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

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 15 - Road Trip!

The Problem...

What do you need to know to plan for a road trip?

Why? 

• Bring together many skills from the Grade 9 Essentials Math Curriculum
• Have students learn skills that are directly applicable outside school
• Interdisciplinary opportunities (business and geography)

I'm starting this entry in a van on the way home from Fond du Lac, Wisconsin  This past weekend I was on a road trip with @emnose and her family to pick up her brother from university.  Long, long drive but great trip!  Their highway bridges are a lot nicer looking than ours (these are the things you notice when you are a Civil Engineer).  Maybe we should start tolling more of our highways... another discussion for another day.

View Larger Map

The curriculum...

@emnose had the the idea to do an entry based on the road trip so I started to think about some of the things that you need to research when you are planning a road trip. I quickly realized that planning a road trip brings together many of the skills in the Locally Developed Essentials Math courses.  I actually taught a Grade 9 Essentials Math course with my AT during one of my practica. I actually think the road trip activity would be an excellent culminating activity for the course.

The Essentials course has a heavy focus on real-world, concrete skills. The Grade 9 course for example had 3 units: money sense, measurement and proportional reasoning.  Really, the activity could be modified to fit into any math course but I thought this was a practical activity for the Essentials students.

In the classroom...

I would start the activity by asking the class what kind of things you would need to research before going on a road trip (I may specify USA because it provides the opportunity to discuss exchange rates and different taxes). Most of the following things should come up in a class discussion:

• Shortest travel time
• Shortest travel distance
• Lowest travel cost
• Exchange rate
• Cost of gas (conversions of volume and currency units)
• Taxes and tipping practices
• Time zone/daylight savings
• Hotel bookings and availability
• Driving rules and other laws
• Vehicle needed and packing allowances

Students could then get in groups, choose their destination and start working on what was discussed.  Deliverables should be based around Skilled Communication of their findings and could take the form of an itinerary sheet, a budget sheet including a total cost of trip, a custom google earth map and/or a travel booklet/infographic with all the info in it.

Equity and 21C...

To be a better example of 21st century learning and for the Knowledge Construction to be authentic, the road trip should actually happen. I know this isn't plausible for most high-schools or affordable by many parents but what if there happened to be a school team going on a road trip to a tournament? The class could help with the preparation of that (including creating a budget and booking the hotel). 

Because of the equity issues involved, I would probably only do this activity if there were a school trip actually planned that the students that were planning it were able to attend!  I think the activity is only worth it (from a 21C perspective) if they actually use the knowledge they construct and the products they create.  For a lot of 21st Century Learning (as well as Critical Pedagogy and Global Citizenship Education), I think it is necessary for a teacher to be highly opportunistic based on what is going on in the school and school community.  That's one of the reasons why I keep these entries fairly vague and open-ended.  I'll post a quick blog entry about this in a bit...

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

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 13 - String Tension

The Problem...

How much force is there on the neck of a guitar?

Why?

• Illustrate relationships between science, math and music
• Students learn to research and collect experimental data in a procedural way
• Connect the Forces unit to the Waves and Sound Unit of Grade 11 Physics

This is an activity I have done with some of my more science-inclined guitar students.  I simplified the problem for them however because I didn't want to take up too much lesson time.  We collected the data over several lessons and I put it in a spreadsheet that tallied the values and gave an answer for all the strings.  The sheet I gave my students looked like this:

In a Science Class...

If I was using this in a classroom, I would let the students come up with ways they could find out the tension in the strings.  I would give each group of students a different stringed instrument (based on what I had available or the music department would be able to provide): guitar, ukelele, bass guitar, mandolin, banjo etc.  Student's could even bring in their own instruments to analyze.  

First, I would have students write down an estimate of what they think the total tension would be.  Again, in problems such as these, its always a good idea to have some idea of what the answer will be before actually calculating it.

They would then work Collaboratively to figure out how they are going to measure the tension.  It's hard to measure string tension directly when the string is on an instrument but there are ways to indirectly find it (see picture above).  If they discover that formula, they will have to think about how are they going to collect data on:

• the length of the string - can be directly measured
• the fundamental pitch of the string - there are many free mobile device apps that will tell you the pitch of a string
• the unit weight of the string (kg/m) - could use the diameter of the string and the density of the string material.  Alternatively, could put a length of string on a scale.
• the diameter of the string - can be directly measured using callipers (diameters also tend to appear on string packages)
• the density of the string material - most likely this would be looked up on the internet

For some of the variables, internet research will suffice and for others, they will need to measure themselves.  They will have to decide themselves what is appropriate for their situation.

Alternatively, they may start by looking at a package of strings, which usually lists the tensions on the back of the pack.  But then they have to think about what they are presented with and read the fine print.  What assumptions are made?  Do those assumptions apply to their instrument?  Probably not.  Also, they may not actually know exactly what brand of strings are on the instrument.

Let them decide...

An important part of Knowledge Construction is to let the students decide how they are going to meet the success criteria.  Although some groups may end up doing more work than others, all groups can present their results back to the class so (hopefully) a variety of creative and innovative ways to measure the tension are covered.

Apply it...

Now that students would have an understanding of how string pitch, length, diameter and density are related, they could apply it by creating their own string instruments.  This could be turned into an interdisciplinary project between science and music or art.  They would have to answer some of the following questions (and more) before starting to build.

• How many strings?
• Will it have frets and will it be based on the Western 12-Tone Equal-Temperament scale like a guitar or a piano?
• What material will the strings be?
• How strong will the support of the strings have to be? (ie. what would the tension in the strings be)

Extend...

This is a cool video that I think would be good for a follow-up on exactly what a string does when it is plucked.  How come they look like that in the video?  Do they see that when they regularly pluck a string?

The curriculum...

This activity would be appropriate for a Grade 11 Physics class because it bridges between the Forces unit and the Waves and Sound unit.  Because of this, I think it would make an interesting culminating project for the course.

More critical...

My self-criticism for this idea is that although it may engage students and contains elements of the 21st Lesson Framework, I think it lacks any real critical analysis or underlying STSE issue; which I believe to be necessary for transformative pedagogy.    Maybe the instruments the students build could be made entirely of recycled materials to draw attention to the incredibly complex life cycle of manufactured goods we take for granted.  Anyways, it's something for me to think about for future entries.

21C...

1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
6. Use of ICT for Learning: entry - adoption - adaptation - infusion - transformation

Day 12 - Infinities

The Problem...

How big is infinity?

Why?

• Opportunity for Math/English interdisciplinary study of The Fault in Our Stars by John Green
• Address the common mathematical misconception that you can treat infinity like any other number in an equation
• Present the mind-boggling idea that an infinite series can have a finite sum
• Illustrate the idea that there are unanswerable questions in math.

The other day, I asked @emnose what I should write an entry about and she had the idea to use the novel The Fault in Our Stars by John Green.  

Today I finished the book.  Great read. Crazy sad but crazy good.  I was already a huge fan of John Green's YouTube channels (VlogBrothers, mental_floss and his brother Hank's channel SciShow) but hadn't read any of his books.  @emnose highly recommended I read The Fault in Our Stars.  Her rationale for using the book in a lesson idea was that a recurring theme is infinity. She's a smart one.  I don't want to give away any of the book so I'm mostly keeping details out of this entry.

Mathematical Infinity...

"Some infinities are bigger than other infinities," a character in The Fault in Our Stars states after explaining Zeno's Paradox.  I thought it would be interesting for students to explore what infinity exactly means in math, and compare it to how it is used (literally and metaphorically) in literature.  

In math, infinity gets messy.  In physics, its where black holes (singularities) appear.  Grade 11 and 12 students discover some of these difficulties when they are trying to plot rational functions or taking limits in calculus.  Some of the most interesting examples of these problems are found when trying to solve the indeterminate forms.  There are subtleties with infinity in math as illustrated by this TED-Ed video (and in Fault in Our Stars):

Interdisciplinary Infinity...

After a student had explored some of these mathematical problems with infinity, they could start to explore how the word is used outside of math.  The Fault in Our Stars is an interesting investigation because it bridges the gap between infinity being used metaphorically and mathematically.  Using The Fault in Our Stars as a starting point, students can explore other places infinity is used in literature.  

Interdisciplinary investigations are critical to 21st Century Learning.  According to the 21C framework, Knowledge Construction must be interdisciplinary to be Transformative. To bring it more into the 21st Century, the investigations can be done Collaboratively in groups (maybe pair up a Grade 12 Calculus student with a Grade 12 English Lit student) and the results Communicated in a variety of forms (writing, video, infographic, art).

To Infinity, and Beyond...

Infinity isn't the only interesting math/science connection in the book.  Here's one of my favourite quotes:

“I believe the universe wants to be noticed. I think the universe is inprobably biased toward the consciousness, that it rewards intelligence in part because the universe enjoys its elegance being observed. And who am I, living in the middle of history, to tell the universe that it-or my observation of it-is temporary?” 

This could be the jumping off point for some interesting philosophical conversations about why we do science and math (or really any other subject).  Along with my Number Bases blog entry, this idea helps students see the more human-created foundations of the way we understand Math.  

The TED-Ed video above also exposes a highly important fact:  It has been mathematically proven that there are questions in math that are unanswerable.  I believe this has huge implications for how we should think about math.  To come back around to infinity, I'll leave you with the awesomely beautiful and mathematically interesting quote from the TED-Ed video, 

"Someone one said the rationals (fractions) are like the stars in the night sky.  Then the irrationals are like the blackness."

21C...

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

Future Lesson Ideas...

• The Philosophy of Math - see this Numberphile video called Do Numbers EXIST?
• Other cool interdisciplinary combos like the Evolutionary Biology in Galapagos (a novel by Kurt Vonnegut)

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)