Welcome to my iFolio! My name is Janice and I have been a student in Canadian International School of Hong Kong for 12 years. I enjoy playing sports, such as volleyball and tennis, reading, baking and cooking and also exploring the great outdoors. This iFolio is a glimpse of my learning experiences throughout PYP, MYP and DP!

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Conjecture Vs. Theorem – Mathematical Thinking

A conjecture is an opinion or conclusion formed based on incomplete evidence. Meanwhile a theorem is a conjecture projected to explain a certain phenomenon with solid empirical evidence. In some cases, these two definitions can collide within a theory. For example, Fermat’s Last Theorem, is an mathematical theory created by Pierre de Fermat in 1673. The first successful theory of this statement however (conjecture turned theorem) was released in 1994 after 358 years of effort by other mathematicians. Through this theorem and it’s investigation, countless other developments such as the algebraic number theory or the modularity theorem was discovered due to the investigation of Fermat’s Last Theorem. However, mathematicians have recently proven that this theorem is notably wrong therefore has transformed back to a conjecture. 

In the TEDtalk, Eduardo Saenz de Cabezon states that Math dominates intuition and tames creativity. Proving this statement, he utilised the example that if you fold a normal piece of paper 50 times, it will reach the thickness from the earth to the sun. He challenged us to do the math to see if he was correct even if our intuition tells us otherwise. To a certain extent, I believe his statement that math dominates intuition is valid. However, math utilises institution to be solved. My friend has the ability to derive the answer to basic mathematical equations inside his head before writing it down. He doesn’t write steps to construct the answer but instead he constructs the answer through building steps within his head. Many believe this to be intuition, another method of solving a equation based on a lot of practice on the specific equation or using another method of solving this.

Maths are eternal because it doesn’t disappear through any subject or mean. For example, within chemistry, observing the electrons, protons and neutrons within an atom requires you to calculate or derive a numerical value from what you are seeing. Math deserves a privileged position in TOK because many believe it to be black and white however there are many layers as to understanding and solving for an answer.

Should math compulsory at school?
To what extent is math pure black and white?
How can problems in mathematics be solved? (clever tricks, experiments, computers, graphic calculators, trial and error, investigation, discussion, textbook answers)
Who should be studying mathematics?
What is mathematics the subject itself about?

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Art Vs. Science and Art and the Truth

Art Vs. Science
Art and sciences are inextricably linked: science can sometimes explain the beauty of art, and art is often used to convey scientific “truths” to the common man. To understand the real truth, both science and art has to be applicable. To understand the truth, it is not only just facts and information, it also includes the fields of emotional attachment. Art provides the emotional attachment to the human experiences associated. Science provides the facts and the information which explains the human reactions.


  • “We know the truth, not only by the reason but also by the heart”
  • Duty of literature (a form of art) to speak and convey the truth
  • Creative work doesn’t care if the truth is ethical, emotional, philosophical, or physical
  • Good and evil are inseparable, past and future are fundamentally related
  • Literature seems unambiguous, use words to define emotions, describe experiences to others
  • Art is to tell the truth
  • books – art form, nothing more powerful than books to retell a story
  • Art has a way to manipulate emotions, it can produce honest and candid portrayal of the truth
  • Other fields of study are factual and accurate but their ability to tell the truth is just information
  • Information + no emotional attachment
  • Truth is not just a precise explanation , it also has experiences of human condition and the impact it laid out there (ie. 10 million people died in the Rwandan genocide vs. people fought with blood sweat and tears against the Rwandan government for justice, 10 million poor souls did not win the battle of life in conclusion)
  • Art and sciences are inextricably linked: science can sometimes explain the beauty of art, and art is often used to convey scientific “truths” to the common man

Art and Truth

The artists have their own responsibility to convey their truth, even if it is upon bias. Their method of communicating this ‘truth’ gives them a type of power because of it’s unique platform. Arts can transmit the truth in different ways possible, unique to the arts, truths can be asserted however often with bias hindering within.


  • Artists have a responsibility to convey the truth
  • Impact of their work gives them another type of power
  • Language is not restricted, factually, information can be given, but arts can transmit truths in many different ways
  • Unique to art – some truths can be asserted
  • Is there a sense to an unbiased picture? There are always two sides to one story, the truth does not classify as one distinct story

Both these essays show that there is knowledge produced within art. It represents how there is always sense to a biased picture. Every story has two sides however the truth is not necessarily a classification of one story. It also represents art as a raw emotional experience of a human. Without art or science, knowledge cannot be produced as facts do not only make up of statistical data but also raw emotional qualitative data.

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“Without the group to verify it, knowledge is not possible.” in the arts

“Without the group to verify it, knowledge is not possible.” 

There are two types of knowledge. Personal knowledge and Shared knowledge. Many believe shared knowledge to be more accurate than personal as it is verified by a group of individuals who share the same beliefs. While personal knowledge on the other hand relies on the experimentations or investigations that one conducts personally with no other confirmation but himself. The definition of knowledge according to dictionary.com is “facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject.”. To regulate and confirm a statement to turn it into a fact, multiple groups/individuals have to agree upon it’s foundation and the validity of the statement. Knowledge is still possible without the group however it is more valid with the group’s confirmation.

Since art is fairly subjective to the individual, many would argue that knowledge is individually produced based on the audience’s perception of the art piece. However, many can compromise and agree upon a similar understanding of a piece and produce a message based on their shared experiences. Therefore there is no distinct group in the production of knowledge, no one to specifically verify what is right or wrong because art has no right or wrong. However, the knowledge in art is shared amongst those with similar beliefs and understandings which form the ‘group’. Art is shared and commented upon by everyone. There is no individual more superior than another as art is a shared community, everyone perceives it differently as it is so abstract and tangible. 

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Knowledge within arts is not objective & therefore not meaningful

Knowledge within arts is not objective & therefore not meaningful.

Science has strict guidelines when transferring knowledge: the boiling point of water will always be 100 °c and humans will always walk before they learn to run. These specific theories will always be valid as they have previously been proven by the discoverer and ‘the group’. While science can be subjective in it’s own ways (qualitative data), people rely on it’s objectivity to draw conclusions due to the ‘group’ approving the statement. Arts on the other hand exert subjectivity. It helps us realise conceptual knowledge such as the ability to feel empathetic as well as form moral knowledge (right from wrong). In terms of art, morals and individual understanding has to be the foundation before art can be applied within our lives. Due to our separate outlooks on life, we will always all have our own perceptions and views towards situations.

Objectivity of a subject is the confirmation of the ‘group’ showcasing it’s value towards society. Public perception affects not only how the knowledge is acquired but also how it is perceived and used. For example, when solving a quadratic equation there are 3 formulas which are distinct and unchangeable [ax2 + bx + c = 0, a(x-h)+k, (x-p)(x-q)]. These three formulas are the basis of solving any quadratic equation. They were derived by multiple individuals who then proven it to ‘the group’ while currently, children in year 7 are implementing and applying this equation to the worksheets they’ve been doing. Objectivity suggests a further extent of validity therefore with art exhibiting individual connections, many believe it is not meaningful as it is only understood by the minority relating to the piece.

The public perception of knowledge is it has to be either scientifically proven by a group of professionals or it is not valid, and I use the term professionals loosely. Empirical data is what people understand, their ability to play with it and interpret it makes them more comfortable with using it in their daily lives. This is why many go on to study the natural sciences, mathematics, engineering or other data based subjects. This automatically leads to the conclusion that art is purely subjective, because it is not black or white. No two humans are alike in every explicit way. However, there are attributes which overlap against each other. Each art piece can affect each individual adversely based on the way they perceive it. Showing that although art is subjective to the artist/audience, it is still meaningful to the individual’s respective means. This is why others believe it to be subjective, because they do not take the time nor have the knowledge the other person obtains to understand that work.

Key Take Aways:

  • public perception: knowledge = scientific knowledge, facts-empirical
  • where does art fit in a modern scientific world
  • science has strict guidelines to transferring knowledge unlike art
  • art doesn’t affect us, it informs us
  • art- conceptual knowledge (our feelings, mental state, allows us to feel empathetic)
  • art- moral knowledge, informing us right and wrong, justified and unjustified
  • viewing art with already pre-made conceptions of individual morality etc.
  • art- a specific framework which can explore possible worlds or further scenarios
  • Art can transfer much more information than we realise, and it can deepen and enrich our aesthetic experience of the world.
  • Aesthetic value is likely a construct made up of many aspects, only one part of which is aesthetic knowledge.
  • Art’s ability to provide knowledge might form just a small part of how we assess an artwork, and this factor is something we do not often address in the visual arts. The fact that we do not often talk about aesthetic knowledge in the visual arts is something that may need to change.
  • For art is doing something quite different to science in terms of knowledge, but art is providing us with knowledge nonetheless.


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English TOK, For something to be Art, it must follow a recognized convention.


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Introduction into Natural Sciences

Recently, I watched a TEDTalk by Naomi Oreskes, a historian of science who firmly believes in using reason to fight climate change denial within current society. Within her TedTalk ‘Why we should trust scientists’, she asked the question ‘Scientist’s tell us stuff, but why should we believe them. From this talk, I had three takeaways; firstly, understanding that science and faith are different however belief is the attribute that ties them together. Faith is understanding and trusting an ideology meanwhile science is the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment. Belief enables us to trust the science behind each living or non living physical matter in our world and forming facts to sustain the knowledge we have today. However, there are three main problems with common attitudes towards scientific inquiry. Firstly, most of us were taught in school that the reason we should believe in science is because of it’s scientific method. The scientists follow a rigid and specific method which guarantees the truth to their claims. The method we were all taught at school was textbook method; involving a independent variable, dependent variable and a few controlled variables to reach an understanding of our data. Through science, we understand that prediction does not work as hypothesis are only a guide to what we sense will occur. The real working aspect of science is the hands on experimentation of the real life situation. Adding on, science does not fit a textbook as it is forever innovative. Ideas and creations are built off of the textbook knowledge however have no limit to discovery.

Ethics, history, religious knowledge systems, indigenous knowledge groups, mathematics, natural sciences, human sciences and the arts are the eight areas of knowledge which people use to investigate upon. Natural Science is different from other areas of knowledge as it requires information drawn from experimentation.

Arts does not require experimentation before a final ideology is presented as it is a creative form. Art can go into many paths and the output of the creation can be drawn from multiple directions. For example when drawing an abstract piece about gun violence, there is no definite way of completing this piece, if you were to ask two people to accomplish this task, they would both have infinitely different pieces due to the creativity within each of their minds. This is the opposite to the Natural Sciences as natural sciences follow a methodology to accomplish a theory they have planned in advance.

Meanwhile within the subject of maths, it requires for a formula or a theory to be constructed. This theory is constructed through a process of trial and error or a build up of previous knowledge. Patterns and investigations are similarly used within the natural sciences when experimentation is done to reach a conclusion.


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Faith and Intuition

Faith is an ideology one abides and follows closely with their morals. For example, some’s idea of faith may be the intention of a religious group such as their faith in the Western God: Christianity. While there are others who believe in a certain ideology or logic but do not abide to that specific ‘group’ or religion. Another concept of faith is commitment, once faith is instilled upon a certain ideology or theory, their ideas and actions expand upon it and their morals build off of their faith.
To better understand the world, faith is used to help us interpret things. This is an individual personal way to looking at the world and the situations that arise. This perspective will allow you to reflect upon how much each situation resides with you and to what extent you agree and believe it to be true.

Meanwhile, similar to faith, intuition is defined as a process which helps with the consumption of knowledge. It is a sense of knowing without any prior thinking required. For example, when putting your hand above a hot stove, through intuition, we know it will hurt therefore we don’t do it. It is a form of common sense which is collected through experience. It is described as a gut feeling for what will happen or the solution to what a problem can be.
This is a way of knowing as it is often classified as a sense of awareness. This way of knowing allows us to have an idea of what will happen through our subconscious mind. Computers do not have senses of intuition therefore it is what makes living organisms such as animals and humans os unique because we have the ability to answer or act upon a ‘I just know’ as justification.

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Memory and Imagination











Imagination is the ability to construct a mental idea of an experience with or without mental stimulus. Another form of imagination is to imagine things different from the way they are and either not accepting the truth or imagining another alternative. Imagination is a common way of knowing, we use it in our daily lives when dealing with situations or as forms of motivation. We use it during the pursuit of knowledge to help extend our thinking and abilities to imagine different scenarios. Without imagination, there would be no extension of further investigation and humans and creatures would be left with the same  extent of knowledge as before. Many classify imagination to be a form of creativity, problem solving or a form of originality however it is often distrusted as it is highly subjective. However, there are a few forms of where medical conditions or special conditions can inflict bias towards the way of knowing, Imagination. People with autism lack an idea of what imagination means to others because of their inability to perceive means through a structured perspective. Their form of imagination is exploding within their minds causing them to be unable to sort their ideas logically. Also, forms of delusion and extreme examples of imagination can cloud one’s judgement disallowing them them to logically think. The form of imagination can be expressed through many forms of language. Media, cultural languages and writing can all aid in our ability to express our imagination and ideas.


Memory is the recollection of the things we know, it is how we recall our prior knowledge to use in distant situations. Adding on, the psychology of memory allows us to imagine nostalgia as a tape which can be played back any time. Experience is also encoded within our memory and the remembrance of an experience is indeed not the original experience recalled, but rather an access of the memory altered during the last time it was accessed.The importance of memory during the pursuit of knowledge is also quite significant. Our past experiences affect how our new experiences are interpreted. Memory plays a big factor in how we gain knowledge in any moment of any time. We do not gain new knowledge through a vacuum, instead we gain knowledge based on our past experiences. For example, when you are in the midst of dating a person, your memory of them is positive however, when you break up, your perception of the guy is different due to the change in memory since the time you experienced the break up. However, memories are not completely reliable because they are inflected with subjective opinions. An example would be the disease Alzheimer’s and how it affects people as they grow older. Particularly, Alzheimer’s affects a growing proportion of countries with ageing population. Although it is an unreliable ‘Way of Knowing’, billions of people rely on their memories within their everyday lives. Memory relates to mathematics because memory is relied upon in order to recall formulas or other mathematical concepts. Without the recall of these concepts, there would be no grip and no connection build upon the previous ideas.

Despite the imperfections of imagination and memory as ways of knowing, the Areas of Knowledge have developed in such as way as to overcome them. Discuss this claim with reference to at least two AOKs.
Despite the imperfections of imagination and memory as ways of knowing, the Areas of Knowledge have developed in such a way to overcome them. For example, in History, the ways of knowing of memory is required to help the future understand the past and how to improve in the future. It also acts as a historical account to help with the current study of the world. Adding on in ethics, imagination helps us determine right from wrong. it controls our ability to control our actions. Imagination sorts right from wrong by eliminating limits for possibilities of the future.

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The validity of an argument is non-reliant of the truth or falsity of its premises. The premises are used as evidence to back up a claim. Premises are used to create conclusions which are statements proving the point of the deductive. The deductive does not have to follow regulations of being ‘common sense’ however the premises have to build off one another and not conclude upon assumptions.

For example:
1. All mushrooms are fungi [True]
2. Some fungi are poisonous [True]
Conclusion: Some mushrooms are poisonous [False]

Deductive: Invalid

Within this example, the first and second premises are statements of a claim the writer has established. In the conclusion, the statement was an assumption of both the first and second premises. The conclusion generalised the statement by simply linking a property both premises obtained. This conclusion is not exhibited as a valid statement however, through logic and common sense, this statement would indeed be coined to be true. Pure logic is only concerned within the structure of arguments. Within this argument, although it is somewhat possible logically that some mushrooms are poisonous, however, given the structure of the arguments and the two premises mentioned above, the conclusion statement is not valid.

In another example,
1. No one under the age of 18 can drink [True]
2. Jen is under 18 years old [True]
Conclusion: Therefore, Jen cannot vote. [Valid]

Deductive: Valid

In comparison to the example above, this deductive is valid due to the conclusion taking both premises into consideration. The conclusion is also not using partial properties or features of the premises. This serves the purpose of the conclusions hence making the realistic link between both premises and their relation to one another. This whole argument is logical and is deemed valid. 

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“The vagueness and ambiguity of language always limits the production of knowledge”.

Language is used to communicate and express our perception of an ideology or thought. However, due to the vagueness and ambiguity of language, it limits the way it is communicated and the way the message is perceived by others. While some areas of knowledge result with clear cut and dry reasoning, others may have multiple ways of expressing conclusive ideas which are opened for interpretation.

In maths, the way people derive answers are through intuitive thinking and or conscious reasoning. Intuition in maths is achieving the final solution through the solvers ability to utilise their personal knowledge to solve equation. Although intuitive thinking in maths is not recognised as mathematical thinking or logical procedure, it is still a method where the answer can be derived. In contrast to intuition, conscious reasoning is commonly used and created by mathematicians. Logarithms, equations, formulas were all found through the method of conscious thinking. It guides people through a step by step procedure to solving the equation which is clear and concise. The way one’s intuition communicates the knowledge it entails is usually filled with ambiguity due to it’s reliance on prior knowledge to understand the piece as a whole.

Arts is a form to express one’s ideas through expressive forms such as writing, singing, painting, dancing etc. However, with many creative methods, each one has a broad range of perception associated with it. The perception of what the art piece is as well as the way it is communicated and expressed to others also differs. Gestalt is the ways of which an image can is perceived through multiple means. For example, this image below.

Some may argue they see a white vase in the picture, however some may also argue they see two human heads facing one another. Both pictures are right, but it just depends on what the person sees and the order to which one they see first. There is also another perception associated if the person told you to look for something and you find what they told you to look for or you find something else along the way. Therefore this image communicates that the method of communicating through language, as well as how broad each individual’s perception is is in art can limit the production of knowledge from one to another.

However, some see Natural Science as the area of knowledge with the most accurate method of communication. Within a lab, conclusive and detailed methodologies are usually expressed to the reader to strictly follow. Although there are some steps which will result with uncertainties of data, most of the procedure will be clear and concise. A lab report is designed for audience’s with the similar ‘textbook’ background information on science to interpret and understand. If I mention a graduated cylinder needs to be filled with NaOH to 100 mL in a step, one with background information on the instruments of laboratory equipment and knowledge about what NaOH is would be able to apply that knowledge to achieve that step. Therefore the accuracy of language used in natural science is often quite accurate due to the clear and universal language communicated to those with common knowledge on the topic.

In conclusion, the vagueness and ambiguity of language usually limits the production of knowledge not regarding the lack of detail within one’s concept but rather how every individual pertains to their own perceptions and everyone has different abilities to communicate something resulting in the misunderstanding of an idea.

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