It's a Matter of Misconceptions

Today I played this video for my Grade 9 Science classes (Academic and Applied):

What was interesting to me was the reaction of the students to the video.

• Students were engaged while watching the video.  They chuckled when somebody in the video couldn't answer what seemed like an easy question and were excited to blurt out the answer when the interviewee couldn't get it
• Students were confident in answering the questions I posed to them after the video.  Maybe seeing others struggle with the same material helped them understand it's perfectly fine to be wrong and there's nothing wrong with taking an educated guess.

Because I saw how well they did with the depth of understanding of the material, I spontaneously asked them why they thought Derek put so many wrong answers in the video.  We had a great discussion about it in both the Academic and Applied classes. 

Here's Derek's own explanation of why he makes videos riddled with people struggling with misconceptions:

Though I didn't show them this video, I had seen it before (and actually read his thesis) and brought up the fact that seeing other people make mistakes can actually lead to a better understanding of the material.  I was impressed with how well the students seemed to understand this.  There was definitely some high level metacognition happening on their part.

Hmmmm... really gets the gears turning.

NDGT in Toronto

On Friday night, I attended a UofT lecture by Neil DeGrasse Tyson.  I really didn't know what to expect going in but I ended up really enjoying it.  I have been a fan of NDGT for a while but didn't know he would be nearly that funny and entertaining giving a lecture. 

Neil discussed his take on Science through a cultural lens.  Some of the things that stood out for me were:

• He showed us his collection of the banknotes of different nations with scientists on them and discussed how this can set a standard for the population of that country. Especially interesting was Germany's 10 Deutschmark note with Gauss on it.  There is even a bell curve on it!
• He discussed how discovery of something leads to the naming of that thing using the periodic table and the planets as examples.  Google 'periodic table country of discovery' and 'year of discovery'.  It's pretty neat to connect the dots with what was going on in those nations at that time.  
• He also touched on more controversial topics such as technology and GMO's and the place of Social "Sciences" and arts compared to Science (his quotations around Sciences not mine).

The most impressive thing about the lecture was that even if you did not have any background in Science, you would still probably have understood most of the lecture and probably would have enjoyed it.  Neil actually touched on this during the question period.  He talked about how a lot of the skepticism toward Science comes from Scientists generally not letting the public into their 'club'. They use fancy words to maintain group exclusivity.  This is the exact opposite of what education should be.  
Knowledge Construction on the other hand occurs when you start with what the student knows and build their understanding from there as opposed to just throwing a bunch of facts and words at them.  Neil did a great job of this during the lecture.  He made a ton of jokes, kept the tone conversational, didn't use any fancy words and even tweeted during the talk!  He did as well as you can do with Knowledge Construction in a lecture scenario.

For me, it basically it boils down to this:
To get people excited about Science (and Math), get rid of the unnecessary pretense and subject-specific lingo and don't be afraid to show your passion for the subject.  

Lastly, Neil insisted he show us the following videos (even though the talk went way later than it was supposed to). Somebody had slowed down his Big Think talk (regular speed and slow motion videos below).  It's pretty funny and it was even more funny to watch Neil's reaction to the slowed down one.

Regular speed video:

Slow motion video:

Oh, and checked the Toronto Star yesterday and today and NO mention of the talk.  Hopefully there will be something in the Monday paper.  It's absolutely nuts what they prioritize over Science and education.

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.

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!