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!
The Problem... Create an ICT artifact that expresses the scale of the really big and really small. Why?
Keep things in perspective!
Creative expression in Science class
Facilitate self-regulation
Facilitate a more intuitive understanding of scale of things discussed in Science
Scale Misconceptions There are a bunch of Science misconceptions that come from a lack of understanding of scale. Here is a video about one of these by Misconception Specialist Derrick Muller of the YouTube Channel Veritasium.
The scale of really big stuff and really small stuff can be really hard to comprehend. Here are some ways that people have tried making it easier:
In a Class... Most of the Grade 9 Science course revolves around the very small (atoms and electricity) and the very large (astronomy) and this activity would be perfect for that class. I would present the above examples to a class and have them create their own artifact to illustrate scale with objects from throughout the course. It could be a long-term project that is introduced at the beginning of the course. The students collect the data throughout. As an ICT Artifact, students could continue to contribute as they move through the grades. It would serve as a good anchor point for some big concepts throughout the Science Curriculum. There are tons of different ways students could present the data: infographics, videos, images, apps and more. I would keep the project relatively open to facilitate Self-Regulation. As the teacher, I would provide them with feedback as they build their artifact over the course as well as providing students to critique others.
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?
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 Solvingand 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.
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.
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 Innovationto 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-Regulatedby 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.
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 hereif 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 EDUthat 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.
Just a general point about my work so far: I have been keeping them very vague and conceptual (and unpolished) for a few reasons explained below.
It's impossible to know whether many of these lesson ideas would actually work with a class until I have a class in front of me and get to know the students Culturally Relevant Pedagogy is critical for student engagement so I wouldn't force any of these lesson ideas on a class unless I thought it would be successful for that group. Keeping it vague gives me the flexibility to change the lesson based on the students in the class and the actual course it would happen in.
One of the reasons I'm doing this blog is to better understand how 21st century learning would potentially look in a high-school math/science class. As well as helping me understand the neXt Lesson Framework for my internship. To me, the hardest part of doing this is generating some really good ideas to get started, which is the purpose of this blog.
Time! To get down all the details of a lesson for each one would take forever. During my internship I don't have that kind if time! (what I'm doing right now takes enough time as it is)
One more point about the levels I have highlighted for each competency at the end of each entry: They reflect the potential of each lesson idea. Where they will actually fall is highly dependent on exactly how the activities are presented to students as well as grade level and course. For example, I have keft Self-Regulation out of many entries but it could end up being a huge part of the activity depending on how the success criteria and project timeline is established.
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.
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 Communicationof 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 Constructionto 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...
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 Constructionstudents 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 Communicationand Real-World Problem Solvingskills 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...
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.
