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Viewing: Blog Posts Tagged with: Mathematics, Most Recent at Top [Help]
Results 1 - 25 of 86
1. A person-less variant of the Bernadete paradox

Before looking at the person-less variant of the Bernedete paradox, lets review the original: Imagine that Alice is walking towards a point – call it A – and will continue walking past A unless something prevents her from progressing further.

The post A person-less variant of the Bernadete paradox appeared first on OUPblog.

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2. Is elementary school mathematics “real” mathematics?

When people think of elementary school mathematics, they usually bring to mind number facts, calculations, and algorithms. This isn’t surprising, as these topics tend to dominate classroom work in many elementary schools internationally. There is little doubt that elementary students should know the multiplication tables, be able to do simple calculations mentally, develop fluency in using algorithms to carry out more complex calculations

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3. Measuring up

My first degree was in mathematics, where I specialised in mathematical physics. That meant studying notions of mass, weight, length, time, and so on. After that, I took a master’s and a PhD in statistics. Those eventually led to me spending 11 years working at the Institute of Psychiatry in London, where the central disciplines were medicine and psychology. Like physics, both medicine and psychology are based on measurements.

The post Measuring up appeared first on OUPblog.

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4. How much do you know about Hypatia? [quiz]

An astronomer, mathematician, philosopher, and active public figure, Hypatia played a leading role in Alexandrian civic affairs. Her public lectures were popular, and her technical contributions to geometry, astronomy, number theory, and philosophy made Hypatia a highly regarded teacher and scholar.

The post How much do you know about Hypatia? [quiz] appeared first on OUPblog.

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5. Teaching teamwork

The capacity to work in teams is a vital skill that undergraduate and graduate students need to learn in order to succeed in their professional careers and personal lives. While teamwork is often part of the curriculum in elementary and secondary schools, undergraduate and graduate education is often directed at individual effort and testing that emphasizes solitary performance.

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6. 25 Books from 25 Years: Grandfather Counts

Lee_Low_25th_Anniversary_Poster_2_LEE & LOW BOOKS celebrates its 25th anniversary this year and to recognize how far the company has come, we are featuring one title a week to see how it is being used in classrooms today!

Today we’re featuring Grandfather Counts by Andrea Cheng and illustrated by Ange Zheng, released in 2003 by LEE & LOW BOOKS:

Grandfather Counts

About the Book: Grandfather Counts is a moving intergenerational story about the universal love between grandparent and grandchild, a love that bridges linguistic and cultural differences. In Grandfather Counts, Helen is excited to welcome her Gong Gong (grandfather), who comes from China to live with her family. But when she realizes that Gong Gong speaks only Chinese, Helen finds a special way to communicate.

Awards and Honors:

  • Reading Rainbow Selection, PBS Kids
  • Choices, Cooperative Children’s Book Center
  • Honor Book Award, Society ofSchool Librarians International
  • Parents’ Choice Noteworthy Product, Parents’ Choice Foundation

In the Author’s Own Words:

“Intergenerational stories come easily to me.  When I was a child, three of my grandparents lived either in our house or within walking distance.  I spent a lot of time with my paternal grandmother, and I think she is the model for many of the grandmothers in my stories.  When my husband and I had children, I could not imagine raising them far from their grandparents, so we moved from Ithaca, New York to Cincinnati where my parents were living.  My father died in 1997, but our children see my mother almost every day, and they spent a lot of time running back and forth between her house and ours when they were younger. Contact between generations is very important to me and seems to find its way into most of my stories.”
–(from an interview with Paper Tigers)

Note: Andrea Cheng passed away in late 2015. We remember her here.

Resources for Teaching With Grandfather Counts:

Book Activity:
Use Grandfather Counts as an opportunity to celebrate the range of languages that students may speak at home. Ask students who are fluent in other languages to share with the class how to count in their languages.

Encourage older students to gather oral histories from grandparents or other relatives for an oral history project.

Did you know?
If you look at the illustrations, you’ll notice that Grandfather Counts features a biracial main character. See all of our books featuring biracial and multiracial main characters.

Purchase Grandfather Counts here.

Other Recommended Picture Books Celebrating Grandparents:

A Morning With Grandpa

A Morning with Grandpa by Sylvia Liu, illus. by Christina Forshay

Seaside Dream

Seaside Dream by Janet Costa Bates, illus. by Lambert Davis

Sunday Shopping

Sunday Shopping by Sally Derby, illus. by Shadra Strickland

Have you used Grandfather Counts? Let us know!

Celebrate with us! Check out our 25 Years Anniversary Collection.

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7. Against narrowness in philosophy

If you asked many people today, they would say that one of the limitations of analytic philosophy is its narrowness. Whereas in previous centuries philosophers took on projects of broad scope, today’s philosophers typically deal with smaller issues.

The post Against narrowness in philosophy appeared first on OUPblog.

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8. Just because all philosophers are on Twitter…

Just because everyone is on Twitter doesn’t mean they’ve all got interesting things to say. I vaguely recall reading that late 19th-century curmudgeons expressed similar scepticism about the then much-hyped technology of the telephone.

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9. Very short facts about theVery Short Introductions

This week we are celebrating the 500th title in the Very Short Introductions series, Measurement: A Very Short Introduction, which will publish on 6th October. Our expert authors combine facts, analysis, new ideas, and enthusiasm to make often challenging topics highly readable. To mark its publication editors Andrea Keegan and Jenny Nugee have put together a list of Very Short Facts about the series.

The post Very short facts about theVery Short Introductions appeared first on OUPblog.

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10. How do people read mathematics?

At first glance this might seem like a non-question. How do people read anything? All suitably educated people read at least somewhat fluently in their first language – why would reading mathematics be different? Indeed, why would mathematics involve reading at all? For many people, mathematics is something you do, not something you read.

But it turns out that there are interesting questions here. There are, for instance, thousands of mathematics textbooks–many students own one and use it regularly. They might not use it in the way intended by the author: research indicates that some students–perhaps most–typically use their textbooks only as a source of problems, and essentially ignore the expository sections. That is a shame for textbook authors, whose months spent crafting those sections do not influence learning in the ways they intend. It is also a shame for students, especially for those who go on to more advanced, demanding study of upper-level university mathematics. In proof-based courses it is difficult to avoid learning by reading. Even successful students are unlikely to understand everything in lectures – the material is too challenging and the pace is too fast – and reading to learn is expected.

Because students are not typically experienced or trained in mathematical reading, this returns us to the opening questions. Does this lack of training matter? Undergraduate students can read, so can they not simply apply this skill to mathematical material? But it turns out that this is not as simple as it sounds, because mathematical reading is not like ordinary reading. Mathematicians have long known this (“you should read with a pencil in hand”), but the skills needed have recently been empirically documented in research studies conducted in the Mathematics Education Centre at Loughborough University. Matthew Inglis and I began with an expert/novice study contrasting the reading behaviours of professional mathematicians with those of undergraduate students. By using eye-movement analyses we found that, when reading purported mathematical proofs, undergraduates’ attention is drawn to the mathematical symbols. To the uninitiated that might sound fine, but it is not consistent with expert behaviour: the professional mathematicians attended proportionately more to the words, reflecting their knowledge that these capture much of the logical reasoning in any written mathematical argument.

Another difference appeared in patterns of behaviour, which can best be seen by watching the behaviour of one mathematician when reading a purported proof to decide upon its validity (see below). Ordinary reading, as you might expect, is fairly linear. But mathematical reading is not. When studying the purported proof, the mathematician makes a great many back-and-forth eye movements, and this is characteristic of professional reading: the mathematicians in our study did this significantly more than the undergraduate students, particularly when justifications for deductions were left implicit.

This work is captured in detail in our article Expert and Novice Approaches to Reading Mathematical Proofs. Since completing it, Matthew and I have worked with PhD and project students Mark Hodds, Somali Roy and Tom Kilbey to further investigate undergraduate mathematical reading. We have discovered that research-based Self-Explanation Training can render students’ reading more like that of mathematicians and can consequently improve their proof comprehension (see our paper Self-Explanation Training Improves Proof Comprehension); that multimedia resources designed to support effective reading can help too much, leading to poorer retention of the resulting knowledge; and that there is minimal link between reading time and consequent learning. Readers interested in this work might like to begin by reading our AMS Notices article, which summarises much of this work.

In the meantime, my own teaching has changed – I am now much more aware of the need to help students learn to read mathematics and to provide them with time to practice. And this research has influenced my own writing for students: there is no option to skip the expository text, because expository text is all there is. But this text is as much about the thinking as it is about the mathematics. It is necessary for mathematics textbooks to contain accessible text, explicit guidance on engaging with abstract mathematical information, and encouragement to recognise that mathematical reading is challenging but eminently possible for those who are willing to learn.

Feature Image: Open book by Image Catalog. CC0 1.0 via Flickr.

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11. Is an engineering mind-set linked to violent terrorism?

In a British Council report Martin Rose argues that the way STEM subjects are taught reinforces the development of a mind-set receptive to violent extremism. Well taught social sciences, on the other hand, are a potentially powerful intellectual defence against it. Whilst his primary focus was MENA (Middle East and North Africa) he draws implications for education in the West.

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12. Addressing anxiety in the teaching room: techniques to enhance mathematics and statistics education

In June 2015, I co-chaired the organising committee of the first international mathematics education conference of the Institute of Mathematics and its Applications (IMA) titled ‘Barriers and Enablers to Learning Maths’ with the University of Glasgow, who also hosted it. The two and a half day conference explored approaches to teaching and learning mathematics and was structured around ten parallel sessions that delegates could choose from, including ‘Addressing mathematics & statistics anxiety’ and ‘Enhancing engagement with mathematics & statistics.’

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13. Let us not run blindfolded into the minefield of future technologies

There is a widely held conception that progress in science and technology is our salvation, and the more of it, the better. This is the default assumption not only among the general public, but also in the research community including university administration and research funding agencies, all the way up to government ministries. I believe the assumption to be wrong, and very dangerous.

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14. Can a robot be conscious?

Can a robot be conscious? I will try to discuss this without getting bogged down in the rather thorny issue of what consciousness –– really is. Instead, let me first address whether robot consciousness is an important topic to think about. At first sight, it may seem unimportant. Robots will affect us only through their outward behavior, which may be more or less along the lines of what we tend to think of as coming along with consciousness, but given this behavior, its consequences to us are not affected by whether or not it really is accompanied by consciousness.

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15. Conversations in computing: Q&A with Editor-in-Chief, Professor Steve Furber

Oxford University Press is excited to be welcoming Professor Steve Furber as the new Editor-in-Chief of The Computer Journal. In an interview between Justin Richards of BCS, The Chartered Institute of IT and Steve, we get to know more about the SpiNNaker project, ethical issues around Artificial Intelligence (AI), and the future of the IT industry.

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16. Does the ‘Chinese room’ argument preclude a robot uprising?

There has been much recent talk about a possible robot apocalypse. One person who is highly skeptical about this possibility is philosopher John Searle. In a 2014 essay, he argues that "the prospect of superintelligent computers rising up and killing us, all by themselves, is not a real danger".

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17. What is information, and should it be free?

When we pay our bills using a plastic card, we are simply authorizing alterations to the information stored in some computers. This is one aspect of the symbiotic relationship that now exists between money and information. The modern financial world is byzantine in its complexity, and mathematics is involved in many ways, not all of them transparently clear. Fortunately there are some bright spots, such as the fact that it is now possible to measure information.

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18. Earth’s climate: a complex system with mysteries abound

We are living with a climate system undergoing significant changes. Scientists have established a critical mass of facts and have quantified them to a degree sufficient to support international action to mitigate against drastic change and adapt to committed climate shifts. The primary example being the relation between increased atmospheric carbon dioxide concentrations and the extent of warming in the future.

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19. Mary Somerville: the new face on Royal Bank of Scotland’s ten-pound note is worthy of international recognition

From 2017, ten-pound notes issued by the Royal Bank of Scotland will feature a new face: that of the great nineteenth-century science communicator Mary Somerville. Her book on mathematical astronomy, Mechanism of the Heavens -- published in 1831, when she was fifty years old -- was used as an advanced textbook at Cambridge for a hundred years. This is a phenomenal achievement for a woman who taught herself science and mathematics.

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20. The consistency of inconsistency claims

A theory is inconsistent if we can prove a contradiction using basic logic and the principles of that theory. Consistency is a much weaker condition that truth: if a theory T is true, then T consistent, since a true theory only allows us to prove true claims, and contradictions are not true. There are, however, infinitely many different consistent theories that we can construct.

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21. Can design thinking challenge the scientific method?

The scientific method has long reigned as the trusted way to test hypotheses so as to produce new knowledge. Shaped by the likes of Francis Bacon, Galileo Galilei, and Ronald A. Fisher, the idea of replicable controlled experiments with at least two treatments has dominated scientific research as a way of producing accepted truths about the world around us. However, there is growing interest in design thinking, a research method which encourages practitioners to reformulate goals, question requirements, empathize with users, consider divergent solutions.

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22. From number theory to e-commerce

The American Mathematical Society held on October 1903 its regular meeting in New York City. The program announced a talk by Frank Nelson Cole (1861-1921), with the unpretending title of 'On the factorization of large numbers'. In due course, Cole approached the board and started to multiply the number 2 by itself, step after step and without saying a word, sixty seven times.

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23. Why know any algebra?

A recent meme circulating on the internet mocked a US government programme (ObamaCare) saying that its introduction cost $360 million when there were only 317 million people in the entire country. It then posed the rhetorical question: "Why not just give everyone a million dollars instead?"

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24. Can one hear the corners of a drum?

Why is the head of a drum usually shaped like a circle? How would it sound if it were shaped like a square instead? Or a triangle? If you closed your eyes and listened, could you tell the difference? The mathematics used to prove that “one can hear the corners of a drum” are founded on […]

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25. Very Short Resolutions: filling the gaps in our knowledge in 2016

Why make New Year's Resolutions you don't want to keep? This year the Very Short Introductions team have decided to fill the gaps in their knowledge by picking a VSI to read in 2016. Which VSIs will you be reading in 2016? Let us know in the comment section below or via the Very Short Introductions Facebook page.

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