May 5, 2008

If you think you know your math, try this math puzzle

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My daughers delight in trying to stump me, with difficult brain teaser math puzzles.

Laura teases “Dad, I bet you can’t solve this one in a hurry”

What’s the sum of numbers from 1 to 100?

Celina mocks me ” come on dad, we have not got all day.”

Now I know what your probably thinking. Gee that’s hard one.

I paused and took a deep breath, as I tried to gather my wits.

After a couple of minutes, my girls start laughing, sensing they’ve beat me.

Suddenly I blurt out 5050

There’s stunned silence.

The girls pleaded with me “But how did you work it out, so quickly”

You could say I had an advantage, as I had read about a 10 year old math prodigy, who was asked the same question by his teacher. His name was Carl Friedrich Gauss.

You see Carl Friedrich Gauss, was a mathematical genius, he recognized there was a pattern. The numbers 1 to 100 were made up of 50 sets, each totaling to 101

Carl Friedrich Gauss imagined the numbers 1 to 50 in one row an in the next row 51 to 100. When he matched up the two row, each set totaled 101

101 x 50 =5050

carl-friedrich-gauss-solves-the-sum-of-numbers-1-to-100.jpg


Now that wasn’t that hard now was it ?

Just in case your wondering Carl Friedrich Gauss, went on to become one Greatest Mathematicians

Carl Friedrich Gauss born 30 April 1777, in Brunswick Germany and died 23 Feb 1855 Göttingen, Hanover.

Here’s formula for solving the math puzzle Carl Friedrich Gauss, the sum of numbers 1 to 100

Carl Friedrich Gauss formula for sum 1 to 100

My girls cried out, “thats not fair, you cheated”

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April 15, 2008

What’s Your Greatest Math Challenge

What math problems do you find the hardest to do?

Blackboard Math

  • Multiplication
  • Long Division
  • Working out percentage

Try this Twitter poll

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March 27, 2008

What’s the difference between a JK Rowling novel and an US Math Book?

What’s the difference between a JK Rowling novel and an US Math book? They both have about 700 to 800 pages. Harry Potter has a plot and follows a logical sequence and is enjoyable to read. That’s more than can be said with my daughter’s math books, its just incoherent.

My daughter’s Everyday Math book is a jumble of math blah blah blah, causing fuzzy math thinking.

I spend a lot of time helping my daughters with their math. It’s no wonder they struggled with math. Have you had a look at theses math books? Pages and pages of unrelated mathematics, which pretends to help kids understand math.

My kids were just confused. Sure, the book cover heaps of math concepts, with lots of pretty pictures. Too much fluff and not enough detail, never finishing a topic. Everyday Math seems to believe, if lacking quality, baffle them with quantity.

These textbooks and the so-called Everyday Math system, is a joke.

It’s funny how my 27 year old math books are more useful for explaining math to my girls.

“In the U.S., we’re trying to teach first-graders 20-some topics.” William Schmidt, professor Michigan State University

These books claim the benefits of Spiral learning, a system of trying to cover a topic with multiple approaches, over and over, but never tying it together. It’s like getting sucked into a whirlpool, your treading water, eventually you drown in a flood of meaningless math concepts.

For years, schools embraced Everyday Math, promising to take us to new learning frontiers. Everyday Math Sucks. it’s a failure because its illogical, unstructured and serves no purpose, accept to sell math books.

My kids were just confused. They never seem to finish any topic, there just left hanging. Everyday math relies on bulk. In fact, the math books are just plain stupid.

Our standings in mathematics have plummeted on the world stage. Once we were regarded as pioneers with the groundbreaking work of John Nash and his colleagues. Now we would be lucky to topple the Muppet’s in a math quiz.

“During most of the 20th century, the United States possessed peerless mathematical prowess – not just as measured by the depth and number of mathematical specialist who practiced here, but also by the scale and quality of its engineering, science, and financial leadership, and even the extent of the mathematical education in its broad population” Foundation for Success, The final report of the National Mathematics Advisory Panel.

If you remember the damming stats from “Highlights from PISA 2006: Performance of U.S. 15 Year Old Students in Science and Mathematics Literacy in an International Context”

The 2006 PISA

This PISA report focuses on the performance of U.S. students in the major subject area of science literacy as well mathematics literacy and on reading literacy.

  • The average score across the OECD Countries was 498, we only managed to average of 474 score
  • Of the 30 OECD Countries, 23 Countries did better than the US. the bottom 25%
  • We managed to sneak over the line, beating fast improving Mexico, Phew!
  • At least we faired better with the 27 non OECD Countries, we were beaten by only 8 Countries
  • 4 Countries increased their average mathematics literacy scores (2 OECDnon OECD countries, Brazil and Indonesia,)
  • So out 57 Counties, we came in an inglorious 32, did we medal?, I don’t think so We couldn’t even beat Azerbaijan, there’s little hope of us even spelling it
  • If we compare the performance of the highest achieving students—those in the 90th percentile—U.S. students scored lower (593) than the OECD It gets worse”

Who said Math is Fun The Math Report Card from Hell a summary of “Highlights from PISA 2006: Performance of U.S. 15Year Old Students in Science and Mathematics Literacy in an International Context”

It’s become such an epidemic that even President George Bush is concerned with the lack of math skills in the US. He commissioned the National Mathematics Advisory Panel to search for “the best available scientific research to advise on improvements in the in the mathematics education of the nation’s children.”

Foundation for Success, The final report of the National Mathematics Advisory Panel.

President Bush created the National Mathematics Advisory Panel within the U.S. Department of Education in April 2006. His Executive Order for the Panel declares: “To help keep America competitive, support American talent and creativity, encourage innovation throughout the American economy, and help State, local, territorial, and tribal governments give the Nation’s children and youth the education they need to succeed, it shall be the policy of the United States to foster greater knowledge of and improved performance in mathematics among American students.”

In 2006 by President Bush charged the panel to address concerns about the lack of home-grown mathematicians, engineers and scientists.

“To keep America competitive in the 21st century, we must improve the way we teach math and we must give more students the chance to take advanced math and science courses in high school,” U.S. Secretary of Education Margaret Spellings said in announcing the appointment of additional members to the panel. “America’s high school graduates need solid math skills, whether proceeding to college or going into the workforce.”

 

On March 13, 2008, after deliberating for 2 years The National Math Panel’s final report, finally released their report aimed at improving math education in this country.

The advisory panel, comprised of 24 mathematicians, cognitive psychologists, and educators, who meet 12 times around the country, reviewing over 16,000 research studies, and scrutinizing surveys from 743 algebra teachers. The offered 45 findings and recommendations on a range of items, including instructional practices, materials, assessments, and teacher professional development

If you got a couple of hour to spare, then you can download The National Math Panel’s 120-page report .Then visit www.ed.gov/MathPanel for the executive summary and full report.

Warning: this is a long-winded report. With the money they poured in to this report, you would think they could afford some commas. The average sentences having 20 to 30 words would be lucky to have any commas as friends. It makes it a hard read.

“Mathematics in the United States is at a mediocre level and needing significant changes to improve our standing with other countries around the world.”

Math Education in the United States “Broken and Must be Fixed”.

The National Math Advisory Panel has declared math education in the United States “broken and must be fixed”. And calling on schools to focus on ensuring that children master fundamental skills that provides the underpinnings for success in higher math and, ultimately, in high-tech jobs.

The panel’s states, we need to change the way we teach math–and how we test it. Teaching Math to kids is simply too broad, too unfocused and repetitious.

Larry R. Faulkner, chairman of the panel and former president of the University of Texas at Austin, said, “the country needs to make changes to stay competitive in an increasingly global economy. He noted that many U.S. companies draw skilled workers from overseas, a pool that he said is drying as opportunities abroad improve”.

Teachers need to focus on skills:

  • Computing with whole numbers
  • Fractions
  • Geometry
  • Measurement.

It’s vital to teach, these skills in a coherent sequence so by late middle school, more students have a sound foundation, so they can unravel the elegant puzzles of algebra. “Students who complete Algebra II are twice as likely to graduate from college compared to students with less mathematical preparation,” the report says.

Math courses must be streamlined, focusing on “a well-defined set of the most critical topics”.


Teaching Math

Core Principles of Math Instruction

  • The mathematics syllabus Grades PreK–8 needs streamling and a well-defined set of the most significant topics in the early grades. Any approach that revisits topics year after year without bringing them to closure should be avoided

  • Proficiency with whole numbers, fractions, and certain aspects of geometry and measurement are the foundations for algebra. Of these, knowledge of fractions is the most important foundational skill not developed among American students

  • Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided.

  • Students should develop immediate recall of arithmetic facts to free the “working memory” for solving problems that are more complex.

  • The Major Topics of School Algebra should be the focus for school algebra standards in curriculum frameworks, algebra courses, textbooks for algebra, and in end-of-course assessments.

  • The Major Topics of School Algebra include Symbols and Expressions; linear equations; quadratic equations; functions; algebra of polynomials; and combinatorics and finite probability.

  • Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical achievement.

  • Our citizens and their educational leadership should recognize mathematically knowledgeable classroom teachers as having a central role in mathematics education and should encourage rigorously evaluated initiatives for attracting and appropriately preparing prospective teachers, and for evaluating and retaining effective teachers.

  • The nation must continue to build capacity for more rigorous research in education so that it can inform policy and practice more effectively.

  • Increase the research on instructional programs developed for pre-schoolers and kindergartners, especially from low-income backgrounds to assure successful implementation of these types of programs.

  • Teachers’ mathematical knowledge is important for students’ achievement. The preparation of elementary and middle schoolteachers in mathematics needs strengthening. Teachers can’t teach what they do not know.

Publishers should make every effort to produce much shorter and more focused mathematics textbooks

Traditional U.S. textbooks are extremely long – often 700-1,000 pages. Excessive length makes books more expensive and can contribute to a lack of coherence. Great length…due to the inclusion of many photographs, motivational stories, and other nonmathematical content…is not necessary for high achievement.” Page xxiv, 56 – National Mathematics Advisory Panel, Final Report

One of the major problems, the textbooks requirements have varied per state, school, and textbook publisher. Textbook publishers should publish editions that include a clear emphasis on the material states and districts agree to teach in specific grades.

Among many recommendations for improvement, the report highlights the necessary changes to math syllabus so students are to be successful. “There is a problem of kids not feeling like they’re getting anywhere…,” says panel chairman Larry Faulkner, president emeritus of the University of Texas at Austin. “Math books are much smaller in many countries with higher mathematics achievement, the panel states. With most curriculum’s consisting of massive textbooks running up to 1,000 pages, they lack coherence and attempt to do everything, everywhere.”

 

The math textbook publishers need to take a leaf from a Harry Potter novel, make it readable and make sense.

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March 11, 2008

World Math Day Results are In

I know you’ve waiting for theTwickenham Solution

Sorry for the delay in providing the solution for The Twickenham Puzzle, I had trouble getting on the Internet, because my daughters have been fighting to get access.

Remember I mentioned world Math Day, my girls have got nuts.

I tell you about it later

Twickenham Solution

Play the counters in the following order: K C E K W T C E H M K W T A N C E H M I K C E H M T, and there you are, at Twickenham. The position itself will always determine whether you are to make a leap or a simple move.

Now that was not so hard.

Lets get back to World Math Day

WOW!

The numbers are staggering

Congratulations to Tatiana D from Team Australia she correctly answered 65,199 questions. Now I know how much effort Laura & Celina put in, this girl doesn’t sleep.

Let me tell you these figures are hard to believe

There were over 1 million students online challenging to answer these Math Questions, from 150 countries

So in 24 hours these kids managed to correctly answer 182,455,169 questions.

The 10 ten students breakdown

  • 3 from Australia
  • 2 from Thailand
  • 1 each UK, United Arab Emirates, Malaysia, China, Hong Kong

These 10 kids answered 544,032

It’s good to see so many kids having a go at Math

My kids loved the challenge, but I ‘m glad its over, I miss my computer.

The countdown has already began for the next World Math Day

I forgot to mention they have left the site up till the 19th of March

If you can’t get enough math puzzles head over to http://coolest.mathspuzzle.ever.com/

Here the link to the previous article Are You Ready, World Math Day is Coming?

 

 

 

 

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March 4, 2008

Are You Ready, World Math Day is Coming?

My daughters have been bugging me about World Math Day.

“Dad we need to use the computer on 5th March, because its World Math Day.”

So I asked whats involved.

Now both my daughters launch into an excited explanation,

You see we’re competiting with our friends to see who can answer the most mental arithmatic questions.

Last year more than, 287,000 kids participated the in the math quiz, from 98 countries.

It’s 24 hours of math helter skelter.

These kids are going for it. They want to smash the record they set last year, of getting 38,904,275 questions right.

As of today there are more than a million kids registered, from 20,000 schools and 165 countries. From as far way as Seycelles, Ethiopia, El Salvador and Romiania.

According to organiser Tim Power “the inaugural competition last year saw more than a quarter of a million children set a world record by collectively completeing 450 math questions per second.”

So you can see there a sense of excitement in our household. The clock is ticking, the countdown to this amazing math project, echo’s throughout the house.

I know my girls have set goals, of how many math question they will answer and get right. The winner last year answered 50,000 question. Can you believe that over million kids are going to strive to knock that benchmark off.

Mr Power reports “that while students participating in the competition improved an average of 30 per cent last year, the free event was all about making learning fun.”

Just in case your kids missed out on registering for this fun learning experience go to World Math Day you only have about 12 hours to go.

 

World Math Day

So what are you waiting for, get your kids to have a go.

If your kids liked these math challenges or your keen to have a go yourself then check out Amusements in Mathematics Making Math Fun

If you want to see how World Math Day went go to World Math Day Results are In

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February 28, 2008

More Amusing Math Puzzles

Did You Work Out, How Many Prisioners Escaped from Alcatraz?

 To refresh your memory check out Escaping Prisoners from Alcatraz, A Math Puzzle

 

When the guards returned the next morning, they were missing prisoners.

The prisoners in rooms with a square number on the door escaped

1, 4, 9, 16, 25, 36, 49

I guess you’d like to try another math puzzle, while you’re here.

Laura has plenty up her sleeve, you can pit your wits against.

Try this one from Amusements in Mathematics

217.—The Twickenham Puzzle

The Twickenham Puzzle

In the illustration we have eleven discs in a circle. On five of the discs we place white counters with black letters—as shown—and on five other discs the black counters with white letters. The bottom disc is left vacant. Starting thus, it is required to get the counters into order so that they spell the word “Twickenham” in a clockwise direction, leaving the vacant disc in the original position.

The black counters move in the direction that a clock-hand revolves, and the white counters go the opposite way. A counter may jump over one of the opposite colour if the vacant disc is next beyond. Thus, if your first move is with K, then C can jump over K. If then K moves towards E, you may next jump W over C, and so on. The puzzle may be solved in twenty-six moves. Remember a counter cannot jump over one of its own colour.

This comes from one of Laura’s favorite puzzle books, Amusement in Mathematics. This was written by Henry Ernest Dudeney 91 years ago. These puzzles will test out your gray matter. If you would like try more maths puzzles check out Amusements in Mathematics

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February 18, 2008

Escaping Prisoners from Alcatraz, A Math Puzzle

Escaping Prisoners from Alcatraz, A Math Puzzle

When I was in San Fransisco last year, I made the trip out to Alcatraz.

It was a slow and bumpy boat trip over to the island.

To keep us amused the tour host challenged us to solve a math puzzle.

I went like this.

See how you go i post answer in a couple of days.

50 prisioners are locked in cells on Alcatraz. The prision guard, not realizing the doors are locked, passes each cell at bedtime and turns the keys once. A second guard comes later and turns the locks in cells 2, 4, 6, 8 and so on, stopping only at multiples of 2. a third guard does the same, but stops at cell, 3, 6,9, 12 and so on, and a fourth guard turns the lock in cells 4,8,12, 16 and so on. This carries on until 50 guards have passed the cells and turned the locks, then all the guards go to bed. Which prisioner escape in the Night?

D-Block Alcatraz

 

To find the solution  Escaping Prisoners from Alcatraz, A Math Puzzle

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February 9, 2008

Why are Our Kids Failing Math at Such an Alarming Rate?

When it to Math on the world stage, we revel in Mediocrity.

Math doesn’t seem to be important anymore.

Take a look at these damming statistics from The OECD PISA 2006 report

“Highlights from PISA 2006: Performance of U.S. 15 Year Old Students in Science and Mathematics Literacy in an International Context”

PISA stands for (Program for International Student Assessment), a program sponsored by Organization for Economic Cooperation and Development (OECD)

Now I know you don’t have time to wade through the 74 Page US Version or the 374 page International Report. So here my Summary “Who said Math is Fun The Math Report Card from Hell”

“I guess they weren’t from the United States
It’s like taking home your school report to your folks. Dread!
If Math were an Olympic sport, the US would struggle to make the heats in the 100 yards.
Unheard of you say, but it’s true.
Don’t believe me then have a look at the latest report, released by the Institute of Education Science on the 4 th December 2007.”

This report is no laughing matter.As a world Superpower, our Math is rated Third World.

This is an international study, we, the US have come up short. We lag behind big times.

Don’t take my word for it, you can read now.


Reading this report will make you Angry

What could we do to raise the bar in learning? Leave a comment

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January 24, 2008

The greatest Math Secret Piratesmath

If you’re looking for your own pirate adventure. You come to the right place.

Captain Abacus knows everybody likes playing pirates and finding treasure.

You’re on a quest, with map in hand looking for buried treasure. You set sail, searching for a treasure chest stuffed with Gold doubloons and pieces of eight.

 

You’re cruising the calm seas, Sexton in hand, plotting a course for treasures, in far away lands

All of sudden, the wind grabs you and starts shaking and rattling your hull. The angry waves try to tear you to pieces, smashing you like road kill. The heavens throw lighting bolts, punching holes in your ship. Your ship is no match for nature’s fury. One last gasp and the sea claims another tortured vessel. Spitting you out, with all the other chewed up debris.

Shipwrecked

After days clinging to the broken mast, you’re washed ashore on a secluded beach in Jamaica. What a stroke of luck its Captain Abacus hideaway. You’re just in time for pirate school.

It doesn’t look like any ordinary schoolyard, littered with, up turned barrels, broken cannons and jagged ship carcass.

You probably wondering why a bunch of pirate misfits, would want to go to school.

You see Captain Abacus understands, there more to being a pirate than having chest full of treasure.

  • Sure there your braves deeds,
  • Make sure you live to tell your tales.

All pirates aspire to find buried treasures, but some look for other easier options, like finding ways of removing from other people

The secret of being a good pirate was not only finding the booty, but also knowing what your share was to keep

The pirates did not have the luxury of whipping out a calculator, they were often in pressure situations where they needed to be able performing maths in a hurried so they developed Piratesmaths.

The greatest secret the was Piratesmath

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January 10, 2008

Twitter Updates for 2008-01-10

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