Knowledge and Mathematics
Choose one of the following questions to explore in your Blog/Journal entry.
- How can we know that current knowledge is an improvement upon past knowledge?
- Are some things unknowable?
- What role does imagination play in producing knowledge about the world?
Remember, A journal entry should be based on a concrete, real life situation (RLS). A RLS can be a response to a personal experience, a topic learned about in school (outside of TOK), a current event, or some form of media (TV show, movie, book, artwork, etc.). This doesn’t necessarily have to be something that happened to you. Your decision about what to write about is up to you.
In your response, you should:
Briefly explain the RLS that you are responding to.
Identify the relevant knowledge question: I will provide a list for each area we are focusing on
discuss your thoughts and ideas on that question.
discuss the connections to TOK. You can discuss the implications of your thoughts or talk about perspective, culture, the definitions of truth, knowledge, or belief, or reflections on the knowledge community you are a part of. Choose a key concept to connect to.
Connect your discussion back to your real life situation.
Rubric
Despite the certainty that can emerge from mathematical tests and equations, there are still things that are unknowable. For example, we know from mathematical proofs that the ratio of a circle's circumference to its diameter is equal to pi, which is approximated to 3.14 in most cases. Although we are able to define and prove pi, it is currently beyond human capabilities to fully know all of its digits.
ReplyDeleteExcellent example of an unknowable concept-for me, all of Math is unknowable. ;)
DeleteImagination plays a large part in producing knowledge through two main aspects, culture and creativity. Word problems in specific play a crutcial role in making use of creativity in order to solve problems. If someone were confused on how to solve an equation, they could use English to better convay what the question is asking. Creativity is important when overcoming situations because it encourages people to look for alternative solutions. Perspective also determines how different cultures are able to take on challenges. The combination of different perspectives derived from multiple cultures allows a collective effort to be made to produce knowledge.
ReplyDeleteCarson, this is a great general response and you are correct about the aspects of culture and creativity. An improved response would include specific examples of where this could be used. For example, many studies have shown that tests like the SAT and ACT utilize western culture based word problems. This makes it more challenging for other cultures to respond accurately to questions.
DeleteWe know that current knowledge is an improvement on past knowledge because it allows us to see a bigger picture with more understanding and certainty. For example in history, our knowledge of things from the past could be limited but as time goes on we learn more and use different details to gain a better understanding of why things happen. In history we are learning more about long term causes of WWI. Before, most peoples knowledge of the start of the war was limited to the assassination of Fran’s Ferdinand, however our current knowledge allows us to see multiple areas of conflicts and issues leading up to the war giving us an expanded understanding of how the war started.
ReplyDeleteThis is an example of how current knowledge can be improved on past knowledge but does not take into account the AOK of math. That was our focus here.
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ReplyDeleteHow can we know that current knowledge is an improvement upon past knowledge?
DeleteThe knowledge available today differs greatly from that of the past, which naturally leads us to question if new knowledge is truly an improvement or not. Many cases of discovery are examples of this, for example John Snow’s discovery of cholera spreading through contaminated water or Galileo Galilei’s discovery of the Earth orbiting the sun and not vice versa. We know these two things to be facts and we would consider these knowledge rather than previous theories, but that wasn’t the case during the two scientists’ lives. The knowledge they presented was actually rejected by others around them even though they were right, which begs the question: why? Why didn’t they believe that this knowledge was an improvement on past knowledge? The answer to these questions and the general “How can we know that current knowledge is an improvement upon past knowledge” fall into the hands of perspective. While it can be argued that we know knowledge is am improvement when it can proven to be the truth, such as the scientific fact that Earth does in fact orbit the sun, not all knowledge can fall into true or false. Additionally, one’s personal values, beliefs and perspective mold their interpretation of “truth,” causing knowledge to differ between people and blurring the lines of improvement and deterioration in knowledge. We are limited in our ability to determine if current knowledge is an improvement upon past knowledge, some past knowledge becomes disproven and rejected by new experiments and discoveries, however, some knowledge can’t be placed in that black and white filter and varies in “true”-ness, making this question vary from person to person.
Excellent examples of the evolution of thought and building on previous knowledge. Another thing to consider in regards to the accepting of truth created by new knowledge is our discomfort with change.
DeleteWhat role does imagination play in producing knowledge about the world?
ReplyDeleteImagination plays an important role in producing knowledge because it allows us to think beyond what we already know and create new possibilities. It helps us make predictions from ideas, and connect information in ways that lead to new discoveries. In freshman biology, we learned how scientists discovered the structure of DNA. Watson and Crick had limited data, so they imagined how the molecule might look and built models to test their ideas. Their creativity helped them propose the double-helix structure, but they confirmed it using Rosalind Franklin's research. This ultimately demonstrates how imagination and evidence work together to produce reliable knowledge. In TOK, this would connect to the concept of evidence, because imagination sparks new knowledge, but proof is needed to make it reliable. Imagination is not just being creative, it is a powerful tool that helps us explore possibilities, deepen our understanding, and create new knowledge about the world.
Great example of the use of imagination to move us forward in our thinking. Connecting evidence to imagination is important-our imagination must be verified by our evidence to advance our knowledge.
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