Math Challenge: Do you know what algorithm this is?

David Wees came up with this challenge. Determine what algorithm this code emulates. You will find the answer more informative if you create a table to see the pattern of moves the code makes. The table can then be used to introduce the algorithm formally to your students. Or better yet, get them to build their own tables from the code. Try a range of integers to test the code. What patterns exist?

 

 

I will post my answer in a couple of days.

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Thinking… Please Wait

 

Hi. It has been a month since I last posted, but I accomplished a lot during that time. And I am very happy I did. I feel like I progressed quite a bit since I last posted.

This is great since I experienced debilitating writer’s block with some of the key posts I have been struggling to publish, and this pretty much stalled me. It happens I guess. I had all these things I wanted to do and I wasn’t advancing.

Thank goodness I had another blog and other professional resources to work on.

Last month I took a rest from Digital Substitute so I could catch up on some much neglected projects that I was just raring to work on. In one of my early posts, Math Lab: Revisiting Technology and Imagination, I exclaimed how liberating it was to take a single day off from blogging, tweeting, PD and other professional activities to just play, and I think the post that resulted was one of my favourites to write, and perhaps my second most popular.

I find most of my posts, and certainly my best ones, result from some emotional or playful encounter. So, I consider the sacrifice of one month worthwhile to recharge myself.

Wandering in the Land of Set-aside

So last month I worked on several fronts.

Teaching Resources

I editted my Teaching Resources site, including adding:

  1. notes I wrote, and links to online archives, from several of my recent PD sessions to my Professional Development Index,
  2. resources, and a Slideshare Pak Liam created in response to these pages, to my Green Pea Analogy pages,
  3. focussing questions and points to my Phronesis page, and
  4. a math term etymology document that apparently was very well received given the tweets and requests for links to it on Twitter.

Writing in Play

I also did a lot of writing this month, something that has sadly been long waiting, including the completion of a short story based on a Figment Theme Prompt and working on a chapter in one of my long stories. I participated in Figment Theme Prompts, doing a little writing each day. And I posted to my Stefras’ Bridge blog. Altogether, a great month of accomplishment for my writing.

Stefras’ Bridge

I blogged about another of my hobbies, oil painting, and linked to one of my essays describing the history and folklore behind the earliest form of Mardi Gras. And I posted my first review and interview — with Malyn Mawby.

The Write Group

I also created a new Twitter account for the Write Group, to which I am migrating my English and writing tweeps and adding tweeps specifically for the Write Group. And I continued to work on our wiki, gathering RSS feeds and bookmarks relevant to our group. It doesn’t look like much now, but wait until I get things up and running!

Flickr, Videos and Coding

Finally, I added some photos to my Flickr photostream, I am working on two cartoon videos for Pi Day — there has got to be a better way to do this than drawing all these pictures … but boy does it look neat (for my first true “movie” videos) — and I am refreshing my coding skills with Code Year.

 

How did I get so busy?

I think I work in there somewhere.

Thinking … please wait.

Revisiting Four Themes

UPDATE: Due to Twitter’s buying and shutting down of Posterous, Malyn’s 10minutes sketchbook blog has been moved to WordPress, The Sketchbook Project 2012 – 10 minutes. Please visit the new site, enjoy Malyn’s sketchbook and sign her guestbook.

Deep passions never die

Last night I had an incredible Twitter conversation with Malyn Mawby about her Playing in Public sketch featured in my last post.

I asked her, since she is part of a sketch tour, whether she was just newly learning how to sketch or if she had started when she was younger. She proudly confessed the latter, and you can tell from the quality of her sketching.

Malyn also mentioned that she had stopped sketching for several years a little while back. For her, the Art House Co-op Sketchbook Project was an opportunity to revisit her sketching and renew her passion for artistic play.

This led to discussion of my passion for creative writing, which I also have enjoyed since childhood and also took a hiatus of several years from.

Hiatuses lead to inspiration

Of course, Malyn asked why I stopped. And I explained my heart transplant to her.

This led Malyn to draw a new sketch … about me.

And here it is. Wow!

 

 

For the colourful story behind this sketch, please read Malyn’s post about this sketch.

Camaraderie expands horizons

I developed many friendships using Twitter. I use the term PLN often, because most of my friends are teachers and most of our communication is professional. But it would undervalue my activity on Twitter and other social media, like this blog, to dismiss the camaraderie developed in my learning journey. My social and professional circles have definitely expanded since I started developing professionally online.

Resparking passion

In addition, I have another blog, maintained much less often than this one, which I dedicate to writing and my writing in particular. This is where I occasionally write about writing.

Last month, I became the new leader of the Write Group. This role is rather daunting, since I am replacing the quill of a great leader who served for 29 years. I expect that as my new duty takes hold, I will post more to my writing blog, particularly since I am designing a resource wiki for the Write Group.

I will also do more writing with the encouragement of my duties, much like Malyn is sketching more with the encouragement of her participation in the Art House Co-op Sketchbook Project.

So from a conversation last night, I have expanded my horizons some more and so has Malyn. Now that is social networking in action.

How about you? What is your passion? And how do you encourage yourself to expand and never lose it?

This post is cross-posted in my writing blog.

Engaging Kids: Outside of the Classroom and into the Club

The first section of this post is cross-posted in my writer’s blog, Stefras’ Bridge.

I have had three deep passions throughout my life so far and the good fortune to experience them all. I love nature, so I became an ecologist. I love learning and sharing my passions, so I became a teacher. And I love storytelling and storycrafting, so I became a writer.

 

 

In a previous post, I discussed the change in teaching style when one engages with students outside of the lesson and in camps and clubs. About a month ago, I attended a Don’t Hibernate Fair in my town. This fair is designed to connect clubs and people. I attended a table and recruited new members into the Write Group.

This was an exhilarating experience for me. I have been in many clubs and organizations, but this was the first time I recruited new members to a club. I had thirteen people sign up and express keen interest. Best of all a few of these are students I sub.

My Students: Engaging Passions

Imagine if you will how profound

It is nice to see students and witness their talents outside of the classroom. We often forget how rich, or conversely how poor, our students’ lives are. And though we spend much time preparing and considering the lessons we teach them, we typically forget in the daily details of our jobs how small, and yet how big, our classes are to our kids. Our influence is cumulative, each class a small part of each school day, yet so important to our students over time.

This in itself is a good argument for making our classes as memorable and impactful as possible, so that our students consciously identify with the concepts we try to help them learn. One of the big goals of our teaching is to contribute to the richness of our students’ daily lives, to keep that excitement that should be every day alive in the people we are raising.

 

 

The hidden factory-style curriculum of traditional education attempts to quash this anticipation so students docily accept factory-style jobs and even factory-style lives.

Our students deserve better, better than turning content, geared curriculum, contrived exercises and lectures. Isn’t the whole point of life to experience and wonder? Shouldn’t our classes go beyond “this is today’s content” to “imagine if you will how profound”?

Imagine if you will how profound. Better starts today, each day, in how we teach each class our students attend. It might be our eighth class we teach today. It might be their eighth class they attend. But it is the one class, the class right now, where we can excite them about learning, about participating, about the concepts we teach and about the possibilities and opportunities and wonders, even about the horrors, of life. We are teaching their lives now. We are teaching their lives in their futures. They deserve the best in this class. So, we have to engage them and rile their passions.

This is certainly a lesson I keep learning. And sometimes it is hard to figure out how to do that with the lesson plans I am given. Sometimes I am exhausted or under the weather. This happens. But I try to remember the key, the key, that this class, this class here, is part of my students’ lives, a part they deserve to be fired up about. Attitude begets attitude; passion begets passion.

Meeting them where they live

I remember when I first really decided to write. It is not the first time I wrote. It is not the first time I slung stories. I was already well into these, for others and for fun. But it was the first time when I thought that writing was really, really, really neat and something I wanted to do more regularly than occasionally, and more for fun than for others.

 

 

I started seriously, playfully, writing when I was eleven, a year older than the lowest age of the students I am teaching. (I currently teach 10 to 21 year olds.) In my time, where I lived, there were no clubs to encourage my writing, no community of people passionate about the same passion. Those of my students who joined the Write Group get to share and grow in their passion with like-minded people of all ages in an environment where, unlike school, they are not judged for the quality of their work, where they can choose to share, what to share, or not, where they can experience the work of others and where they can open their minds to new and beautiful worlds.

The Write Group is experiential. It is as good as what is shared.

In the Write Group everyone is equal and the only criteria is the love of the written image, the spoken story. I look forward to witnessing my students engaged in their passions, sharing that which stokes their pride and celebrating what they love.

The Camp, the Club and the Class

Our students require a lot from us. Sometimes they need a class. Sometimes they need a camp. Sometimes a club. A lab. A project. These types of teaching should:

  1. reflect the content of our lessons — the form of the lesson should reflect the structure of the content.
  2. reflect the knowledge, skills, curiosity, skepticism, problem solving and innovation we want our students to learn.
  3. reflect who are students are, what they are interested in and how they learn.
  4. provide authenticity and relevance of our lessons to our students.
  5. provide a variety of learning opportunities and styles to invoke and promote a variety of thinking and physical skills.
  6. invoke curiosity, awe, confidence, mastery and gratification from our lessons or their learning in our students.

 

 

A class, under controlled circumstances, explores content and skills. A lab and a project duplicate a class but invoke handling content and skills. A lab is more immediate and cooperative than a project; a project delves deeper and ranges farther. A camp combines class and lab in open and unfamiliar circumstances. And a club combines each of these in an open, guided, non-critical, low-stakes milieu.

When was the last time you taught in a club-style? What lessons coming up can best be learned if they were experienced as a club rather than a class?

Engaging Kids: A Little Classroom Humour

 

 

There has been a recent rash of puns spreading around one of the schools I sub at. It has infected kids at all grade levels from 5 to 12. Of course, being called in to teach occasionally, I happened to walk into this contagious disease with no warning and no defence last Thursday and Friday.

My kids tried to infect me twice with puns on Thursday. Unfortunately, I was rather vaporous on that day, so I did not catch on to either attack and thwarted the jokes.

The Mistaken Challenge

The first attack came from my Science 9 students. I can not remember the pun and ruined the joke anyway. The students grudgingly revealed what they were trying to get me to say (without getting in trouble). I remember being glad I didn’t. My guess now is that the pun must have been inappropriate to school anyway.

(At this point, I should confess that I am a stickler when it comes to swearing or inappropriate topics from my kids. This deters my kids for about 15 seconds after I warn them not to engage in such behaviour. Then the fun begins: trying to find ways to tease Mr. Urban. This particular pun was their latest effort.)

Still, my kids were unaware that I hadn’t caught on. I am sure they have taken my sidestepping of the pun as a challenge, so I expect more cunning attempts to get me to break one of my own rules.

These kids just crack me up. They are so eager and clever. And for the most part, when I ask them to, they willingly engage in the learning activity at hand.

There is always room to play and enjoy class. My kids like joking with me; I am easy enough to let them bait me, yet usually wise enough to get out of their traps.

 

 

The Unintended Lesson

The second attack came from my Grade 12 math students. My Grade 12s were a little more cautious with their pun, choosing one that was barely offensive.

But, again, I did not catch on. And how spectacular the result.

I have watched these kids grow up from Grade 7 and am absolutely fascinated at how mature and confident they have become. I can’t tell you how awed and full of pride of them I am. So, yes, I was targeted again.

The pun was simple. My kids asked me “what is that under there?” and I was supposed to reply “under where?”

I did not.

Being obtuse

 

Really, it never occurred to me to even ask that. Over there were cabinets and shelves sitting without gap on the floor and a well raised table clearly with nothing under it.

I was supervising a probability quiz and wrote it myself along with them. (Probability, permutation and combination just confuse me. I can not make heads nor tails out of them. The quiz had a few sporting coin questions in it by the way.)

So I was thinking mathematically, systematically and about test question quality. I ended up pitching against the ambiguity of vague questions with my kids, particularly the one they were asking me, and they in turn kept trying rather desperately to get me to ask that magical pun-question. Dialogues of the obtuse are so amusing.

It all ended up in laughter and teacher-student bonding that would never have happened had I clued into the pun at any time.

One boy grinned that the joke turned out better than my kids had planned. A girl told me that I really got her thinking about clarity and definitions. Everyone, including me, ended the day with renewed energy and a smile.

Yeah, I was thick on Thursday. I normally take questions and comments at face value. I rarely look for ways to make this or that perverse by some lateral interpretation. I am eager to help.

And I love the way I am, and my kids. They can fool me any time they want, so long of course that doing so does not interfere with their learning activity.

I feel much closer today to these two classes of students, particularly the Grade 12s, as a result of this jocularity.

A little humour in the classroom is engaging and builds strong bonds. I am ecstatic that I subbed these kids on Thursday. A lot was won.

 

 

Math Challenge: The Odds and the Evens

Bon Crowder has recently been exploring the similarities between the addition of even and odd addends and the multiplication of positive and negative factors. Read her post on this topic to find what she has discovered.

 

 

I was taught to think of a negative number as a positive number times negative one; so, in this way the only real negative number is -1 and it is a direction vector. Similarly, i is the only real imaginary number, since all other imaginary numbers (not complex ones) are real numbers times i, the “imaginary vector”.

This is not a math challenge in the sense I have normally been applying the term. There are no computations, but there is a puzzle, one which I have yet to explore.

In Bon’s post, she connects the addition of odds and evens to the multiplication of negatives and positives. I wonder then if there is a way to express an odd number in terms of an even value times an “odd vector”? What would that odd vector be?