the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.
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How to Fix Our Math Education - NYTimes.com - 63 views
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Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.
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A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.
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For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.
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Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.
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Traditionalists will object that the standard curriculum teaches valuable abstract reasoning, even if the specific skills acquired are not immediately useful in later life. A generation ago, traditionalists were also arguing that studying Latin, though it had no practical application, helped students develop unique linguistic skills. We believe that studying applied math, like learning living languages, provides both useable knowledge and abstract skills.
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In math, what we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).
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Maths Charts - 104 views
www.amathsdictionaryforkids.com/mathsCharts.html
maths charts number addition subtraction multiplication division fractions decimals percentages ratio algebra data statistics probability geometry measurement time money
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A great new resource from the creator of 'A Maths Dictionary for Kids'. Download and print beautifully designed and wonderfully useful maths posters on a good range of topics. Your classroom walls will never be the same again. http://ictmagic.wikispaces.com/Maths
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Maths duck - 92 views
mathsduck.co.uk
maths number algebra data shape and measure game multiplication addition subtraction
shared by Martin Burrett on 02 Aug 11
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A superb site with lots and fun maths games on a wide range of topics across the maths curriculum. http://ictmagic.wikispaces.com/Maths
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MathsPad - 99 views
www.mathspad.co.uk
maths numeracy angles shapes area perimeter transformations negative numbers fractions percentages place value algebra sequences data handling
shared by Martin Burrett on 02 Jul 12
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A great maths site with flash resources, online tests and worksheets on a range of maths topics to print or use on your whiteboard. http://ictmagic.wikispaces.com/Maths
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Math is Fun - Maths Resources - 131 views
www.mathsisfun.com
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shared by Martin Burrett on 07 Nov 11
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A simple site with well written explanations, examples worksheets and games of maths topics from across the curriculum. http://ictmagic.wikispaces.com/Maths
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Mathopolis - Math Games - 175 views
www.mathopolis.com
maths games measurement geometry space numbers decimals fractions memory data handling
shared by Martin Burrett on 25 Oct 11
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A superb place to find games and questions for the whole of the maths curriculum. Join for free to track progress or just play the games. http://ictmagic.wikispaces.com/Maths
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How Big Data Is Taking Teachers Out of the Lecturing Business: Scientific American - 0 views
www.scientificamerican.com/article.cfm
adaptive learning pedagogy education ASU Arizona Knewton math
shared by Maureen Greenbaum on 19 Jul 13
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David Heckman, a mathematician, was accustomed to lecturing to the class, but he had to take on the role of a roving mentor, responding to raised hands and coaching students when they got stumped
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Like institutions at every level of American education, it is going through some wrenching changes. The university has lost 50 percent of its state funding over the past five years.
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more efficient way to shepherd students through basic general-education requirements—particularly those courses, such as college math, that disproportionately cause students to drop out
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That fall, with little debate or warning, it placed 4,700 students into computerized math courses. Last year some 50 instructors coached 7,600 Arizona State students through three entry-level math courses running on Knewton software. By the fall of 2014 ASU aims to adapt six more courses, adding another 19,000 students a year to the adaptive-learning ranks.
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The End of Theory: The Data Deluge Makes the Scientific Method Obsolete - 137 views
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sociology. Forget taxonomy, ontology, and psychology. Who knows why people do what they do? The point is they do it, and we can track and measure it with unprecedented fidelity. With enough data, the numbers speak for themselves.
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The big target here isn't advertising, though. It's science. The scientific method is built around testable hypotheses. These models, for the most part, are systems visualized in the minds of scientists. The models are then tested, and experiments confirm or falsify theoretical models of how the world works.
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But faced with massive data, this approach to science — hypothesize, model, test — is becoming obsolete.
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article discussing whether math models can replace other tools for understanding the world.
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I dissagree. Maybe for someone who can cope with the massive scale Google works with but for the average student bah humbug. As far as the students I see the scientific method still needs to be taught as they need a lot of help learning how to gather reliable information from the web. As far as google is concerned the students simplistic, unevaluated searches are as valuable as someone who actually understands what they are looking for or maybe more valuable because more students are doing almost thoughtless searches. The real need is a good course, hopefully online, to teach students how to do a reasoned search. agoogleaday is a start.
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The Coach in the Operating Room - The New Yorker - 37 views
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I compared my results against national data, and I began beating the averages.
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the obvious struck me as interesting: even Rafael Nadal has a coach. Nearly every élite tennis player in the world does. Professional athletes use coaches to make sure they are as good as they can be.
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They don’t even have to be good at the sport. The famous Olympic gymnastics coach Bela Karolyi couldn’t do a split if his life depended on it. Mainly, they observe, they judge, and they guide.
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always evolving
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no matter how well prepared people are in their formative years, few can achieve and maintain their best performance on their own.
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For decades, research has confirmed that the big factor in determining how much students learn is not class size or the extent of standardized testing but the quality of their teachers.
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So, instead of having students take test after test after test, why don't we just have coaches who observe and sit and discuss and offer suggestions and divide the number of tests we give students in half and do away with half? Are we concerned about student knowledge? student performance? student ability? student growth or capacity for growth? What we really need to identify is what we value!
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California researchers in the early nineteen-eighties conducted a five-year study of teacher-skill development in eighty schools, and noticed something interesting. Workshops led teachers to use new skills in the classroom only ten per cent of the time. Even when a practice session with demonstrations and personal feedback was added, fewer than twenty per cent made the change. But when coaching was introduced—when a colleague watched them try the new skills in their own classroom and provided suggestions—adoption rates passed ninety per cent. A spate of small randomized trials confirmed the effect. Coached teachers were more effective, and their students did better on tests.
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they did not necessarily have any special expertise in a content area, like math or science.
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The coaches let the teachers choose the direction for coaching. They usually know better than anyone what their difficulties are.
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The conversation with the coach and the coach listening and learning what the teacher would like to expand, improve, and grow is probably the most vital part! If the teacher doesn't have a clue, the coach could start anywhere and that might not be what the teacher adopts and owns. So, the teacher must have ownership and direction.
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teaches coaches to observe a few specifics: whether the teacher has an effective plan for instruction; how many students are engaged in the material; whether they interact respectfully; whether they engage in high-level conversations; whether they understand how they are progressing, or failing to progress.
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must engage in “deliberate practice”—sustained, mindful efforts to develop the full range of abilities that success requires. You have to work at what you’re not good at.
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most people do not know where to start or how to proceed. Expertise, as the formula goes, requires going from unconscious incompetence to conscious incompetence to conscious competence and finally to unconscious competence.
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The coach provides the outside eyes and ears, and makes you aware of where you’re falling short.
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So coaches use a variety of approaches—showing what other, respected colleagues do, for instance, or reviewing videos of the subject’s performance. The most common, however, is just conversation.
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“What worked?”
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“What else did you notice?”
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something to try.
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Good coaches, he said, speak with credibility, make a personal connection, and focus little on themselves.
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“listened more than they talked,” Knight said. “They were one hundred per cent present in the conversation.”
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trying to get residents to think—to think like surgeons—and his questions exposed how much we had to learn.
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one twenty-minute discussion gave me more to consider and work on than I’d had in the past five years.
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watch other colleagues operate in order to gather ideas about what I could do.
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routine, high-quality video recordings of operations could enable us to figure out why some patients fare better than others.
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It’s teaching with a trendier name. Coaching aimed at improving the performance of people who are already professionals is less usual.
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modern society increasingly depends on ordinary people taking responsibility for doing extraordinary things
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We care about results in sports, and if we care half as much about results in schools and in hospitals we may reach the same conclusion.
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The Default Major - Skating Through B-School - NYTimes.com - 41 views
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Dr. Mason, who teaches economics at the University of North Florida, believes his students are just as intelligent as they’ve always been. But many of them don’t read their textbooks, or do much of anything else that their parents would have called studying. “We used to complain that K-12 schools didn’t hold students to high standards,” he says with a sigh. “And here we are doing the same thing ourselves.”
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all evidence suggests that student disengagement is at its worst in Dr. Mason’s domain: undergraduate business education.
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“Business education has come to be defined in the minds of students as a place for developing elite social networks and getting access to corporate recruiters,”
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It’s an attitude that Dr. Khurana first saw in M.B.A. programs but has migrated, he says, to the undergraduate level.
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Second, in management and marketing, no strong consensus has emerged about what students ought to learn or how they ought to learn it.
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Gains on the C.L.A. closely parallel the amount of time students reported spending on homework. Another explanation is the heavy prevalence of group assignments in business courses: the more time students spent studying in groups, the weaker their gains in the kinds of skills the C.L.A. measures.
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The pedagogical theory is that managers need to function in groups, so a management education without such experiences would be like medical training without a residency. While some group projects are genuinely challenging, the consensus among students and professors is that they are one of the elements of business that make it easy to skate through college.
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“We’ve got students who don’t read, and grow up not reading,” he says. “There are too many other things competing for their time. The frequency and quantity of drinking keeps getting higher. We have issues with depression. Getting students alert and motivated — even getting them to class, to be honest with you — it’s a challenge.”
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“A lot of classes I’ve been exposed to, you just go to class and they do the PowerPoint from the book,” he says. “It just seems kind of pointless to go when (a) you’re probably not going to be paying much attention anyway and (b) it would probably be worth more of your time just to sit with your book and read it.”
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“It seems like now, every take-home test you get, you can just go and Google. If the question is from a test bank, you can just type the text in, and somebody out there will have it and you can just use that.”
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This is not senioritis, he says: this is the way all four years have been. In a typical day, “I just play sports, maybe go to the gym. Eat. Probably drink a little bit. Just kind of goof around all day.” He says his grade-point average is 3.3.
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History and philosophy, on the other hand, provide the kind of contextual knowledge and reasoning skills that are indispensable for business students.
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when they hand in papers, they’re marked up twice: once for content by a professor with specialized expertise, and once for writing quality by a business-communication professor.
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a national survey of 259 business professors who had been teaching for at least 10 years. On average, respondents said they had reduced the math and analytic-thinking requirements in their courses. In exchange, they had increased the number of requirements related to computer skills and group presentations.
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what about employers? What do they want? According to national surveys, they want to hire 22-year-olds who can write coherently, think creatively and analyze quantitative data, and they’re perfectly happy to hire English or biology majors. Most Ivy League universities and elite liberal arts colleges, in fact, don’t even offer undergraduate business majors.