K-12 Integer Sequences

The K-12 Integer Sequences Conference was organized by my good friend Dr. Gordon Hamilton (Dr. Pickle) of MathPickle.com and Dr. Neil J. A. Sloane, the founder of the On-line Encyclopedia of Integer Sequences (OEIS). I was fortunate enough to attend as a math educator among other educators, math professors, and curriculum developers.



The goal of the conference was to identify 13 integer sequences that could be promoted for use in classrooms from K-12. The sequences would help students practice or learn level appropriate curricular goals, but they would also introduce the students to the wonderful world of mystery found in integer sequences. You can watch our large group sessions in these videos. Three sessions were spent in smaller groups - mine sought to identify sequences for grades 10-12.



The event was hosted by the Banff International Research Station (BIRS) at the Banff Centre which means they provided the hi-tech and comfortable conference facility (pictured behind me) and the lodging for the attendees. BIRS is dedicated to math research and collaboration.



Naturally, if you are still reading this, you are keen to learn which sequences will be promoted as a result. As with many collaborative conferences, there are still some **loose ends to tie up. I will feature a few here though.



Kindergarten: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, ...

A034326 This is the clock sequence. I think it's brilliant. You can have kids do some skip counting on it where they will be exposed to factors of 12 (when you skip by 4s, you will always land on the same 4 numbers, when you skip by 5s, you don't!). There is of course the excellent recursive nature of this sequence which mimics time.

Grade 3: 14, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 24, 22, 11, 9, 18, 16, 32, 30, 15, ...

A254873 This sequence is a modified Recamán sequence developed by a 15-year old student. Starting at the seed number (14) the sequence continues by dividing, subtracting, adding or multiplying by the step number (2). Division gets precedence over subtraction which gets precedence over addition which gets precedence over multiplication. The new number must be a positive integer and not previously listed. The sequence terminates if this is impossible.



Grade 5: 4, 9, 7, 20, 6, 33, 13, 23, 16, ...

Starting with 1, on the first step add 1/n, and on subsequent steps either add 1/n or take the reciprocal. What is the smallest number of steps needed to return to 1? This number of steps is the nth term of the sequence. (Note: the n=0 and n=1 terms are not defined, so the sequence actually starts with the 2nd term.)

eg. let n=2: 1, 3/2, 2, 1/2, 1 therefore the number generated is 4 because it took 4 steps
eg. let n=3: 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 1/3, 2/3, 1 took 9 steps
eg. let n=4: 1, 5/4, 3/2, 7/4, 2, 1/2, 3/4, 1 took 7 steps

This one is a lot of work, but I think it works to help students see that just because you work with increasing fractions, it doesn't necessarily mean it will require more steps. It really depends on the factors of n.



This time, I brought Amber along since I knew she would enjoy the tranquility, beauty and opportunity to relax in such surroundings.

My mom took the kids for most of the weekend, then Jasen for the last bit - we are very grateful.



Getting away to Banff now means being able to chow down and drink at the Banff Ave Brewing Company. Their beers are notable - especially their recent addition of an imperial IPA. Their food portions are ridiculously huge. I ate one burger for two meals.



The sequences have been determined in full! Here they are at the OEIS.org.

Hi-Pi

3.1415.. = π
3.14.15  = today

Math 30-1 Diploma Exam

In January, my grade 12 math students wrote their diploma exam, a provincial requirement and a university placement helper. They did superbly! I have to brag a little since I had a class of 24 with wide ranging skills and because of a schoolwide scheduling change 15% less instructional time to deliver the course than what was previously allotted (and recommended, and possibly required...).

The course is very demanding with nine pre-calculus units:

• Functions  and  Relations   
• Transformations on Functions 
• Exponential  and  Logarithmic  Functions
• Applications   of   Exponential   and   Logarithmic  Functions
• Polynomial  Functions  and  Equations
• Permutations  and  Combinations
• Analyzing  Radical  and  Rational  Functions
• Trigonometry  –  Functions  and  Graphs
• Trigonometry  –  Equations  and  Identities

My students scored on average 10% higher than the province (which had a 24% failure rate). We also had a tight standard deviation of 15.5 whereas the province had a spread of 20.1.

So! Congratulations to my stellar students!

Zaakistan 2013

January

Sick Day. Snow Day. Gaming weekend in Canmore. Concerts: Living with Lions, Whitehorse. Semester 1 ends: Math 10C, Math 20-2, Multi-Media

February

Dragonfly Cohousing Social Media Blitz. Man Scouts Beer Tasting. Demitor Visit in Edmonton. Peter turned 80 in High River. Semester 2 begins: Calculus, Math 30-2, Multi-Media. 

March

Mother-in-law visit. Turned 37. Fundraising Beer Tasting. Visit to South Africa: Waldrons, Seed of Hope, Game Reserve.

April

Visit to Malawi: World Renew, Kamanzi, Lake Malawi, Participatory Rural Apraisal. Morning stroll in Amsterdam. Daughter turned 6. Sister-in-law visit. Weekend in Radium with friends. Budget cuts at work.

May

Son learns to ride a bicycle. Dragonfly Cohousing Groundbreaking. Minhas Brewery Tour. Book Sale. Inglewood Bird Sanctuary. Mumford and Sons. Graduation. 

June

Calgary is flooded/Exams cancelled. Dragonfly Cohousing grinds to a halt due to construction bids coming in way over budget. Ultimate Frisbee (go Vicious Circles). Allan Family Reunion in Canmore. Bladder Infection.

July

Despicable Me 2 with kids. Son turns 8. Camping and hiking in Banff with friends (sickness). Anniversary Ride to Rocky Mtn House with sister. Montreal: Sister/Brother-in-law, Shakespeare in the Park, Biodôme/Botanical Gardens/Insectarium/Planetarium, Microbrew visits, Alouettes, BBQ.

August

VIA Rail NB: Papa/Step-Mother, Memere, Fern/Gail, Beach, Pugwash Campmeeting, Canoeing, 13th Anniversary, Dieppe Kite Festival, Plovers, Building a Geodesic Dome, Visit to Sackville, Mémere turns 87. Camping at Little Bow with Friends. Visit to Vulcan. Meadery tour.

September

Semester 1 begins: Math 10C, Math 30-1, Math 30-2. Camping in Rocky Mtn House with family and friends. Tennis with friends. Dragonfly Cohousing hires a new project manager. FallCon 26. Peter's Memorial Service. Kids begin homeschool. Beer Tasting.

October

Corn Maze with Dragonfly. Re-Design Workshops. Mom's Birthday. Reflektor is Released. Family Visit to Red Deer. Beer Tasting. Cystoscopy. Nenshi Re-Elected. Teachers Conference.

November

Glenbow Museum. Sleeping Beauty Ballet. Banff Mtn Film Fest. Wife turns 35. First Batch of Beer. K-12 Unsolved Conference in Banff. Visit Demitors in Westlock. Old Fashioned Family Portrait. Grey Cup Party.

 December

Son gets his Yellow Belt in karate. Re-Design Workshop. Hobbit 2 Premiere showing. Snow Day and a half. Power Out Day. Beer Tasting. Second Batch of Beer. Friend goes missing in Belize. Christmas in Calgary. Nutcracker. New Years Eve Fondue with Family in Red Deer.

K-12 Unsolved Math Conference

In November, I attended a math conference with another 24 people at the Banff International Research Station for a weekend. The conference was organized by my friend Dr. Gordon Hamilton of MathPickle.com fame (visit his site for more info on the conference). It was meant to discuss and identify 13 unsolvable math problems that could be introduced at each grade level from kindergarten to grade 12 as puzzles or games that have curricular connections. Among the attendees were math educators, education consultants, puzzle pros, and mathematicians, each bringing expertise to the table.



First of all, I was blown away by the Banff Centre where BIRS is just one of the many buildings used to promote scientific research, artistic residencies, and host internationally acclaimed cultural events. The facilities are state of the art and staff are wonderful (I took the Greyhound to and from Banff for the event. When I was checking out, the door man asked where I had parked my car and when he discovered I was walking to the bus station (2 km away), he locked up the storage room and shuttled me to the station, insisting this was necessary and that me walking there would be absolutely tragic.). The food is also stellar and I must thank my school for covering the food costs.



The weekend was full and we spent a lot of time debating the merits of various problems, how they should be presented, their relevance, and especially how we could go about promoting the concept of teachers using unsolved problems in their classrooms (no easy task in this age). One of the ideas we tossed around for a long time was the offering of a $1 Million award for anyone who solved one of the problems. The trick here isn't so much the money, which insurance could cover, but the vetting of the solutions - who would do it?

In the evenings we played games and talked math. One of the lead guys attending was James Tanton, currently the visiting scholar of the Mathematical Association of America. He had some really innovative ideas that I can't pretend to explain here. Check out his website for some mini courses - especially the one on disappearing dots.

My hunch though is that Gord did all of this so that we could find a way to introduce every living student to Pick's Theorem - which I have to say, is pretty cool, and fun to play with.

A Personal Update: Zaak aged 37 and 1/4

I'm involved in a lot of stuff. A lot. So I haven't been a mental state to articulate thoughts on my experiences in Africa, recent beer tasting, cohousing activities, educational philosophy, political musings, musical tastes, and Christian thought. At least not on this blog. I have been in conversation about all of these things on a daily basis with a wide variety of people. Maybe this fact brings into question the purpose and role of this blog. I'm currently 95 movies behind on my movie blog too (incidentally, Man of Steel didn't shake me up any).

I got back from 3 wonderful weeks spread over South Africa and Malawi back in mid April. I left with a great feeling of encouragement and rich for having walked alongside Africans.

I continue to love my church where I am appreciating the diversity of our membership and the growth I am experiencing in my life with God. I'm reading Wendell Berry and listening to podcasts by Tim Keller, This American Life, and CBC's Ideas. These keep me engaged intellectually.

Two weeks ago, our family joined 20 of my relatives in Canmore. They came from Washington, Florida, New Mexico, British Columbia, North Carolina, Alberta, and Nevada. It was really quite wonderful to reconnect with aunts, uncles, cousins, and my grandmother - all of whom I hadn't seen in 13-21 years.

The way we are delivering education at my school is changing. We are focusing on giving the students more responsibility for their learning and we teachers become more facilitators and guides and resources for them. This is not an overnight transformation, but some big changes are being implemented. For me the greatest change will be as the only high school math teacher (at some points, there were three of us). I will be teaching 6 different math courses through the year - and that's it.

My children continue to amaze me and humble me and love me. My wife continues to charm me and support me and love me. I am very grateful to have them in my life and to them lovingly mould me as their husband and father. Blaise is going to lose one of his top front teeth soon. Acadia is the first person I talk to every morning. Amber and I joined an ultimate frisbee team - go Vicious Circles! We have another family living in our home and it has been a joyous experience to share so much and to be living in community.

As time passes, I am less and less interested in national and international politics (I follow it generally through CBC Radio, Colbert Report, & HuffPost). I'm far more interested in local civic issues and process. My city is still recovering from the greatest natural disaster it has ever seen and my esteem for our mayor has only swelled to greater depths (Naheed Nenshi has the highest rating of any mayor in any North American city - or so I am told).

Lately, I've been listening to Atoms for Peace, The National, Band of Horses, Mumford and Sons (who we saw in concert a few weeks back), Sufjan Stevens, and City and Colour. Certainly some favourite songs which I may blog about in the near future.

Beerwise, I'm looking forward to tasting some local brews while in Montreal. Lately, I've been quite enamoured with 8 Wired Superconductor, a double IPA from New Zealand. As a regular drink, I am quite content with Co-op's Classic Premium Ale (it's the very same Big Rock Traditional Ale) and Lagunitas Maximus (another glorious imperial IPA). Picked up a 4-pack of Fuller's London Porter the other day and I'm enjoying that too.

Cohousing. Well, we were flying really well until 3 weeks ago. We had 33/36 units sold and more members lined up to buy in the coming week. We had $8.7M worth of financing lined up. Our building permit was essentially approved by the city as our building documents were completed. Then the bids came in and our contractor had to break the news (about 8 months too late in our mind) that it was going to cost 75% more to build than he initially told us. We are looking at various options which basically mean way more time for this project to be completed. A couple members have dropped out. The community (myself included) is feeling pretty stressed out.

Tutoring Calculus in Bhekulwandle [Seed of Hope]

Carl hooked me up at Seed of Hope with one of their after school programs led by a great guy name Musa. Musa leads tutorials and discipleship programs with jr and sr high students living in an impoverished area between holiday town Amanzimtoti and Durban township Illovo.

The students who showed up were told to bring questions and questions they did bring. The junior high students worked on multiplying fractions and I showed them how to break numbers down to their factors. Four grade 12 boys arrived with curve sketching questions from their calculus class - a unit I am in the middle of teaching to my class back in Calgary.





One of the challenges that I could see the students are faced with attempting to complete rather complex math operations and tasks without very clear understanding of the roots of these operations. Fortunately, the boys are very diligent and bright, but I fear a lack of access to a willing teacher hampers their ongoing understanding.





Very fun to help out, but I'm not fooling myself into thinking that they will be impacted long term by this. I do hope they were able to get through the week with a little less stress.

Conservatives "Economic Stability" and e

I read in the Calgary Herald earlier this week that the priorities of my Conservative MP Diane Ablonczy are "the economy and stability." Considering conservative policy on the economy (deregulation, privatization, lower taxes, fewer tariffs, foreign investment and ownership, etc.), this seems like the worst way to promote stability. I think Ablonczy should simply say her priority is unmitigated economic growth despite future costs to communities, small businesses, the environment, the disadvantaged, and pretty much every Canadian, very few of whom will be able to afford the inflated costs of living.

As an example: Alberta. Following a conservative economic policy for the past several decades, the province has a bloated infrastructure and skyrocketing prices in energy, food, housing, education and healthcare. How did it happen? They allowed economic growth to happen too quickly. People flooded the province seeking work causing more demand on just about everything. Private industry was willing to pay outrageous wages and prices for services and supplies making it impossible for the public and non-energy sectors to keep up with livable wages. The gap between rich and poor widened shockingly and as history has demonstrated over and over again - the bubble popped and citizens and province are left with things they can't pay for.

In mathematics we have a number, e, which represents the natural growth constant. It is a number related to everything in the universe that grows. It is also called Euler's Number and it's value is roughly 2.7182818284590... (it's irrational). If things grow at a faster rate, I believe it is unsustainable. If it grows at a slower rate, there is a risk of it failing or dying.

It's not that I don't understand the Conservative's policy. They want to lower corporate taxes so more national and international corporations will park themselves in Canada, create more jobs and in turn generate more revenue for the government. The fallacy is twofold. The larger and wealthier these corporations become, the more political power they gain over than the people (gov't) and their interest is not a public one. Second, the money pools at the top and the benefits are not enjoyed by the most of the population.

The Conservative Party of Canada is promoting a get rich quick scheme that is not-sustainable and that puts our nation's proud federal services and increasingly less stable economy at risk.

I believe the greatest challenge we face is that Canada feels it must compete with the United States with tax rates so our jobs won't flow south. If we operate out of fear rather than out of our identity, we risk losing ourselves completely.

If you choose to not vote Conservative, I encourage you to vote strategically (seriously, visit this site). The Green, Liberal and New Democrat Parties are not very far from each other ideologically whereas the Conservatives are drifting further and further to the right.

Teaching Calculus

This year I picked up Math 31 in my teaching assignment. It is an introductory course to calculus that only students with

a: high post secondary ambitions

b: a love of math

c: lots of spare time

consider taking. All of my students fit into categories a and b.

I've loved the challenge and content of calculus since I took my intro class in grade 12 and I am enjoying revisiting these amazing concepts after a 12 year hiatus. The real joy is working with such dedicated students. The class average is an impressive 90%.

At the moment, my class is finishing their chapter 3 test on related rates - lots of furrowed brows, focused stares, sketching and calculator buttons being pushed. Such fun!!

Facebook Forced Me

25 random things about me. If you've been tagged on FACEBOOK, then you're supposed to make a list too.

1. I miss having long hair.

2. I am currently in the middle of 10 books.

3. I am a very slow reader.

4. Since April 15, 2007, I have watched 299 movies and have blogged about them all (except the last 6 which I plan on doing this weekend).

5. Math was always my favorite subject in school and now I teach Pure Math 10.

6. I am a worst case scenario thinker. I discovered this on my first day cycling across Canada.

7. I have owned 3 different models of the iMac (G4, G5, Intel Duo Core)

8. Since the age of 12 I have kept longer fingernails on my right hand so that I could play classical guitar.

9. I get very worked up about politics because most people aren't aware of underlying issues that aren't discussed in the media.

10. I am a non-denominational Christian.

11. I was the yearbook co-editor of my school in grade 11.

12. I turned down a large scholarship at a prestigious Canadian university and went to Canadian University College instead.

13. My favorite food is fresh cherries. I've eaten them once in the last 3.5 years.

14. I've spent 4 years of my life living on foreign soil.

15. I've played tuba, trombone, and french horn in 5 different concert bands.

16. I want to live on a commune. I want this badly. That was even my goal stated in my grade 11 yearbook.

17. Making lists is enormously enjoyable.

18. I do my own taxes. And Amber's too. I learned how to do them while observing a low level high school math class when I was training to become a teacher.

19. This is my fourth year teaching in Canada and the only course I've taught twice is grade 10 math. I'm a pro at first year teaching.

20. My favorite composer is Jean Sibelius - an alcoholic Finn who wrote melancholy symphonies and tone poems.

21. Nehemiah is my favorite book of the Bible. My favorite verse is John 21:25

22. I manage money quite well.

23. My favorite contemporary author is Douglas Coupland.

24. I cry easily. Guatemala was tough.

25. I am the same height as my wife.

I'm 100000

I've gained one more digit in binary today. It'll be another 32 years before I get another and it took 16 to get this one. The fact that 2 X 2 X 2 X 2 X 2 = 32 makes 32 a better number than 30 (or 31 for that matter). Interesting note on a couple of alphanumerical systems L = 30 and B = 2 so LB = 32. I would have thought - different alphabet, different amounts for each letter. The Mayan representation (3 dots over 2 lines) is counter intuitive to how you might imagine it to mean: the top dot represents 20, the next two dots represent 2 and each line represents 5. Notice how the Roman, Egyptian and Babylonian (bottom right) are so similar.

The merging of culture and mathematics.

Thanks to all my birthday wishers and especially my wife and spawn who are making the day super special. You're a kind bunch.

One Laptop Per Child

One Laptop Per Child is a project that has been in the making for 40 years. The concept involves a sophisticated, economical, durable laptop that can be placed in the hands of every child on earth.
The current laptop prototype:

• costs $100
• 366 Mhz processor
• built-in video camera/mic/speaker
• 1 megapixel swivel screen
• flash hard drive (no moving parts)
• game controllers
• wireless networking
• LED lights for the keyboard
• 3 USB 2.0 ports
• various language keyboard layouts
• when shut, it's impervious to rain and dust

The philosophy behind it is that this will be a tool to allow creativity among the world's underprivileged children (90% of all children) and provide an inexpensive and reliable education tool.

My feelings are mixed. Of course I think the technology and partnerships involved are stellar. The possibility of creating video, music, art and limitless access to literature and news is awesome. Computers are wonderful tools - I spend a good portion of my day in front of one. What concerns me is the innate learning that happens when we touch, write, taste, and work. It's the same question as to whether we should give children calculators to learn math. Could we turning the rest of the world into N.America's generation Y?

Got this from the Québecois eMagazine Le Studio 1.

Bound for the Grove

We have been accepted to rent an apartment in Spruce Grove this fall. It will be smaller than the huge place we have now, but that will give us the opportunity to shake some of our materialistic headspace in exchange for a simple home. We know we will only be in Spruce Grove for one year.



I'm pretty stoked about teaching music to kids aged 5 to 17 this year. How fun is waving a baton and having music happen? And little kids singing with me. Total blast! I'm also going to teach grades 7 and 8 math and elementary P.E. and some non-core classes. The classes are nice and manageable to the point where I can get to know all of the students better and where more possibilities for learning can happen. This is a fantastic opportunity.