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.
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)
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:
Organize! Students determine roles for constructing the model.
Model the classroom - including desks, lab desks, teachers desk, windows, doors, intercom, materials storage and anything else of note.
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!
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.
Material DistributionProcedure - What is the best way to distribute lab materials/chemicals - come up with a plan!
Emergency plan - Plan for an emergency and try it out! With everyone sitting at their desks (in the model) re-enact the procedure.
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.
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.
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...
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.
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.
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.
The Problem... How do excercise apps/machines determine how many calories you have burned? Why?
Critical examination of the algorithms behind ICT
Make mathematical connections between variables
Experimentation and control variables
I have often wondered about how exercise bikes and running apps are able to calculate the amount of calories burned. What assumptions do they make to find that number? This question is an opportunity to combine math and biology (the science often seen as having to do the least with math), as well as tying both into physics.
These are the stats of one of my runs (from last year when I was in way better shape) collected using the free iPhone app RunKeeper. Apparently, I burned 403 calories. Not too shabby.
I think an interesting activity would be to try and reverse-engineer where that 403 calories comes from. Collect some data... Students could form groups and collect data on their own devices on a variety of apps and experiment by playing with different variables (if you look hard enough on the RunKeeper website, there is actually a list of variables used to calculate the calories, but it doesn't tell you how its calculated). This is a good introduction to control variables. Students will have to understand they can only change one variable at a time to get useful results. For example, they may change the weight that is input and see if the calories burned varies linearly with weight. **If a school has exercise bikes available, they may be a good starting point because there are usually less variables to deal with and the method they use for calculating calories is much simpler (and usually just linear with distance travelled). What assumptions does the software in these machines make? Critique and Create... After coming to some conclusions about how the apps calculate calories, students should critically evaluate the assumptions in the calculation. I think an interesting way of evaluating this would be for the students to decide what other variables may be important and come up with their own algorithm for calculating calories burned. They could then submit their recommendations to the app developers.
Curriculum...
This activity encourages the use of control variables and has students creating their own experiments. They have to think about the mathematical relationships to establish an understanding of the cause and effect of the variables in the app, a critical part of the Scientific Method.
This activity is also a good introduction to metabolism:
What are calories?
Why do we use the unit calories instead of joules?
To give some scale of energy, how many calories does a lightbulb use in an hour?
How many calories does a litre of gasoline contain?
We can also tie in physics:
In physics, we say that the total energy in has to equal the total energy out. Is this true of humans?
What other ways do we use energy besides going for a run or bike ride?
21C...
Students participate in Knowledge Constructionby performing their own experiments. They should have the freedom to choose what apps they want to analyse and work in groups to establish the relationships between the variables.
Problem... Why are there 10 symbols in our numbering system? Why?
Start a discussion on biases and assumptions implicit in the way we look at math
Introduce programming and logical reasoning into math classes
There is a lot in math that tends to be taken for granted. For example: our number system is in base 10. In other words, we have 10 different symbols: 0,1,2,3,4,5,6,7,8,9. When we add one more, we end up reusing the digits 1 and 0 to make 10 and continuing from there: 11,12,13 etc. Why 10? Essentially, its completely arbitrary. The most commonly cited reason is that we have 10 fingers for counting on. The inspiration for this post is Alex Bellos' book Here's Looking at Euclid. In addition to many other topics, Bellos discusses the concept of different bases and how they were used in different cultures throughout history (bases 20, 60 and 12 are the most common). Below is a screenshot from the app Number Base Conversion.
It blows my mind that I didn't really hear about number system bases until Grade 11 Computer Science, where it tends to be a common intro to how computers work. I find it strange that it never appears in the math curriculum because it is fundamental to how we think about numbers. The base 10 bias is never really explored or explained in school. Programming in Math Class... Conrad Wolfram (brother of Stephen Wolfram, founder of the awesome math/everything tool Wolfram Alpha) is a big proponent of utilizing programming as a tool for helping students understand concepts in math classes.
He believes the act of writing a computer program requires a much more in-depth understanding of the concept. Once the program is written, students can use it to solve problems for them. This way, they don't have to waste a lot of time doing arithmetic and other mundane tasks that aren't part of the curriculum. Thats what we have computers for after all. This is highly representative of how problems are approached in the real world as well. We aren't trying to teach students to be human calculators, were trying to teach them to be problem solvers.
The topic of number bases and base conversion would be an excellent example for using programming in a math class. Students could write programs that convert base 10 number to other bases. They could then use their program to explore strange bases like base 1, negative bases, irrational bases (like pi) and fractional bases. This is a perfect example of the 21st Competency Use of ICT for Learning. Students would be able to create a usable artifact. Another interesting investigation is looking at how arithmetic works in other bases. Curriculum connections... Understanding number bases requires the use of exponents, logic, and a deep understanding of place value and how numbers work on a fundamental level. Though the topic is not directly in the curriculum, I see it as a way for a teacher to formatively asses students' comfort with basic math concepts and their problem solving ability.
Critical Math... It is important to be able to step back and examine our biases. Examining why we use base 10 is a good way to bring to light the fact that a lot of math is actually rather arbitrary as a product of history and culture as opposed to a given fact of nature. It is an opportunity to challenge our basic assumptions with math and opens the door to discussion and the critical examination of other things that we may take for granted (example: why are there 12 semitones in an octave in our music, why does the major scale have 7 notes?). We can ask questions such as: If we primarily used a base 12 system for math, would we see things in different ways? Would we have made certain discoveries that we have not made yet or would we have missed certain discoveries? Would our world be different? 21C Continuum... 2. Knowledge Construction:entry - adoption - adaptation - infusion - transformation 6. Use of ICT for Learning:entry - adoption - adaptation - infusion - transformation Future Lesson Ideas
Examine the music/mathematical relationships in the 12 Tone Equal-Temperament system
