(by Eileen Dombrowski, from OUP blog) This week, I want to add a couple of ideas, just lightly, to what I said last week. I was presenting an argument back then, feeling the urgency of TOK’s goal to engage critically with the world. In a more mellow mood today, I’m recommending much “softer” class materials, with a gentler touch that leaves educational goals implied.
After all, students surely learn more than we teach. Along with our explicit messages – the focused questions, the concepts we’re developing, the analytical tools we’re practising – we’re also communicating attitudes and values. We don’t have to spell out everything. By choosing materials and focusing examples with a bit of resonance, we can teach indirectly, giving support to both TOK and the broader IB. Continue reading
(by Eileen Dombrowski, from OUP blog) May in the northern hemisphere. The return of long daylight. But also IB exams. Tired students. Tired teachers. Time to take a class into the calm and beauty of pattern, with gentle TOK reflection on the deep intersections of mathematics, nature, art and technology. 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. Continue reading
(by Eileen Dombrowski, from OUP blog) Hans Rosling, who passed away earlier this month, made numbers tell significant stories about the world. A self-proclaimed “edutainer” — educator and entertainer — Professor Rosling championed a worldview based on facts. He had a genius for revealing large patterns in human development by making people see the data on population, inequality, and global education and health. He leaves to teachers resources on numbers, facts, and large patterns that can continue to help us in our classrooms — and also leaves us, in less practical terms, the inspiration of his love of knowledge. Continue reading
(by Eileen Dombrowski, from OUP blog) Is the study of mathematics really a gateway toward empathy? I’m not fully convinced by the argument presented by mathematician Roger Antonsen, but I like him for making it. We need all the empathy we can get in our world. Certainly, his mathematical visualizations do demonstrate the importance of mental flexibility and imagination in mathematics, and do stand metaphorically for being able to see from different points of view. And his argument leads to some interesting knowledge questions about perspectives and empathy. Continue reading
(by Eileen Dombrowski, from OUP blog) Often it takes dramatic illustration to convey just why certain abstract concepts are so important to thinking critically about knowledge. For demonstrating the significance of concepts of “bias” and “implications”, try this online game with your students. “The Parable of the Polygons” provides an attractive, interactive – and startling! – visualization of what can follow from accepting some initial ideas, or from being influenced by only a little bit of bias! Students can play the game online, make their own choices, and see the graphic results form before their own eyes. Continue reading
April 1, 2016. Sets of prominent mathematicians rallied today to demand the release of an imprisoned mathematics teacher on the anniversary of his arrest. Ten years ago, he was apprehended boarding an international flight while in possession of a ruler, protractor, setsquare, and calculator. He is being held in Geometer’s Bay, charged with transporting weapons of math instruction.
A spokesman for Heavily Organized Armed Security (HOAX) declared that the man is dangerous. “He belongs to a cult that derives its teaching from a code known as the Axioms. These people are highly calculating.” It has been rumoured that the detainee is a member of the powerful group Al-Gebra, who follow their Ruler, reputed to be a straightforward hardliner. A dogmatist, he asserts that just two points are enough to determine his unique party line. Continue reading
(by Eileen Dombrowski) Who needs critical thinking when we have Google? A team of computer scientists working for Google has proposed an improvement on what comes up when we enter our terms in its search window. They suggest a method of calculating a “trustworthiness score” for webpages based on their factual content: “We call the trustworthiness score we computed Knowledge-Based Trust (KBT).” An avid Googler myself, I am awash with both admiration and amusement. What would our students, many of them also consummate Googlers in face of essay assignments, make of the knowledge questions that instantly arise about the nature of facts, truth, and reliable sources? Continue reading
(by Theo Dombrowski) When we hear the much quoted claim, “There’s lies, damned lies, and statistics,” many of us smile ruefully, suspecting that we have been duped by statistics at some points in our lives. How should we react, therefore, when we read a detailed report, accompanied by graphs and numbers, that, in the U.S., non-whites are more concerned about global warming than whites? After all, though we’ve known for a long time that statistics can be manipulated, we also know that statistics are much more effective and precise than words for communicating relationships such as proportions or correlations. Can we trust this report correlating race and attitudes to global warming? With the increase in “data journalism” the need for critical thinking is probably more acute now than ever before. Continue reading
(by Eileen Dombrowski, from OSC TOK blog) Mathematician Alex Bellos was intensely irritated by the question. Was that person in the audience mocking him, or possibly ridiculing what he’d been saying about mathematics, to ask such a bizarre and irrelevant question at the end of his lecture? The audience member had asked him, as others had done before, “What’s your favourite number?” In this podcast conversation from Radiolab, Bellos describes his abrupt shift of perspective as he realizes that the questioner is asking in sincerity. Quickly, he discovers that half the members of his audience have “favourite numbers”. And so begins his own investigation into emotional and imaginative associations with numbers, and the non-rational characteristics that many people attribute to a numbering system he had previously seen exclusively in terms of reason.
(by Theo Dombrowski, OSC TOK blog July 2, 2014) “As it develops, mathematics moves both towards the abstractions of the mind, and also towards the connection with the world.” Thus begins the section on “Pure and Applied Mathematics” in the ToK Course Companion. (p. 357). The nature of the relationship between the abstract nature of mathematics and “the world” is one of several issues examined in a new book on mathematics Continue reading