Posts Tagged ‘Math’

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_______ Politicians vs Reality ______ Why BACK-to-BASICS Maths FAILS

December 8, 2019

“There are many such examples of excellence across Australian schools. But there are not enough. While individual schools might shine, the results of international tests, released earlier this week, suggest our education system as a whole is stagnating. For the first time, Australia failed to exceed the OECD average in maths, and the nation’s results in reading and science have declined since Programme for International Student Assessment (PISA) testing began in the early 2000s.” More here.

What about SINGAPORE?

Meanwhile, SINGAPORE students do well in maths because they have very ENTHUSIASTIC teachers. If you want to see how Singapore and other countries promote maths in the classroom go to Maths News: Around the World from International Congress of Mathematical Education 2016.

Here we go again!

I wrote the following post in 2014 and here we are, 5 years later, back where we started. 

Louis CK Quote

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Is maths becoming a dead language?

mathspig fractionsIn the 1980’s American restaurant chain A&W was going to kick Mcdonald’s marketing butt. How? Instead of a quarter pounder burger they brought out and promoted a third pounder!!!! The promo failed. Why? Americans didn’t get fractions. More frightening, in Why do Americans stink at maths?, Elizabeth Green, The New York Times ( 23 JUL 2014), was the US study that found 17 percent of medication errors were caused by maths mistakes made by doctors or pharmacists.

Meanwhile, students in Australia, the USA, and the UK are dropping out of maths like flies.

Something is seriously wrong with the way we teach maths.

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Vote 1 Me. (Probably can’t count to 2 anyway.)

vote slip 2

Politicians around the world use education to win votes. We will raise numeracy standards they promise. Of course, this may not help your child, just the state averages.

Nevertheless, Back to Basics concepts are constantly pushed in the UK, the USA, and Australia by politicians.

us flagIn 2009 Obama backed “common standards” and “common core” curriculum in maths supported by $USA 4 Billion in grants. (Why do Americans stink at maths?, Elizabeth Green, The New York Times, 23 JUL 2014).

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uk flagLater this year a new ‘Back to Basics’ Curriculum will be rolled out in the UK with an emphasis on times tables and mental maths. (Schools must go back to basics to raise maths standards, Graeme Paton, The Telegraph, UK, 18 FEB 2014)

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aus flagAustralia has introduced a National Curriculum and National Testing (NAPLAN) in numeracy and literacy in recent years. The current government just put up $22 million to back Direct Instruction in Indigenous Schools across Qld, NT and WA (Noel Pearson’s learning engine, Jamie Walker, The Australian, 5 JUL 2014) Direct Instruction is a commercial product involving very rigid and proscriptive Back to Basics curriculum and testing program from National Institute of Direct Instruction based in Eugene, Oregon.

Teachers use strict guidelines and must keep within the program. Eg:

Picture 2

Picture 3……………………………………

Do back to basics programs work?

Maybe. It depends on what you are measuring. Students can improve some maths skills. The worksheets are very clear and that is to be applauded. And so, in time, standards may rise on paper.

But there are still two huge problems.

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We have ways of teaching to make you hate maths!!!!

Firstly, there is the McMath Element. Do you want Pythagoras with that quarter pounder? Repetitive, pre-packaged, parrot-style learning is easily forgotten. According to Professor Roediger professor of psychology at Washington Uni ‘effortful, varied practice builds mastery’. (How tests make us smarter, New York Times, 18 Jul 2014).

Secondly, rigid drilling is boring. Students grind through the exercise after exercise being constantly reminded that maths is dry, dull and boring on a coma-inducing scale. Students will, as is the current trend, drop maths as soon as they can.

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Why do some kids think maths is a cruel and unusual punishment?

According to Peter Sullivan, Professor of Mathematics Edu at Monash University students drop maths because it is:

not related to the real world,

repetitious,

boring

and restrictive.

See STOP THE PRESS: Maths Teaching Fails

But it is not just students who find maths boring. Teachers who are forced to adopt rigid, repetitive and monotonous prepackaged courses also become disillusioned.

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One size does not fit all and local knowledge counts

Grade 3Elcho Island MapI’m sitting in a Grade 3 classroom in a remote Indigenous School on Elcho Island off the coast of NT. (Last week I ran some fun/creative workshops for staff.) The young enthusiastic teacher (with the help of two indigenous interpreters) was teaching the students to count to 10 and write the numbers from 1 – 10.

Students arrive at school speaking only the local Indigenous language. They must acquire literacy skills in their own language before they are taught English in Grade 4. There is a good deal of catching up to be achieved in numeracy skills. Many Indigenous languages only name the numbers 1, 2, 3 and many. The teachers on the island are familiar with the difficulties facing their students and work hard with empathy and enthusiasm to overcome multiple disadvantages of their students.

Teachers on the island have developed extraordinary resources and create programs to engage their students in learning maths. Imposing a rigid curriculum regime like Direct Instruction on Elcho Island schools will further disadvantage the students and also demoralize the dedicated staff.

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Ways of teaching maths that work

Here are two teaching methods that are not only flexible and fun, but they have also been proven to work in the classroom.

The Walker Learning Approach

Walker learningKathy Walker is an Australian educator, author and early years curriculum expert. Her books include What’s the Hurry? and Play Matters. The Walker Learning Approach, which is used in many schools around Australia including Elcho Island, is an evidence-based strategy that encourages play-based discovery and learning as well as explicit instruction in numeracy and literature (K – Year 8). More here.

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Magdelene Lampert: Learning by Communication Method

teaching probMagdalene Lampert, until recently professor of education at the University of Michigan in Ann Arbor and author of “Teaching Problems and the Problems of Teaching, has replaced ‘answer-getting’ with ‘sense-making.(Why do Americans stink at maths?, Elizabeth Green, The New York Times, 23 JUL 2014)

She advocates incorporating communication in maths as ‘being able to explain your thinking so that someone else grasps your ideas’ improves your understanding ( as any teacher knows from their own experiences in front of the classroom.)

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LET TEACHERS TEACH

Mathspig Pedagogy

Yeah! MATHS: Guaranteed to be boring one day and scary the next but always a complete waste of time – there’s a product that’s not going to sell.

Let teachers teach. This should be a campaign slogan to put maths teaching back into the hands of the people, who know what is going on in the classroom. Imposing rigid regimes on teachers is counter productive as the teachers become as bored, as angry and as disenfranchised as their students. I mean ‘why bother?’ We need teachers with passion, enthusiasm and creativity to teach maths, not Mathsbots pre-programmed by politicans to win votes.

Politicians do not teach your children. Teachers do. If politicians and the bureaucracy make teachers lives miserable, this misery will be passed onto their students … Your children. There must be checks and balances – and cliches, I guess – but it is the teacher who passes on their love or hatred of maths to your children. If the community gives teachers the chance to teach maths creatively and with humour, they will take up the challenge and your child will benefit.

Mathspig Let Teachers Teach

I was taught by a young and enthusiastic Maths teacher at a small rural hgh school in the sixties. That’s almost 50 years ago – OMG! Don’t do the maths. His name was Barry Underhill.

Mathjspig a gogo 1I’m Mathspig. And I love maths.

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Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . USA UNITS

November 13, 2019

mathspig-smoke-jumpers With the catastrophic Californian fires burning into November and wildfires currently burning in NSW and Qld, Australia, I had to repost this firefighter maths for middle school classrooms.

Radiant Heat Stats WA Fire Dept FACEBOOK, Australian Bushfires 14 NOV 2019 MyFireWatch WA

 Wildfires USA 2019 Map: Ecowest,

mathspig-usa-units-fire-math

 

USA UNITS

Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

HOW FAST CAN YOU RUN?

USA UNITS

Time Trial:

Mark out a 30ft course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 30/tav   ft/sec

mathspig-firefirghter-maths-1

HOW FAST IS A GRASS FIRE?

This will, of course,  vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 12mph (up to 20mph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)

                           = 17.6 ft/sec

                           = 18 ft/sec

mathspig-firefighter-maths-2

CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 10 ft/sec

Average Running Speed Girl 13–14 yo = 8 ft/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

mathspig-fire-fighter-table-4

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

mathspig-cfa-diag-usa-units

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the fire front speed doubles.

mathspig-fire-fighter-table-5

Now you can calculate the distance travelled up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here

mathspig-fire-fighter-table-6

Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra Worksheet and solutions  here.

CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 70 mph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front in a strong wind can reach 140 mph, 210 mph and up to 280 mph.

20o-angle-mathspig-2

What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.

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Braindead Math for Halloween

October 29, 2019

Tarantino, being a connoisseur of Fake Blood, used several types of Fake Blood in the film Kill Bill II ranging from good splatter to free-flowing blood. According to one fanzine, in this film, Uma Thurman killed 88 opponents with a sword.  So the numbers(above)are in the right ‘blood-soaked’ ballpark. More survival math (The Hunger Games) here.

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1. Stuntman Math: Car Stunts

October 20, 2019

“With enough stupidity you can get any car to roll over” (MSN AUTO)

What stuntmen and women need is maths!

Maths is essential to the process, from calculating speeds and braking distances to looking at the ratio of the amount of film shot to the length of time of the end sequence. The stunt and crash is outlined, and the co-ordinator explains how he must calculate speeds and stopping distances carefully.

So you want to be a stuntman?

First think of the pain.

Mark Eiden, 52, a professional stuntman (pictured) who is not only afraid of heights, but was once told he likely wouldn’t walk again. Eiden’s had surgery on both arms and shoulders, five knee surgeries, six nasal reconstructions, foot and hand surgery and a facial cast. He fell off the top of a stunt car at 40 mph when the tyre blew. He gaffer taped his ear and continued, despite severe concussion. Northern Express Michigan

1 J Mark Eiden Northern Express

If you still want to be a stuntman do the Maths:

Rolling a Car:

You can use quick handbrake turn, speed around a corner, fishtail into the curb or some other lunatic thing. The most controlled way to roll a car is to use a ramp.

ramp caranddriver.com

These ramps often have a kicker at the end to add extra lift. Ramp calculations can be complicated, but the simplest way to look at the maths is to determine the angle a car will roll ie. When the Centre of Gravity moves over the base.

Centre of Gravity vs Base Width

The distance between the front wheels in cars is often called the track width.

1a Centre of Gravity

2 Stable Couch3 SUV angleBase vs CofG SUVsTable from Accident Reconstruction Website

4 Bus Centre of Gravity

5 Small car centre of gravity

6 Lambogini Diablo Centre of Grvity

So the Lamobgini Diablo is very hard to roll (build a higher ramp) and it therefore beats the SUV for stability every time.

Balancing on 2 Wheels

A more skilled stunt involves driving a car on two wheels. A very skilled stunt driver can lift the car onto wheels by snaking the car back and forth across the road until it balances on 2 wheels.

From the Centre of Gravity vs Base angles above you can see that the SUV is the easiest car to balance of 2 wheels.

But there is nothing quite as crazy as this SUV stunt:

Saudis changing car tyres, just insane.

Picture 1

View full video here.

Safe Driving Info here

 

 

 

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3. STUNTMAN MATH: Motorbike Jump

October 9, 2019

This is a repost of Mathspig’s very popular Stuntman/woman series.

Star Stuntmen

Picture 2

Star Stuntmen Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”

1. perlin_stunt_ Terminator 3

Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman

Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.

2 Evel Knievel JUNE-23-1973

His injuries are legendary:

3 the-many-injuries-of-evel-knievel1

More Evel Knievel

Ramp Design

4 Ramp Design Angle of final kicker

The angle of the kicker in ramp design can vary from 100 – 700 (See below)

5 Robbie Maddison's 2008 New Year's Eve jump Arc de Triomphe at the Paris Las Vegas

Picture 2

 

Moto-X Ramp Jump Maths

6 motorbike -parabola Mr Reid

7 bike jump 1 Method 1



8 bike jump Method 1 final

 

9 bike jump method 1 final

 

Picture 2


10 bike jump method 1 final

 

As any bike nut knows increasing speed and angle of take off will increase jump distance.

Here is a graph from final gear for speed vs angle to jump 90m.

12 optimising ramp angle

 13bike jump Method 2

METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.

You will find a thoroughly detailed calc for STUNT JUMP MATHS here:

And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here. 

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Outdoor Math Adventures___________ Middle School

September 9, 2019

As the weather improves – Spring in Melbourne, my city & Autumn in USA & UK – it is an ideal time to take math outdoors. Here are some fab exercises for Middle School Math.

Outdoor maths middle school 1 mathspig

Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!

 

Outdoor Maths Middle School 2 Mathspig

McGill Uni link here.

Outdoor Maths MIddle School 3 Mathspig

Don’t forget to throw in Mathspig’s lame protractor jokes.

Outdoor Maths Middle School 4 mathspig

You’ll find full calculations at the Maths is Fun blog.

Outdoor Maths Middle School 5 Mathspig

You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.

Outdoor Maths Middle school 6 Mathspig

Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.

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Can you escape a FALLING TREE?

August 24, 2019

Tragically, 5 people have been killed by falling trees in Victoria, Australia, this Winter. 

In 3 separate accidents, 4 died when trees crushed the occupants in cars. One victim was a pedestrian.

So if you were walking through a park could you escape a falling tree if you either heard a cracking sound or saw the tree starting to fall?

With thanks to Physics Stack Exchange.

For an inverted pendulum near the top of its arc, there is no period, but the quantity ℎ/𝑔 does represent a characteristic time scale for this system. The tree will take a few of these characteristic times to fall.

Mathspig hates seeing an old tree felled, but it does give us the necessary time data.

 

There are many assumptions in these calculations.

*You’d be hit by the tree trunk, not a branch which would hit you sooner.

*There is no wind pushing the tree over.

*The tree falling is an approx to a reverse pendulum.