A more detailed description of this activity can be found on the [https://www.exploratorium.edu/snacks/spinning-cylinder Exploratorium's Science Snacks archive, which includes a mathematical explanation and some additional inquiry methods that students can use to understand the phenomena.
A more detailed description of this activity can be found on the [https://www.exploratorium.edu/snacks/spinning-cylinder Exploratorium's Science Snacks archive, which includes a mathematical explanation and some additional inquiry methods that students can use to understand the phenomena.
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[[Category:Lesson plans]]
[[Category:Lesson plans]]
Revision as of 16:27, 21 August 2023
Without scientific optimism, the idea that science is necessarily iterative and if we as scientists keep looking we will eventually gain insights, scientists would have discovered far less than they have.
The Lesson in Context
This lesson teaches students that one's optimistic and persistent attitude towards scientific problem solving is just as important as understanding the philosophical underpinnings of the scientific method. Throughout the semester, we teach students how science or human reasoning can go awry, and it is important to balance this healthy skepticism with the optimism that iterative progress is still possible in problems big and small. Students will experience this hands-on in an activity in which they have to solve various puzzles that build upon each other.
Knowing that our perception and measurement of external reality are inevitably imperfect, it is still possible to collectively make iterative progress towards improving our understanding of the shared reality.
Scientific predictions are inevitably imprecise, but the precision (and accuracy) can be numerically estimated (credence level) and iteratively improved over time.
Persistance and a "can-do" attitude in problem solving can be developed by harboring a growth mindset and recognizing the value of iterative progress.
Understanding a complex system fully can seem intractable. Often, a first step in understanding is to make a first-order description of the system. One can then make incremental improvements by tackling second- or third-order effects.
One often mistakes scientific progress as a series of correct ideas confirmed by experiments. In reality, experiments are often designed to falsify a given idea, and only a small number of ideas survive. The rejection of ideas by experimentation is itself a form of incremental scientific progress, rather than failure.
Takeaways
After this lesson, students should
Appreciate how the "can-do" spirit of inquiry (and inventive experimental techniques) counter-balances the difficulties of discovery/innovation.
Appreciate that iterative work on a problem is the norm in science and the most productive approach (and in some cases the only way of being productive), even when it looks like it's not getting anywhere. Persisting on difficult problems will eventually pay off with interesting insights.
Recognize that an optimistic view of the tractability of a problem and/or one's ability to solve it eventually can in itself affect one's actual capacity to solve the problem.
Feel optimistic about the possibility of "enlarging the pie" in societal problems, rather than resorting to playing a "zero-sum game."
Scientific Optimism
The can-do attitude of problem solving that pushes one to persist in working iteratively on a problem.
Scientific optimism does not refer to the belief that science is always right, or that it can solve all the world's problems, or that one is inherently intellectually superior to others.
Iterative Progress
The practice of checking how an idea/solution/policy is playing out, and adjusting it in light of new evidence, often repeatedly or in frequent small steps.
Meno
"I do not insist that my argument is right in all respects, but I would contend as far as I can, in both word and deed, that we will be better people, braver and less idle, if we believe one must search for the things one does not know, rather than if we believe it is not possible to find out what we do not know and that we must not search for it."
- Plato, in the voice of Socrates
Cosmic Distance Ladder
Over time cosmologists have been able to measure distances to farther and farther objects. Several centuries ago the best that could be done was having approximate distances to the moon and other planets. But, by gradually building on each others techniques, we now know the distances of the farthest objects in the observable universe. They can start by using parallax to get estimates based on how the relative locations of stars shift in the night sky as the Earth rotates around the sun. Then, by comparing the luminosity of ever brighter (and rarer) objects of consistent known brightness, astronomers have been able to create a series of standard candles that make up a "cosmic distance ladder" reaching all the way to the edges of the known universe. Astronomers have now developed several independent cosmic distance ladders. But, the classic one begins with using nearer and farther Cepheid variables then eventually type 1A supernova to measure the most distant objects.
Poincaré Conjecture
After proving the longstanding Poincaré Conjecture and being offered the prestigious Fields Medal, Grigori Perelman rejected the prize, stating that his work merely built upon his predecessor Richard Hamilton's. Even though it is the final triumph that is publicised and celebrated, it is the countless hours of incremental work that lays the foundation for that triumph.
Katalin Kariko
The daughter of a butcher in Hungary, decided she wanted to be a scientist even though she'd never met one. She spent her entire career studying mRNA, convinced it could be used to make vaccines. As grant after grant was rejected, and the University of Pennsylvania rejected her tenure, Dr. Kariko nevertheless persisted in her project. Recently, in her 60s, she and her colleagues made the breakthrough that led to the mRNA vaccine for Covid-19. Scientists are now hopeful that this breakthrough may lead to other vaccines for a wide variety of major diseases, including malaria, cancer, and AIDS. (Info)
Many people have tried to solve this problem of increasing illiteracy and failed, so we shouldn't throw more good money after bad — some problems are just intractable.
Even tiny improvements can be quite substantial in changing people's lives. Additionally, even though progress may be slow or invisible (only in certain communities, etc.), its cumulative effect can be enormous.
Scientists have been trying to figure out what dark matter is for decades, and we still basically have no idea. We'll probably never know, so it's not worth working on.
We may not know exactly what dark matter is. But, scientists have managed to substantially expand the list of things it isn't. This is still progress and could ultimately give us real insight about the nature of dark matter.
Very carefully read through the tangram activity, make sure the GSI and TA know their respective jobs, and make sure you have access to all the equipment you need.
Conduct the tangram activity. Any pairs that don't take the whole time should be free to work on their Project 2 proposals and talk them over with the GSI.
15 Minutes
Discussion questions from the Tangram activity.
30 Minutes
Have students come up with a Project 2 idea and discuss with the GSI/TA.
Lesson Content
Warm-up Question
Which of the following is NOT an example of scientific optimism?
A physicist keeping herself working on a problem by persuading herself that she is making incremental progress.
The public believing that scientific research will eventually cure cancer.
A biologist in the 1940s, when the role of DNA had yet to be discovered, extensively researching the new idea that genetic material is carried by polynucleotides rather than proteins, despite the majority of his colleagues' believing that nothing of interest will come of it.
Mathematicians continuously trying to prove Fermat's Last Theorem for 3 centuries following the original conjecture by Fermat in 1637.
Physicists continuing to design experiments searching for other new elementary particles after failing to find some particles they predicted.
Explanation
The public is not actually doing the research themselves, so their optimism is not active.
Tangram
In this activity, we aim to demonstrate the importance of iterative progress in problem solving by giving the problem solver a sense of continued motivation. The students will be asked to work on a series of Tangram puzzles, which are designed so that the solutions to simpler puzzles may help one solve more difficult ones. The class is secretly divided into two halves, with one side given puzzles in the intended order (optimistic, from easy to hard) and the other in a somewhat reversed order (pessimistic, from hard to easy). We hope to see that the optimistic pairs feel more motivated to persist than the pessimistic pairs.
Supplies
Let [math]\displaystyle{ n }[/math] be the number of pairs of students in your section. (If you have an odd number, just make a "pair" of three students.)
[math]\displaystyle{ 2n }[/math] complete sets of Tangram puzzles (One complete set consists of seven pieces. You can reuse these from a previous section as long as they're still complete.)
[math]\displaystyle{ n/2 }[/math] printed copies of the optimistic puzzles
Randomly divide the numbered sticky notes into two piles of equal size. One pile is for the pairs that will receive the optimistic puzzles. The other is for the pairs with pessimistic puzzles. On a separate document or piece of paper note down which numbers are in which piles.
Logistics
Make sure to not distinguish between the optimistic and pessimistic pairs as you implement this!
Two instructors must attend this section. We'll call them instructor 1 and instructor 2.
Students work in pairs.
Split the classroom into two halves. Instructor 1 manages one half and instructor 2 manages the other. Instructor 1 holds all the optimistic puzzles and sticky notes from the optimistic pile. Instructor 2 holds all the pessimistic puzzles and sticky notes from the pessimistic pile.
Give out one sticky note per pair of students. The instructors will give out sticky notes to their halves of the room.
Display your prepared spreadsheet on the projector, where each pair's success/failure will be recorded and publicly shown.
Explain the activity using the following script as a guide.
Each pair is given their first puzzle. The timer begins!
Script
In this activity you'll be given a set of Tangram puzzles to solve. For each puzzle you'll be given a sheet of paper with some shape to make and a set of 14 plastic pieces with which to fill in that shape. Some puzzles may have leftover pieces at the end but each shape must be exactly filled in. There's eight normal puzzles as well as one "bonus" puzzle if you get them all done. You'll be given the puzzles one at a time and your progress will be shown in the projected spreadsheet. If you complete the puzzle, loudly announce "We did it!" and the instructor that gave you your pair number will come over. They'll check your work, take your old puzzle, give you the next one, and mark down that you successfully solved that puzzle on the spreadsheet. You can also choose to skip a puzzle. In that case, you must loudly announce "We're skipping!" and your instructor will come over. The instructor will take your old puzzle, give you the next one, and mark down that you skipped the puzzle on the spreadsheet. When you skip or complete a puzzle, you can request to go back to a previous one and the instructor will give you that puzzle instead. The first pair to complete every puzzle other than the bonus one will win a fabulous prize!
Instructions
If a pair completes their puzzle, they call the instructor that handed them their sticky note over to check their solution. The instructor can then collect their current puzzle and give them the next one or a previously skipped one, their choice. Mark on the public spreadsheet with a "success".
If a pair decides to skip their puzzle, they also call the instructor over to exchange their current puzzle for the next one or a previously skipped one. Mark on the public spreadsheet with a "skip".
When a pair finishes all the puzzles, record the time on the spreadsheet. The pair that solves all of the puzzles first gets some prize. If a pair finishes early, they can work on the bonus puzzle.
Reminder
Make sure to figure out the students' fabulous prize!
Discussion Questions
Immediate Activity Follow-up
Ask the following questions of the entire class.
How do you feel?
Did you use knowledge from an earlier puzzle on a later one?
How did you decide when to skip a puzzle or keep working on it?
Here's one more Tangram puzzle. How long do you think it would take you to solve it?
Is there something else you noticed?
If you want, you can ask the first question of only the best and worst performing pairs of students.
For the second to last question, show a slide with the extra Tangram puzzle. Have the students do a show of hands for under 5 minutes, 5-10 minutes, and above 10 minutes.
The Reveal
At this point, the instructor reveals that there are two different orderings of the puzzles, one optimistic and one pessimistic. The optimistic ordering encourages incremental progress by providing partial puzzles whose solution can be used in a later puzzle. You can put what pair had what ordering in the "?" column of the spreadsheet with labels. Then, sort column A.
Tip
The spreadsheet will automatically color the cells in if you fill them with "O" for the optimistic pairs and "P" for the pessimistic pairs.
Final Questions
Now ask the following questions of the class as well.
Did the optimistic pairs perform better?
Do you think there's such a thing as a "Tangram person" like there may be "math person" or "music person?" Why or why not?
Give the students the morals of the story.
The Morals
Reiterate the first three learning goals.
One can stay motivated by recognizing the value of incremental progress even when you feel you're nowhere close to the "big" goal.
The "error" part of trial and error is an important type of incremental progress.
Remind them of the "growth mindset" from 3.2 Calibration of Credence Levels. You can improve in your persistence and "can-do" spirit by recognizing the value of incremental progress instead of feeling dejected over not having completed the overall goal.
