Today was the 16th annual TCDSB "Special Needs Mini Olympics". The 21C/AICT team provided tech for the rest station and was responsible for running it (with the help of several student volunteers). It was awesome to see all the students having such a great time. There was great energy from all the student volunteers and teachers. Kudos to the organizers on accommodating such a large and diverse group of students! All the events were great and the Hangar at Downsview was the perfect venue. Really inspirational stuff. It was an awesome day.
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 Collaborativelyto 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 Constructionis 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.
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 beTransformative. 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."
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:
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 Collaborativelydecide 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 Solvingand 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 Constructionwould 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?
How does the song I.S.S. (Is Somebody Singing) illustrate physics concepts and how has Chris Hadfield's stay on the ISS impact the way the public thinks about Canada's contribution to Science?
Why?
Exposure to seldom heard Canadian point of view on space exploration
Illustrates how Science can directly impact Society
Deepen understanding of physics concepts and address misconceptions
Chris Hadfield is a Canadian astronaut and has been the commander of the International Space Station (ISS) for the past few months. From orbit, he has been taking stunning pictures of the Earth and tweeting them.
Nice pic of Toronto in this tweet:
Tonight's Finale: Toronto, Ontario. Interesting the different things that become more visible at night. twitter.com/Cmdr_Hadfield/…
Hadfield has drawn tons of media attention for the tweets and videos he has created. This entry is inspired by the completion of Chris Hadfield's stay on the ISS (he returns to Earth tomorrow evening). Have a safe journey home Chris!
The Song...
While on the ISS, Chris Hadfield co-wrote a song with Barenaked Lady Ed Robertson (who was on Earth). The media attention has been surprising (I have heard the song on several different radio stations over the past week).
I think it would be interesting to have a Science class examine some of the lyrics in the song to pick out and examine some of the concepts presented. This blog entry contains some background information on the writing of the song as well as the lyrics and sheet music complete with guitar chords. To turn this into an in-class activity, I would flip the video to the class for homework and provide them with some questions to prompt them thinking about the physics concepts mentioned. I would then provide them with the lyrics in class and would task groups of students with making the connections and checking the claims (and see how much creative license Hadrield and Robertson take!). They could then present their results to the rest of the class to start discussions on the topic. This activity requires student-directed Knowledge Construction because essentially they have to generate their own questions and figure out how to solve them. Below I have identified some of the lyrics that may be used in class discussions:
"Pushed back in my seat/Look out my window/There goes home"
At what point in the mission is Hadfield 'pushed back in his seat'? What is he experiencing? What is the physics behind that feeling? (an illustration of inertia and acceleration)
What would he feel this while orbiting in the ISS?
There is a common misconception about the lack of gravity an orbiting astronaut would experience. Really there is gravity, the weightlessness is attributed to the fact that the ISS is actually in free-fall around the earth.
"I can hear your voices bouncing off the moon"
This is more than just a metaphor! What is he referring to?
"All black and white just fades to grey/Where the sun rises sixteen times a day"
Why does the sun rise 'sixteen times a day'?
Why does the ISS not fall to earth?
This is a good way to introduce the concept escape velocity
This site contains interesting facts on the orbit of the ISS.
"Eighteen thousand miles an hour/fueled by science and solar power"
This also relates to escape velocity and can be used to calculate kinetic energy of the ISS (see below)
"At half a thousand tons/Ninety minutes Moon to Sun/A bullet can't go half this fast"
Check the validity of this statement! How fast do bullets generally travel?
How much kinetic energy does the ISS have compared to a bullet?
The ISS started a pieces on Earth. How did we get the kinetic energy of the ISS to that value?
"What once was fueled by fear/Now has fifteen Nations orbiting together here"
and...
"You can't make out borders from up here/Just a spinning ball within a tiny atmosphere"
These quotes give us some perspective and are an opportunity to explore deeper questions about our place on the planet and in the universe and the role of science in our society
Curriculum...
This lesson is flexible because of the student-constructed knowledge aspect. They ask the questions that they will answer. Because of this, it could potentially be appropriate in any high school Science/Physics class.
There's some interdisciplinary opportunity here too. Hatfield's Twitter pictures would be awesome to study in a physical geography class. It could also potentially be an appropriate topic of discussion for a civics class. The obvious connection is to a music class...
21st Century...
Students will have to use internet resources to answer their questions about the lyrics. The fact that the material is presented as a song (and video) will appeal to a broad range of high school students. It also models another possible medium that they can use to present material for assignments: through song!
Other internationally funded Science projects (Ex. The Large Hadron Collider)
More material... Here's another Ed Robertson blog entry on Science and Songwriting. Awesome quote: "If you want to improve your songwriting, work on your math and science." Some trivia: the Barenaked Ladies do the theme song to Science-laden TV comedy Big Bang Theory. This is another cool Hadfield video where he talks about how he takes the pictures from the ISS.
For the record, I have gone back through the lesson ideas I have created so far and made a few modifications:
I formalized the entries by starting with a Problem Statementat the beginning of each entry. This is more representative of the type of Inquiry-Based Learning I plan on implementing in my future classroom.
After the Problem Statement, I have added a section called 'Why?' or 'Why is this a good topic for a lesson?' It is basically a few points rationalizing what the purpose of turning that idea into a lesson is.
I have tagged each entry based on the 6 neXt Lesson competencies as well as subject area. In his session on Blogging as Portfolio, George Couros made a good point about organizing your blog with tags so that individual competencies or subjects can be accessed by themselves. This reflects how a resume would be organized into categories.
I have put a scale at the end of the entries that shows where on the neXt Lesson continuum the idea falls in each competency (see below).
While making the above changes to my entries, I realized I could fairly easily improve each idea with a few tweaks. Hopefully this realization will help me create more 'transformative' ideas going forward. Also, I'm a day behind because this blogging is hard work! I'll catch up over the weekend.
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.
