To Fix Math Education, See It as a Program That Needs an Update | Mathematics - Walter Bradley Center for Natural and Artificial Intelligence

Part 1: How can we really fix the way math is taught? First, we must understand why we teach math in the first place. Math teaches students how to think more clearly in all areas of life but it mostly performs this function silently, invisibly.

Part 2: Straight talk about fitting the math curriculum to the student. We need to avoid pushing too much too soon, lest students come to see themselves as “bad at math” when they are just not ready for it. About math drills: Every algebra teacher I’ve ever met will tell you that instant recall of math facts is the best predictor of algebra success.

Part 3: Helping students see how math benefits them in the long run. To keep them motivated, we need to answer the “Why bother?” question honestly and directly. Most mathematics topics teach a specific logical skill that will help students solve problems on any career path.

See also: Bartlett’s calculus paper reviewed in a mathematics magazine. The paper offers fixes for long-standing flaws in the teaching of elementary calculus.

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Jonathan Bartlett, senior software R&D engineer at Specialized Bicycle Components inform, In this series we are looking at ways that math education can be reformed. 

Photo: aleonmail via Flickr

In contrast to some other math reform efforts, we are not trying to fundamentally rewrite what math education is doing but to simply admit that we can do better and see where that takes us. (See Part 1, Part 2, and Part 3.) Here in Part 4, let’s look at specific content issues that, I will argue, we could improve when we do a curriculum revision.

Mathematics is an old subject. We have inherited quite a bit of mathematical thought. We must educate future generations so as to make sure that this hard-won knowledge is not lost. But one of the biggest impediments to our task is simply the way in which mathematics is presented.

Here is an illustration that may help: In computer programming we sometimes talk about “legacy code.” Legacy code consists of working programs that have been handed down to us, usually from earlier programmers. Oftentimes, as change requests have come in, one programmer after another bolts features into the code. After a while, the bolt-ons start making the code itself confusing. As a result, later programmers have a hard time making sense of how everything fits together.

Eventually, the code must be “re-factored.” This means that we pull the code apart and rebuild it so that it makes a lot more sense to those who are currently using and developing it.

I think the same process is needed for math education...

A great math problem would be a practical one. For example, ask students to create a formula for a catering budget based on a head count, and then to modify that formula to see, given a particular budget, what the head count would be.

Too often, formulas in mathematics simply seem to fall from the sky and students are merely asked to use and obey. That works well for younger students who just need a thinking tool to begin with. But our goal is to eventually get students to think for themselves and generate their own solutions to their own problems. Math can help with this but only if we train students to think in a logical way as a normal routine.

Read more... 

Source: Walter Bradley Center for Natural and Artificial Intelligence

Four German-speaking philosophers in search of a theme | Philosophy - Spectator.co.uk

Steven Poole, Author, The Spectator Australia writes,Wolfram Eilenberger credits Heidegger, Wittgenstein, Benjamin and Cassirer with inventing modern thought. But a shared language was all they ever had in common.

Martin Heiddeger.
Photo: Getty Images

How do you write a group biography of people who never actually formed a group? Such is the challenge Wolfram Eilenberger sets himself in a book about the philosophers Martin Heidegger, Ludwig Wittgenstein, Walter Benjamin and — the surprisingly unstarry fourth subject — Ernst Cassirer, an urbane and now nearly forgotten neo-Kantian who might have deserved the made-up title of ‘symbologist’, thus far reserved for the heroes of Dan Brown’s novels.

What these men have in common is that they spoke German and were philosophically active during the 1920s, but that is about it. Heidegger and Cassirer met and traded rhetorical blows at a celebrated philosophy conference in Davos; Benjamin was envious of Heidegger’s success and Wittgenstein at least had heard of him. But they were all ploughing very different furrows — unless you ascend to the highest levels of abstraction and say, along with Eilenberger, that they were all interested in human beings’ relationship with language. Well, sure. Aren’t we all?

The book starts at the end of its chronological period: in 1929, Wittgenstein receives his PhD at Cambridge, while Heidegger and Cassirer arrive at Davos, and Benjamin is ‘troubled by concerns of quite a different order’ — his girlfriend has just kicked him out...

In the end the reader is prompted to wonder whether it was indeed these four men, and only they, who ‘invented modern thought’. Plenty of other candidates of the era come to mind, philosophical and otherwise — why not Niels Bohr and the other quantum physicists? (As it happens, Cassirer wrote a well-received book on Einsteinian relativity, as well as a later treatise on the idea of indeterminacy in quantum mechanics.) As for Heidegger, his membership of the Nazi party is still in the future as the book closes, and so Eilenberger absolves himself from having to address the thorny question of what that episode means (if anything) for an assessment of his philosophy.  

Read more...

Recommended Reading

Time of the Magicians:
The Invention of Modern Thought, 1919-1929

Source: Spectator.co.uk

16 of the best maths books 2020 | Reading lists - BBC Focus Magazine

The best books to help you understand the maths and statistics that govern life here on Earth by BBC Focus Magazine. 

Photo: Jimmie via Flickr

Maths. As a word, it may bring up terrible memories: row upon row of algebra equations, hours of precious childhood spent on confusing and complex sums. Even in our adult lives, some of us avoid using maths wherever possible – even physicists opt for research that has fewer mathematical equations on the page.

But it doesn’t have to be that way. These easy-to-understand non-fiction books will help you get a grip on geometry and be more confident using cosine, sine and tan… or they might just help you help with GCSE maths homework. Some will also shed light on the history of maths, through memoir or even fiction.

Read more... 

Source: BBC Focus Magazine

Beyond Socrates and Aristotle: Philosophers you might know | Greek Studies - Neos Kosmos

When citing Greece’s contributions to world culture – from democracy to theatre and athletics – philosophy is one of the first that come to mind by Neos Kosmos.

Busts of great philosophers.
Photo: PXFUEL

Unsurprisingly, its name is Greek, from philosophia meaning “love of wisdom”.

Unlike other practices and bodies of knowledge, such as architecture and visual arts, which were perfected but not invented by Greeks, Greece is believed to be the birthplace of Western philosophy, in that the notion of philosophy as the study of the basic axioms that comprise knowledge was actually created there.

There are of course older philosophical systems in the world, such as the Hindu Samkhya tradition, but they are generally believed to have developed independently, and there is no substantial historical evidence of contacts and exchanges between these cultures -until the times of Alexander the Great- that would suggest an influence of one over the other. Similarities between Hindu and early Greek thought are therefore generally considered incidental.

When thinking about Greek philosophy, certain names inevitably crop up. Figures like Socrates, Plato and Aristotle – each a disciple of the former- are held to universal acclaim and may often be referred to even by people completely unfamiliar with the study of philosophy...

We begin with the pre-Socratics, the philosophers that either preceded Socrates, or were his contemporaries but developed completely independent schools of thought with no influence from him. All the philosophers that followed Socrates, Plato and Aristotle were to some extent influenced by some or all of them, even if only by their differences.

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Source: Neos Kosmos and Greek News Agenda

Digital Credentials: A Better Way Capture And Communicate Learning | Education - Forbes

There is an invention opportunity to better credential units of learning. Listed are six opportunities to better capture and communicate learning, notes Tom Vander Ark, Building the future of learning. 

Learner's Lifelong Learning Journey
Photo: Badgr.com

For hundreds of years we’ve relied on time as the primary measure of learning. Sit through a class and get credit. Accumulate enough credits and you get a degree. But a list of classes passed (a transcript) tells little about what a learner knows and can do. Add grades and the reputation of an institution and you get a little signaling value but the standard high school or college degree is a terrible communications of capabilities. 

 

There is an invention opportunity to better credential units of learning, to open up individual learning pathways, to better communicate capabilities, and to reduce friction in talent transactions. 

The pandemic is accelerating this shift to verified credentials...

There are six opportunities to better capture and communicate learning.

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Source: Forbes 

Creating an environment for effective learning measurement | Measurement - Chief Learning Officer

If we truly embrace our people as our most valuable corporate asset, invest in them as we would to maintain and grow physical assets, and surround them with opportunities to acquire new skills that directly align with corporate goals, the return on learning investment will naturally find its place among our top business KPIs, according to Andrew Temte, president and global head of corporate learning at Kaplan North America.

Creating an environment for effective learning measurement
Photo: Adobe Stock

I’ve spent most of my working career within the realm of professional education, focused on helping individuals achieve “yahoo!” moments in their lives through the attainment of industry-recognized licensures, designations and certifications. In this corner of the educational landscape, the measurement of learning efficacy boils down to a fundamental relationship between the credential and its ability to signal workplace competency, which ultimately unlocks new opportunities and improves the recipient’s lifetime earning power. In relative terms, the progression is simple: The learner does research (in consultation with mentors) and decides on the credential that fits with their career aspirations, fills any minimum requirement gaps, registers for the exam, studies a prescribed curriculum and passes the test. The process is deemed successful as doors open and pay and responsibility improve. Examples of industry-recognized credentials include CPA, CFA, PMP and a host of other acronyms.

In contrast, learning and development within an organization is more likely to be viewed as a cost and not an investment due to the lack of direct evidence that learning interventions lead to a demonstrable improvement in skill and competency for the learner or cohort and that skill improvement is tied to better organizational performance...

Changing the equation

One of the reasons learning takes a backseat to more tangible areas of the business is that it’s deemed to be unmeasurable. As a result, companies don’t invest what they should to maintain and grow their most valuable asset. Instead, learning is viewed as a cost and is the first thing to go when times get tough.

How can we align our actions and words with regard to our most valuable asset? How can we change the perception of learning and begin viewing it as an investment?

Read more...

Source: Chief Learning Officer

Number 10 cherry-picked 'spurious' Covid data to justify England's second lockdown and may have intended to frighten the public, top Cambridge statistician claims | Covid-19 - Daily Mail

• Sir David Spiegelhalter suggested the Government tried to 'manipulate' Britons
• Cherry-picked 'worst-case scenarios' to 'instill a certain emotional reaction'
• No10 lambasted for its apocalyptic graphs and spurious data shown to public

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Eminent statistician Sir David Spiegelhalter suggested the Government tried to manipulate Britons rather than genuinely inform them on the true scale of the crisis. 

The 4,000 deaths per day scenario was based on the assumption that there would be 1,000 per day by the start of November. There are on average 441 occurring across the UK as of November 23

Number 10 cherry-picked 'spurious' coronavirus data to justify England's second lockdown and may have intended to frightened the public, according to one of Britain's top experts.

Eminent statistician Sir David Spiegelhalter said ministers had 'broken pretty much every code of conduct' by choosing only to show worst-case scenarios, which were often based on out of date data.

The Cambridge professor told MPs today: 'I don't want to ascribe motivation to anyone of course. But if someone was really trying to manipulate the audience and frighten them and persuade them that what was being done was correct, rather than genuinely inform them, then this is the kind of thing they might do.'...

What I'm objecting to strongly is the fact such spurious data and graphs were being presented to the public as a justification for the decisions that were being made.

'You didn't need that graph, you just needed quite short-term projections to tell something needed to be done or we could be in real trouble very quickly.

'There is good data available and yet at some point the need to persuade people, to instill a certain emotional reaction in people seems to take over at really quite a high level of decision making. I think it's quite unfortunate.'...

The statistician was giving evidence to the House of Commons Public Administration and Constitutional Affairs Committee today.

Read more... 

Source: Daily Mail

Quantum magic squares | Mathematics - Mirage News

 /Public Release. The material in this public release comes from the originating organization and may be of a point-in-time nature, edited for clarity, style and length. View in full here.

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The magic of mathematics is particularly reflected in magic squares by Mirage.

Detail from Melencolia I by Albrecht Dürer
Photo: National Library of Spain CC BY-NC-SA 4.0

Recently, quantum physicist Gemma De las Cuevas and mathematicians Tim Netzer and Tom Drescher introduced the notion of the quantum magic square, and for the first time studied in detail the properties of this quantum version of magic squares.

Magic squares belong to the imagination of humanity for a long time. The oldest known magic square comes from China and is over 2000 years old. One of the most famous magic squares can be found in Albrecht Dürer’s copper engraving Melencolia I. Another one is on the facade of the Sagrada Família in Barcelona. A magic square is a square of numbers such that every column and every row sums to the same number. For example, in the magic square of the Sagrada Família every row and column sums to 33...

In a new paper in the Journal of Mathematical Physics, Tim Netzer and Tom Drescher from the Department of Mathematics and Gemma De las Cuevas from the Department of Theoretical Physics have introduced the notion of the quantum magic square, which is a magic square but instead of numbers one puts in matrices.

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Source: Mirage News

How To Improve Your Software Development Team? | Tech - SociableBlog

Rebecca Jordan, social media and content marketing strategist explains, Software development is a complex and volatile job that requires a combined effort from various individuals in order to succeed. 

How To Improve Your Software Development Team?
Photo: SociableBlog

With rapid technology advancement, volatile requirements, tremendous competition in the industry, and a rise in customer demands, it can be a challenge to increase performance and maintain high levels of productivity in your software development teams.

The good news is that you can boost overall team productivity and performance without extending your working hours or hiring more people. Besides developers, an effective software development team often involves different kinds of specialists including UI/UX designers, business analysts, project managers, quality assurance specialists, and marketing professionals. As such, teamwork has to be a prime focus of your software development project to drive innovation, increase efficiency, and encourage creativity.

Here are some steps you can take to not only minimize challenges but also improve the performance and productivity of your software development team.

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Source: SociableBlog

Software Development in a DevOps World | DevOps Culture/Practice - DevOps Online

Throughout the software development process, developers are usually required to spend a lot of time fixing bugs and vulnerabilities, so as everything works as planned for the delivery by constance drugeot.

However, with DevOps practices, these problems can be a lot easier to manage and secure.

That is due to the fact that software that uses DevOps practices are constantly maintained and improved, making it faster to deal with errors and problems. Hence, developing software within a DevOps world brings many advantages when looking at security and speed...

DevOps also help developers to better fix vulnerabilities, by implementing the right processes and procedures. However, cybercriminals become more and more cunning and adapt their strategy according to the new releases, so it is a never-ending loop...

Conclusion

With the DevOps model, organizations are ensuring the security of their products and infrastructures. By automating security in the development process, software developers can deliver safer products quickly.

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Source: DevOps Online