Engineering Forum - 3D Imaging

Wow, has it been a while since my last post.  Blogging hasn't been my priority since I have been teaching since the beginning of the semester.  It's March Break now though so I thought I would try to fit in some blogging.

3D Imaging Technology

Last night, I attended this year's Engineering Innovations Forum at the Ontario Science Centre with a few of my Engineering friends.  The topic of discussion was 3D imaging technology.  The presenters talked about 3D scanning and modelling for Construction Design, Forensic and Medical applications.  There is some really cool and interesting tech out there.  Particularly interesting to me was the discussion of Photogrammetry (using photographs to find measurements and model in 3D).  Eugene Liscio, president of AI2 3D talked about how taking pictures with any digital camera can be used to generate a 3D model which he uses in Forensic applications.  He mentioned the Autodesk app 123D Catch, which can create a 3D model from photographs with any Apple mobile device.  Pretty neat.  Now how could I use this in my classes?  Something to think about over the next week...

3D Printing Technology

Turning 3D computer models into tangible objects for the Medical field was the theme for another one of the presenters.  You must check out the pictures at this link for 3D Printed casts.  They look awesome.

Breathing

Anyways, the presenter talked about how he was involved in designing a mask to be used to analyze breathing in sleep studies.  He needed to find the optimal spot for the microphone so it picked up the sound of breathing from the nose and mouth at the same time.  To find where to put it, they went outside when it was cold and snapped a picture of the condensing breath.  They used this to find the ideal location of the microphone.  The picture he showed us looked something like this (red lines indicate direction of breath):

Application problem time!  My Grade 10's are starting the unit on solving linear systems so I could get them to overlay an axis and grid on the picture and determine the location of the ideal microphone spot.  Here is a screencap of a Geogebra model of it that I threw together.  I didn't scale it to the size of the face but that would be necessary to solve the problem:

Also, here's a link to a Desmos graph of the same thing.

This could be a quick activity to show the students how this stuff can actually be used in real-life.

And then they could use their answers to design a mask which could be printed on the school's 3D printer.... ok maybe that's not that realistic yet.  It would be AWESOME if every school had a 3D printer.  Only $2500 each!  Somebody needs to get on that.  Real-world problem solving to the MAX.

This is why I still go to Engineering events when I can.  It gives me some ideas for presenting concepts in new ways and helps me stay current with the technology that's out there.  Engineering PD is teaching PD for me as a math/science teacher.

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.

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 17 - Canoe Trip Physics

The Problem...

How can you use an understanding of physics to make a canoe trip more enjoyable and less work?

Why?

• Opportunity for students to use physics concepts to help plan for a canoe trip
• Opportunity to bring sustainability discussions into a Physics class
• Interdisciplinary math, science, biology, physics, ecology, geography

Check out this blog entry from a few years ago by @emnose.  Canoe tripping is awesome.  The planning, driving, paddling and portaging all pay off when your alone on a lake in the middle of Ontario enjoying the silence and the stars.

In a class...

I would only use this activity in a class if right opportunity presented itself:  if students were actually going on a canoe trip (I know a bunch of high schools that regular do canoe trips). Students working on their Duke of Edinburgh are actually required to do a trip so it would be a good opportunity for them to earn some of the requirements.  

The Physics...

Believe it or not, there is actually a ton of physics that can be found in canoe tripping.  Here are some examples:

1. Buoyancy and hydrodynamics

• What canoe shape, size, depth is appropriate for the trip.  Can study the drag/friction of the canoe in the water.
• Optimal weight and number of people per canoe.  Too heavy and the canoe will sit too low in the water and be inefficient to paddle!
• Number of canoes needed for the trip.
• Optimal paddle length and shape.  There is some statics involved in the best paddle length.  The shape has to do with hydrodynamics.
• This site has a whole bunch of canoe recommendations and images including the one below.  A good question may be which one would be most appropriate canoe profile for the trip.

2. Distance-time relationships

• Best route to a destination (connections to contours in geography and optimization in math).  Students would have to develop some criteria for what 'best' route entails.  Easiest? Quickest? Shortest travel time?  In the picture below, what would be the best route from the Three Legged Lake Access Point to Clear Lake? 

Map is of Massassauga Provincial Park.

Clear Lake is a route we've done a few times.

3. Statics

• What is the best way to pack a hiking pack in terms of physics.  Would it be better to pack the heavier stuff closer or further away from your body?  This can be interpreted as a simple statics problem (see below).  How does your body adapt if the centre of gravity of your pack is further away from your back.

Drawn in Penultimate

• Carrying a canoe - In terms of statics, is it better to carry a canoe with two people or one?  What are some advantages and disadvantages of each.  I've never had a problem with 1 person...

Canoes are designed to be carried by one

 person but at first it doesn't seem to make 

sense from a physics standpoint.

These are just a few examples of how to look at canoe tripping through a physics lens.  I'm sure there are plenty more though.

Transformative Environmental Education

As a Scout leader, I have the opportunity to fairly regularly organize and participate in trips with groups of Scouts.  It's something I think every high school student in Toronto should have a chance to experience.  We talk about Environmental Sustainability but sometimes we forget what we're actually trying to sustain.  Living in the city all year, I sometimes forget about my connection and dependance on nature.  

In an article I read at OISE for my cohort class (Global Citizenship and Sustainable Development), Julie Johnston stresses the importance of stepping outside the curriculum box by practicing Transformative Environmental Education.  She presents education as the primary source of social reproduction and thus where we must start the cycle of understanding, caring for and protecting our environment.  Two examples of Transformative Environmental Education she provides (that I could utilized in this Canoe Tripping activity) are:

• Sky Awareness - promoting the importance of just looking up! Talking about how the sun tracks across the sky and how you could navigate by the stars.  This is easily tied to physics (astronomy).
• Bioregion-Based Education - understanding your connection to your immediate environment.  Understanding the ecosystem in which you live.  This ties nicely into biology and ecology concepts.

21st Century...

Students will be using Real-World Problem Solving and Innovation to help them plan their trip.  Concepts from Physics and other courses can help make an actual trip more enjoyable and less laborious.  

The activity also has the potential to be fairly long term and Self-Regulated by students, culminating in the actual trip.  Journals kept by students during the trip could be used to self-assess the effectiveness of their plans.

Lastly, there would be few more interdependent activities than a canoe trip, which basically forces everyone to do their part in order for the group to get to a destination.  It's an excellent opportunity to demonstrate Collaboration.

1. Collaboration: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
5. Self-Regulation: entry - adoption - adaptation - infusion - transformation

Day 16 - Lab Safety

The problem...

What is the safest layout for a Science lab/classroom?

Why?

• Cover the Science Lab-Safety curriculum expectations in an engaging way
• Utilize Third Teacher principles (environment as third teacher) that enables students to take more ownership of their classroom environment (while considering safety)

Minecraft Classroom Image from:

http://dbatty.wordpress.com/2012/06/23/minecraft-brings-about-so-many-opportunities/

Each science course has a lab safety component to the curriculum.  It makes sense.  Lab activities use dangerous chemicals and apparatus.  There needs to be procedures in place to ensure safety that the students are aware of.  Usually, lab safety is taught over a day or two followed by a quiz. Why not make the way they learn about safety engaging?  

Minecraft!

What I propose is give the choice for students to model the classroom/lab in Minecraft and then experiment to determine the safest way to arrange the classroom would be.  They could also figure out procedures for dispensing and collecting dangerous chemicals and the best way to store apparatus.  I probably wouldn't force them to use Minecraft.  It would be one way they could attempt to solve the problem.

The Lesson...

First, to facilitate Self-Regulation, I would discuss with the class what would make a successful classroom layout and have them establish some success criteria.  They would then come up with some sort of method for carrying out the task.  It may look something like this:

1. Organize! Students determine roles for constructing the model.
2. Model the classroom - including desks, lab desks, teachers desk, windows, doors, intercom, materials storage and anything else of note.  
3. Label the safety equipment in the model - fume hood, eye wash station, sinks, fire blanket, sprinkler, fire extinguisher and anything else.  Students will really know where all the safety equipment is after this!
4. Layout - In groups, students discuss how to improve safety by rearranging and experimenting with the layout.  Not all safety items are movable but desks and storage of equipment are.  This is where students can take ownership of their classroom environment.  Different layouts can be discussed and actually implemented in the class.
5. Material Distribution Procedure - What is the best way to distribute lab materials/chemicals - come up with a plan!
6. Emergency plan - Plan for an emergency and try it out! With everyone sitting at their desks (in the model) re-enact the procedure.  
7. Make a video.  Groups create videos of the student's avatars interacting with their models acting out safety procedures (what to do when there is an acid spill, chemical distribution, etc). Each group could choose a different procedure to demonstrate. They can post their videos on YouTube to share with the rest of the class.  

Students could continue to modify the model throughout the year if a layout isn't working or if there is a more unconventional lab that will happen.

Why Minecraft?

Whenever tempted to use some form of ICT I think it is important to ask yourself if that is the best way to deliver a lesson or you are just using the tech for the sake of using the tech. If you can't rationalize the tech actually enhancing the learning experience for the students, don't do it. In this case I chose Minecraft for a few reasons:

• It provides a Collaborative environment for groups of students to experiment with designs
• Students can try different designs in a short amount of time.  It's a good platform to support Real-World Problem Solving.
• The first person perspective is more personal and engaging for students
• The digital environment may be more comfortable to students who would not normally contribute in group discussions
• Really, I'm just excited about the idea of using Minecraft in a class

There are limitations to what furniture/equipment you can build in Minecraft but if students are creative enough, they would probably be able to model anything they need for this exercise.  

One criticism of this may be that students wouldn't take lab safety seriously but I am fairly confident a student is more likely to remember the procedure from a classmate made video about what to do if there is a chemical fire in the class than from a teacher-directed lecture.

Ultimately, I students should decide how they want to come up with their ideal (safe) classroom.  They could use Minecraft if they wanted to.  For example, an alternative to Minecraft would be Trimble Sketchup (formerly Google Sketchup) or other 3D modeling software. The downside to that would be a loss of the collaboration and first-person immersion within their environment.  Experimenting with the classroom in real life may not be practical but is another option.


1. Collaboration: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: 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

• Retrofit school to accommodate classes in portables (can be tied into math: measurement, etc)
• Classroom layout using magic plan or other app to get dimensions

Minecraft and Education

At the Connect 2013 conference I attended a few weeks ago, I saw a group of middle-school aged kids walking around.  The conference was mostly attended by teachers, administration and salespeople so I was a bit confused as to why they were there.  Turns out they were a group of Grade 7 students from a school in Hamilton that were there with their teacher hosting a poster session on a really cool project they worked on: redesigning Hamilton's West Harbour... using Minecraft.  Apparently, they presented their design to city officials.  This CBC article has a slideshow of the creation process.  Unfortunately, I missed the poster session and found out about it from my supervisor later (she was super excited about it).

What is Minecraft?

In case you haven't hear of it, Minecraft is an extremely popular 'sandbox survival' game.  What does that mean?  You build stuff out of blocks and try not to die.  There are 2 main modes to play in: creative and survival.  In creative mode you don't have to worry about the dying part so you can just create. Further explanation here if needed.

Minecraft and Education...

I am a gamer.  I love video games. I think they are a largely untapped source of educational potential so when I hear video games + education I get really excited.  As a  player of Minecraft, I can see tons of ways the game can provide fun and entertaining ways of teaching math and science.  

Just to be clear, Minecraft and Education is not a new idea.

In fact, there is a version of the game called Minecraft EDU that is specifically tailored to education.  Teachers have more flexibility with the environments their students create in.  Here's a video about the growing Minecraft EDU community:

As mentioned in the video, the creator of Minecraft EDU is Joel Levin, the Minecraft Teacher.  Most of his work is directed at elementary level students.  Check out some gameplay footage from his YouTube Channel.

Playing in the Sandbox...

In the documentary Minecraft: The Story of Mojang. Peter Molyneux (famous and sometimes controversial ex-Microsoft game developer) compares the evolution of video games to the evolution of Lego.  

Lego used to be a bunch of blocks that you dump on the floor and build whatever you want with.  Now, it is a kit made up of a bunch of specialized pieces that you follow the instructions to build.  After you finish building it, you put it on a shelf and leave it there to collect dust.

Similarly, Molyneux states the best selling video-games have overwhelmingly become linear, polished products.  Though they serve their own purpose as a form of interactive media, they generally leave little room for real creativity or creation.  When your done playing it, you put the game it in its case and put the case on the shelf to collect dust.  

On the other hand, there is Minecraft.  Notch (the creator of Minecraft) has done the exact opposite.  There are essentially no set goals or creative limits (other than gravity).  Minecraft has brought gaming back to the original lego bricks; back to playing in the sandbox. 

I like to think this analogy applies to education as well.  We generally have courses with predetermined outcomes and use the same lessons year after year for different students.  So much of what students learn feels useless to them after they pass the exam.  Instead, we should be providing students with the tools and environment to create and continue to learn by themselves.  Minecraft is one such environment and toolbox that enables students to set their own goals to create without limits in a highly collaborative environment.  

Teaching with Minecraft in High School...

The Hamilton West Harbour and Joel Levin's classroom are examples of elementary school Minecraft projects.  Would the game be able to engage high school students in the same way?  I think so.  Because the game is so open-ended, I believe a teacher could potentially come up with projects that addresses the curriculum from any course.  Some projects having to do with physics and math that immediately come to mind are:

Physics

• Find gravity in the game by experimenting with falling objects.  How does it compare to gravity on earth?
• Measuring momentum and velocity of a mine cart
• Measuring friction on a mine cart track
• Study circuit operation using redstone
• Examine gravitational and potential and kinetic energy and use it to design and build a roller coaster track

Math

• Find optimal ways to mine for diamonds (related to maximizing surface area)
• Cost to build different numbers of things (related rates)
• Surface area/volume relationships of structures
• Analysis of how the random world is spawned based on a seed (ties into Computer Science)

I'll try to explore these ideas and others in coming entries.

Why Minecraft?

The creation of a product is an integral part of the 21st Century Learning framework, especially for Knowledge Construction, Real-World Problem Solving and Use of ICT to be authentic and transformative.  If this is the case, why use Minecraft at all?  Why not physically build something?  Having a physical product isn't always practical.  Time, money, material and size constraints limit what is possible in the physical world.   

Resources and space are practically infinite in Minecraft.  Fairly complicated works can be built fairly quickly, especially when there is effective Collaboration.  In addition the game itself is cheap, user friendly and is available on almost any platform.  Its accesibility makes it appealing from an equity standpoint. In addition, students on the same server are accountable for their actions and interdependent on the cooperation of all players.  After all, there is nothing stopping from one student from completely destroying the work of the rest of a class.

Minecraft has potential for awesome Self-Regulation as well.  The game responds to the players actions as opposed to telling the user what to do.  Students can challenge themselves with goals they collaboratively set with the each other and the teacher.  

Basically, Minecraft is able to tie in all the neXt Lesson competencies.

Learning from Minecraft...

In addition to using Minecraft to teach, educators can learn from the game's success in engaging players and inspiring creativity.  This article from teachthought.com called '5 Lessons to Learn from Minecraft in Education' highlights some of them.  I would add 'Be Collaborative' as number 6 the list.  Though Minecraft does not have to be played collaboratively, some of the world's largest and most intricate Minecraft constructions are a result of the combined efforts of groups of people.  

Education should be about providing students with the tools to create and share their creations.  What those Grade 7 students in Hamilton accomplished is an example of how transformative 21st Century Learning can be.  Minecraft is just one platform that makes this kind of creation and collaboration possible but it sets a new standard on the possibilities of education.

Day 14 - EQAO and Equity

The Problem...

What educational equity issues become apparent when looking at EQAO results?

Why?

• Provides relevant context for statistics concepts
• Opportunity to turn a social justice lens on inequity in education
• Potential for Grade 12 students to help Grade 9 students get prepared for EQAO testing

This idea comes from a lesson example that I developed for a curriculum interrogation assignment at OISE.  It's an interesting lesson idea that I thought would be good to improve by looking at it through a 21st Century lens.  

The Math Curriculum...

I have stated before that the math curriculum is very concept-heavy (at least compared to Science which distinguishes STSE and skills expectations from concepts).  This generally leaves little room for deep investigations about culturally relevant and engaging topics.  

The vast majority of examples of using social justice education, global citizenship education, culturally relevant/responsive pedagogy or critical pedagogy in math class that I have heard have been based on statistics.  Unfortunately, in the high school math curriculum, statistics really only seriously comes into play in Grade 12 Data Management.  I think one way of increasing student engagement in math classes would be to spread out the Data Management concepts throughout the grades (another may be providing teachers with a bit more flexibility with the concepts).

Because Data Management is the obvious math course for the delivery of social justice education, I have stayed away from it in my blog.  Up until this point, my math entries have focused more on being critical of bias in math in general.  This however is an investigation about how we can use math to look at equity in society.  It fits in directly with a bunch of the Data Management expectations.

EQAO and Equity...

The following plot compares Primary EQAO data to Stats Canada Data on average family income.  Each dot represents a school's average result.  The article this plot comes from can be found here (it was published by EQAO in 2008).  This plot alone can be the starting point for a serious discussion on equity in standardized testing and education. 

I thought a good way to start the class would be to hand out a bunch of questions from a past Grade 9 EQAO test.  This will get them in the frame of mind of a Grade 9 student.  They can start to think about what factors may give students students trouble with those questions.  Note: A bunch of past secondary EQAO tests and other EQAO related resources can be found here.  

Find the relationships...

Then they could start looking at data.  The above plot can be found online but to facilitate Knowledge Construction students should be going to the EQAO website to get the raw data.  They can then draw their own relationships.  Some of the simple relationships they can get directly from the EQAO data are gender and stream comparisons.  Questions that may be good discussion starters are:

• does the division between genders seem to be increasing or decreasing over time?
• does the division between academic/applied seem to be increasing or decreasing over time?

Other sources of data students can compare the EQAO results to are Stats Canada data and even the Fraser Institute Rankings (which frankly scare me because of how seriously they seem to be taken).

Critical analysis...

After establishing relationships, students can begin discussing why some of the relationships exist.  As a teacher, this is where things can become difficult and exciting.  The discussion is the part of the investigation that can be most thought provoking and interesting but often gets left out for the sake of saving time.  I believe we're talking about 21st Century Fluencies, that excuse is unacceptable.  Bypassing the discussion doesn't help students develop the Skilled Communication and Real-World Problem Solving skills necessary for the 21st Century Learner.

I think another huge topic of discussion is taking a step back and looking at standardized testing in general.  What is the purpose of EQAO?  Really it is to evaluate teachers and schools.  Is this the best way to do this?  Is it a good representation of the academic strength of the school?  How else should schools be evaluated?  What equity issues may arise because of standardized testing?  What biases are present in both the test itself and the data it produces?  

It would also be interesting to look at the standardized testing situation in the United States, where it is much more pervasive and compare it to Ontario.

Action!

Now, how can these results be used by the Grade 12 Data Management Students?  I would say it's a good opportunity for the Grade 12 students to help the Grade 9 students that are preparing for the EQAO.  If they find relationships in the data that could be beneficial to the younger students then they could share their results.  Most likely, they will not be able to directly influence any of the factors that cause inequity but they can at least advocate for and educate the Grade 9's.  Most students probably never think back to EQAO after they write it but I think this is a good opportunity to build some school community and leadership skills by having Grade 12 students setting up tutoring sessions for Grade 9's.  There's the Collaboration!

21C...


1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
4. Skilled Communication: entry - adoption - adaptation - infusion - transformation

Day 11 - Hockey Stats

The Problem...

• How are all those hockey stats collected and what do people do with them?

Why?

• Engage students with the data collection and management behind sports
• Expose students to the real-world application of statistics
• Entry point to talking about the cultural impact of hockey in Canada

This entry is coming a day late because I was too upset to write one after the Leafs loss to the Bruins in overtime in Game 7 yesterday.  It's fresh on the minds of Leafs fans so I decided I would blog about it and somehow tie it to math.  Below is an nhl.com screenshot of the top 10 players from the 2012-2013 NHL regular season:

http://www.nhl.com/ice/playerstats.htm?season=20122013&gameType=2&team=&position=S&country=&status=&viewName=summary#?navid=nav-sts-indiv

That is a lot of stats to collect for each player!  In addition to analyzing the data on the site in a Grade 12 Data Management class, the question of how and why they collect these stats at all would be an interesting way of pulling the topic into the 21st Century Classroom.  

Close to home...

I think an awesome activity would be for a class to organize in order to collect an array of statistics of a team's season.  Ideally it would be a season played by their own high-school team so small groups of students could go out to collect stats for each game.  The class could consult with the coach/team at the beginning of the year in order to Collaboratively decide what statistics would be most beneficial for the team. They could analyze the stats over the course of the year and create reports to the coach who could ideally use them to improve the team's performance, supporting both Real-World Problem Solving and Skilled Communication.

In addition to potentially providing the coach with tools for improving the team's performance, the purpose of this activity would be to expose students to the process for the collection of data and some of the complications that may arise.  This Knowledge Construction would not occur if students were just studying stats taken from nhl.com.

Note: this obviously doesn't have to be a for a hockey team.  It could be any sport. Hockey is just what I had on my mind at the time of writing.

Digging deeper...

Once they have collected the data, they could start asking the deeper questions about collecting data in sports.  For example: in what ways are the data collected in hockey games are used?  Below are some things that may come up:

• Help teams improve their performance:  find ways to improve their team or find weaknesses in other teams
• Scouting for the NHL: the site behindthenet has a comprehensive report on how junior player's stats are projected to estimate what their performance in the NHL would be
• Fans love stats!  Stats get fans more engaged.  It is a source of revenue for the teams and leagues.
• Provide research for medical studies (for example: the concussion epidemic)

Here are some other questions that may be good discussion starters: 

• How much money is spent to collect stats in the NHL?
• Is it worth all the money to collect the stats?
• How many people does it take to collect stats for one NHL game?
• How might projecting a Junior players stats into the NHL be problematic?

21C...

1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
4. Skilled Communication: entry - adoption - adaptation - infusion - transformation

Future lesson ideas...

• Along the same lines but for Baseball: the math behind Moneyball (the movie)

Day 9 - Crossing the Chasm

The problem... 

Experiment with designs and materials to build a structure that enables a truck to cross a chasm (between 2 desks).    

Why?

• Build an intuitive understanding of forces and load paths
• Make use of the engineering design process
• Encourage collaboration, knowledge construction and real-world problem solving

Ode to the Bridge Builder...

While reading this blog post, feel to play what I like to think of as the Anthem of Civil Engineers: Ode to the Bridge Builder by the awesome Kyle Gabler from the awesome game World of Goo (available for desktop, iOS, Wii and more)


Bridges are awesome (I use the word awesome a lot when I talk about Civil Engineering stuff because it is all awesome.  Big + heavy + awe-inspiring = awesome).  

The bridge building challenge has been a key go-to for physics and science teachers.  Usually it goes something like:  use the provided materials (toothpicks, spaghetti, balsa wood) to span the gap between two desks.  The team with the bridge that supports the most weight is the winner.  Its Collaborative nature also makes it a standard team-building exercise.  I want to pull this classic into the 21st Century by tweaking the challenge a bit.

Into the 21st Century...

The modifications I would make are as follows:

• Success Criteria: Bridge is able to support the weight of a (weighted toy) truck crossing over it while satisfying the constraints.  
• The usual challenge of building the bridge that supports the most weight isn't representative of Real-World Problem Solving.  Instead, if a teacher chooses to make it a competition, the winner may be the cheapest bridge (the ethics of the lowest bidder standard is a good discussion topic in classes!)
• Instead of providing the students with the materials to build the bridge, provide them with nothing.  They will have to experiment to find out what materials are best to use.
• Real constraints!  Set a material price limit.  I would set this very low (a few dollars?) to prevent them from using just a straight 2x4 or steel which would be acceptable based on the success criteria.
• Make the span huge.  Note: huge is a relative term.  It depends on how long you want students to spend on it!

Time to Play...
Students may want to dive straight into the building of the bridge but it should be stressed that they should do some research and planning before building.  This doesn't have to be boring research though.  It can be hands on and engaging.

Having the students decide what materials to use supports Knowledge Construction.  Students will have to experiment with a host of materials, taking into account their strength, weight, and cost.  They will also need to decide what to affix the members together (if it even ends up being constructed with multiple members).  

Physically experimenting with different designs can be time consuming, and time is money.  Student can experiments with different designs using simulations instead.  I say the more fun, the better.  Save the boring simulations for the pros (at least in younger grades).  Although World of Goo is not your typical physics simulation program, it helps develop an intuitive understanding of structural design (as long as they are reflecting on what they build and how they can improve their designs while playing).  Another (free) web-based game that is more specifically for bridge design is called Cargo Bridge.  Ultimately, the groups should decide what simulation program they would like to use.  

Screenshot from World of Goo

Curriculum Connections...

I see this activity as at the beginning of a physics course or at the beginning of a unit on forces.  It is a good formative assessment for a teacher to learn about students' preconceptions about forces and building.  During the design process, students can analyse the external forces in the structure, a part of the grade 12 physics curriculum.  If done at the beginning of the unit, the teacher can use it as context for the rest of the unit.  

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

• Formalize the engineering design process