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https://education.gov.scot/improvement/learning-resources/numeracy-in-expressive-arts/

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This document can be used in a variety of ways. The exemplars can be used to support practitioners to consider real and relevant contexts which could be used to develop learners' skills between numeracy and expressive arts. It can also be used to support interdisciplinary learning through planning of particular projects or school events.

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A collection of free videos and downloadable worksheets to help adult learners improve reading, writing and numeracy skills.

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to skillsworkshop, the home of free adult literacy, numeracy and Functional Skills resources since 2001.

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Motivating and engaging students in FE maths

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Motivating and engaging students in FE maths

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Mathematics in Music (Lesson Plans & Printables)

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Help students find the connection between mathematics and music with these lesson plans and worksheets.

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Teaching health and safety - risk assessment calculations

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Embedding Functional Skills Maths in Acting

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Embedding Functional Skills Maths in Acting

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Embedding Functional Skills maths into Acting. 

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What I want you to learn Effective ways to embed maths and spark learners interest. We still have a way to go, but our reforms to English and Maths will raise the aspirations of learners and improve the quality of teaching”. Boles (2014:1) When embedding the skills during

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Your Money Matters - helping explain maths through financial education

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Your Money Matters - helping explain maths through financial education

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All 3,400 state-funded secondary schools in England will get 100 free copies of a financial education textbook this week, thanks to a £325,000 donation from MoneySavingExpert.com founder Martin Lewis.

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First-ever financial education textbook lands in schools - funded by Martin

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All 3,400 state-funded secondary schools in England will get 100 free copies of a financial education textbook this week, thanks to a £325,000 donation from MoneySavingExpert.com founder Martin Lewis.

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Great Ted Talk: Understanding the world with Maths?

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Great Ted Talk: Understanding the world with Maths?

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Math is the hidden secret to understanding the world | Roger Antonsen

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Math is the hidden secret to understanding the world | Roger Antonsen

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Embedding English and Maths

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Ten mainstream movies that feature math in the premise

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Ten math based movies where math or its principles are part of the plot or premise of the movies, and where without math the movie would lose its edge.

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Sarah K-B has this in her bag, so you can take a look on Tuesdays and Thursdays

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Buy English and Maths in Your Pocket by Dan Williams (ISBN: 9781326275631) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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The Potential Benefits of Using Film as Part of Literacy Lessons

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The Potential Benefits of Using Film as Part of Literacy Lessons

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look at the ref list too

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Potentially a good approach for visual and kinaesthetic learners

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adding fractions visually: colouring workbook

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Adding Fractions Visually: Colouring Workbook

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Buy Adding Fractions Visually: Colouring Workbook 1 by Eng S Jama (ISBN: 9781726331043) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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Percentages in every day living.
Karen Lawrence

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~An overview of basic business math skills provides the foundation of arithmetic, mathematics and measurements used in common business and industry practices. Further into the basic business math program, trainees build on these skills and delve into algebra, geometry, and trigonometry, learning to apply these topics to their day-to-day work.

Popular with anyone new to a workplace environment, this valuable program helps trainees to:

Add, subtract, multiply, and divide whole numbers, fractions, and decimals.

Measure lengths and distances.

Calculate areas, volumes, and weights.

Measure temperature in Fahrenheit and Centigrade, convert from one system to the other, and select the appropriate type of thermometer to be used at given temperatures.

Perform the basic arithmetic operations with signed numbers and signed terms, and transform and solve an equation.

~

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Supporting Maths & English in Post-14 Education & Training by Jo-Ann Delaney and Amanda Cope

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Supporting Maths & English in Post-14 Education & Training by Jo-Ann Delaney and Amanda Cope

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supporting maths & english in post-14 education & training (uk higher education humanities & social sciences education)

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language teaching & learning (other than elt)

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Supporting Maths & English in Post-14 Education & Training (UK Higher Education Humanities & Social Sciences Education)

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Buy Supporting Maths & English in Post-14 Education & Training (UK Higher Education Humanities & Social Sciences Education) UK ed. by Jo-Ann Delaney, Amanda Cope (ISBN: 9780335264100) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

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http://passyworldofmathematics.com/mathematics-of-photography/

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Inclusion for programming, but also in design concept work.

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Math is an absolute fundamental foundation to successful game development and game design.

Math is everything when it comes to games. From having the ability to calculate the trajectory of an Angry Bird flying through the sky, to ensuring that a character can jump and come back down to the ground -- without the help of mathematics, games simply wouldn't work.

A character wouldn't be able to walk up a slope, slide down a slide, fire a bullet from a gun, or even jump without the help of the mathematics.

The most basic of games use some form of math to the most complex of games.

Math is essential to the production of games. It is the flour to the cake that game developers are trying to bake. Without it, the cake wouldn't rise.

Math is used in every aspect of game development, including art. Maya is a math based program that plots out the vertices and normals in mathematical form while the artist just uses a tool that allows them to create stunning 3d graphics without worrying about math. Simply put, you could model Godzilla in notepad and push it into Maya, if you knew were to plot the points in numerical form (which is extremely difficult).

However, a lot of the math is computed at runtime and handled by the game engines that render back face culling, and the other nitty gritty things that would be too cumbersome to do without the use of using an engine to alleviate the math calculation portion at runtime.

A lot of math in gameplay scripting is fairly simple, but math used in game engine architecture is far more complex and a lot more taxing mentally. Math in game development is simulated either by the developer or handled by the engine at runtime by running computations to calculate the operation that is needed.
Here are some examples.

Ocean waves crashing nicely against your boat in ASC: Black Flag? Math.

Those bullets flying over your head in Call of Duty: Ghosts? Math.

That fancy UI animation that's procedurally generated? Math.

Sonic being able to run fast and Mario being able to jump? Math.

Drifting around that corner in Need for Speed at 80mph? Math.

Snowboarding down a slope in SSX? Math.

That rocket blasting off in Kerbal Space Program? Math.

Here's an expanded example using Mario's jumping mechanic.

When Mario jumps he isn't just going straight up and down on the Y-Axis but rather creating a parabola to jump up and down. It would be quite silly for Mario to beam up and then beam across on the X axis and then straight down on the Y-axis. Certainly, it would look goofy and not quite right.

Another example for instance is, Kerbal Space Program; a game that relies heavily on math. The entire game is pretty much all math when you think about it.

Newtonian physics are heavily simulated in KSP. Without the use of math in KSP, the game wouldn't be able to do much. Your rocket wouldn't be able to get off the ground and out of the atmosphere into space. The simulations in the game would be boring, and quite frankly the game wouldn't be able to do much. A rocket wouldn't be able to get off the ground because thrust doesn't exist, and or be able to pitch,yaw,and roll when in the sky.

In game development we're allowed to get away with faking math so that it is to work with the design of a game, but a lot of the time the math in games mirror real world physics and math principles. Math helps out with calculating everything from what a particles velocity should be, to the spread of a shotgun blast, to using gravity to bring a ball back down to the ground, and vice versa. These are all very basic math principles that a lot of games use. And their is still much more sophisticated and advanced math used in AAA games that I haven't covered.
What are the main branches of math used in game development?

Algebra

Discrete Mathematics

Trigonometry

Calculus

Linear Algebra

Applied mathematics

And much much more....

Some of the most important math used in games.

Dot Product, Cross Product.

Scaling Vectors, Unit Vectors, and Vectors.

Reflection, Matrices.

Scalar Manipulation.

COS,SIN,TAN.

Delta Time.

Domain and Range.

Most of these math topics are all used all together in very advanced games. But, in simpler games the math may only require trig and algebra, to a handful of math using only scalar multiplication.
How is math used in game programming and game scripting?

Math in game programming can be as easy as adding x + y, to calculating and manipulating cos, sin, tan with added variables while stringing it to your function, all the while their is still much much more advanced ways to use math in games.

Let's take a look at creating a constant variable called MAX_SPEED and MIN_SPEED (vectors) and adding that to the game update loop while adding a speed to a spaceship so that it can move, to creating an array that runs an algorithm that loads a random level every time the game is played, to simply altering a child's X (vectors) in the update loop, or to adjusting the angle of rotation once it hits a wall (reflection) on a spin wheel when a ball hits it. Doing any sort of basic thing, such as movement in a game will incorporate some form of math.

Math is essential ingredient that is necessary to the production of games. Without the use of math in games we would just have pretty art that's semi-interactive. Math adds a whole new element to entertainment by blending the sciences and arts into a whole.

With that being said, mathematics allows games to do incredible things that the real world cannot simulate by allowing new ways for the game script and engine to handle calculations on the fly that would not be feasible to do in the real world. So next time when you question your math teacher if you're going to ever use "Algebra" in the real world when you're done with your studies, you sure will especially if you pursue a career in game development.
What can math do in game design?

Fluid water simulation.

Animation.

Algorithms.

Game engine architecture.

Gameplay scripting. (walking, shooting, jumping)

Analytics and data mining. (analyzing players interaction)

Timers programming (delta time, etc).

Physics programming (inertia, friction, etc).

Graphics/Shaders programming (matrices,etc).

Path finding/AI.

Procedural level design.

Handling Polygon rendering.

And much much more.

The things listed above are only but a fraction of what math is able to help out with in game development and game design.
Here are some books I recommend reading.

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How is math used in video game designing and programming?

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Answer (1 of 10): > Math is an absolute fundamental foundation to successful game development and game design. Math is everything when it comes to games. From having the ability to calculate the trajectory of an Angry Bird flying through the sky, to ensuring that a character can jump and come ba...

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Calculating volume and area

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Math Antics | Math Video Lessons for Free plus more

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ildiko

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The Tutor Pages - Art and Design Tutor Article: Embedding key skills into arts teaching

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Ildiko

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Teaching maths and art - Continuing Professional Development - UAL

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Learn how to embed maths into your creative teaching strategies at this one-day CPD event from UAL Awarding Body

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Embedding maths into dance
Clip from mathsdance.com

Who look at using dance to understand mathematical problems.
Vic

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Why should you choose between maths and dance when you can do both at the same time? To find out more, visit www.mathsdance.com, join us on facebook Maths Dance, LinkedIn MATHS DANCE and/ or follow @Maths_Dance on twitter.

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How to embed Maths within Functional Skills English

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How to embed Maths within Functional Skills English

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http://www.anngravells.com/information/embedding
AP

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http://blogs.arts.ac.uk/ualawardingbody/2016/10/26/the-benefits-of-teaching-maths-with-art-and-design/?_ga=2.179431588.1261162049.1506604889-339695534.1506604889

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https://denobis.wordpress.com/2014/05/19/math-in-the-film-industry/

Bee

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Maths and Photography - Camera sensors sizes and quality of image.

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Maths and Photography - Camera sensors sizes and quality of image.

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http://www.techradar.com/how-to/sensor-sizes-explained-what-you-need-to-know

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Embedding maths within Sound Engineering

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Embedding maths within Sound Engineering

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Dan Tregenna
https://mathspig.wordpress.com/tag/sound-engineers-need-math/

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Embedding maths within Functional Skills English

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Embedding maths within Functional Skills English

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Shocking sugar levels in High Street hot drinks

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Topical resource based on a news story. Reading comprehension at 2 levels (E3 and L1/L2) plus two writing extension activities with writing frames. Some embedded maths (including a chart in the L1/L

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FE and other post-16 tutors are increasingly being asked to embed and develop English and maths skills in their lessons, and the revised common inspection framework from Ofsted places an increased emphasis on this. You may lack confidence or the required background knowledge to do this, or be struggling to find ideas that will engage and motivate your learners.

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Stephen Levenson

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An Introduction to Computer Programming and Mathematics : nrich.maths.org

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This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

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From Hannah R

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Basic math skills are a must for a business owner.

Creatas/Creatas/Getty Images

Business ownership requires more than skill in creating a product or talent at providing a service. Overseeing the finances of your company is key to survival and success. Understanding basic business math is necessary for profitable operations and accurate record keeping. Knowing how to add, subtract, multiply, divide, round and use percentages and fractions is the minimum you need to price your product and meet your budget. If math is not your strength, partner with someone who can take over that role or hire a trusted employee to help your operation stay in the black and grow responsibly.

Calculate Production Costs

Before you formally establish your business, you must estimate the cost to manufacture or acquire your product or perform your service. Adding all expenses associated with making or buying items helps you realize if you can be competitive with other companies and profitable enough to sustain your business and make a reasonable income. In addition to the standard costs of production, such as materials and machinery, add accompanying expenses, such as shipping, labor, interest on debt, storage and marketing. The basis to your business plan is an accurate representation of how much you will spend on each item.

Determine Pricing

To ensure you can operate your business and produce enough cash flow to invest into your enterprise, you must charge enough for your product to be profitable. Markup is the difference between your merchandise cost and the selling price, giving you gross profit. If your operations require a large markup, such as 70 percent, you may not be competitive in your industry if other companies sell the same items for less. Once you have determined your markup, one way to calculate the retail price is to divide using percents or decimals. For example, if a product costs $10 to produce and your markup is 35 percent, subtract .35 from 1 (or 100 percent), which gives you .65, which is 65 percent. To calculate the price of your product, divide 10 by .65, which rounds to $15.38.

Measure Profits

If you want to determine the net profit for a certain time period, you will need to subtract returns, costs to produce an item and operating expenses from your total amount of sales, or gross revenue, during that time. Discounts on products, depreciation on equipment and taxes also must be calculated and subtracted from revenue. To arrive at your net profit, add any interest you earned from credit extended to customers, which is reflected as a percent of the amount each person owes. Your net profit helps you understand if you are charging enough for your product and selling an adequate volume to continue to operate your business or even expand.

Analyze Finances

To analyze the overall financial health of your business, you will need to project revenue and expenses for the future. It's important to understand the impact to your accounting records when you change a number to reflect an increase or decrease in future sales. Estimating how much an employee affects revenue will indicate if you can afford to add to your staff and if the profits realized will be worth the expense. If a competitor starts selling a cheaper product, you may need to calculate the amount by which your volume must increase if you reduce prices. You may need to know if you can afford to expand your operations to improve sales. Using basic business math to understand how these types of actions impact your overall finances is imperative before taking your business to the next level.

About the Author

Carol Deeb has been an editor and writer since 1988. Her work has appeared in magazines, newspapers and online publications, as well as a book on education. Deeb is a real-estate investor and business owner with professional experience in human resources. She holds a Bachelor of Arts in English from San Diego State University.

Photo Credits

Creatas/Creatas/Getty Images

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The Importance of Basic Math in Business

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Business ownership requires more than skill in creating a product or talent at providing a service. Overseeing the finances of your company is key to survival and success. Understanding basic business math is necessary for profitable operations and accurate record keeping.

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Joe Hiscock

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The world around us is full of relationships, rhythms, correlations, patterns. And mathematics underlies all of these, and can be used to predict future outcomes. Our brains have evolved to survive in this world: to analyse the information it receives through our senses and spot patterns in the complexity around us. In fact, it's thought that the mathematical structure embedded in the rhythm and melody of music is what our brains latch on to, and that this is why we enjoy listening to it. It is perhaps not surprising then that there is a great deal of overlap between mathematics and the art that our brain finds so pleasing to look at.

This article is a whistle-stop tour of some of the types of art with a strong mathematical component, or conversely where a mathematical visualisation has an astonishing beauty.

Geometric patterns

The "Flower of Life" pattern

Simple arrangements of mathematical figures, like circles and triangles, have been extensively used in decoration throughout history. For example, the "Flower of Life" can be seen on the Temple of Osiris at Abydos, Egypt, which dates back about 5,000 years. This pattern, as seen to the right, consists of an array of circles positioned in rows, each one centred on the circumference of circles in the neighbouring rows. (This arrangement provides an interesting geometric problem to solve. If each circle has a radius of 1 unit, can you show that the rows are √3/ ₂ apart? Hint: think about the type of triangle formed by the centre-points of three neighbouring circles, and your sine and cosine rules about triangle sides).

Mosques throughout the world are decorated with extremely elaborate geometrical patterns of simple shapes. This is because Islamic art (in contrast to that of other faiths, with their murals, paintings and stained glass windows) traditionally avoids the depiction of people and animals, and instead involves repeating geometric patterns. These regular arrangements are said to symbolise the divine order of the Universe. However, the artist often includes a deliberate mistake in acknowledgement of the belief that only Allah is truly perfect.

The Golden Ratio

The ancient Greeks did some of the finest maths in history - we owe much of our understanding to them. One of the numbers that particularly interested them is known as the Golden Ratio. A rectangle constructed with sides in proportion to the ratio of 1 to 1.618 to 3 decimal places (to be precise, ) has a very interesting property. Removing the largest square contained in the rectangle leaves a smaller rectangle, with exactly the same proportions as the original. This means that you can keep on removing squares to leave smaller and smaller rectangles. Joining up the corners of these rectangles produces a spiral that has been named the Golden Curve due to its graceful aesthetic look.

The Golden Curve

The value 1.618 is itself very curious. It was discovered by the Greeks as the positive solution to the basic quadratic equation x ² - x - 1 = 0. The ratio of successive terms of the Fibonacci sequence, where each new term is the sum of the two previous (i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...), also tends towards this value of 1.618.... This series turns up throughout nature, from the number of petals in a flower, to the pattern of seeds in Sunflowers to the swirl in a Nautilus shell.

The Greeks appreciated the special nature of the Golden Ratio, and thought that objects in this proportion were particularly pleasing to the eye. It is said that they used it to ensure the beauty of statues and architecture, for example in the dimensions of the Parthenon. This practice was apparently passed down through history, so that even the figures in Leonardo Da Vinci's paintings, or Michaelangelo's David are proportioned according to this ratio. You can find out more about the use of the Golden Ratio in art in The golden ratio and aesthetics from a previous issue of Plus.

However, although there is strong support for the presence of this Fibonacci "Golden" ratio in nature, whether Ancient or Renaissance artists really did use it in their work or whether it is only a numerological coincidence is much more contentious. In fact, recent psychological experiments have failed even to show that people have any preference for this proportion, compared to either "thinner" or "squatter" rectangles. There is a very interesting article by Keith Devlin on the facts and fictions of the Golden Ratio in art on the website of the Mathematical Association of America.

Geometric abstractionism

Piet Mondrian was one of the founding members in 1917 of a Dutch art movement called De Stijl (meaning "The Style") or neo-Plasticism. Mondrian's style of painting involved the use of strictly horizontal or vertical black lines to create a grid of rectangles, some of which were filled in with black or white, or vivid red, blue or yellow. You can see an example of Mondrian's work at the website of the Museum of Modern Art in New York.

Mondrian believed that, despite their complexity and variability, natural scenes are composed of basic components and regularity. So he tried to create faithful reproductions by painting only these fundamentals and their relationship with each other, using only the prime colours and elements of geometric mathematics - straight lines, right angles and quadrangles - to create his reflection of reality.

Abstract paintings from graphs

Crossing at the Left Border, by Margaret Leiteritz

Margaret Leiteritz was always intrigued by the graphs in her scientific journals and books about chemical engineering. She was fascinated by the way that a simple line on a graph could represent something real about the energies and motions of the universe, such as combustion or viscosity of a liquid, as well as the innate aesthetic appeal of many of the curves. Between 1961 and 1974 Leiteritz produced a series of "painted diagrams". One piece from this period is named Crossing at the Left Border, which she painted from a graph labelled in the paper only as "Figure 13: Separation as a function of flow rate with plate spacing as parameter". It's amazing that something with such a dry and unimaginative name inspired such a colourful and dynamic piece of art.

Tessellations

M.C. Escher's "Regular division of the plane".All M.C. Escher works © 2002 Cordon Art - Baarn - Holland (www.mcescher.com).

All rights reserved. Used by permission.

Maurits Cornelis Escher (1898-1972) is well known for his graphic art. He enjoyed playing with aspects of surfaces and reflection (including spherical mirrors), perspective, symmetry, and impossible figures such as the paradoxical staircase depicted in Ascending and Descending. He sometimes included polyhedra in the background of his drawings, and was particularly interested in mathematical curiosities such as the Möbius Strip, a surface with only one side. He also produced a great number of tessellating patterns composed of irregular shapes. You may have learned at school that only certain regular polygons can be repeated indefinitely and all fit together without any gaps - triangles, squares and hexagons can make tiles, but pentagons cannot. Escher made an art form out of colourful patterns of tessellating reptiles, birds, fish and even crabs and sea-horses.

Origami

Origami is the Japanese craft of creating wonderful three-dimensional shapes and models solely by folding paper - usually a single square sheet ( ori meaning folded and kami meaning paper). The links between this ancient art and mathematics are profound. If you unfold a finished model you will see a complex geometrical pattern of creases made up of triangles and squares, many of which will be congruent (because they were produced by the same fold). The construction step known as a "push fold" is mathematically equivalent to bisecting an angle.

The regular polyhedra. Image used by permission of Polycell

Maths classrooms are often decorated with models of the nine "regular polyhedra". These are the three-dimensional solids that have every face the same. Five of them are convex, that is, the straight line joining any two points lies entirely inside the solid. These are often known as the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron. The other four were not known to the Greeks, and are sometimes known as the stellated (starlike) regular polyhedra. The classroom models are usually made from card with scissors and glue, but they can also be made by origami. In fact, mathematicians have been able to prove not only that any polyhedron can be constructed by origami, but also that any outline drawn with straight lines (such as a star symbol *, or arrow →) can be cut out from a sheet of paper using a single scissor cut, once the sheet has been folded in the appropriate way.

Anamorphic Art

The Ambassadors (1533), Holbein

"Anamorphis" is a form of art that was first experimented with during the Renaissance and became particularly popular during the Victorian era. It involves distorting an image so that it is unrecognisable unless viewed in the right way. For example, Hans Holbein's The Ambassadors (1533), at the National Gallery in London, contains a skull (symbolising the transience of life) that has been grossly stretched. It only becomes recognisable when viewed from a very oblique angle, by standing practically alongside the left-hand edge of the painting.

Anamorphic art is a good demonstration of the mathematics of transformations. Translations, rotations and reflections don't tend to distort an object in interesting ways, but stretching along one axis (like in The Ambassadors) is a popular method. However, another very striking effect is produced when an image is transformed through an "inverse curve". If the curve used is a circle then the image only becomes recognisable in the reflection of a cylindrical mirror. One good example is "The Well", drawn by István Orosz (1998), which contains a portrait of Escher (you can see a copy of this image and the hidden portrait at planetperplex). The image shown to the left is of an inverted chessboard that only appears normally if a cylindrical mirror is placed in the gap in the centre.

Fractals

A fractal is usually defined as a mathematical structure that exhibits some sort of "self-similarity", meaning that if you zoom in on one, the same type of structure will keep appearing. For example, a fern leaf is built up of leaflets and fronds with the same reiterative structure. They are also often defined as shapes that have fine detail at all scales, and it is this combination of repetition and intricacy that makes them so aesthetically interesting.

When the sensitivity of a complex system to small changes is mapped on the plane, the result is often a fractal. When this map is colour-coded, the result can be strikingly beautiful. The "Lyapunov Exponent" fractal on the left is one example, and you can find out more, and see some more beautiful images, in Extracting beauty from chaos from issue 9 of Plus.

Minimal energy surfaces

A rope hung between two points, like a clothes drying line, describes a particular mathematical curve. It is sagging under its own weight, but is also constrained because the rope cannot stretch much. So the curve produced is a compromise - it sags as low to the ground as it can get. The rope is said to have found a "minimum energy solution" (in this case it is potential energy that is being minimised).

Minimisation problems can also be solved in three dimensions. The spherical shape of a soap bubble is due to all the molecules in the surface attracting each other and pulling the thin film into the smallest possible area. A raindrop on a leaf is under further constraints and the resultant "minimal energy surface" is distorted into a flattened droplet shape.

Mathematicians have used computers to work through the same equations that are solved by nature, but given them much more complicated constraints. The picture to the left shows the surface that would be adopted by a soap bubble formed within a cube connected to its neighbours, if it never popped and wasn't subject to gravity.

Some artists have appreciated the beauty of such forms and incorporating them into their work. For example, Bathsheba Grossman, who has a maths degree from Yale and a Masters degree in sculpture, describes herself as an explorer of the region between art and mathematics. Her "Antipot" sculpture is an example. You can find out more about Grossman and her work at her website.

This article can give only a brief glimpse of the enormous region of overlap between mathematical patterns and processes, and the world of art and aesthetics. A web search reveals many more examples, and it would be well worth keeping your maths hat on when you visit a gallery....

About this article

Lewis Dartnell read Biological Sciences at Queen's College, Oxford. He is in his second year of a four-year combined MRes-PhD program in Modelling Biological Complexity at University College London's Centre for multidisciplinary science, CoMPLEX. In 2003 he came second in the THES/OUP science writing competition, and in 2004 he came second in the Daily Telegraph/BASF Young Science Writer Awards. You can read more of Lewis's work at www.ucl.ac.uk/~ucbplrd.

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The world around us is full of relationships, rhythms, correlations, patterns. And mathematics underlies all of these, and can be used to predict future outcomes. Our brains have evolved to survive in this world: to analyse the information it receives through our senses and spot patterns in the complexity around us.

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Functional Skills Maths within a reading compre

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Functional Skills Maths within a reading compre

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https://www.theguardian.com/teacher-network/teacher-blog/2013/jan/16/teaching-maths-poetry-oulipo-classroom

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https://www.mymathdone.com/top-ten-math-movies/

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Creative Approaches to Maths Across the Curriculum

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Creative Approaches to Maths Across the Curriculum

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Creative Approaches to Mathematics Across the Curriculum : nrich.maths.org

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Suggestions for teachers about exploring maths in different contexts: art, history and so on

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Kayleigh Russell

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Teaching maths and art - Continuing Professional Development - UAL

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Learn how to embed maths into your creative teaching strategies at this one-day CPD event from UAL Awarding Body

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Embedding numeracy in sport/physical education

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Embedding numeracy in sport/physical education

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Developing Functional Skills in Art and Design (Secondary)

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Wuzzit Trouble, from InnerTube games, is new in the app store this week.

Innertube Games is a learning-games studio founded by four enthusiasts, including the world famous Dr. Keith Devlin: the NPR Math Guy and Stanford Mathmetician. It has taken InnerTube two years from forming the company to release their first game: Wuzzit Trouble.

Although they consider it a soft release, I'm excited to let my kids play Wuzzit Trouble in its current iteration (and to play it myself!). The game fulfills one of the great promises of game based learning: the ability for a game to teach multiple skills simultaneously. That is not to say that everyone who plays will walk away having learned a multiplicity of skills, but rather that the game offers puzzles that work on multiple levels. Therefore, players are able to practice and develop math skills and comprehension appropriate to their particular age and skill level. Innertube puts it this way:

InnerTube Games does not build video games to 'teach mathematics.' Rather, we build instruments which you can play, and we design them so that when you play them, you cannot fail to learn about mathematics. Moreover, each single game can be used to deliver mathematical challenges of increasing sophistication.

Wuzzit Trouble has a unique interface that's based on turning gears. Devlin describes it as an "instrument on which to play mathematics." He likens it to piano keyboard: you can't help but learn something about music if you sit down and tinker. Manipulating the Wuzzit Trouble's game mechanics is enacting the functions of arithmetic, in the same way that pressing a piano's key creates tone. Put those functions together and you're doing math. Put those tones together and you've made music.

I love the instrument analogy because I'm often explaining to my students why the Ancient Greeks saw math and music as part of the same realm--that area of experience that belonged to the god Apollo. Of course, the relationship has to do with intervals. But both math and music are also related to Apollo's other domains, such as light, prophecy, healing, etc. The connection has been hard to understand from the rigidly measured viewpoint that has dominated Western thinking since Nietzsche inadvertently cemented the Apollonian into strict opposition with the Dionysian in The Birth Of Tragedy. From Apollo's standpoint, space and interval reign. And where we focus on distance, it is hard to see the way things touch, or blend into one another. Unfortunately, this dichotomy is pervasive in education. As Cathy Davidson writes in her book, Now You See It:

Everything about school and work in the twentieth century was designed to create and reinforce separate subjects, separate cultures, separate grades, separate functions, separate spaces for personal life, work, private life, public life, and all the other divisions.

Then the internet came along. Now work increasingly means desktop computer. Fifteen years into the digital revolution, one machine has reconnected the very things--personal life, social life, work life, and even sexual life--that we'd spent the last hundred years putting into neatly separated categories, cordoned off in their separate spaces with as little overlap as possible.

Game based learning will lay the foundation for new ways of thinking, encouraging us to look at the process of learning traditionally Apollonian subjects from a Dionysian perspective.

I asked Keith Devlin to explain some of the great thinking that underlies Wuzzit Trouble, and the pedagogical thinking that permeates the InnerTube vision.
Your book, Mathematics Education For a New Era, argues that video games are the best way to teach math to middle school kids. Can you briefly explain why you feel that way? Mathematics is an activity. It's not stuff you know, it's things you DO (and can do). Natural selection equipped us supremely well to learn actions by actually doing them. In fact, any other way is hopelessly inefficient. eg. Try learning to ride a bike by sitting in a lecture or reading a book - or even watching a video! It doesn't work. The studies of Street Mathematics show that pretty much anyone can become proficient at mathematics if they pick it up in the course of actions relevant to them. If designed suitably, video games are activity simulators with a dopamine reward system. When someone plays ANY game, they are learning something. The challenge for the math educator is to make that learning be about DOING mathematics. You've related math games to a musical instrument, imagining a platform on which you play mathematics. Share some thoughts about how you think about the relationship between a math game and a musical instrument? What I think is truly unique about Innertube's games in the current landscape of math ed video games, is that our games are literally just instruments designed and built to act as representations of parts of mathematics. The mathematics itself is separate. Just as a piano, say, is not music, but can be used to play music. For instance, DragonBox, which you and I both love, is super for helping people master the solution of linear equations. But it cannot go beyond that. (At least, I don't see how it could.) It's locked in to that one specific part of algebra. With Wuzzit Trouble, in contrast, we can add another room of 25 puzzles as often as we want, aiming them at 8-year old learners or 80 year old former Nobel Prize winners. Designing the game as an instrument on which certain mathematics can be "played" means our games are very versatile. As we build our games out we intend to add a feature where players can design their own challenge problems to share with their friends. Teachers too could prepare problem sets that load into our game. I expect that people will come up with ways to embed other parts of number theory into the game. Why did you decide to build Wuzzit Trouble around Integer partitions? The goal was to design the game so that any action in the game was a direct action on numbers: adding, subtracting, or multiplying them, in increasingly sophisticated, algorithmic ways. (Acting on the abstract numbers themselves, that is, NOT by way of a symbolic hindu-Arabic representation. We bypass the standard notation just as a piano can bypass musical notation.) The challenge then was to do so in a way that yielded a fun and challenging GAME, that in its playing required the player to develop and use those increasingly sophisticated thought processes. Integer partitions was simply the best option we could think of. It asks you to look at ways a given integer can be obtained from others using the three basic arithmetical operations. Having built the game and played it, I know just how engaging and challenging it can be. But even though I always felt confident it would work, I have to admit I was surprised at just how well it works as a game concept. One of the things I love about Wuzzit Trouble is that it doesn't dis-empower teachers. Players can learn on their own, but that learning will be enriched with serious instruction. How do you imagine that games like Wuzzit Trouble will change the way math is taught in schools? For the later puzzles in the game (and even more so for some fiendish puzzles we haven't dared include in this first release which is aimed as much as anything at helping us raise money to build further), there is no hope of getting a top score without stopping the game and doing some good-old-fashioned paper-and-pencil algebra. I'd love it if kids get sufficiently hooked that they go along to the math teacher for help. Just think, when there are three cogs, there are 30 choices for each move, so 900 two-move sequences, 27,000 three-move sequences, 810,000 four-move sequences, and 24,300,000 four move sequences, etc. So plain luck is out of the question. A player who wants to solve a three cog puzzle in 4 to 10 moves inescapably has to think mathematically. Trial and error is out of the question. When we have the money, we'd like to prepare a teacher demo version of the game, probably in HTML5 for Web access, absent the glossy front end but with mathematical annotations, that a teacher can use in class for demonstrations. That would also require providing teachers with support: lesson plans, classroom ideas, etc. We felt that the game is the game, and should hold its own among all the other games, and teaching is for the teacher. We did not want to try to do in our game what a good teacher can do SO MUCH BETTER in the classroom. So we see our instruments as resources for teachers, not apps that try to do things for teachers. But we also see them as just plain fun games! In your view, what does game-based learning mean for the future of learning, or the future of schooling in general? When the big supertanker that is systemic education finally gets fully on board, and has seen enough examples of good educational video games to be able to separate the wheat from the chaff (currently it's mostly the latter that is out there), then I think that video games will play a significant role in mathematics education. Video games are a much better representation system for learning mathematics than are symbolic representations on a static page. If the technology had been available in 350BCE, Euclid's Elements would have been a video game. All Euclid's arguments are instructions to perform actions: draw an arc, drop a perpendicular, circumscribe the square, etc. It would be much more efficient, both as a communicative medium and for the student learning, if instead of writing instructions in words, the student was presented with opportunities to perform those ACTIONS. A change in how we teach math will inevitably also change how we think about math, and therefore, what math is--big picture: how will incorporating games like Wuzzit Trouble into school curricula change math and provide new possibilities for mathematical applications? What's next for InnerTube games? We have plans to build out Wuzzit Trouble by adding a lot more rooms of puzzles, each aimed at different audiences, from 8 to 80 years old, of different ability levels. (We will charge for some of those. Our basic philosophy is to provide the basic games for free, so everyone can benefit educationally, and make additional puzzle sets available for a fee so those who simply love the puzzles and will buy as many as we can provide). We will build a data analytics back-end. We designed the game to make that possible, but did not have the financial resources to do it before launch. We will need that back-end for game development, teachers will need it if they want to use our game in class, and education researchers will be able to use it to carry out learning research using our game. (Our super-stellar educational advisory board are eager to start that phase. By being on our board, they have an edge over their colleagues in getting us to put in algorithms to collect the data as they want it!) We have another twenty or so different games that exist in prototypes of various stages of Flash implementation, many of them kids tested, and we want to start building them. In our first year post-launch, we'd like to bring out two more, one based on algebra, the other on geometry - thereby demonstrating that we can span the three basic food groups of mathematics learning. But we can't do any of that without a fairly sizable injection of funding, probably a commercial investment. A video game like ours needs a support staff to handle updates as platforms advance, deal with customer problems, fix bugs, etc., etc. The only way to do that is to generate a revenue stream. Right now, I think our best way to do that is to sell great puzzle sets to older folks - folks like me actually. I pass many hours on long airplane rides doing math-based puzzles. Because we can target our game -- the same instrument -- to kids in school and their grandparents, simply by providing different datasets to generate the individual puzzles, we can take money from the latter and use it to provide free games to the former. I call it the Robin Hood business model. No one is going to get rich in this business. But then, if it were about getting rich, none of us would be in education, would we? Jordan Shapiro is author of FREEPLAY: A Video Game Guide to Maximum Euphoric Bliss and co-editor of Occupy Psyche: Jungian and Archetypal Perspectives on a Movement. For information on his upcoming books and events click here.

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Video Games Are The Perfect Way To Teach Math, Says Stanford Mathematician

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Wuzzit Trouble, from InnerTube games, is new in the app store this week. Innertube Games is a learning-games studio founded by four enthusiasts, including the world famous Dr. Keith Devlin: the NPR Math Guy and Stanford Mathmetician. It has taken InnerTube two years from forming the company to release their first [...]

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When I was a graduate student in art history, I read many explanations of abstract art, but they were invariably inadequate and misleading. So after completing my PhD, I went on to learn the history of biology, physics, and astronomy, and to publish a book detailing how modern art is an expression of the scientific worldview.

Yet many artworks also express the mathematics and technology of their times. To research Math and Art I had to learn maths concepts like calculus, group theory and predicate logic. As a novice struggling to understand these ideas, I was struck with the poor quality and confusing content of illustrations in most educational books. So I vowed to create for my book a set of cogent math diagrams that are crystal-clear visualizations of the abstract concepts.

As a lecturer at the School of Visual Arts in Manhattan, I wrote this book for my students, such as Maria, who told me she was never good at history because she couldn't remember dates, and for Jin Sug, who failed high school algebra because he couldn't memorize formulae. I hope they will read this book and discover that history is a storybook and that math is about captivating ideas.
Here are ten images followed by descriptions:

Throughout history, scientists have discovered mathematical patterns in nature, such as the paths taken by electrons as they flow over the hills and valleys of tiny "landscapes" that are measured in microns (one micron equals one millionth of a meter). Paths of electrons in this digital print were recorded by Eric J. Heller, who studies rogue waves (freak waves, killer waves) on large and small scales. When a wave of electrons flows through a computer, a freak wave in a semiconductor can suddenly threaten the smooth functioning of the device.

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Jim Sanborn (American, b. 1945), Kilkee County Clare, Ireland, 1997. Large-format projection, digital print, 30 × 36 in. (76.2 × 91.4 cm). Courtesy of the artist.

Western mathematics proceeds by increasing abstraction and generalization. In the Renaissance the Italian architect Filippo Brunelleschi invented linear perspective, a method to project geometric objects onto a "picture plane" from a given viewpoint. Three centuries later the French mathematician Jean-Victor Poncelet generalized perspective into projective geometry for planes that are tipped or rotated. Then in the early twentieth century the Dutchman L.E.J. Brouwer generalized Poncelet's projective geometry to projections onto surfaces that are stretched or distorted into any shape-so-called rubber-sheet geometry-provided that the plane remains continuous (with no holes or tears), which is the subject of this photograph. The contemporary artist Jim Sanborn created it by projecting a pattern of concentric circles onto a large rock formation at night from about 1/2 mile away. He then took this photograph with a long exposure at moonrise.

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Reza Sarhangi (Iranian-born American, b. 1952) and Robert Fathauer (American, b. 1960), Būzjānī's Heptagon, 2007. Digital print, 13 × 13 in. (33 × 33 cm). Courtesy of the artists.

Knowledge of ancient Greek mathematics, such as Euclid and Ptolemy, was lost to the medieval West, but Islamic scholars preserved their writings in Arabic translations. In the ninth century, caliphs established the House of Wisdom in Baghdad as a place for scholars to acquire and translate foreign texts in mathematics and philosophy. Ptolemy's thirteen-volume work is known today by the name they gave it, Almagest (Arabic for "the greatest").

Two contemporary mathematicians, Reza Sarhangi and Robert Fathauer, pay homage to the Islamic mathematician Abū al-Wafā' Būzjānī (AD 940¬-98), who worked at the House of Wisdom, where he wrote a practical text, On Those Parts of Geometry Needed by Craftsmen. He showed how to construct a regular heptagon (a polygon with seven equal sides and angles), which is in the center portion of this print. Around the perimeter of the heptagon Sarhangi and Fathauer wrote Buzjani's name seven times in Farsi, the language of Persia (modern Iran).

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Robert Bosch (American, b. 1963), Knot? 2006. Digital print, 34 × 34 in. (86.3 × 86.3 cm). Courtesy of the artist.

With the development of railroads in the nineteenth century, the topic of finding an optimal route for a journey was of practical interest. The topic entered the mathematics literature in 1930, when the Viennese mathematician Karl Menger described it as the "messenger problem" ( das Botenproblem) of finding an optimal delivery route. It was soon dubbed the "travelling salesman's problem": given a list of cities and the distances between each pair, find the shortest route that visits each city once and returns to the city of origin

The American mathematician Robert Bosch drew this continuous line based on the solution to a 5000-city instance of the travelling salesman problem. From a distance, the print appears to depict a black cord against a grey background in the form of a Celtic knot. But on close inspection the apparent "grey" is actually a continuous white line moving on top of a black background. The white line never crosses over itself-it is a network rather than a knot-and so the punny answer to the title is "Not."

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Karl Gerstner (Swiss, b. 1930), Polychrome of Pure Colors, 1956-58. Printer's ink on cubes of Plexiglas, 1 1/4 × 1 1/4 in. (3 × 3 cm). ea., fixed in a chrome-plated metal frame, 18 7/8 × 18 7/8 in. (48 × 48 cm) ea. Courtesy of the artist.

In 1905, Albert Einstein discovered the symmetry of mass and energy-mass can be converted into energy, and vice versa (E = mc2). Then in the early decades of the twentieth century, physicists and mathematicians, including Einstein, gathered in Zurich and employed group theory in their exploration of the symmetry of nature.

Swiss artists such as Gerstner created patterns that resonate with these mathematical descriptions of nature in terms of symmetry. Like the mathematicians, these artists established basic aesthetic building-blocks-units of color and form-and arranged them using rules that preserve proportion and balance.

In 1956 Gerstner devised a modular system-a movable palette with 196 hues in 28 groups-for experimenting with progressions that link form with color. Gerstner's palette of 196 squares has 28 groups with 7 squares each. Shown here are four of myriad possible arrangements, which the artist describes using the mathematician's terms: groups, permutations, algorithms, and invariance.

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Karl Gerstner (Swiss, b. 1930), Polychrome of Pure Colors, 1956-58. Printer's ink on cubes of Plexiglas, 1 1/4 × 1 1/4 in. (3 × 3 cm). ea., fixed in a chrome-plated metal frame, 18 7/8 × 18 7/8 in. (48 × 48 cm) ea. Courtesy of the artist.

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Karl Gerstner (Swiss, b. 1930), Polychrome of Pure Colors, 1956-58. Printer's ink on cubes of Plexiglas, 1 1/4 × 1 1/4 in. (3 × 3 cm). ea., fixed in a chrome-plated metal frame, 18 7/8 × 18 7/8 in. (48 × 48 cm) ea. Courtesy of the artist.

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Karl Gerstner (Swiss, b. 1930), Polychrome of Pure Colors, 1956-58. Printer's ink on cubes of Plexiglas, 1 1/4 × 1 1/4 in. (3 × 3 cm). ea., fixed in a chrome-plated metal frame, 18 7/8 × 18 7/8 in. (48 × 48 cm) ea. Courtesy of the artist.

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Karl Gerstner (Swiss, b. 1930), Color Spiral Icon x65b, 2008. Acrylic on aluminum, diameter 41 in. (104 cm). Collection of Esther Grether, Basel, Switzerland.

Scientific insights into the deepest levels of the natural world are explanations based on symmetry, which the artist Karl Gerstner symbolizes with this circular "icon" for the secular age of science and technology. The most symmetrical geometric form is a sphere (all points equidistant from a point in three-dimensional space). In the late twentieth century, scientists concluded that the universe began in perfect symmetry as a point that exploded into a sphere of plasma. As the infant universe expanded, the primordial sphere cooled, and matter condensed from the plasma to form the first particles, then atoms, gas clouds, and stars. At some point the original symmetry of the universe was broken; the resulting asymmetries appear to be the result of random shifts analogous to mutations during evolution. Today physicists are recreating samples of this primordial spherical plasma to determine the degree to which the universe retains traces of its original symmetry.

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Simon Thomas (British, b. 1960), Planeliner, 2005. Bead blasted stainless steel, 23 5/8 in. (60 cm) diam. × 2 1/4 in. (5.55 cm) high. Courtesy of the artist.

Simon Thomas is a young British artist whose work, such as this sculpture, is a visualization of a mathematical formula. He studied visual arts at the Royal College of Art in London in the 1980s and went on to create sculpture with striking geometric patterns, serving as artist-in-residence at the University of Bristol, both in the department of physics (1993-95) and mathematics (2002).
Mathematics and Art: A Cultural History by Lynn Gamwell is out now. This is a guest post on Alex Bellos's maths blog. Alex's most recent book is a mathematical colouring book, called Snowflake Seashell Star in the UK and Patterns of the Universe in the US.

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Why the history of maths is also the history of art

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In her new book Mathematics and Art, historian Lyn Gamwell explores how artists have for thousands of years used mathematical concepts - such as infinity, number and form - in their work. Here she choses ten stunning images from the book that reveal connections between maths and art.

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Social model of dyscalculia

Cooper (2009) highlights the move away from a deficit model of disability where the responsibility is on the individual learner and their deficits, to a social model of disability (Oliver, 1990), which acknowledges our responsibility to provide a barrier-free learning environment. Cooper outlines the social model of Dyslexia (external link) and an example of such an initiative is the British Dyslexia Association's (BDA) ' Dyslexia Friendly Schools ' (external link).

Inclusive practice in education reflects the social model of disability (external link).

Recent legislation, the Equality Act 2010 and the Disability Discrimination Act 1995, also reflects a greater focus on the social model of disability in the workplace (external link). Dyscalculia is considered a disability within the law.

Another development of the social model is highlighting the strengths of the learner.

As well as having difficulties, dyscalculic people often have strengths, such as:

creativity

strategic thinking

practical ability

love of words

intuitive thinking

problem-solving.

( www.brainhe.com/students/types/dyscalculiaforstudents.html)

Other social factors and poverty

There is a strong association between what children achieve in mathematics both early on in school and later, and their social background (Nunes et al., 2009). As has been found in many areas of schooling, children from more prosperous families perform better in the mathematics classroom and in examination conditions. Despite the widespread effect of social background very little is known about how this effect is caused. Multiple hypotheses have been proposed to explain this social influence on numerical learning.

Ginsburg and Russell (1981) found that pre-school children with different social economic status (SES) backgrounds performed differently in various mathematical problems, showing an effect of the home environment before any formal schooling takes effect. It is possible the home environment experienced by the children affects mathematical learning opportunities. A child living with access to a computer or surrounded by clocks may have more opportunity to explore mathematics, learning to tell the time or being able to practise concepts online or with computer games. Siegler and Ramani (2009) studied the effect playing board games can have on young children. Participating in a game with an experimenter, such as Snakes and Ladders, was found to improve the child's performance on subsequent numerical tasks. Therefore, a child will stand to gain in their schooling from living in a home with board games available.

It is also proposed that the school curriculum has two aspects, the explicit and implicit. Children from higher SES homes could benefit from the choices made in the curriculum, with their strengths being exaggerated by the mathematical skills being tested in schools. Children of lower SES families could be skilled in mathematical areas that are not tested by the schools examination curriculum, getting results that put their intelligence below its true level (Apple, 1979). It is also possible these children have less knowledge of the implicit curriculum than those in higher SES families so get left behind when this isn't taught in their lessons.

It is possible the children of higher SES backgrounds have parents/carers with higher education and more tendencies to discuss mathematical concepts with their child, encouraging them to think and analyse mathematics when away from school. These children are not necessarily more skilled in mathematics but the chance to explore and practise gives them an advantage when being tested later in school (Nunes et al., 2009).

These hypotheses could all be working in conjunction, all adding to any differences between mathematical ability of children from different SES backgrounds. Social effects will also stretch to the school itself. The SES backgrounds of classmates can have an effect on a child's achievement, no matter what their own SES level (Opdenakker and Van Damme, 2007).

Ethnicity also seems to have an effect on general educational and specific mathematical achievement. Green, Dugoni, Ingels and Cambum (1995) found an effect of ethnicity on mathematical achievement while controlling for SES levels.

Concerning adults, research indicates that entry level numeracy for adults is insufficient for success in employment and the subsequent consequences in later life such as the cycle of poverty (Parsons and Bynner, 2007). Recommendations are made to ensure that numeracy teaching to adults is available wherever adults are, e.g. community, classroom, workplace and through initiatives such as parent numeracy groups within schools (National Literacy and Numeracy Framework, Wales), and that it is made relevant to their lives.

References

Apple, M. W. (1979) Ideology and Curriculum. London: Routledge and Kegan Paul.
Cooper, R. (2006) A Social Model of Dyslexia. London South Bank University.
Ginsburg, H. P. and Russell, R. L. (1981) 'Social class and racial influences on early mathematical thinking'. Monographs of the Society for Research in Child Development, 46 (6) pp1-69.

Green, P. J., Dugoni, B. L., Ingels, S. J. and Cambum, E. (1995) A Profile of the American High School Senior in 1992. Washington, DC: U.S. Department of Education.

Nunes et al. (2009) 'Development of Maths Capabilities and Confidence in Primary School' (2009) DCSF-RR118.

Oliver, M (1990) The Politics of Disablement. Palgrave Macmillan.

Opdenakker, M. and Van Damme, J. (2007) 'Do school context, student composition and school leadership affect school practice and outcomes in secondary education?' British Educational Research Journal, 33(2), 179-206.

Parsons, S. and Bynner, B. (2007) 'Illuminating disadvantage: Profiling the experiences of adults with Entry level literacy or numeracy over the lifecourse'.

Siegler, R. S. and Ramani, G. B. (2009) Playing linear number board games - but not circular ones - improves low-income preschoolers' numerical understanding. Journal of Educational Psychology,101 (3) pp 545-560.

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Barriers to numeracy learning: poverty and social factors

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Social model of dyscalculia Cooper (2009) highlights the move away from a deficit model of disability where the responsibility is on the individual learner and their deficits, to a social model of disability (Oliver, 1990), which acknowledges our responsibility to provide a barrier-free learn...

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Importance of Numeracy - research evidence

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Importance of Numeracy - research evidence

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Last year, more than 510,000 international students took part in survey focusing on mathematics. Of the 65 countries involved, the US ranked 36th - a poor result that points to the growing problem of innumeracy.

Here's why we need to be literate in math, and why our failure to do so is spelling bad news for our careers, life choices - and even our mental health.

Of all the primary academic subjects, mathematics causes the most stress and trepidation. Many students are genuinely terrified of math, a sentiment driven by a culture that's consistently trying to convince us that math is hard, or that it's useless.

But as we head deeper into a knowledge-based economy, and as our personal and professional lives become increasingly dependent on our ability to comprehend and process numbers, it's becoming increasingly imperative for us to have at least a rudimentary knowledge of math.

More Than Just "School Math"

Math literacy, also called numeracy, doesn't imply proficiency in some of the more advanced areas of mathematics, like calculus or trigonometry. Rather, it describes the knowledge and skills required to effectively manage the mathematical demands of diverse situations. Numeracy doesn't require the knowledge of "school mathematics," but rather a minimal level of competency required to grasp and handle numbers.
Related: How to comprehend incomprehensibly large numbers
The Organization for Economic Cooperation and Development (OECD) offers a more precise definition, but one with a similar message. Numeracy is defined as,

an individual's capacity to identify and understand the role that mathematics play in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual's life as a constructive, concerned and reflective citizen.

Literacy in math, therefore, is less about the hard skills and more about its ability to play a role in our lives, such as our ability to carry out mechanical operations with numbers and symbols. As noted by the Australian Council for Educational research, it

encompasses the ability to put mathematical knowledge and skills to functional use as well as the ability to pose and solve mathematical problems in a variety of situations and having the interest and motivation to do so.

Numeracy can be divided into three specific areas, including the understanding of mathematical content (areas like quantity, space and shape, change and relationships, and uncertainty), mathematical processes (including the use of mathematical language, modelling, and problem solving skills), and situations (namely the ability to recognize any context in which math can be applied, including personal, educational, occupational, public and scientific).

Numeracy can also involve what mathematician Sol Garfunkel calls "quantitative literacy" - the ability to make quantitative connections whenever life requires (such as being confronted with conflicting medical test results, but we need to decide whether to undergo a further procedure) and "mathematical modeling," the ability to move practically between everyday problems and mathematical formulations (like deciding whether it is better to buy or lease a new car).

A Tool For Life

The need for numeracy has never been greater. It has a pronounced influence on our fiscal choices, literacy, and even perceptions of risk as it pertains to health. Perhaps surprisingly, it has even been associated with a reduced susceptibility to framing effects (a cognitive bias in which people react to choices depending on whether or not it's presented in a positive or negative light), the tendency to choose logic over emotion, and a greater awareness of risks that have a numerical component.

Just as importantly, numeracy also has a significant impact on our careers. Atif Kukaswadia says it's a necessary skill for the 21st century. Given that that the world is moving towards a knowledge based economy, he says the lack of mathematical literacy is a big concern: "Now more than ever the ability to critically evaluate information presented to us to draw our own conclusions, rather than have someone tell us what they mean, is of the utmost importance."

Indeed, many professions require people to have at least a rudimentary sense of numeracy, including accounting, actuarial work, risk analysis, finance, engineering, architecture, social sciences, urban planning, and many others - including those jobs outside of specialized areas. Innumeracy reduces employment opportunities and promotions, resulting in unskilled manual careers, low-paying jobs, and unemployment.

Late last year, the Programme for International Assessment (PISA) survey - which is organized by the Organization for Economic Cooperation and Development (OECD) - assessed nearly 510,000 students aged 15 to 16. The tests considered three primary areas, namely reading, science, and (especially) math. The emphasis on math was on account of it being a key indicator for post-secondary success. PISA says proficiency in math is a strong predictor of

positive outcomes for young adults, influencing their ability to participate in post-secondary education and their expected future earnings...The OECD's new Survey of Adult Skills finds that foundation skills in mathematics have a major impact on individuals' life chances. The survey shows that poor mathematics skills severely limit people's access to better-paying and more-rewarding jobs; at the aggregate level, inequality in the distribution of mathematics skills across populations is closely related to how wealth is shared within nations. Beyond that, the survey shows that people with strong skills in mathematics are also more likely to volunteer, see themselves as actors in rather than as objects of political processes, and are even more likely to trust others. Fairness, integrity and inclusiveness in public policy thus also hinge on the skills of citizens.

Each year, countries around the world invest over USD$230 billion in mathematics education in schools. OECD admits this is a major investment - but the returns are many times larger.

Looking at the results of last year's PISA survey, Asian countries did the best, occupying the first seven spots in the rankings. Canada finished in 13th, the UK 26th, and the US 36th. Boys scored higher than girls in math in 37 out of the 65 countries (more on this gender gap later).

In response, US Education Secretary Arne Duncan said that the findings

show our education system hasn't done enough to help Americans compete - or position our country to lead - in a global economy that demands increasingly higher skills.

Other figures are just as discouraging. From the New York Times:

Nearly 90 percent of high school graduates say they're not interested in a career or a college major involving science, technology, engineering or math, known collectively as STEM, according to a survey of more than a million students who take the ACT test. The number of students who want to pursue engineering or computer science jobs is actually falling, precipitously, at just the moment when the need for those workers is soaring. (Within five years, there will be 2.4 million STEM job openings.

Anxiety - and Even Pain - Inducing

Low numeracy rates, and even the reluctance to focus on more advanced areas of math, are in large part the consequence of an anti-math culture. It's not uncommon to hear students complain about how boring it is, or how difficult or useless it is. Clearly, the culture surrounding math has got to change, but we also need to be aware of the anxiety that math can produce.

Indeed, math anxiety is actually a thing - one with potential downstream mental health consequences.

According to Mark Ashcraft and Elizabeth Kirk, math anxiety is "a feeling of tension, apprehension, or fear that interferes with math performance."

Their work has shown that individuals with pronounced math anxiety have smaller working memory spans. This reduced working memory capacity, say the researchers, results in a pronounced increase in errors when mental addition is performed along with a memory load task. Ashcraft and Kirk say it's likely caused by a disruption of central executive processes.

Indeed, previous studies have shown that math anxiety is associated with poor math performance on tests, negative attitudes about math, and outright math avoidance.

Trouble is, math avoidance results in less competency and confidence, resulting in even greater levels of anxiety. Further, Ashcroft says an empirical dilemma arises as a result of this avoidance; it presents a chicken-and-egg scenario. His work shows that there's a correlation between accuracy and math anxiety.

There's also the self-reputational threat to consider when it comes to poor math performance. Studies have shown that women do better on tests when they fake their names. By assuming an alias - whether it be a male or female name - women can overrule the self-reputational threat - the fear of doing poorly when they're concerned that it'll be taken as proof of a stereotype. Removing this pressure appears to alleviate the fear and the distraction.

Revealingly, research done by Sian Beilock and her group at the University of Chicago shows that math anxiety is not simply about being bad at math. Using brain scans, she determined that the brain areas active when highly math-anxious people prepare to do math overlap with the same brain areas that register the threat of bodily harm - and in some cases, physical pain.

"For someone who has math anxiety, the anticipation of doing math prompts a similar brain reaction as when they experience pain - say, burning one's hand on a hot stove," noted Beilock in a statement.

Indeed, it was the anticipation of having to do math - and not actually doing math itself - that looked like pain in the brain. The brain activation does not happen during math performance, meaning that it's not the math itself that hurts, but rather it's the anticipation of math that's painful.

Fixing the Problem

So how do we alleviate math anxiety? And how can we cast aside the prevalent anti-math culture?

It all comes down to the quality of education and how math is presented. Math doesn't have to be boring. And as Sol Garfunkel has noted, different sets of math skills are useful for different careers - and math education has to reflect that. He continues:

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.

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. The former is how algebra courses currently proceed - introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities - for instance, Einstein's famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.

Garfunkel asks us to imagine replacing algebra, geometry, and calculus with such things as finance, data, and basic engineering. In other words, teach the math within the context of the larger discipline or subject itself. So, in the finance course, for example, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. And in the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers.

"Science and math were originally discovered together," says Garfunkel, "and they are best learned together now."

Image: 21 Jump Street

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Why Neglecting Math Can Be Hazardous To Your Life

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Last year, more than 510,000 international students took part in survey focusing on mathematics. Of the 65 countries involved, the US ranked 36th - a poor result that points to the growing problem of innumeracy.