Archive for the ‘Senior School’ Category

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Crazy Ways to Make Middle School Maths Cool

November 11, 2016

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I started my maths workshop in Hamburg by stirring up some friendly rivalry.  And what better way to do this than by using statistics.

Which is the biggest country?

Australia is 21.5 times the area of Germany. So I counted off 22 workshop participants and pointed to one saying ‘Your’re Germany! Ha!’ Here’s another way to compare areas:

area-of-australia-vs-germany-in-schnauzers

Which country has the largest population?

Germany has 3.5 times the population of Australia.

But the really interesting questions are:

Who drinks more beer?

Who eats more meat?

Here are the answers to these and other interesting questions from the introduction to my workshop with apologies to Brisbane and Perth:

Here are some amazing ways to make middle school maths AMAZING:

1. Defronting the Maths Classroom

2. Amazing German Maths Blog

3. m&ms and Exponential functions

4. Take a Mandelbrot Set Selfie

5. Best Fun with Algebra Ever

6. The Multi-legged Beast that Walks

7. Maths You Hold in Your Hand

8. Are you Maths Blind?

9. Real World Maths Selfies 

10. Magical Music Machine built with Maths

And don’t forget:

Maths News from around the World

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2. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

October 19, 2016

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Funky, Fab and Fantastic INTRO

IMAGINARY

IMAGINARY is a German website where ART and MATHS combine. It is AMAZING.

Schools, museums, students, anyone can download interactive Computer Programs like MORENAMENTS (below) to create art, maths demonstrations and public exhibitions. IMAGINARY also contains maths/art films, an art gallery, programs for printing 3D-sculptures, maths texts and exercises, and more.

morenaments-interactive-program

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It is FREE.

It is written in ENGLISH.

Here are a few highlights picked by Mathspig, but you have to explore the website yourself.

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SURFER

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 SURFER is a program that allows you to put in any equation and test the resulting 3D image. There is a brief video explaining how it works and you can download the program here.

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WORKSHEETS

You can download worksheets for every school level, but get ready. Here is a worksheet for 5-7 year olds. But why not? Five year olds can look at sheet music without running away screaming, why not show them ALGEBRA too?

imaginary-worksheet-5-7-year-old

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Mathematicians Just Wanna Have Fun

The following videos show mathematicians having fun! If your middle-school students think maths is ‘boring’ show them just one of these videos.

 

Explore IMAGINARY. Enjoy.

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3. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

October 10, 2016

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Funky, Fab and Fantastic INTRO

mathspig-at-icme-hamburg-2016Mathspig tried the m&m Algebra Challenge in her ICME 13 Workshop in Hamburg.

BUT … I bought PEANUT m&ms. OH Nooooooooo!

They were the WRONG SHAPE. Deformed m&ms bounced everywhere. All I could do was collect the m&ms in my gloved hands and hand them out to the workshop participants. They seemed to enjoy the failure.

But Mathspig does not give up that easily.

Here is the m&m ALGEBRA CHALLENGE with PLAIN m&ms.

The Great m+m ALGEBRA CHALLENGE

Method:

1. Open a packet of PLAIN m&ms. (Wear white Gloves like the m+ms)

2. TIP onto table. (Put a few books around the edge to define an area.)

3. Sort the m&ms into:

m -UP pile.

m-DOWN pile.

4. REMOVE the m-UP pile.

5. PICK up m-DOWN pile and TIP again.

6. REPEAT until only 1 m+m is left.

The pattern should follow the exponential equation here:

mm-equation

Did it work? Check it out below.

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Who knew one family packet had 366 m+ms?

You’ll find a worked ‘theoretical’ example here.

mm-table

Here’s the ANSWER:

mm-algebra-challenge-answers

Try it. Middle school students have to see

that applying maths in the real world can be tricky but logical.

And a lot of FUN too.

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8. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

August 26, 2016

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Funky, Fab and Fantastic INTRO

One reason why students think maths is a waste of time is because they do not see it in their world. It’s not just middle school students. We are all maths blind.

Here is the challenge. At the beginning of your next maths class:

Ask your students what ‘mathsy’ thing they have on them and see what happens. Mathspig started her ICME 13 Workshop with that question and maths teachers from around the world struggled to answer. Here is what happened.

More ideas below.

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Note: I missed the significance of ‘Standing on the Shoulders of Giants’ Quote. It was from the great mathematician Sir Isaac Newton, 1776.

More Maths on or around you: 

*food snacks: nutrition information, calories, cost.

*medication: recommended dose, concentration eg. 5 mg, quantity, cost.

*room temperature: weather forecast.

*Light Bulbs: Watts, brightness (lumens, inverse quadratic function)

*Flooring: Wood (parallel lines), carpet (tessellations), coefficient of friction (Don’t want people to slip in the wet).

*Windows, doors: Hinges (Fulcrum, Effort as a Hyperbolic function), opening/closing door is an equation of a circle, angles, fly screens (pattern), windows (pulleys sometimes), handles (knob or lever impacts on effort)

Table/desk/chair: Based on statistics to fit majority of students.

Leaning back on chair: Centre of Gravity. Watch out. 

Sharpening pencil: Circular motion, sharpness of blade reduces force needed. Why?

Pens, books dropping on floor: Good old gravity. Works every time. Quadratic fn.

Fonts: Size. Based on statistics for readability. Watch the small print.

Jewellery: Geometric shapes & patterns, but also symmetry of diamond facets, weight of diamonds in carats, purity of gold in carats (different carat).

Zips: Interlocking pattern hopefully not interlocking with your skin.

Heating: Flow rate, cost, vent locations.

Architecture: Of building involves length, height, area and cost. 

External Noise: Wall thickness. Sound proofing.

Rubbish: Recycling. Why do it?

Tights: You buy them using a height weight graph on the back of the packet. 

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9. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

August 26, 2016

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Funky, Fab and Fantastic INTRO

Here is a fabulous idea for prompting students to ‘see’ maths in the world. This activity was designed by Axelle Person Faughn, North Carolina University (Below).

Mathspig Maths Selfies 1

The idea is simple.

Ask students to take pictures of maths they see in their lives. The photos below were taken by Axelle’s students.

Alternatively, you can give students an equation and ask them to find a picture representing that equation. Axelle gave Mathspig a slip of paper with the words ‘Demonstrate limits’. I sent back a picture of curly hair and a link to the equation of a helix.

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Mathspig Maths Selfie 2

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Mathspig Maths Selfies 4

Is that pasta really a Sine Curve?

Mathspig Maths Selfies 5

 

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Maths News: Around the World

August 9, 2016

MATHSPIG ICME 13 HAMBURG

Mathspig’s head is almost exploding with the maths ideas she picked up at the ICME 13 maths conference in Hamburg last month. Mathspig’s interest is in ‘Popularising’ maths. Enthusiastic conveners of this group were:

Patrick Vennebush (Discovery Channel, USA), Carlota Pires Simoes (University of Coimbra, Portugal), Prof Chris Budd (University of BAth, UK) and Christian Mercat (Universite Claude Bernard, Lyon, France).

QUICK SUMMARY:

HARNESS CURIOSITY: Maths educators from many countries have found that informal styles of maths education encourage students’ interest in maths.

ENCOURAGE INVOLVEMENT: Maths educators from around the world have found maths activities engage students more in mathematical concepts than simply opening text books or handing out worksheets.

POLITICAL INTERFERENCE: Politicians of all flavours believe they know more about maths eduction than maths educators and use funding to push their ideas into the classroom.

CURRICULUM CONFLICT: Politicians around the world have virtually opposing views on ‘good’ maths teaching methods. See UK vs SINGAPORE vs AUSTRALIA. 

So here are some of the fabulous ideas from the International Congress of Mathematical Education ICME 13 plus some additional research and links.

UK: Screen Shot 2016-08-09 at 3.39.28 PM

The UK govt has offered £41 million to encourage half their primary schools to adopt Asian-style methods of teaching maths used in Singapore, Shanghai, Hong Kong (The Guardian, 12 July 2016) and return to using math text books. One favoured (and expensive – try  £4000 for a text book package) program is INSPIRE, which is a very visual and very structured text book series. But, as maths educator Dr Jennie from University College London commented, just because something works in Singapore does not mean it will work in London.

SINGAPORE:        Screen Shot 2016-08-09 at 3.53.51 PM

Meanwhile maths educators from Singapore are adamant that there is no such thing as SINGAPORE MATHS. There are just a lot of maths teachers working hard. While parents, teachers and cultural expectations also make a contribution. In fact, there are many struggling maths students in Singapore. Tin Lam Toh from the National Institute of Education, Singapore, gave a – dare I say – ‘inspiring’ talk on the use of maths comic books to engage reluctant students. Would the UK government be happy if some of that £41 million was spent on COMIC BOOKS? But it is SINGAPORE MATHS! (The Straits Times, 30 May 2016)

 

PORTUGAL:        portugal

Andreia Hall, University of Aveiro, and Sonia Pais, Polytechnic Insitute of Leira demonstrated the power of maths magic from their MATHEMATICAL CIRCUS PROJECT. Their Circo Matematico road show has delighted and astounded many students and teachers. (More info on this project coming soon). 

Portugal pic

But others explained that Maths education in Portugal has its problems. Every time the government changes, the maths curriculum changes because – you know how it is – politicians know more about maths education than maths educators. And guess what? After 3 years of a disastrous regressive curriculum, there has been a change of government. ‘So what will happen next?’ maths teachers wonder.

COSTA RICA:      Cost Rica

Costa Rica has, however, avoided some of Portugal’s curriculum headaches. The very cheerful, Angel Ruiz, University of Costa Rica, explained that he and others schmoozed the politicians of all political flavours before each election so that educators remained in control of the curriculum. There is a clear message for maths associations around the world in this news.

FRANCE:      French

Glorious France. The French have long admired philosophers and mathematicians so it is no surprise that some amazing maths projects are taking place in France. Martin Andler, University of Versailles St Quentin, described the exciting Animath Project, which has been running for the last 4 years. With a €2 million government grants expanded to almost €6 million with private contributions, the project funds maths clubs, expositions, websites, competitions, prizes and more. (More info on this project coming soon. Look at Animath Facebook for now.)

 

GERMANY:     German

Wow! Andreas Matt and Bianca Violet, Mathematisches Forschungsinstitut Oberwolfach, Germany, introduced the extraordinary Imaginary Project.

This free, open source, collaborative website encourages involvement from around the world. Imaginary is funded by a Philanthropic Foundation and embraces concepts from Cloud Conferences to shopping mall displays to 3D printing competitions. It is mind boggling in its mathematical breadth and creativity. Just go to the website for a quick shot of amazement. (More on this project soon). And it is in ENGLISH.

USA:     USA

My good maths friends at the National Council of Teachers of Mathematics provide resources, conferences and support for maths teachers. The NCTM are, significantly, not shy about making public comments on maths education topics from the teachers’ perspective. The NCTM is highly critical of the misuse by governments et al of high-stakes testing and the No Child Left Behind initiative, which produced a maths curriculum focused on ‘mostly low-level and disconnected skills’. Meanwhile, it was Marta Civil, Arizona, who highlighted the challenges faced by the individual math teacher especially in a multicultural classroom. Here, for instance, are two samples of long division USA-style and the Mexican Method.

Long Division Mathspig

No wonder some students and their parents get confused.

CANADA:   CANADA

Frederic Gourdeau, University of Laval, Canada, is one of the editors of the maths magazine, ACCROMATH, that has been promoting math in Quebec for the last 10 years. The success of the magazine – apart from the vibrant layout, fascinating topics and broad mathematical content – is based on tireless testing of the articles until they appeal to a broad range of students and teachers. The magazine is in French, of course, but if you Google Accromath images you’ll get the picture.

FINLAND:    FINLAND

Finland is held in high esteem among maths educators because of its consistently high math scores in the PISA tests for 15 year olds. But Prof Matti Heilio, Lappeenranta University of Technology, Finland, advises caution before jumping to conclusions. Yes! Teachers are highly trained and school quality is consistent across the country. But Finland’s success in maths education doesn’t necessarily flow onto their tertiary level.  As Prof Heilio explained ‘we need maths fundamental to the sustainable development of a technologically-based society’. Meanwhile, my favourite comment by a Finnish educator: ‘Our mission as adults is to protect our children from politicians’.

But, at least, Finland did give us ANGRY BIRDS.

AUSTRALIA:    AUSTRALIA

Last year the Australian government granted $1.5 million to Prof Robert Fitzgerald of INSPIRE Centre, University of Canberra (Not the Singapore Inspire) to bring back STUDENT ‘fascination’ with maths and science because, according to the professor, the ‘old text book approach is not working’.

Meanwhile, the mining conglomerate BHP has donated $22 million to fund the Australian Mathematical Sciences Institute ‘Choose Maths’ program to do what? Guess? Produce text books! And these text books do not appear to be very exciting at all – definitely not up to $22 million worth of excitement. Go here to have a look at The Laws of Arithmetic and their use in Algebra for Year 7. This approach could excite you into a coma! What’s going on?

NEW ZEALAND:   NZ

In his keynote address (Full video recording here) Bill Barton, The University of Auckland, NZ, emphasised how little maths education had changed since Felix Klein criticised teaching methods over a hundred years ago. If maths students were apprentice carpenters then we would subject them to 14 years of repetitive tests of their hammering and sawing skills without ever letting them build even the smallest dog kennel. His talk was a plea for innovative thinking in maths education. He also criticised streaming students into ability groups as a form of Human Rights abuse. Think about it. The lowest ability group is always given a watered down curriculum, which is against their rights to a standard education.

RUSSIA:    RUSSIAN

Sergei Pozdniakov, Saint Petersberg Electrotechnical University, Russian Federation, spoke magnificently as if driven by the full force of Russian history. Yet he did not speak about tradition but rather the need to enhance the ‘bookish’ approach to maths education with activities for students of all ages. These activities included websites with algorithm challenges for all ages (See pic below) and Olympiad competitions with open and difficult problems. In each case students are encouraged ‘to build their own solutions and also find individual paths of searching for the solutions’. 

RUSSIAN PIC 2

THE NETHERLANDS:   NETHERLANDS

Bumping into middle-school maths teacher Jeroen Spandaw proved that a creative approach to maths education was alive and well in The Netherlands. In one maths challenge  for his students, he asks  ‘if all the people in China – the world?- stood on each other’s shoulders would they reach the moon?’

ISRAEL:    ISRAEL

Nitsa Movshovitz-Hadar, Israel Institute of Technology, had a unique approach to popularising mathematics. She runs public lectures open to all. It is astounding to learn that, say, 85 members of the public would turn up and pay a fee to listen to a lecture on Infinity. But they do. The fee supports grants for innovation in maths teaching. Nitsa carefully prepares each lecture and wins the audience with intriguing titles such as ‘The wonders of logic or: A mathematician’s April fool trick’ and ‘How many guards are needed to protect an art gallery?’

SOUTH AFRICA:   SOUTH AFRICA

Duduzile Mkhize, University of Johannesburg, South Africa, described the program she has developed to help some of the poorest students in her country. This Outreach program works beyond curriculum to improve high school students self-perception. Teenagers are forming their identities and it is as this time they decide they are NOT mathematicians. This 10 day residential program aims to change this view. Students are immersed in mathematics and return to their schools feeling more confident about their maths abilities. And this new found confidence persists throughout their education.

INDIA:   INDIA

Rajaratnam Athmaraman Veeravalli, The Association of Mathematics Teachers of India, explained that maths education is celebrated in India with TV shows, competitions, displays, Maths Awareness Months and even a National Maths Day celebrated on 22nd Dec, the birthday of the celebrated mathematician, Srinivasa Ramanujam, whose life was portrayed in the film ‘The man who knew infinity’. Nevertheless, the attitude to maths in India is not good. Many think maths is not useful so efforts to popularise maths will continue. And ‘the target audience has to be almost the entire population—young and old, the well educated as well as the poorly educated, and, of course, men and women. Sometimes, it may have to include reluctant mathematicians.’

TURKEY:  TURKEY

Education is a servant of politics. This became sadly apparent when we learnt that the Turkish presenter for my popularising maths group, who I will not name, was prevented from attending the conference. The audience sat in stunned silence as we watched his video presentation of a very normal, busy middle-school maths classroom filmed only 4 days before the political turmoil began in Turkey.

ITALY:   ITALY

Marco Turrini, MMLab-University of Modena e Reggio Emilia, described how his Laboratory of Mathematical Machines is used to popularise maths in Italy. Students work with or create similar machines to develop an understanding of the underlining mathematical principles (see pic below).

ITALIAN MACHINES

ICME 13 photographs 

ICME 13 2016 2Row 1: 1.ICME 13 Hamburg Opening Ceremony, 2. Friendly Helpers at Congress, 3. Fabulous French PhD maths students Alix Boissiere and Lisa Rougetet,

Row 2: 4. Patrick Scott, IACME, USA and Angel Ruiz, University of Costa Rica, 5. Mathspig and Christian Mercat as a comcam Mandelbrot set,

Row 3: 7. Dr Axelle Faughn, Western Carolina University, 8. Jana Sierk Mintfit HamburRow

Row 4: 9. Christian Mercat  at the Mayor’s Reception City Hall hamburg, 10. Mathspig’s Workshop ICME Hamburg, 11. Mathspig at her Hamburg Workshop

Row 5: 12. Amazing image from the IMAGINARY website, 13. Prof Matti Heilio, Finland, 14. Patrick Vennebush (Discovery Channel, USA), Carlota Pires Simoes looking as if they’re giving  Prof Chris Budd (Looking like his head as a trophy, The Popularising Maths Group.

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One Second

June 27, 2016

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