-what-suit-th...

Rossiter, M. (2010, May 09). [Big fish eat little fish]. Retrieved February 6, 2011, from http://swittersb.wordpress.com/2010/05/09/fly-tying-brook-trout-streamer-big-...

Science 21 essential questions [Pdf]. (n.d.). Retrieved February 06, 2011, from http://www.pnwboces.org/science21/pdf/EssentialQuestions.pdf

YouTube - TEDxNYED - Dan Meyer - 03/06/10. (2010, March 06). YouTube - Broadcast Yourself. Retrieved February 06, 2011, from http://www.youtube.com/watch?v=BlvKWEvKSi8

YouTube - Tom Lehrer: New Math. (2010, April 10). YouTube - Broadcast Yourself. Retrieved February 06, 2011, from http://www.youtube.com/watch?v=DfCJgC2zez. [Lip-synced parody of Tom Lehrer's original song -- http://www.tomlehrer.org/.]

 

I have been blogging for Wilkes University for nearly 2 years and left my own blog to languish in the process. Now that I have graduated with an M.Sc. in Instructional Media it's time to gradually migrate away from my work for Wilkes and reconnect with my own blog. I'm also doing a couple of courses through P2PU (Peer to Peer University).

(click the pic)

From their website --  “All P2PU courses are free and based on materials and resources openly available on the web. Anyone can volunteer to run a course. You don't have to be an expert! At P2PU groups of peers come together to learn course materials collaboratively.”

I’m pursing my interest in math education, so will take 2 courses: one about using Twitter in math classes. Twitter is a tool I don’t use much unless I’m at a conference and want to enjoy the feeds. To do that more easily, I now have a TweetDeck which will separate out various streams from the Twitter feed for me.

I can watch all of my friends, or search on specific hashags, and set up a separate stream for direct messages coming in just to me. There’s also a great post of ‘twitformation’ for people like me who have used Twitter in the past, but really don’t get the most out of it. I don’t have a web-enable cell phone so only use Twitter from my computer and another about using Tweetdeck which is free. I can see that if you want to use Twitter for a classroom, you’d need to organize a group, set up a hashtag, and use a tool like this to stream the class’s twitters into one column on the deck to make it easier to follow a class discussion.

The other course is being offered by Maria Droujkova of the Math 2.0 Interest Group and Natural Math network. I have to admit I started the course late and might not have taken it except for the presence of Blair Miller – a teacher who lives nearby me here in Surrey, BC. I’ve wanted to get to know Blair’s work with his grade 8’s better for some time and this is a perfect opportunity to do that. Also, I’ve started looking for a doctoral program in Australia. Some of the universities there offer what are called ‘Research doctorates’ which can be done in as little as 2-3 years. They don’t require formal course work but enable you to pursue a deep inquiry into an area that will bear fruit for other educators. I’m after something that will combine my passions for improving math instruction in light of the new findings in the field of cognitive neuroscience and involving the use of non-math specific tools to help students connect to their math in a more meaningful way and process the content more deeply.

I hope to use my experiences in these two courses to begin to clarify these ideas and pull together the research I was exposed to last summer at the Brain Development and Learning  conference here in Vancouver.  The next months’ posts here will be dedicated to the work in these courses. I’m still posting about tools on the Wilkes Instructional Media blog which can also be followed on Facebook and in CEET.

Meanwhile – please enjoy my math video pick of the week. Happy Sunday from soggy Surrey, BC.