Trapped by the seasons

As a Scout group, we have traditionally done 4 camps each year: 

• Fall camp is at the beginning of October (2 nights)
• Winter camp is at the beginning of February (2 nights)
• Spring camp is at the beginning of June (2 nights)
• Summer camp is in August at Halliburton Scout Reserve (7 nights).  Less Scouts tend to come to summer camp though because it is a big financial commitment for parents/guardians and is a week long so I hesitate to count it as a camp

I was skimming a report the other day from a University of Waterloo student titled Membership Retention in Scouts (Morland, 2007).  One of the recommendations that caught my eye was to have more activities and camps.  Morland proposes an outdoor activity each month including 6 camps throughout the year.

Why have we always stuck to 4 camps?  Maybe it's just because there happen to be 4 seasons so it's convenient to refer to them by the season they occur in.  This is reinforced by the fact that there are the 'Year-Round Camper' Badges divided by the seasons (though Fall/Spring is one badge).

Essentially what I'm getting at is that it's fairly arbitrary that we have 4 camps.  Why don't we do another Winter camp in December before the Winter break? Or in January shortly after we get back from the break.  Or maybe one in April to fill the gap between Winter and Spring camp.  Or how about a shorter camp earlier in the summer?  

One of the arguments against an additional camp is that it will require more planning time for leaders and another weekend lost.  I would argue that the Scouts should be doing the bulk of the planning and preparing anyways and the independence and confidence they gain from the process is much more valuable than the skill of learning to tie 4 different types of knots.  In terms of the time commitment for leaders, not every leader needs to come to every camp.  Too many leaders at camps has lead to a lack of Scout participation around camp which leads to a lack of them acquiring important camping and survival skills.  Too many leaders and it undermines the independence we are trying to foster among the Scouts.  An additional thing to consider is that camps could be 1 night instead of 2.

As head leader, I'm making it a Troop Goal for the program to follow Morland's suggestion of having at least 1 outing per month.  Also, we will have a 5th camp.  I think being outside as often as possible and fostering independence are 2 key ingredients in keeping Scouts year to year.  

Eglinton-Scarborough Crosstown

As a teacher, it pays to be opportunistic.  At least in terms of student engagement.  Take Toronto transit planning for example (or more like a ridiculously embarrassing lack of transit planning in the GTA).  Some students are bound to know about the most recent craziness surrounding a subway line in Scarborough.  Bringing it up may get other students interested in current events.  Nothin' like a good ol' subway debate to get a class riled up and excited for some learnin'.

Anyways this week I came across this map:

When a construction company is tendering a job, an estimator (or intern) may need to do take-offs: a fancy way of saying figuring out how much stuff they need to buy so they can put a cost to a job.  Here's a good math question:

Using the map above, how much material will they need to remove to construct the tunnels in the underground section of the LRT?

You may say there's not enough information there, which is probably true unless you make some big assumptions.  You can find the length of the tunnel using Google Earth.  If you explore the Eglinton Crosstown website you can find this rendering of the tunnel boring machine launch site:

From the picture, it's apparent that there are 2 adjacent tunnels.  Based on the size of a person (maybe 1.6 or 1.7 metres), you can estimate the diameter of the tunnels.  Using the length of the tunnel and the diameter, you can calculate a volume (after some unit conversions most likely).

Real-World Problem Solving

There are many other ways to find out the size and lengths of the tunnels from reports and construction drawings.  That's the awesome thing about these kinds of questions.  Plenty of ways to an answer.  Also, the answers may vary depending on what assumptions are made!  You can have a good class debate to try to figure out who is closest and why.  

You could also put some numbers to it.  How much would it cost to remove the rock/dirt?  Where should it go?  How big would a pile of it be?  How do I make sure I cover my assumptions?  These are all questions an Estimator has to deal with when pricing a job.  And it all comes from some simple geometry!  Great for any math class.  A lot of Construction and Engineering problems can be boiled down to simple math.  

This is also a perfect opportunity for some Problem-Based Learning.  The Eglinton LRT could be a theme for a unit.  The problem would be to estimate the cost of the whole rail line.  Several math concepts could be brought in to help solve the problem: areas and volumes, slopes of lines, finance, scale, understanding and creating graphs.  It's a way to give a bunch of disparate and lonely math concepts some common context and interest.  There is also the human factor to consider: the impact on the communities and the environment.  Definitely some interdisciplinary potential there.

I do foresee a problem however.  If I was ever to do this activity with a class I'd probably get so excited I'd end up talking about tunnel boring machines for an hour and put everyone to sleep.  The woes of being a Civil Engineer... not everyone cares about dirt as much as you do.  Vince understands.

Root 2

The other day, I posted this Vine:  

[Note: I just started using Vine last week.  I know I'm late to the party with Vine but it's not too late to state that it's an awesome way for students to document and share their ideas and creations.  Doesn't require any video editing skills.  Just a steady(ish) hand and a smartphone or tablet]

Root 2

You can figure out the relationships between the green, white, yellow, red and grey rods from the Vine using a bit of geometry.  Its a nice exercise that really makes you realize how smart the inventors of K'NEX were.  It also becomes obvious why I titled the Vine 'Root 2'.

There are actually hundreds of math questions that you can generate from the Vine.  Questions involving shapes, proportion, angles, colours, similarity, scale, pattern recognition, length, measurement, area, parallel and perpendicular lines, special triangles, manipulating root expressions, polar coordinates and more.  These topics cover every grade and even some university stuff.  K'NEX is a great tool for teaching a wide variety of math to students of any level or ability.  I can't believe I didn't use it for one of my lesson or unit planning assignments for OISE.

Extend...

Once you figure out the relationships between the lengths of the rods, you can start to ask some more interesting questions.  For example:

• What lengths can be made by combining the pieces and what lengths can't be made
• Is it possible to construct a 3-4-5 triangle with K'NEX?  The math gets interesting because you have to mix rational and irrational numbers.  
• How about this question: Is there a piece or combination of pieces that will perfectly join two opposite corners of this cube (below)?  Prove it.  With math.  Even if you had a piece that was the correct length, would you be able to connect it? 

Answers and more K'NEX to come...

Internship Debrief

This internship with the TCDSB 21C/AICT team was the last piece of my OISE education.  The 5 short weeks flew by!  Throughout the internship, I met whole bunch of interesting, inspirational and fearless people that taught me so much in such a short amount of time.  It's super refreshing to see positive change happening in education, even if it is one teacher at a time.  It is only a matter of time before momentum takes care of the rest.

When I started the blog, I knew that you should always plan lessons with your specific students in mind but what I realized is that it is also really hard do do if you don't actually have any class your doing it for.  I thought the freedom of not having a specific class or course would enable me to generate tons of ideas but I actually think that made it more challenging.  Ideas were broad and I didn't really know where to cut off each entry.  I think my more successful entries were the ones that were less general and I tailored more specifically to one course or unit.  Despite that, I think it was a great exercise for me to really learn the neXt Lesson Framework and start thinking about what my future classroom would look like.  I was able to complete entries on 20 lesson ideas (although I was actually there for 23 days).  

The most valuable lessons I learned come from hearing the stories of teachers' challenges and successes of implementing 21st Century Learning.  Here's just one example that stands out for me:  At a workshop, one teacher talked about how she used Minecraft in her class to teach her Grade 6 students about surface area and volume.  The idea actually came from one of her usually disengaged students.  He and the rest of the class loved it and didn't believe it when the teacher told them that they were doing math. 

As my education at OISE comes to an end, I see one big challenge (in addition to just getting a teaching job):  professional development.  How in the world do I keep up with new and ever-changing pedagogical research, educational policy, and all that lingo?  This might find its way into future blog entries.  For now, I will continue to surround myself with people who care about education and hope to learn from them. 

Thanks to the TCDSB 21C/AICT team for having me as their intern!  It was a dream internship.  Way more than I ever could have hoped for.  I hope to be attending your workshops as a teacher someday soon!

Day 20 - To Scale...

The Problem...

Create an ICT artifact that expresses the scale of the really big and really small.

Why?

• Keep things in perspective!
• Creative expression in Science class
• Facilitate self-regulation
• Facilitate a more intuitive understanding of scale of things discussed in Science

Scale Misconceptions

There are a bunch of Science misconceptions that come from a lack of understanding of scale.  Here is a video about one of these by Misconception Specialist Derrick Muller of the YouTube Channel Veritasium.

The scale of really big stuff and really small stuff can be really hard to comprehend.  Here are some ways that people have tried making it easier:

1. Original Powers of 10 Video - http://www.youtube.com/watch?v=0fKBhvDjuy0
Old school, but effective!  There is also a good Simpsons couch gag parody of the Powers of 10.

2. Scale of the Universe 2 App - http://htwins.net/scale2/
Interactive scale app.  The Planck Length, the Universe, and everything in between.

3. This pic from I F______ Love Science

from https://www.facebook.com/IFeakingLoveScience

4. Khan Academy Video: Scale of the Large: Attempting to comprehend the scale of the large

In a Class...

Most of the Grade 9 Science course revolves around the very small (atoms and electricity) and the very large (astronomy) and this activity would be perfect for that class.  

I would present the above examples to a class and have them create their own artifact to illustrate scale with objects from throughout the course.  It could be a long-term project that is introduced at the beginning of the course.  The students collect the data throughout.  As an ICT Artifact, students could continue to contribute as they move through the grades.  It would serve as a good anchor point for some big concepts throughout the Science Curriculum.

There are tons of different ways students could present the data: infographics, videos, images, apps and more.  I would keep the project relatively open to facilitate Self-Regulation.  As the teacher, I would provide them with feedback as they build their artifact over the course as well as providing students to critique others.

21C...

2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
4. Skilled Communication: entry - adoption - adaptation - infusion - transformation
5. Self-Regulation: entry - adoption - adaptation - infusion - transformation
6. Use of ICT for Learning: entry - adoption - adaptation - infusion - transformation


Future Lesson Ideas...

• Create a directory of unit equivalencies (ie. 1 Newton is approximately the weight of an apple on Earth)

Day 19 - Saving at the Pump?

The Problem...

The price of gas is going up tomorrow.  Should I go fill up my tank?

Why?

• Illustrate the human factor that complicates apparently simple math problems
• Discussion of sustainability in transportation
• Practical application of linear relations, unit conversions
• Facilitates critical thinking

This is the dilemma: 

You are at home in the evening and you hear on the news that the price in gas is going up 5 cents over night.  You know you will need to fill up soon anyways.  You are faced with a choice:  Go out now to fill up or just go on the way into school/work tomorrow morning.  You know if you go now, there will probably be a line at the pumps.  How much will you save if you go tonight?  Is it worth the inconvenience?

from:http://www.energyblogs.com/blackswanblog/index.cfm/2013/5/14/The-Black-Swan-Blog-No-soft-landing-for-the-PV-Solar-Industry 

I know most high school students don't drive so it might not be a great question for them.    Or maybe its a calculation they can share with their parents.  Regardless, it's a question I have wondered whenever I hear gas prices are going up and I see line ups of cars at gas stations.

From my calculations, I would save about $2.00 to fill up 50L by driving out to the gas station.  Assumptions listed below and will vary by model of car and other factors:

• Fuel Efficiency = 10L/100km (from the dashboard display on my parents' car)
• Distance to Gas Station = 1.5 km
• Idling consumption = 0.1 L /10 minutes (I found this on one site. Very unsure about the accuracy)
• Assume a 10 minute line up for gas (idling) before the price goes up
• Assume a fill up is 50 L

In a class...

Because most likely a lot of students won't have vehicles of their own, I would probably present them with the above scenario and results.  Really, the point of this would be to start a deeper discussion about how we often oversimplify decisions like this.  This activity could really be done in any Science class.  It's a valuable lesson on how complicated Real-World Problem Solving and decision making can be.

I would pose this question to them:

Given the fact that you will save $2.00 if you fill up tonight (instead of tomorrow), will you go fill up?The first instinct may be to be purely economical and say yes of course.  Maybe students could look at trends in gas prices over the year and see how often big price drops/increases occur to try to predict how much they would save over a whole year.

Challenge the Assumptions

I would expect students to inquire about how I got the $2.00.  I would then explain my method to them and they could further critically analyze the assumptions I used to arrive at the answer.  Something that may come up is the gas consumption unit of L/100 km (or MPG in the States).  Where does that measure break down? Idling!  When you are idling, the gas consumption should theoretically be infinity L/100 km because you aren't going anywhere but are still using gas but most cars that report 'instantaneous' fuel consumption in the console will show 0 L/100 km.  If you calculate the average fuel consumption using the instantaneous values, the average will be biased downwards because of this.  So what do car companies report when they advertise efficiency?  I don't know.  Something to discuss!

Time is Money

I would then challenge them a bit and ask how much them how much their time is worth to them.  This is something they would not think about if they don't have a job.  Say it takes 25 minutes to drive to the station, wait in line, fill up, and return home.  Is it still worth it?  Quantifying how much a persons time is worth is an interesting topic (engineers use it when optimizing public transit routes and schedules).  For a high school student, would they consider minimum wage ($10.25) to be how much their time is worth? If so, the 25 minutes it takes is not worth it!  It also depends on how busy they are.  Do they have an exam coming up the next day?  Or are they not doing anything anyways?  The Human Factor can complicate things.

Internalize the Externalities

What about the environmental implications of going out to fill up?  How much carbon dioxide is released during the trip and while idling?  Idling is actually very inefficient on gas and produces a relatively large amount of CO2 for not moving anywhere.  This is a good way to get into discussions about the impacts of elevated greenhouse gases and the carbon tax debate.  We pay for water, electricity and gas.  If we are using up clean air by polluting it, why aren't we paying for that as well?


According to Wikipedia, the Energy Density of Gasoline is 36 MJ/L.  I calculated 0.4 L of gas for the trip to the gas station and back.  Thats 14.4 MJ or 4 kWh - the equivalent of leaving a 40 W lightbulb on for about 4 days.  In terms of energy used, it's not insignificant (though it would only cost about 40 cents of electricity because our electricity is ridiculously cheap).  This highlights how much energy transportation actually uses.  Remember, that the 14.4 MJ is only for driving 3 km and idling for 10 minutes. 

21C...

Students could weigh all these options and come to conclusions which they can share with the class or discuss in a discussion board.  The topic can be used as a jumping off point for a whole host of STSE issues as well.

Okay so maybe this is a bit of a mundane way to illustrate the complexity of problem-solving and decision making that doesn't demonstrate 21C all that well.  There are probably much better examples of cost-benefit analysis (such as the Exploding Ford Pinto Debacle), but I was curious about filling up the tank before the price goes up so that's what I decided to write about.

2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation

Future lesson topics...

• Ethics in Engineering and problem solving/decision making
• Optimal vehicle speed for fuel efficiency/GHG emissions

Day 18 - 4 Pics 1 Word

Problem...

Create a Science/Math 4 Pics 1 Word puzzle for your classmates

Why?

• 4 Pics 1 Word is engaging.  Harness that!
• Students demonstrate a deep conceptual understanding of concepts

What is 4 Pics 1 Word?

It is a popular puzzle game available on mobile platforms (iOS version here).  This is a screencap of a question (the level I was stuck on at the time of writing this):

On my Practicum...

In my Grade 9 Applied Math Class on my practicum, I often caught students playing 4 Pics 1 Word on their phones when they were supposed to be working together on a question.  Instead of telling them to put their phones away, I would walk up behind them and tell them the answer to the level they were struggling with.  This would often result in groans of "Sirrrrrrrrrrrrrrrrrr.  Why did you give it away???" at which point they would get the picture and get back to work on their math.  They really, really wanted to come to the answers themselves and their faces lit up when they found it.   

The strange thing about this is that it's generally the COMPLETE opposite of what students are like when doing a math/science problem.  Usually they want you to give them the answer or tell them exactly how its done and there isn't that same satisfaction of coming to a conclusion as there was with 4 Pics 1 Word.

This tells me that 

a) there is something wrong with the way we teach and 

b) there is something huge we can learn about student engagement from casual games like 4 Pics one Word.  

In Blooms Taxonomy lingo, my Grade 9 Applied Students were using Higher Order Thinking Skills  (Analyzing and Evaluating) when playing 4 Pics 1 Word.  And it is self-directed and collaborative!  I hardly ever saw a student working on the game alone.  Making the word associations in 4 Pics 1 Word are highly dependant on prior knowledge and experiences so certain answers come easy to some people and are more difficult for others.  I have been stuck staring at questions for a loooong time and then somebody comes by and gets it instantly.  Thus, the nature of the game makes it conducive to  collaborative.  Education should be the same.  It shouldn't be a chore to work together.  It should be necessary and fun and embedded in the task!

As a teacher, this would be an excellent activity for a unit review:  Have groups of students Collaboratively come up with a 4 Pics 1 Word question for their classmates.  This pushes 4 Pics 1 Word to the highest level of Bloom's Taxonomy: Creating.  Students have to synthesize their understanding of the units concepts and be creative to make their problem tricky for other students.  They can take pride in making their question hard for others to figure out.  I think this is a form of Skilled Communication.  They have to express their understanding of a concept in an indirect, yet targeted way.

I'll come up with a physics/math example and post it here SOON.  It's late and sleep is good.

Students decide!

I think one of the biggest reasons I saw so many students play 4 Pics 1 Word is that it is not teacher-mandated or evaluated.  Students hear about it from friends and online.  It is self-directed!  They have a choice to play the game and there are no time limits for each level.  Also, there is no penalty for asking a friend to help, unlike a test or assignment.  

Because I think the reason so many students play it is because they have a choice to play it or not, asking your students to create a 4 Pics 1 Word problem for fellow students would potentially undermine some of its appeal.  This why giving students choices and letting them decide how they want to study/present material is so important.

21C...

This activity doesn't do so well on the neXt Lesson continuum.  I think its strength is in conceptual thinking though and is worth giving students as an option for a review exercise.


1. Collaboration: entry - adoption - adaptation - infusion - transformation
4. Skilled Communication: entry - adoption - adaptation - infusion - transformation