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Table of Contents
Knowledge and the Knower.................................................................................................................................. 3
Introduction to TOK (and me!)..........................................................................................................................................4
Perspectives ...........................................................................................................................................................................8
Scope ...................................................................................................................................................................................... 17
Scope, Part 2 ....................................................................................................................................................................... 21
Methods & Tools ................................................................................................................................................................ 24
Ethics, Part 1 ....................................................................................................................................................................... 35
Ethics, Part 2 ....................................................................................................................................................................... 40
AOK: The Arts ......................................................................................................................................................... 45
The Arts: Scope & Perspectives ................................................................................................................................... 46
The Arts: Methods & Tools ............................................................................................................................................. 56
The Arts: Ethics ................................................................................................................................................................... 67
AOK: Natural Sciences ......................................................................................................................................... 73
Natural Sciences: Scope.................................................................................................................................................. 74
Natural Sciences: Perspectives .................................................................................................................................... 79
Natural Sciences: Methods and Tools ....................................................................................................................... 84
Natural Sciences: Ethics .................................................................................................................................................. 93
AOK: Mathematics ................................................................................................................................................. 99
Mathematics: Scope ...................................................................................................................................................... 100
Mathematics: Perspectives ......................................................................................................................................... 106
Mathematics: Methods & Tools ................................................................................................................................. 113
Mathematics: Ethics ....................................................................................................................................................... 121
AOK: Human Sciences ....................................................................................................................................... 128
Human Sciences: Scope ............................................................................................................................................... 129
Human Sciences: Perspectives.................................................................................................................................. 139
Human Sciences: Methods & Tools.......................................................................................................................... 147
Human Sciences: Ethics ............................................................................................................................................... 157
AOK: History ........................................................................................................................................................ 163
History: Methods & Tools ............................................................................................................................................. 164
History: Scope & Perspectives ................................................................................................................................... 171
History: Ethics .................................................................................................................................................................. 178
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Knowledge and
the Knower
Introduction to TOK (and me!)
TOK is an introduction to __________ which studies the nature, sources, and
__________ of knowledge.
The TOK Knowledge Framework
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Scope
What do I know?
How do I know it?
What might I not know?
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#RLS – Indonesian Cinema Reopening
Do you agree or disagree with the following knowledge claim: Going to the movies
can prevent COVID-19.
How does this knowledge claim work with the rules of logic?
How does this knowledge claim cohere to what we know about medicine and biology?
Perspectives
#RLS - Panguni Uthiram
Our __________ provide a lens that serves as our __________ to the things that we
experience, witness, and know.
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Methods & Tools
The Ways of Knowing:
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Chairs can break. So why are you sitting in a chair? (Connect with a WOK)
What do you KNOW is true without evidence? What are you certain of, right down to
your bones, without proof?
TOK is established on the belief that to know something you must have a __________,
__________ __________.
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Ethics
What we __________ to do in a given situation or when having knowledge.
Who would you kill?
TOK is concerned less with your answer and more with the reasoning behind the
answer!
Why did you answer the way you did?
TOK Terms
Validity, understanding, bias, implications, certainty, assumptions, interpretation,
reliability, evidence, belief, culture, experience, explanation, interpretation, intuition,
justification, truth, values.
How to sound TOK-y: Address __________, __________ ___ __________, and TOK terms.
By acknowledging our perspectives and how they create our interpretations, we can
become open to __________ perspectives. We become open to __________ knowledge
and information.
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Perspectives
The First Question
You tell your friend to meet at 1 p.m. She shows up at 1:15.
Assuming that this was not caused by an accident, why might she
have chosen to show up at this time?
Our __________ provide a lens that serves as our perspective to the things that we
__________, __________, and __________.
What person has influenced you more than anyone else?
What experience has influenced you more than anyone else?
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What idea or belief drives you each day?
If these influences give conflicting information, which are you most likely to follow?
Why?
Click here to access the Political Compass quiz. After taking it, take some guesses –
think about your response. Are you surprised? Why or why not?
What influences and/or experiences might have caused you land where you did?
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What Are Your Influences?
What year were you born?
How might your age affect both what you know and your attitude towards gaining
knowledge?
How is your perspective different than that of an adult alive today?
What gender are you?
How does your gender role affect how you see the world?
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Does it influence your expectations of what knowledge you should gain in your
education?
Did you grow up in an urban or rural area?
How might living in a city, suburb, or rural area affect what and how you know?
Have you always had enough to eat, felt safe and been able to get education?
How do you think having these needs met, or not, affects your present knowledge?
What areas of knowledge interest you most?
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How about what is least interesting to you? What impact do your interests have on
how you view the world and people around you?
How would you describe your spiritual worldview?
How might one’s religion impact knowledge acquisition?
What is your SES (Socio-economic Status?)
How does this affect the things you know and think?
What kind of school do you go to?
How is this different than other people in your country.
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Perspective, Opinion, & Facts
Do you agree with the following knowledge claims? Why or why not? What
experience created the perspective that provided your answer?
Cryptocurrency is a scam.
Government should fund domestic healthcare systems.
The world is flat.
It is important that all perspectives be protected.
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It is important to be on time.
Patricia Piccinini is a good artist
When experts disagree, who do you trust?
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The Big Question
What is something that you are certain about? What would it take
to change your mind?
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I Am Smart
Your first closing activity will be listening to a podcast (I love podcasts & videos)
featuring an interview with a woman who grew up in Westboro Baptist Church. If you
don’t know about the WBC, you may want to Google them first. They are not kind
people (nor are they affiliated with the Baptist denomination of Christian Churches).
Megan grew up believing many things that she now believes to be false. In this
interview she details what experiences helped her to evaluate and eventually change
her beliefs. Please note: this interview discusses the behavior of people who are racist,
homophobic, and just plain mean.
Click here to listen to the podcast.
After finishing the podcast, answer these questions:
1. What caused Megan to change her mind?
2. What is a significant belief or opinion that has changed as you’ve grown up?
How was your mind changed?
3. Why do we believe people when we disagree with them? What leads to
changed minds?
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Scope
The First Question
When was a time in which you messed up because you didn’t
have knowledge? Why is knowledge important?
#RLS – Where Ukraine At?
Key: Our knowledge of ___________ may inform our opinions about __________.
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The Ladder of Inference
Inference can lead to __________ and __________. We use these to make knowledge
claims.
Types of Knowledge Claims
First Order Knowledge Claims
Second Order Knowledge Claims
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You believe the knowledge claim that Hydrogen is the lightest element. Why?
How many times does the white team complete a pass?
Empirical Claim
Normative/Value Claim
Analytic Claim
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Metaphysical Claim
Revelatory Claim
How does your knowledge affect the way you watch this video?
TAKE A BREAK!
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Scope, Part 2
A Priori Knowledge
A Posteriori Knowledge
What is Knowledge?
Write any true statement below. It can be stupid or brilliant.
Justified
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True
Belief
Video: The Gettier Problem
#RLS – Miasma Theory
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The Big Question
What do you think? Does something have to be true for it to be
counted as knowledge? Can you know something that is false?
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Methods & Tools
The First Question
Is this real or not? How did you come to this conclusion
(influences, ways of knowing, areas of knowledge)?
Plato’s Allegory of the Cave
Come up with reasoning for both sides of this argument:
What we call reality is real.
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There is something beyond our reality that we cannot see.
Can you think of something that is 100% always true?
The Coherence Test for Truth
Does this fit with what I already __________?
Does this fit with what I have __________?
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The Coherence test relies on a body of truth that is based on____________ knowledge.
Black Swan Events
“A black swan is an ________________ event that is beyond what is normally expected
of a situation and has potentially severe consequences. Black swan events are
characterized by their extreme_______________, severe impact, and the widespread
insistence they were obvious in _______________.”
From Taleb:
Black swans are __________.
Black swans have major __________.
In retrospect, people will rationalize that it should have been __________.
Examples & Notes:
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Correspondence Test for Truth
This test asks if a knowledge claim corresponds to what is __________ in reality.
“Truth consists in a relation to reality: truth is a relational property involving a
characteristic __________ to some portion of reality.”
Thomas Aquinas: “A judgment is said to be true when it __________ to the external
reality”
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Examples & Notes:
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Pragmatic Test for Truth
Beliefs that lead to the best "payoff", that are the best justification of our actions, that
promote success, are truths, according to the pragmatists."
The Pragmatic Test deals with __________, _________, and __________.
Examples & Notes:
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Consensus Test for Truth
Truth is whatever people __________ upon.
Examples & Notes:
What are some problems (and problematic RLS) with the Consensus Test?
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Minor Tests for Truth
Test of Time
Divinity/God
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Authority
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The Big Question
Think about the las time you were frustrated or confused about a
choice that you had to make. Which test for truth did you use?
Which other tests might have helped you out?
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I Am Smart
I could talk about the tests all day. There were some videos that I chose not to include
for the sake of time. But they are so interesting! Watch these videos and ponder the
age-old question, ‘What is Truth?’
Truth isn’t Truth
What Nietzsche meant by ‘God is Dead’
Washington Group Challenges Gender Identity Controversy
Rachael Dolezal ‘I Definitely Am Not White’
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Ethics, Part 1
The First Question:
If you were guaranteed not to get caught stealing a snack from a
convenience store, would you do it? Why or why not?
Where does right and wrong come from?
At its simplest, ethics is a system of moral principles. They affect how people make
decisions and lead their lives.
Ethics deals with the word ought. It’s what you ought to do in a certain situation.
What principles, ideas, morals, ethics, or experiences guided your decisions in the
Moral Machine?
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If you were accused of doing something immoral what might you have done?
If you were accused of doing something unethical what might you have done?
Ethics – guidelines that originate from an __________ source.
Morals – guidelines that come from __________ you.
Absolutism & Relativism
Moral absolutism argues that there are some moral rules that are __________ true,
that these rules can be discovered and that these rules apply to everyone.
Moral relativists say that if you look at different __________ or different __________ in
history you'll find that they have different moral rules.
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Ought a teacher cite their research for a simple lesson like this one? What is the
dilemma here?
Waterboarding: Would you torture terrorists in order to prevent further terrorism?
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Moral Framework Research
Spend a few minutes learning about the following moral frameworks. Though there
are many frameworks used today, these are some of the most common and universal.
You can read articles about these, watch videos on YouTube, or do something else.
As you learn about each one, write down the following:
1. What does this framework believe?
2. How would they communicate to a country that might panic if told the truth
about COVID-19?
Egoism
Utilitarianism
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Kantian Ethics
Divine Command Theory
Aristotelian Ethics
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Ethics, Part 2
Why do parents work hard for their children? Why do they buy gifts for their children?
What different reasons can you come up with?
It often turns out on closer inspection that acts of apparent __________ are really
selfishness in disguise.
How might buying a gift for your child be an act of selfishness?
#RLS – The Selfish Gene
When it comes down to it, why don’t you cheat on exams?
When it comes down to it, why would you really give money to help a friend?
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When it comes down to it, why don’t you murder classmates that annoy you?
What are your thoughts on Dawkins and The Selfish Gene? Do you agree or disagree?
Why?
#RLS – Racism in the West
Is it moral to be tolerant of intolerant people?
Is it ethically justifiable to pour coffee on a racists face during a livestream? Why?
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Is it ethically justifiable to punch a racist in the face? Why?
Is it ethically justifiable to shoot a fascist?
The Paradox of Tolerance
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The Big question
I shared why I believe relativism is wrong. Do you agree or disagree
with me? Why?
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I Am Smart
Watch this video about how ethics work in the natural world. What do you think?
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AOK: The Arts
The Arts: Scope & Perspectives
The First Question
Who, in your opinion, is an artistic genius? How did you come to this
opinion? What makes someone an artistic genius?
Is It Art? Why or why not?
1.
2.
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3.
4.
5.
6.
7.
8.
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In your opinion, what makes something art?
#RLS – Duchamp & the Society of Independent Artists
#RLS – Salon des Refusés
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Before you begin lesson #2, click here to listen to Hallelujah, an episode of the podcast
Revisionist History.
Listen to the three versions of Hallelujah below:
Leonard Cohen’s Original Version
John Cale’s Cover Version
Jeff Buckley’s Cover Version
Which version of the song is the best?
How do you decide on the version that is the best?
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Does your opinion matter? Why?
The Two Kinds of Genius
Why do we value Conceptual geniuses?
Why do we value experimental geniuses?
Which kind of genius do we value more? Why?
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What criteria do we use for evaluating art?
1. The intentions of the artist.
2. The Quality of the Work
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3. The Audience’s Response
Should art exist just to anger a target audience?
Was Soul a Black film?
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Should a white person direct a film about Asians?
Should an Asian person direct a film about White people?
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The Big Question
What is the role of knowledge authorities in the AOK of The Arts? Is
this role good or bad? Why do you say this?
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I Am Smart
What is the difference between knowledge expressed in the Arts versus other AOKs?
(What makes Arts special?) Provide one example of something that could only be
expressed through art. Then provide the opposite.
Be sure to save these, as these could be pieces of evidence for either TOK assessment!
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The Arts: Methods & Tools
The First Question
What is it about art that is so good at conveying emotion and
knowledge that might be hard to express? Think about a song that
you really connect with. Why is it so meaningful?
Tool 1: Genres
Why are genres good? Bad? Necessary? Unnecessary?
What/who creates the specifications for a genre of art? How do they do it?
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What is (or what makes) a western?
What is (or what makes) country music?
#RLS – Old Town Road
Is this country music or not? Why?
What knowledge helps you decide?
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Where did this knowledge come from?
Tool 2: Formal Techniques
Think about an art form that you have learned. What were the disciplines or tools that
you learned to become “better.”
Is having knowledge of the arts necessary for being able to make great art?
What is the relationship between mastery of skill and the quality of the artwork?
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Evaluate These Artworks
Old Town Road
1. What were the intentions of the artist?
2. What was the technical quality of the work?
3. What was the response of the spectators?
Christiano Ronaldo Bust
1. What were the intentions of the artist?
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2. What was the technical quality of the work?
3. What was the response of the spectators?
The Mona Lisa
1. What were the intentions of the artist?
2. What was the technical quality of the work?
3. What was the response of the spectators?
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A 3D Chalk Sketch
1. What were the intentions of the artist?
2. What was the technical quality of the work?
3. What was the response of the spectators?
Crucifix Artwork
1. What were the intentions of the artist?
2. What was the technical quality of the work?
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3. What was the response of the spectators?
Tool 3: Emotion
Click here to read the article Students Learn from People They Love by David Brooks
in the New York Times.
Can you think about a time in which this story was true or not in your life?
Provide a solution: what can be done about this situation? How would you try and
solve it?
Brooks demonstrates that knowledge being __________ is insufficient for it to be
__________ as true!
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#RLS – Malcolm Gladwell & Friends
#RLS – The Emotional McGurk Effect
#RLS Reason & Emotion by Disney
How did this film manipulate the very thing that it sought out to teach?
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How was emotion used to convey knowledge (and opinion)?
Why is emotion often seen as a negative thing? Why is being logical a compliment?
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The Big Question
How does the medium used change the way that knowledge is
shared or understood?
Pick two artworks and compare them.
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I Am Smart (required)
This activity is both required for understanding the next lesson and is also the best
single piece of evidence I will share in this course. Click here to listen to the episode of
Revisionist History called Foot Soldier of Birmingham. After finishing, respond to the
questions below:
1. Would you say that this artwork is ethical?
2. Would you say that the statue conveys truth? Why or why not?
3. Do we need the information that Gladwell provided in order to experience the
art? Why or why not?
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The Arts: Ethics
The First Question
When you listen to a song or look at a painting, how much do you
think about the artist? Why?
Do artists have ethical responsibilities? Why or why not?
What experience, moral, or authority instilled the perspective that you used to answer
the previous question?
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Should art be accurate? How accurate ought art to be?
Thinking about Foot Soldier:
What is the purpose of the statue? How did you decide this?
Does it matter that the “Foot Soldier” wasn’t a Foot Soldier at all?
#RLS – Rick Griffin & Sniffy the Rat
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What was your reaction to Gibson’s art? Is it art? If not, what is it?
What knowledge does Griffin’s “art” communicate? What do we learn?
What is forbidden in the arts? Why? How did you make this rule?
#RLS – Singers Won’t Back Down
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#RLS – Cancel Culture in Art
Should we enjoy someone’s art if they live an immoral or disagreeable lifestyle?
If meaning in art is up to the audience, do ethics matter?
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The Big Question:
What are the benefits and drawbacks to a post-Duchamp
paradigm in which everyone’s perspective is valid?
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I Am Smart
Listen to one more episode of Revisionist History – this one is about white artists rerecording the songs of Black artists. As you read that last sentence, what were your
initial feelings or perspectives?
Click here to listen to the podcast. When you are finished, answer the questions below.
1. What were your original opinions about the concept of white artists covering
Black artists’ songs, especially knowing that it was for a white audience?
2. Discuss the ethics of Pat Boone and Elvis Presley. What are your opinions of
the ethics of the situation?
3. Should Pat Boone be in the Rock & Roll Hall of Fame?
4. Did Malcolm change your mind or not? If yes, what techniques were employed
to change your mind? If no, what would it have taken for Malcom to change
your mind?
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AOK: Natural
Sciences
Natural Sciences: Scope
The First Question
What makes something scientific? What makes something
unscientific (or a pseudoscience)?
“Science is a _____________ much more than it is a body of knowledge.”
Do you agree with this quote?
Do you think that Maths and the Natural Sciences are the most reliable AOK? Why
or why not?
Natural sciences studies the _____ using the scientific method as a route to gain
______ knowledge.
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Pure Science:
Applied Science:
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What is science, really?
Karl Popper coined the phrase falsificationism. How can you summarize this
concept?
Notes on Nancy Segal:
How do we become confident in scientific knowledge?
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The Big Question
Think about the biology and the astrology. How might falsification
show that one is a science, and the other a pseudoscience?
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I Am Smart
What do you believe is true even though you cannot prove it? Think about your
answer. If you can’t prove it, then why do you believe it?
This question was asked to a bunch of smart people. People even smarter than me! I
love what they said. Check out their answers.
https://www.edge.org/responses/what-do-you-believe-is-true-even-though-youcannot-prove-it
After reading some of the responses, ponder to yourself this question: why do we
believe things that we cannot prove? Can an unjustified belief count as knowledge?
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Natural Sciences: perspectives
The First Question
What is something that you used to believe that you don’t anymore?
What changed your mind? What makes an explanation persuasive?
Paradigms:
Kuhn’s definition of paradigm:
My definition of a paradigm:
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Examples of paradigms:
#RLS – Miasma Theory
Why do paradigms exist?
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#RLS – Barbara McClintock
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BIG QUESTION
Is certainty achievable in the Natural Sciences? Provide a historic
example in support of both perspectives.
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I Am Smart
Big Question: Look at two or three paradigm shifts (starting with Wikipedia is fine).
What led to the shift? What are some similarities and differences in how the shifts
occurred?
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Natural Sciences: Methods and Tools
The First Question
In what situation, or in which areas of reality, may the scientific
method not be sufficient for gaining knowledge?
How have you used the scientific method outside of a science class?
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How Discoveries Are Made
Roentgen discovered:
How Roentgen gained knowledge:
Von Humboldt discovered:
How Von Humboldt gained knowledge:
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Jenner discovered:
How Jenner gained knowledge:
Plank discovered:
How Plank gained knowledge:
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Fleming discovered:
How Fleming gained knowledge:
Brown discovered:
How Brown gained knowledge:
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Some common methods and tools in the Natural Science
1. _______________________________________________________________________
2. _______________________________________________________________________
3. _______________________________________________________________________
Way of Knowing - Reason
How would you change your school administration’s mind to prevent yellow jumpsuits
as uniforms? Write down as many ideas as you can (even if they’re crazy!).
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Inductive Reasoning:
Deductive Reasoning:
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Syllogisms:
Way of Knowing: Sense Perception
When are our senses good for gathering information?
When are our senses not good for gathering information?
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#RLS – The McGurk Effect
#RLS – The Dress
#RLS – Baseball
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The Big Question
Why are some methods and tools able to create more certainty than
others? What makes an explanation believable?
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I Am Smart
If you were to ask someone ‘how do you know that reality is real?’ you might be
surprised with their answers. As you think about Sense Perception, this may be your
only way of proving that what we call the real world is, in fact real! Read the following
article and ask yourself why you believe that anything that you are experiencing is, in
fact, real. Then answer the questions below. Click here to read the article
1. Were the perspectives used to support Simulation Theory compelling to you?
Why or why not?
2. What makes an argument persuasive?
3. How much can we trust our sense perception?
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Natural Sciences: Ethics
The First Question
If you were a scientist and discovered a gun that could blow up a city,
what would you do? Why?
“In some sort of crude sense…the physicists have known ________; and this is a
________ which they cannot lose.” - J Robert Oppenheimer
Creating a weapon capable of wiping out humanity is an ethical choice. Yet
Oppenheimer (and Einstein) believed that it was ethical. What was their justification?
In your opinion, was it valid? Or should they have kept their knowledge secret?
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Scientists ought to…
Scientists know that they ought to
Some basic ethics of Natural Scientists
1. __________________________________________________________________________
2. __________________________________________________________________________
3. __________________________________________________________________________
4. __________________________________________________________________________
#RLS - He Jiankui & Embryonic Gene Editing!
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How do we decide upon (or who gets to decide) the ethicality of commercial gene
editing?
Big Ethical Issues in Scientific History
(Un)ethical Scientists: for each #RLS shared, note their justification for choosing to
perform the experiments that they did. Some of these are quite horrible, by the way!
J. Marion Sims/Nazi’s
Japanese Unit 731
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Tuskegee (United States) Syphilis Study
Testing on animals
How do scientists decide whether or not they should research
dangerous ideas?
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The Big Question
Who or what is the guiding force in scientific ethics today? Who most
often is allowed to ‘draw the line’? Who is drawing the lines of
acceptable investigation?
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I Am Smart:
Reading: “What Scientific Idea is Ready for Retirement?”
https://www.edge.org/responses/what-scientific-idea-is-ready-for-retirement
Browse through this site and read multiple perspectives regarding what ideas need
to be retired. Please don’t try to impress me with a perspective that is confusing or
heady. Choose something that you can understand and discuss.
1. Pick one response: what are the reasons offered for retiring an idea? Is the
opinion convincing to you or not? Why?
2. In the natural sciences (and this article) what makes an opinion compelling,
believable, or persuasive?
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AOK:
Mathematics
Mathematics: Scope
The First Question:
We tend to treat Maths as the AOK with the most certainty. Some
people call Maths the universal language. Why is there so much
confidence and certainty in Maths?
Video: How Did Maths Begin?
Video Clip: Contact
“The universe cannot be read until we have learned the __________ and become
familiar with the characters in which it is written. It is written in mathematical
language, and the letters are triangles, circles and other geometrical figures, without
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which means it is humanly impossible to __________ a single word. Without these, one
is wandering about in a dark __________.” – Galileo
Do you think we invented mathematics to explain things? Or is its the “language of
the universe” and we just discovered math? Explain your answer.
“The patterns and relationships studied by the mathematicians occur __________ in
nature: the symmetrical patterns of __________, the often complicated patterns of
__________, the orbits swept out by __________ as they move through the heavens.
Because it studies such abstract pattens, mathematics often allows us to see – and
hence perhaps make use of – similarities between two phenomena that at first appear
quite different. Thus, we can think of mathematics as a pair of conceptual __________
that enable us to see what would otherwise be invisible.” – Keith Devlin
Eugene Wigner’s Mathematical Miracles (kind of…)
Miracle #1:
Miracle #2:
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Miracle #3
Richard Haming’s Counterpoints:
Non-Miracle #1:
Non-Miracle #2:
Non-Miracle #3:
Non-Miracle #4:
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Who do you agree with? What is mathematics, really?
What is the goal of mathematics?
Michio Kaku on Maths…and other crazy stuff:
Video #1 Notes:
Video #2 Notes:
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The Big Question
According to Kaku, the goal of mathematics is to find and explain
reality. Do you agree or disagree?
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I Am Smart
Pythagoras’ Revenge
Don’t worry. This isn’t a B-movie where the mathematician murders people. Rather,
in this article Sam Baron reveals how animals have known things about Maths before
we did!
Click here to access the reading. After finishing, answer the questions below.
1. What is something that math helps you know?
2. What is something that math does not help you know?
3. We will watch a video about Max Tegmark in an upcoming lesson. What did
you think about his perspective (and those of the Pythagoreans in general).
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Mathematics: Perspectives
The First Question
Aliens time: If an Alien asked you what Math was, what would you
tell them? How could you explain math to someone without a
concept of math?
Pure Mathematics/Pure Science:
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Applied Mathematics/Applied Science:
Max Tegmark Video Notes:
Deep (or crazy) Questions:
What are numbers, really?
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Do numbers exist?
Are numbers things?
Three Main Mathematical Perspectives
Pause the video to copy down definitions.
Platonism:
Nominalism
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Fictionalism
Video: Equations that Rule the World
#RLS Planar-Crystallographic Symmetry
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If something was proven by two completely different groups of people, did the concept
exist outside of humanity and we just realized it existed?
Is math as separated from politics (power) and perspective as we thought?
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The Big Question
What is it about mathematics that enables mathematical results to
remain unchanged over time?
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I Am Smart
Click this link to learn more about equations that rule our world. Each of these can
work as a piece of evidence in any TOK assignment. As you read through these, ask
yourself the following questions.
1. How do we know that the equations are true?
2. What makes something persuasive in the AOK of Mathematics?
3. What role does authority play in the acceptance of these equations?
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Mathematics: Methods & Tools
The First Question
If someone asked you what fifteen percent of 90 was, what would
you do? Describe your mental process.
If someone asked you what eight eights equaled, what would you do? Describe your
mental process.
Tool #1: Shared Knowledge
One of the ways that the __________ __________ creates knowledge is through peer
review and the community working together and challenging each other. Maths must
not exist __________ but within the scope of many people reviewing ideas to avoid
errors. Maths must not exist independently but within the scope of many people
reviewing __________ to avoid errors.
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#RLS: Fermat’s Last Theorem
Do you think that Fermat had actually solved the problem? Why or why not?
What else was needed to solve this equation beyond mere logic – after all no one
could do it for 350 years?
“When mathematicians prove theorems…the __________ of the arguments is
determined by the scrutiny of other mathematicians, in informal discussions, in
lectures, or in journals…the means by which mathematical results are verified is
essential a social process and is thus __________.”
– American Mathematical Society.
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Do you agree with the last statement regarding the claim of infallibility?
Tool #2: Technology
#RLS: Four Color Theorem
What if no human can verify something, but a computer can?
Settle an argument: could technology be an official way of knowing?
How do you use technology to gain knowledge? How do you use technology to know?
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#RLS: Keller’s Conjecture
If we can’t check something to be true, how do we know that it’s true?!
What role does faith play in mathematics?
Tool #3 : Axioms, Theorems, & Reasoning
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I use inductive reasoning when…
I use deductive reasoning when…
Tool #4: Intuition
Have you ever had a “gut feeling” about something and been right? When did it go
wrong?
Intuition Video Notes:
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"Intuition," as used by the modern mathematician, means an accumulation of
__________ (including beliefs and opinions) derived from experience, both individual
and cultural. It is closely associated with mathematical knowledge, which forms the
basis of intuition. The role of intuition in research is to provide the "educated
__________," which may prove to be true or false; but in either case, progress cannot
be made without it and even a false guess may lead to progress. Thus intuition also
plays a major role in the __________ of mathematical concepts.
Rope Around the World:
#RLS - Getty Kouros
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The Big Question
How is an axiomatic system of knowledge different from, or similar
to, other systems of knowledge? What are the similarities and
differences?
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I Am Smart
Continue the exploration of technology as a way of knowing (both in Maths and in
general) by reading this article about a computer potentially being used to solve
another challenging conjecture. After you read, answer these questions:
1. Why do these questions need to be answered?
2. Why does mathematical knowledge bother with “pure maths” at all?
3. If we need computers to know things, can we claim that we know the answer?
4. What role do humans have in the creation of knowledge that is assisted by
technology?
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Mathematics: Ethics
The First Question
When has Maths been used to do something good for humanity?
When has Maths been used to do something bad for humanity?
Mathematicians ought to:
Math ought to be used for:
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From the IB: Is it ethically justifiable for mathematicians to spend time doing research
that does not have immediate useful applications (pure math)?
Mathematicians are considered smarter than other people. Why is this?
What are the implications (effects) of treating mathematicians smarter than experts
in other fields?
Have you ever felt like a “lesser” person because you were not good at math? Why is
this?
If math is the strongest and most believable AOK, then we value mathematicians
more than dancers or mothers or soldiers. Is this ethical or not?
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#RLS – Racist Math
All teachers teach with a certain way or method. Does that mean that it is wrong? Or
is it white supremacy to teach only in a specific manner?
Is there only one right way to do Maths? Is there only one right answer to some
problems?
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I gave my opinion. Do you agree or disagree? What is your opinion? Is the way that
we teach math racist? Is it a part of white supremacy culture? Why or why not?
#RLS - The Importance of Ethics in Mathematics
When math stuff is really (really) confusing, who gets to decide what should happen?
The mathematicians? Government? Voters? Companies?
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Collateralized Debt Obligations:
Blockchain Technology & the CryptoCrash
Mathematicians & Big Tech
Judicial Algorithms
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The Big Question
On what criteria could we decide whether mathematicians should be
held responsible for unethical applications of their work?
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I Am Smart
Continue reading about the way that algorithms are used in the United States’ legal
system. Click here to read an article about it, but if you would like to read other articles,
feel free to do so. After doing some research, come to your own opinions and answer
the following questions:
1. Who should decide if algorithms should be used or not?
2. What is a solution to this problem?
3. What is the role of the mathematician in creating an algorithm like this? What
is not their role?
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AOK: Human
Sciences
Human Sciences: Scope
The First Question:
Which provides more certainty:
A scientific study of penguin mating habits in Antarctica.
Or
A scientific study of college freshmen mating habits in UCLA.
Why did you answer the way you did?
Why the woman might be drinking wine:
Human Sciences vs Natural Sciences
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Both sciences inductive reasoning, via observation, to do experiments, develop
theories, and confirm conclusions. However, what makes them different?
One main difference is that the Natural Sciences observe principles of nature, while
the Human Sciences observe principles of social nature. This makes the N.S. more
__________, and __________, while the H.S. are more __________, and __________,.
Human Sciences is often considered less certain because we cannot always be sure
that what we __________, is true in all cases.
The Human Sciences can be compared to a __________,: they are able to make
zoomed-out __________,. This is also true of the Natural Sciences, but to a lesser
extent.
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Human Sciences are unique, however, because of their ability to be anchored in
specific __________,. and give information about particular __________,.
Reasons why the lions are drinking water:
The key difference is one of __________. Whereas natural scientists study objects and
organisms that are unaware of their own existence, human scientists are concerned
with organisms that are.
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Oxford University List of Human Sciences:
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Human Sciences & Cigarettes
#RLS – Stanford Prison Experiment (Zimbardo)
Why do some people treat others badly? Is it nature? Nurture? Something else?
Video 1 – What happened? Summarize it as you watch.
What does this study teach us about human nature?
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What reasons can you think of that might cause us to not believe the findings of the
study?
Video 2 – Some problems arise with the study
Did this study provide us with knowledge of humans? Was it reliable? What did it
actually study?
How could we be certain of the reliability of the things that we learn from this?
Different human sciences can be used to understand different issues. Which human
sciences can be used to better understand the following RLS?
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2008 Financial Crisis
Mask Mandate Controversy
Bullying in Schools
Gun Control in the United States
Syrian Refugee Crisis
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The Big Question
Do you think that human behavior is too unpredictable to study?
Why?
What is something that you think is reliable enough to be studied? Why?
What is something unreliable that should not be studied? Why?
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I Am Smart
One of my favorite TV shows of all time was called Community. Set in a terrible
community college, each episode seemed to take on a different angle of things that
might be academic subject. And yes, there were paintball episodes, too. Multiple.
A recurring character in the series was John Oliver’s Professor Duncan. Watch the
episode below in which he takes some students through a study that he created,
which could be nearly as unethical as the Stanford Prison Experiment. Click here to
watch the clip of the experiment.
As you can see, one single person was able to invalidate the Duncan Principle. What
does this mean? Is the principle true? False? Sometimes true? Often true? This gets
back to the heart of the scope of knowledge in the Human Sciences. How often we
can trust it is essential for understand the AOK. Don’t worry – at the end of lesson 4 I
will give you my perspective.
To continue thinking about this, create your own experiment on your own. Study your
friends, families, or classmates.
Aim to provide a stimulus and measure the responses. Some of my favorite unethical
experiments include:
•
Hiding cigarettes in conspicuous places.
•
Staring at people’s foreheads during conversation.
•
Calling people during a conversation.
•
Speaking softly.
•
Speaking loudly.
•
Running at people and stopping right before the collision.
The possibilities are endless! Just don’t be a jerk.
1.
2.
3.
4.
5.
6.
After you conduct your experiment, answer the questions below:
What did you learn in your study?
How certain are you that the findings are true?
Are the findings always true? Or true just about the people that you studied?
What would confirm your findings?
What would invalidate your findings?
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Human Sciences: Perspectives
The First Question
Imagine that you see a child steal a piece of candy from a
convenience store. What, in your mind, is to blame for this behavior?
Nature vs Nurture
What is a behavior that you believe is determined by our biology?
What is a behavior that you believe is determined by our culture?
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Plato & the Greeks believed:
Darwin might say:
John Locke said that:
What do you think?
Thought Experiment: Papuan student at an IB School
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#RLS – Milgram Shock Experiment
Why do people do evil things?
What kinds of insights does Milgram give?
Do you think that the study gives accurate and reliable information? Why or how?
How could we be certain of the reliability of the things that we learn from this?
Can this (or should this) be replicated?
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The fact that they are referred to as sciences gives them a responsibility to be fairly
__________ in how they approach things… All sciences have to be methodical.” - Dr.
Marianna Koli
Perspectives in Disciplines are WEIRD
#RLS – Margaret Mead & Derek Freeman
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Measuring the Immeasurable
“Measure what is measurable, and make measurable what is not so.” – Galileo
Is it worth it to attempt to measure happiness? Why or why not?
Can this be considered knowledge? Why or why not?
Is it valuable to try to measure personality types?
Why are personality tests so popular if they aren’t reliable?
What knowledge do tests like this actually convey?
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Is it valuable to try to measure intelligence?
What assumptions are being made about the basis of intelligence?
Why is logical knowledge highly valued?
What kinds of knowledge is not valued? Why?
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The Big Question
If two competing paradigms give different explanations of a
phenomenon, how can we decide which explanation to accept?
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I Am Smart
This is one of my all-time favorite TOK Essay prompts:
To what extent do you agree with the directive to "measure what is measurable and
make measurable what is not so" (Galileo Galilei)? Answer with reference to the
human sciences and one other area of knowledge.
Find one Real Life Situation (or example, or study) that shows why it is good, valuable,
or important to measure what is not measurable. Then find one piece of evidence that
shows the opposite! Then answer the question.
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Human Sciences: Methods & Tools
The First Question
It is very common for people to mention scientific studies in casual
conversation. Why might we believe scientific claims that we read
about?
Tool #1: Academic Journals & Studies
#RLS - Good Samaritan Experiment
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Can we ask these critical questions about anything in the Human Sciences?
Tool #2: Field Work
#RLS - Bronislaw Malinowski
Can a researcher be both detached and involved when studying a people group inperson?
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Tool #3: Statistics & Models
How would you measure the success of a presidency?
Pick a human science. What method would you employ to measure the success of the
same presidency?
If someone asked you if the economy was good, what processes would you undertake
to decide upon an answer? What questions would you ask? What methods would you
use to figure out the answer?
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Gross Domestic Product (GDP) & Using Math to Predict Behavior
Why is GDP so commonly used and accepted?
What are the effects of economists being able to communicate through the AOK of
Maths?
How accurately can we predict human behavior?
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How do we know when they’re right?
Three Kinds of Data
Quantitative Data
Qualitative Data
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Anecdotal Evidence
Tool #4: Replicability
#RLS – Many Labs 2
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How do you decide whether or not to believe a claim in psychology?
What do you think? Is psychology dead?
Tool #5: Experiments
Think about experiments that you’ve done in any of your DP classes – did you trust
the results? Why?
What assumptions are made when engaging on an experiment?
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#RLS – Addiction, Rat Park, & Kurzgesagt
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The Big Question
Think about some of the methods and tools mentioned in this less.
Think about other ways of learning about human nature. How
scientific are the human sciences, really? Provide one reason why
we should call the Human Sciences scientific, and one reason why
we shouldn’t.
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I Am Smart
Click here to read How Did Economists Get it So Wrong? This article explores how the
usage of math in economics presents some problems for both economists and people
who believe them. After reading the article, answer the questions below:
1. According to the article, why do people trust economists so much? Why is their
knowledge so highly valued?
2. What is it about a scientific claim that makes it believable?
3. Find any economic theory, formula or claim that uses math. Why does the
author believe it? What makes it persuasive? How could it be wrong?
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Human Sciences: Ethics
The First Question
If you have ever cheated on an assignment or test: How did you
justify it?
If you have never cheated on an assignment or test: Why did you
not do it?
When conducting a human sciences study, what ethical responsibilities do scientists
have?
Scientists ought to…
Was it ethically correct to ‘fake’ an experiment, and mislead volunteers as to the
nature of what was being investigated?
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If we don’t lie to people being studied, can science exist? Is this an example of a just
lie?
Where was your line of ethical scientific boundaries? What is it OK to study? What is
it not OK to study?
Should we study the effects of bullying on 5-year-olds? Why or why not?
Should we study the effects of withholding/supplying government aid to poor
countries? Why or why not?
Is it ethical to use mathematical algorithms to influence jail sentences? Why or why
not?
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Should we conduct scientific behavioral studies on infants? Why or why not?
#RLS - Little Albert
Who gets to decide upon the ethical boundaries of experiments in the human
sciences?
Who Draws the Line?
1.
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2.
3.
#RLS - Al Jolson & Development Studies
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The big Question
Should key events in the historical development of the human
sciences always be judged by the standards of their time?
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I Am Smart
Finding unethical scientific experiments is one of the easiest things to do online. TOK
Essays are filled with examples of scientists (in both sciences) doing unthinkable and
questionable things. To further your understanding of the ethical boundaries of
investigation find a scientific study (you can choose Natural Sciences if you lean
towards that AOK) that is considered unethical or questionable. Then answer these
questions:
1. What was questionable or unethical about the study?
2. Why did the scientist perform the study? How did they believe that they were
not crossing a line?
3. Did anyone disagree with the study? Where and/or how would they have
drawn the line?
4. If the study was stopped, why and how was it stopped?
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AOK: History
History: Methods & Tools
The First Question
What is something that you know happened 100 years ago? How do
you know this actually happened?
How certain are you? Why?
History is the __________ of the past and the body of knowledge that __________ from
that study.
Historians use many methods and tools to find __________. The __________ and
providing of __________ makes it an Area of Knowledge.
Carr says that the main tool of the Historian is their ability to __________ and be
__________.
History is Not a Fact
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The main methods and tools of History are __________, __________, __________ and
__________. They are intangibles.
Historians have many tangible tools available to them. Some of them are __________
__________, photographs, films, reading __________ and __________ sources, studying
pre-historic __________ and artistic representations of the past.
All methods and tools attempt to find and create a __________ __________ of the past.
Oral Histories
What unique information does an oral history provide?
What does it not provide?
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Why might oral knowledge be criticized, especially in the modern, technological west?
Is knowledge less valuable because it was not written down? Is it less believable?
The two most replicated ancient texts, The Odyssey and The Bible are both based on
oral tradition, communication, and knowledge. But only The Bible is criticized for being
unreliable. Why do you think this is?
166
Facts in History
A historic fact that I know:
How do you know that this is a fact?
Who/what did you rely on to get this fact?
What makes something believable in History?
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History & Technology Video
How do you think you could use technology to learn the truth about the past?
What are some ‘facts’ that this computer model teaches us?
How reliable are these facts?
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The Big Question
If we will never have all the facts from a certain event, is it possible
to know the truth about history? Or is history just unknowable and
we should give up on it?
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I Am Smart
TOK is often split into units that study each AOK on its own. That’s what I did! But
knowledge doesn’t always work this way. Read this article about how researchers in
the Natural Sciences helped us understand the history of the worst pandemic in
history.
Click here to read the article about the origins of the bubonic plague. After finishing,
answer these questions below:
1. How can knowledge in The Arts help us understand a certain culture or time
period more? Find one example.
2. How can knowledge in the Human Sciences help us understand a different
point in history? Find one example.
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History: Scope & Perspectives
The First Question
What is a folktale, legend, or myth from your culture? Is it true or
made up? Why do people in your culture tell this story?
Language as a Way of Knowing
When you use the word pre-historic what do you mean by this? Who or what is prehistoric in today’s world?
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How do we still use oral history, tradition, myth, and religion to explain and make
sense of the past?
If language is a conduit for history, how has your culture’s history been shaped by
stories and tales?
Notes on Herodotus
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What do you call these things?
Photo of Cars:
Photo of boy:
Photo of people in office:
Person sitting on the street:
Photo of people with body paint:
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If the rioters on Jan 6 succeeded, how might they be described by historians in the
future?
In the AOK of history, an understanding of a historian’s __________ is as essential as
understanding what they __________.
The most important events of the 20th Century…according to me:
1. __________________________________________________________________________
2. __________________________________________________________________________
3. __________________________________________________________________________
4. __________________________________________________________________________
5. __________________________________________________________________________
How might your list be affected by your nationality?
How might your list be affected by your age?
174
How might your list be affected by your education and SES?
What was most responsible for the end of WWII?
175
The Big Question
How might the existence of different historical perspectives be
beneficial to historical knowledge?
176
I Am Smart
Though History may just be a study of different perspectives, the subjective nature of
knowledge in this AOK does not mean that it shouldn’t be explored! In fact, the
opposite is true! To explore the scope of knowledge in History, and to practice a great
Methods & Tool, you will now conduct an oral history!
Contact someone who is at least 50 years old. Before conducting the interview,
research some major events that they would have experienced in their lifetime. Pick
one or two and let them know, in advance, what you want to talk about. Come up
with a list of questions and interview them for at least 20 minutes. After the interview,
answer these questions.
1. You performed what historians call an oral history. What kind of knowledge
was best communicated in this way?
2. What knowledge or information do you believe was reliable and corresponds
well to historical records?
3. Where might your interviewee’s perspective have influenced their opinions or
beliefs?
4. What might you use this kind of information for? What is the best use of
knowledge gained from interviews and oral histories?
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History: Ethics
The First Question
How certain are you that you received a true history education?
Explain your answer.
What ought we to do the with knowledge we learn from History?
What ought we to do with the uncomfortable knowledge we learn from History?
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#RLS - History Books
Who should be in charge of writing history textbooks? Who gets to decide what goes
in them? Why?
What’s the difference between education and indoctrination with regards to teaching
history?
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#RLS – The Rape of Nanking
Can only historians report on history?
Can someone with a vested interested in a topic be believed when researching about
history? Why or why not?
180
#RLS – The Act of Killing
What responsibility do countries have to teach history that is harmful to its image and
reputation?
What do we do with controversial knowledge of the past?
Should a government promote “patriotic” education? Should a government promote
education (and history) that makes students respect the government more?
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#RLS – Patriotic(?) Education
The 1619 Project
The 1776 Report
What is your opinion on this #RLS?
182
Why do historians disagree (both in this RLS and in general)?
Who gets to tell the story of a people and what is at stake in the telling?
Is it unfair to judge people and actions in the past by the standards of today?
Thomas Jefferson wrote ‘All men are created equal,’ yet he owned slaves. How should
he be remembered? Studied?
When it comes to statues, whose opinion matters the most? How do we decide this?
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#RLS - San Francisco School Board
What are your initial thoughts and opinions on this?
Were these men evil? Or were they just a product of their times (Nature vs Nurture)?
How ought people to be remembered when their morals contrast with modern
morals?
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#RLS - South African Truth and Reconciliation Committee
What ought be done as a result of truth and reconciliation discoveries about people
who were harmed (even generations) in the past?
What about your country or culture? What situations like these do you have?
In America, we have shared knowledge about the crimes committed against slaves.
These are accepted. What ought to be done about this?
185
The Big Question
Is it unfair to judge people and actions in the past by the standards
of today?
186
I Am Smart
Having knowledge means that you may have the responsibility to act on it. As we saw
with the Truth and Reconciliation Committee in South Africa, this can mean that it is
ethical to take big actions. Read this article that explains the situation regarding
Canada’s Truth and Reconciliation Commission and what they suggested based on
the country’s Native American boarding schools. Click here to read the article. After
finishing the article, answer these questions:
1. What is meant by the headline: “Canadians need truth, not just reconciliation”?
2. What, in your opinion, should be done in the case of Canada and the issue in
the article?
3. How does reconciliation occur in a situation like this? What steps can bring
people together?
4. What ethical implications arise as a result of having historical knowledge?
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Thank you for being a part of TOK Masterclass! I appreciate
your support and hope that you had a fun, and funny, time
learning about a bunch of weird stuff. If you made it this far,
please shoot me an email and tell me a joke.
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