How big is infinity?
Why?
- Opportunity for Math/English interdisciplinary study of The Fault in Our Stars by John Green
- Address the common mathematical misconception that you can treat infinity like any other number in an equation
- Present the mind-boggling idea that an infinite series can have a finite sum
- Illustrate the idea that there are unanswerable questions in math.
The other day, I asked @emnose what I should write an entry about and she had the idea to use the novel The Fault in Our Stars by John Green.
Today I finished the book. Great read. Crazy sad but crazy good. I was already a huge fan of John Green's YouTube channels (VlogBrothers, mental_floss and his brother Hank's channel SciShow) but hadn't read any of his books. @emnose highly recommended I read The Fault in Our Stars. Her rationale for using the book in a lesson idea was that a recurring theme is infinity. She's a smart one. I don't want to give away any of the book so I'm mostly keeping details out of this entry.
Mathematical Infinity...
"Some infinities are bigger than other infinities," a character in The Fault in Our Stars states after explaining Zeno's Paradox. I thought it would be interesting for students to explore what infinity exactly means in math, and compare it to how it is used (literally and metaphorically) in literature.
In math, infinity gets messy. In physics, its where black holes (singularities) appear. Grade 11 and 12 students discover some of these difficulties when they are trying to plot rational functions or taking limits in calculus. Some of the most interesting examples of these problems are found when trying to solve the indeterminate forms. There are subtleties with infinity in math as illustrated by this TED-Ed video (and in Fault in Our Stars):
Interdisciplinary Infinity...
After a student had explored some of these mathematical problems with infinity, they could start to explore how the word is used outside of math. The Fault in Our Stars is an interesting investigation because it bridges the gap between infinity being used metaphorically and mathematically. Using The Fault in Our Stars as a starting point, students can explore other places infinity is used in literature.
Interdisciplinary investigations are critical to 21st Century Learning. According to the 21C framework, Knowledge Construction must be interdisciplinary to be Transformative. To bring it more into the 21st Century, the investigations can be done Collaboratively in groups (maybe pair up a Grade 12 Calculus student with a Grade 12 English Lit student) and the results Communicated in a variety of forms (writing, video, infographic, art).
To Infinity, and Beyond...
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):
After a student had explored some of these mathematical problems with infinity, they could start to explore how the word is used outside of math. The Fault in Our Stars is an interesting investigation because it bridges the gap between infinity being used metaphorically and mathematically. Using The Fault in Our Stars as a starting point, students can explore other places infinity is used in literature.
Interdisciplinary investigations are critical to 21st Century Learning. According to the 21C framework, Knowledge Construction must be interdisciplinary to be Transformative. To bring it more into the 21st Century, the investigations can be done Collaboratively in groups (maybe pair up a Grade 12 Calculus student with a Grade 12 English Lit student) and the results Communicated in a variety of forms (writing, video, infographic, art).
To Infinity, and Beyond...
Infinity isn't the only interesting math/science connection in the book. Here's one of my favourite quotes:
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,
“I believe the universe wants to be noticed. I think the universe is inprobably biased toward the consciousness, that it rewards intelligence in part because the universe enjoys its elegance being observed. And who am I, living in the middle of history, to tell the universe that it-or my observation of it-is temporary?”This could be the jumping off point for some interesting philosophical conversations about why we do science and math (or really any other subject). Along with my Number Bases blog entry, this idea helps students see the more human-created foundations of the way we understand Math.
The TED-Ed video above also exposes a highly important fact: It has been mathematically proven that there are questions in math that are unanswerable. I believe this has huge implications for how we should think about math. To come back around to infinity, I'll leave you with the awesomely beautiful and mathematically interesting quote from the TED-Ed video,
"Someone one said the rationals (fractions) are like the stars in the night sky. Then the irrationals are like the blackness."
21C...
1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
4. Skilled Communication: entry - adoption - adaptation - infusion - transformation
Future Lesson Ideas...
- The Philosophy of Math - see this Numberphile video called Do Numbers EXIST?
- Other cool interdisciplinary combos like the Evolutionary Biology in Galapagos (a novel by Kurt Vonnegut)
Lots of good ideas! I like that this might help engage students who aren't necessarily interested in math.
ReplyDeleteAnd I especially like the shout out to me ;)