The Math Student’s Manifesto

Posted on by Denise Gaskins

[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]

Note to Readers: Please help me improve this list! Add your suggestions or additions in the comment section below…

What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.

(1) I can make sense of problems, and I never give up.

  • I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
  • I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
  • I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
  • I like to compare my approach to the problem with other people and hear how they did it differently.

Continue reading The Math Student’s Manifesto

Two Ways to Do Math

Posted on by Denise Gaskins

Two-Ways-to-Do-Math

There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.

— Raoul Bott

CREDITS: Today’s quote is from Raoul Bott, via The MacTutor History of Mathematics archive. Background photo courtesy of Swedish National Heritage Board (no known copyright restrictions) via Flickr.

Fractions: 1/5 = 1/10 = 1/80 = 1?

Posted on by Denise Gaskins

[Feature photo is a screen shot from the video “the sausages sharing episode,” see below.]

Fractions: 1/5 = 1/10 = 1/80 = 1?

How in the world can 1/5 be the same as 1/10? Or 1/80 be the same as one whole thing? Such nonsense!

No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.

Here’s the problem:

  • How can you divide eight sausages evenly among five people?

Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.

What Do You Notice?

Continue reading Fractions: 1/5 = 1/10 = 1/80 = 1?

Math Teachers at Play #70

Posted on by Denise Gaskins

800px-Brauchtum_gesteck_70_1[Feature photo above by David Reimann via Bridges 2013 Gallery. Number 70 (right) from Wikimedia Commons (CC-BY-SA-3.0-2.5-2.0-1.0).]

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 70th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 42+ links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Click here to continue reading.

A Good Problem Requires Dreaming Time

Posted on by Denise Gaskins

A-good-problem

A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some “dreaming” time.

— Howard Eves

CREDITS: Today’s quote is from Howard Eves, An Introduction to the History of Mathematics. Background photo courtesy of Brenda Clarke (CC BY 2.0) via flickr.

Math Teachers at Play #66

Posted on by Denise Gaskins

[Feature photo above by Franz & P via flickr. Route 66 sign by Sam Howzit via flickr. (CC BY 2.0)]
Route 66 Sign

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

By tradition, we start the carnival with a couple of puzzles in honor of our 66th edition.

Let the mathematical fun begin!

Puzzle 1

how crazy 66

Our first puzzle is based on one of my favorite playsheets from the Miquon Math workbook series. Fill each shape with an expression that equals the target number. Can you make some cool, creative math?

Click the image to download the pdf playsheet set: one page has the target number 66, and a second page is blank so you can set your own target number.

Continue reading Math Teachers at Play #66

Rate × Time = Distance Problems

Posted on by Denise Gaskins

I love how Richard Rusczyk explains math problems. It’s a new school year, and that means it’s time for new MathCounts Mini videos. Woohoo!

Continue reading Rate × Time = Distance Problems

How to Think like a Mathematician

Posted on by Denise Gaskins

Would you like to learn how to think like a mathematician? Stanford professor (and NPR “Math Guy”) Keith Devlin is teaching a free online course through Coursera. It starts in just a few weeks. I’ve signed up. Will you join us?

The prerequisite is to be taking or have finished high school math. If (like me) you took it so long ago that you can’t quite remember, don’t worry: The focus of the course is not on long-forgotten mathematical procedures, but on “learning to think in a certain (very powerful) way.”

Mathematical thinking is not the same as doing mathematics — at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself.

The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box — a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

— Keith Devlin
Introduction to Mathematical Thinking

Continue reading How to Think like a Mathematician

Olympic Logic

Posted on by Denise Gaskins

I love logic puzzles! Nrich Maths offers four fun Olympics Logic puzzles. And be sure to check out the rest of their Nrich Olympics Math as well.

Medals Count

Given the following clues, can you work out the number of gold, silver and bronze medals that France, Italy and Japan got in this international sports competition?

  • Japan has 1 more gold medal, but 3 fewer silver medals, than Italy.
  • France has the most bronze medals (18), but fewest gold medals (7).
  • Each country has at least 6 medals of each type.
  • Italy has 27 medals in total.
  • Italy has 2 more bronze medals than gold medals.
  • The three countries have 38 bronze medals in total.
  • France has twice as many silver medals as Italy has gold medals.

Go to Nrich Maths and try all four puzzles!