That event in the past: what do we make it signify in the present? WOK rarely function in isolation, the TOK will explore how WOKs work, and how they work together with different areas of … We cannot accept conclusions in the sciences unless we can trust the methodology that produced them. 9:22. Math relates more to reasoning as it’s based on facts and specific rules that are learnt. Great videos on mathematics, beauty and proof, 10 female mathematicians who changed the world, "hidden figures": a film about the Black female mathematicians who helped win the space race, The story of Maths: prehistoric Mathematics, BBC Documentary: The history of mathematics, Blog: The neuroscience of mathematical beauty, Stanford encyclopedia of philosophy: Philosophy of Mathematics. If people should object to this, I am quite willing to confine my statements to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure knowledge. How are unethical practices such as “data dredging” used by statisticians to deliberately manipulate and mislead people? How significant have notable individuals been in shaping the nature and development of mathematics as an area of knowledge? Possibly. Indeed, a common method of mathematical research is to reduce a problem to one already considered. First, then, the basics. What should most leap off the page is that the graphs bear a striking similarity. Why does mathematics enjoy a privileged status in many education systems? What, though, is the premise (arguably there is more than one) that lies behind such an answer? New College of the Humanities 333 views. Mathematics and the world (1) We can use mathematics successfully to model real-world processes. Quotes on the foundations of mathematics. ( Log Out /  Loading... Unsubscribe from 3liony? These concepts often cause a dilemma. The questions may appear a little leading, since this part of the process is most illuminating if students give the same answers–the same reasonable answers, importantly–as malaria researchers generally give. We just don’t have enough evidence to decide whether they are wrong or right when major flaws emerge in the methods of gaining evidence. A Professor at the University of New South Wales in Australia and head of the “Complex Systems in Biology Group”, Dr. Davenport is using as a primary weapon not what most would expect: he is using mathematics. On the one hand it seems to supply a certainty often missing in other disciplines. Consuming the news: Is knowing harder than dieting? The research and experiences of IB graduate Dr. Change ), Backward Brain Bicycle: memory and knowing how, supplied by the Gates Foundation, Creative Commons, 2018 TOK blog posts compiled for download, Facts and feelings: knowing better by knowing ourselves. Is there a distinction between truth and certainty in mathematics? Do mathematical judgements and ethical judgements face similar challenges in terms of the evidence available to support them. Mathematics, he argues, unlike most other research tools used in immunology work, is crucial in finding patterns in the detail produced by most research: “What we urgently need are some ‘lumpers’ [as opposed to ‘splitters’], who search for the overarching rules which help us understand how the different phenomena arose and how they fit together.”  “The discipline that mathematical analysis imposes on the field is the need to state how different factors will interact and what outcomes we predict.” ( p. 363). The foundation of scientifi c frameworks is the science principle and scientifi c research methods. What do mathematicians mean by mathematical proof, and how does it differ from good reasons in other areas of knowledge What is Mathematical Proof How to prove it? Retraction of major research on eating: a failure in scientific methodology, or a corrective in the process? 5-Minute Crafts TEENS Recommended for you. I’m getting myself organized. In fact, the opposite is true. Announce that, if time permits, they should continue solving the same equation using multiple methods. Critical thinking and critique of methodology. Making links of this sort is what is meant by analysis in TOK. The student activity to echo some of his own team’s research methods starts with a chess board and a hand full of rice (or similar bits and pieces). How is an axiomatic system of knowledge different from, or similar to, other systems of knowledge? ( Log Out /  Drop the rice grains loosely onto a chess board and see where they land, says Dr. Davenport. Is mathematics better defined by its subject matter or its method? Is all apparent immunity merely the result of chance? Question: Would one of these groups seem to you more likely than the other to have natural immunity? Mathematics Notes - Theory of Knowledge I know you'll find this TOK Mathematics notes helpful, but there is an even better version available to our supporting members here (the full Mathematics notes) --along with some very helpful TOK videos and other sources for your TOK essay and presentation. TOK Monday, May 18, 2015. Step Two: Look at a standard graph of random distribution–in other words, a “bell curve”. TOK Thoughts Tuesday, May 12, 2015. ​Is mathematical reasoning different from scientific reasoning or reasoning in other areas of knowledge? 9:31. 3. On what criteria could we decide whether mathematicians should be held responsible for unethical applications of their work. What is it about mathematics that enables mathematical results to remain unchanged over time? Since the subject is a very factual knowledge, it is rarely influenced by the society and culture it lives in. Do Nobel prizes distort public understanding of scientific knowledge? Love, luck, literature, and logic: Who will win the lady? The scientific method is a key feature of what makes the natural sciences so scientific. In fact, the opposite is true. And remember question 4? Though you might find the question becomes too complex to introduce, you may note that those who would argue for examining children first are actually introducing something akin to a utilitarian ethic. This is what Dr. Davenport and his team conclude in the recently published paper: “We find that under most circumstances, the distribution of time-to-infection [i.e. While conceding that it is children who are most vulnerable to the disease and suffer most, he points out that it is only in adults that real natural immunity might effectively be detected. Question: Since children generally suffer more severely than adults when they are infected, would you target children in your research or merely include them in your study? Count squares with 0, 1, 2, 3 etc. The mere fact that mathematicians use their own 'language of symbols' raises interesting TOK questions about the role of language within the methodology of an area of knowledge or discipline. Is it ethically justifiable for academic researchers to spend time doing research that does not have useful applications? We can all hope that they close in sooner on what they — and we! ... Natural Sciences methodology and use of equipment and it has a more traditional approaches. 19 SURPRISING MAGIC TRICKS - Duration: 9:22. There is a bit of a trick here. For this kind of pattern-finding, ways of knowing of, What does this example suggest about the importance of finding. They underlie the methodology of the areas of knowledge 2. This has every guarantee of success, provided one is sufficiently skilful in the standard method. The slightly less obvious answer–but one that could easily be teased out–is that you are likely to identify two apparently resistant types: 1. those who don’t seem to catch the disease even after considerable time 2. those, who having the disease, don’t seem to develop severe symptoms. The second, Dr. Davenport’s specialty, is less obviously fundamental–applying mathematics. Why might this be the case? Everything around you is numbers. Dr. Davenport suggests that confronting some of the problems that researchers face in important contemporary research encourages students to recognize that critical thinking is not always obvious or easy. Here there is no clear “correct” answer. Mathematics Knowledge Framework 1. The full paper goes into details in making recommendations on the most likely methods of finding resistant individuals–and improving methodologies. Everything around you is mathematics. Why the improvement? Members will find questions on these quotes in the Exploration Points section below. While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. This year, my favourite vehicle is the animated sculpture of John Edmark, especially with the video “ Creating the Never-Ending Bloom ” in which the designer is commenting on his work. TOK double vision: lofty overview but critical engagement in the world. What is meant by the term “proof” in mathematics, and how is this different similar to or different from what is meant by this term in other areas of knowledge? And there are plenty more statistics where these came from: In 2013, there were about 198 million malaria cases (with an uncertainty range of 124 million to 283 million) and an estimated 584 000 malaria deaths (with an uncertainty range of 367 000 to 755 000). – all want: a prevention or cure for malaria. Draw a graph, he says, recording distribution. Miles Davenport provide excellent insight into the methods currently being employed in the biological sciences to combat this huge health issue faced principally by the world’s poor. At this point, we shift to the second main aspect of this problem–enter mathematics! These are lecture notes for AME 60611 Mathematical Methods I, the first of a pair of courses on applied mathematics taught in the Department of Aerospace and Mechanical Engineering of the University of Notre Dame. Modern math teaching methodology offers various possibilities for solv-ing the above mentioned problem. Tik Tok Verse Recommended for you. In a sense a Knowledge Question is a TOK-style research question. Theory of Knowledge: Maths, Dr George Zouros - Duration: 9:31. Question: If you were looking to develop a vaccine against malaria what population group might you first examine? On the horizontal axis enter the number grains of rice in each square. These quotes offer thoughts on the nature and scope of mathematics, methods we use to study it, and reasons for studying this area of knowledge. Are mathematicians the people best placed to create codes of ethics for professional mathematicians. The level of difficulty of this quadratic equation has been chosen so that some students may struggle and others may work through at least four methods. Change ), You are commenting using your Google account. (It turned out that this was because they had developed a natural immunity from exposure to cow pox, a closely related but less dangerous pox than small pox.) Does mathematics only yield knowledge about the real world when it is combined with other areas of knowledge? SPOT and the cloak of invisibility: cognitive biases. Class activity: understanding random processes. (Dis)trusting statistics: a one-page guide, Facts matter after all: rejecting the “backfire effect”, History: writing the past, drafting the future, “How am I supposed to appreciate it?” Art, science, and some silly assumptions, Download TOK resource: 2017 TOK blog posts, collected, “Those experts!”: cartoon, class discussion activity, Signed language, symbolism, and reflections on inclusion. In TOK terms, we might rephrase to say that the methodology is flawed, giving insufficient justification for the conclusions reached. An important contribution to advance in science is critique of the methodology itself. Step One: The process is deceptively simple. rate of infection] is consistent with this simply being a random process. We may not even begin to understand this particular mathematical formula, but we can all appreciate how mathematics is being used in a rigorous and powerful manner! “ The scientific method, as far as it is a method, is nothing more than doing one’s damnedest with one’s mind, no holds barred. Some students may feel that mathematics and Theory of Knowledge do not have much in common. Well, I am currently in the first year of IB and our teacher has set us a prep to prepare a presentation regarding one of the "Arts" and I chose photography. This branch of mathematics developed quickly in the early 1800s, sparking new interest in geometry and leading to a heated debate about whether geometry should retain its “pure” Euclidean roots of diagrammatic proof, or if it was best understood through algebra. The third, least studied, subject deals with emotional interventions, and it investigates methods of intentionally influencing emotions during mathematical activity. In the end, the scrupulously close study of data leads Dr. Davenport and his team to conclude that it is only by using a particular method of detection of infection (described in the paper) and only by applying it to a group within a 1. narrow age group and 2. within the same geographical area that researches can legitimately expect to find individuals with natural immunity. Do mathematical symbols have meaning in the same way that words have meaning? Is absolute certainty attainable in mathematics? TOK teachers can handle this.” Astrology & belief. Step Three: Compare the 2 graphs. Mostly, it seems, from two causes: increased availability and use of both insecticides and mosquito nets over sleeping areas. ​Why is mathematics so important in other areas of knowledge, particularly the natural sciences? 1:53. CT4ME provides this information in our section on Standards. “Deepfakes” and TOK: more trouble ahead for critical thinking? According to yet further statistics, this horrifying number is not as bad as it was just a few years earlier. Beyond demonstrating the ways in which two AOKs, mathematics and the natural sciences (and biology in particular) are interdependent, this example of current research in malaria raises at least the following knowledge questions: Those who are intrigued by the role of mathematics in this kind of analysis –and that should be all of us!–might be equally intrigued by glimpsing a tiny sample of the papers’ methods of analysis: This is not a joke! The first concerns those elements absolutely basic to gaining scientific knowledge–making observations, collecting data, making assumptions, and formulating hypotheses. Either answer, arguably, is reasonable. What you, as teacher, know in advance, however, is that, according to Dr. Davenport, most of these answers could well be wrong, or, at least, oversimplified. ( Log Out /  Is this enough to strike a chill into the heart of any malaria researcher? Thus this new paper is a warning to those researchers pouring resources into malaria prevention by focusing on those who seem resistant to becoming infected that they may well be fundamentally wrong in their approach. Does personal experience play any role in the formation of claims in mathematics? The exploration points enable students to develop a deeper understanding of this aspect of TOK via extensive additional media sources and unpacking suggestions, links to TED talks, guidance on how to draw on the 12 key concepts of TOK… The Methodology of Mathematics by Ronald Brown and Timothy Porter Introduction This essay is based on a talk given by the first author to students and staff of the Departmento de Geometria e Topologia at the University of Seville in November, 1993. An example can be see at this website. BUT…they might still be right. Other Maths ToK questions for discussion. This method is probably a part of every successful research project. Math is a language as it is developed and understood differently in many other cultures. We find that age, method for detection of infection, and underlying force of infection are all factors in determining whether time-to-infection is a useful correlate of immunity.”. For example, the reliability of knowledge within an AOK will depend critically upon the methods used to produce it. Areas of knowledge are specific branches of knowledge, each of which can be seen to have a distinct nature and different methods of gaining knowledge. “Moral robots” and that messy human factor, Red lines and “complex moral duality”: TOK and ethics of witnessing, How much does this example demonstrate the common assertion that, of all the natural sciences, biology is most difficult to quantify and most difficult in which to find general laws? Is progress harder to make in mathematics than in other areas of knowledge? 1. How do mathematicians reconcile the fact that some conclusions seem to conflict with our intuitions? ( Log Out /  Possibly. Does this suggest that attempts to decode the biology at play in individuals with “natural resistance” are based on entirely false premises? Do you have a prompt for what you are supposed to do? A TOK class for exam month: mathematics, nature, art, technology…and peaceful contemplation of beauty, Exercise for awareness: facts, feelings, and changing your mind. ), they would see that it, too, looks almost exactly like a graph of randomness. The WOK have two roles in TOK: 1. And, at this point, we need to consider another problematic issue with most current research. Evolutionary biologists suggest that even in day to day living–quite apart from scientific research–we humans tend to find significant patterns because our survival has depended on our doing so. 2. chess board, “Creative Magic”, Pixabay, Creative Commons. The second, less frequent focus is on emotional states, and it investigates interactions between emotional, cognitive, and environmental factors when completing mathematical tasks. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. The conclusions could be wrong. Is personal experience more important or less important in mathematics compared to other areas of knowledge? Exploration points for mathematics. Malaria is, after all, as the paper shows, a complex disease–and different levels of resistance or immunity can occur at various stages in the process of the parasite’s development. Course description. ​If mathematical knowledge is highly valued, does this place special ethical responsibilities on mathematicians when they are making claims? They provide a basis for personal knowledge. Second, how does mathematics help to examine the methods? 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