Calculus on the Khan Academy

I'm doing a lot of Calculus marking lately, and starting to think about matching up the Ontario MCV4U curriculum with the Khan Academy videos and practice dashboard (sorry, now known as the "Knowledge Map").

Their Derivatives 1 questions provide practice in finding the derivative of polynomials (only quadratics, in fact).  The Power Rule questions add simple negative exponents of -1 or -2.

The best place to start for Optimization questions (Lesson 12 in my world) is probably this link:
https://www.khanacademy.org/math/calculus/derivative_applications/calc_optimization/v/minimizing-sum-of-squares
Unfortunately the Knowledge Map currently stops with taking derivatives, so there are no practice questions on the topic.

This link seems like the best place to start for Vectors:
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra--introduction-to-vectors
There are exercises for scaling and adding vectors; so you have to spot 2a and add a and b, but there none where you have to find 2a+b for vectors (and students invariably need to practice the distributive step).

Yoga

Yoga is something that I've been enthusiastic about many times over the years.  I've attended classes at at least two places of work that offered them, at my local community centre in both Toronto and on the Island, and at the occasional studio.

Searching the blog I see that I've never written about it.  At this particular point in time, with life crazy but about to slow down, with loss pervading my thoughts, yoga seems like a logical practice to pick up again.  In January I set no resolutions, but my mantra became "a quiet mind in an active body".  I had some success and it's time to revisit.

Use a strategy for happiness

I'm only on the second habit of happy people, and already it feels like he has copped out on me.  His suggestion is that I use a strategy for happiness; figure out what makes me happy and make it happen.

The research he has based it on, though, says that good and bad things happen in the same proportion to happy and unhappy people.  The difference is that happy people spend about 2/3 of their time thinking about the happy things, and the unhappy people spend 2/3 of their time thinking about the unhappy things.  So that suggests to me that what I should actually be doing is monitoring my thoughts and gently guiding them back into happy paths.

It turns out that's actually much easier to do than emptying my mind, so I've been fairly successful at it.  I even find that I've associated thoughts, so that common negative thoughts are closely followed by their corresponding positives, with very little effort on my part.  My daily emails have been going well, and I've gotten some nice responses.  I'm not running out of people to send to yet, so I'll keep it up for a little longer while I explore the next "secret".

My life has purpose and meaning

I've been re-reading David Niven's The 100 Simple Secrets of Happy People, which my husband bought me years ago, knowing that I'd be interested in a review of research rather than a self-help book.  Rather than resolutions this year I'm trying to meditate on the 100 principles he identifies.

So, for the past week or so I've been constantly turning over in my mind his first point, that my life has purpose and meaning.  My very existence has touched the lives of many people and enriched some of them.  (I had to stop myself from insert "hopefully" there.)

My perfectionism wants to blow this out of proportion, and as I've been thinking I've found I have to constantly remind myself that this doesn't mean:

• that every day, hour, or minute of my life has to have purpose or meaning
• that I don't need to do some grand, amazing thing with my life to create that purpose or meaning
• that it's perfectly okay if the bulk of what I did in my life is behind me, and I lead a quiet existence taking care of myself for a while, or even the rest of my life if I'm so inclined

Strangely, I also find that I'm constantly reminding myself that the foster parenting we are doing right now is purposeful, meaningful, and also highly visible and earning us the respect of many people.  Because it has just become what life is for us, I can go for days without thinking of it as "special" in any way.  I'm making more of an effort to be gentle with myself about the stress I feel, but also give myself credit for what I'm doing.

It would be helpful if I can make a habit or routine out of each point so that I can integrate the principles of happiness into my life.  For this one I've settled on a habit that I will try at least for a week, and see how it goes; I will email one person each day that I haven't communicated with in a while.  I'll pick people whose lives I think I've enriched; I do a good job already of remembering to send emails at intervals to people who have been important to me, but I don't look the other direction.  To help it become a habit I've picked a time to do it - right after the baby goes down for his first nap of the day, because it's quiet then - and I've got a box on my Unschedule for the week so I can see my line of unbroken Xs.

So... baby's down for his nap... someone will be getting an email from me within minutes!

Rural Real Estate

I drive from Toronto to Tobermory and back many times in a summer, and I usually take the same route every time.  I enjoy seeing how familiar landmarks change over the season, and from year to year.

I did the drive up and back last Wednesday, and I was surprised to see more houses for sale than usual.  Here are a selection of the ones I saw.

On the road heading south out of Wiarton, there is a long row of beautiful Victorians on the hill, looking out over the sound.  This one is a former B&B with five bedrooms.  376 Berford Street, MLS listing X2405187, asking $299,900.

This beautiful brick Ontario farmhouse is on Highway 10, south of Owen Sound.  It's only $399,900 for 89 acres.  ComFree listing #194849, 777502 #10 Highway.

The house is a little topheavy for my taste, with all those dormers.  The garage is just about as cute as a garage can be, though, and the kitchen has really cool red kitchen cabinets that look as though they've been lacquered.  ComFree listing in the little town of Markdale, for $229,900; a good price for a house in town, walking distance to everything you need.

This 1905 beauty is near Flesherton.  The wraparound porches look out on 72 acres of gardens and outbuildings.  $579,900 on ComFree.

Because statistics make me feel better

469 children aged 1 to 14 died in Canada in 2009.

28 of them were homicides.

However, homicide is only the 5th leading cause of death in those aged 1 to 14.

Five times as many died of accidents; car crashes, falls, burns.

Four times as many died of cancer; mostly leukemia and cancer of the brain or central nervous system.

More than twice as many died of congenital abnormalities.

One more died of influenza or pneumonia.

Almost as many died of heart disease or suicide.


I guess my point is that if you want to protect your children, it's the annoying, every-day things you have to be aware of - like using a car seat correctly, and turning the handles of your pots to the back of the stove.  Because those happen singly, our limited human brains don't calculate the risks effectively.

The Khan Academy

I love the website KhanAcademy.org, and I'm continually recommending it to my students.

I'd like to do a matching of their topics to Ontario curriculum.  It's a rather big job, which I'll probably never get around to doing in full.

However, here's one to start.  To review probability and cover the material in permutations and combinations in Grade 12 Data Management (fondly known as MDM4U), start with this link:
http://www.khanacademy.org/math/probability/e/permutations_1

Follow the topics on the left-hand side.  Part of what I love about the site?  Notice the "Stuck? Watch a video!" on the right-hand lower corner.  It's on every question!