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Lockhart’s Measurement

Posted on by Denise Gaskins

After watching the video on the Amazon.com page, this book has jumped to the top of my wish list.

You may have read Paul Lockhart’s earlier piece, A Mathematician’s Lament, which explored the ways that traditional schooling distorts mathematics. In this book, he attempts to share the wonder and beauty of math in a way that anyone can understand.

According to the publisher: “Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living. Favoring plain English and pictures over jargon and formulas, Lockhart succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable.”

If you take any 4-sided shape at all — make it as awkward and as ridiculous as you want — if you take the middles of the sides and connect them, it always makes a parallelogram. Always! No matter what crazy, kooky thing you started with.

That’s scary to me. That’s a conspiracy.

That’s amazing!

That’s completely unexpected. I would have expected: You make some crazy blob and connect the middles, it’s gonna be another crazy blob. But it isn’t — it’s always a slanted box, beautifully parallel.

WHY is it that?!

The mathematical question is “Why?” It’s always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it.

So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.

— Paul Lockhart
author of Measurement

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

Introducing the “Let’s Play Math!” Book, Beta Version

Posted on by Denise Gaskins

This blog originally grew out of my Homeschool Math Manuals series published in the 1990s, and when I typed a post, I often added new tips, activities, or examples. Now the stories are coming full circle: I’ve entered the enriched blog-post versions back into the book manuscript, fixed all the typos I could find, deleted obsolete references, and added a list of my favorite “living” math books and internet links.

But no writer can accurately judge her own work. A professional editor is helpful, but he or she can’t see the book with a real homeschooler’s eye. Most writers look for beta-readers among their friends or acquaintances. As we live in a rural area, my supply of potential victims helpers is limited. So I decided to try an ebook experiment: Use Amazon.com to find readers willing to pay the price of a Caramel Macchiato for a pre-publication beta version of my book.

All of the books in the Math Ebooks Beta Series are designed to supplement your current math program — to help you teach math with ANY curriculum. If you would like to help me improve the books, please grab a notepad and jot down your thoughts as you read:

  • Let’s Play Math:
    How Homeschooling Families Can Learn Math Together, and Enjoy It!
    Discover new ways to explore math as a family adventure, playing with ideas. True mathematical thinking involves the same creative reasoning that children use to solve puzzles. Introduce your children to the “Aha!” factor, the thrill of solving a challenging puzzle, and build thinking skills with toys, games, and library books. Find out how to choose math manipulatives, or make your own, and learn how to tackle story problems with confidence. Let’s Play Math will give you a wealth of motivating, hands-on ideas for teaching home school math.

Edited to Add a Clarification

If you are interested in my book but don’t have time to take notes and send me comments, that’s OK. Feel free to take advantage of the beta price anyway — there’s absolutely no obligation.

I hope you and your children enjoy the adventure of learning math together!

Sample from the Introduction to Mathematical Thinking Class

Posted on by Denise Gaskins

I’m really looking forward to Keith Devlin’s free Introduction to Mathematical Thinking class, which starts in mid-September. There are more than 30,000 nearly 40,000 students signed up already. Will you join us?

These days, mathematics books tend to be awash with symbols, but mathematical notation no more is mathematics than musical notation is music.

A page of sheet music represents a piece of music: the music itself is what you get when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive and becomes part of our experience. The music exists not on the printed page but in our minds.

The same is true for mathematics. The symbols on a page are just a representation of the mathematics. When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive — the mathematics lives and breathes in the mind of the reader like some abstract symphony.

— Keith Devlin
Introduction to Mathematical Thinking

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

5 Stars at Home School Book Review

Posted on by Denise Gaskins

Wayne at Home School Book Review just posted a very kind review of my daughter’s book:

Banished is a captivating fantasy story with a well-thought-out plot that would be a credit to any writer. But it is especially remarkable coming from a thirteen-year-old student who has been homeschooled all her life.
…
However, be forewarned. When you reach the final page and find the words, “Not the End…,” you will cry, “Oh! No!”
…
I for one feel as if I simply can’t wait to read the next installment to find out what happens to Chris and his friends. It’s that good!

Mathematicians Love to Play

Posted on by Denise Gaskins

Mathematicians love to play with ideas. They experiment with puzzles. They tinker with the connections between shapes and numbers, patterns and logic, growth and change. To a mathematician, the fun of the game is in experimenting, in trying new things and discovering what will happen. Many modern strategy games were invented primarily for the fun puzzle of analyzing who would win.

Continue reading Mathematicians Love to Play

Math Teachers at Play #53 via Motion Math Blog

Posted on by Denise Gaskins

We’re excited to celebrate the availability of Motion Math’s Pro editions and Motion Math: Hungry Guppy with this week’s Math Teachers at Play blog carnival, a monthly round-up of math-related blogs. We had some great submissions we’re excited to share with you — thanks to everyone who participated!

Let’s start with some math learning experiences —

Go read the post at Motion Math Blog!

Mathematicians Ask Questions

Posted on by Denise Gaskins

Wise mathematicians are never satisfied with merely finding the answer to a problem. If they decide to put effort into solving a math puzzle, then they are determined to milk every drop of knowledge they can get from that problem. When mathematicians find an answer, they always go back and think about the problem again.

  • Is there another way to look at it?
  • Can we make our solution simpler or more elegant?
  • Does this problem relate to any other mathematical idea?
  • Can we expand our solution and find a general principle?

Continue reading Mathematicians Ask Questions

How Can I Teach Math If I Don’t Understand It?

Posted on by Denise Gaskins

Our childhood struggles with schoolwork gave most of us a warped view of mathematics. We learned to manipulate numbers and symbols according to what seemed like arbitrary rules. We may have understood a bit here and a bit there, but we never saw how the framework fit together. We stumbled from one class to the next, packing more and more information into our strained memory, until the whole structure threatened to collapse. Finally we crashed in a blaze of confusion, some of us in high school algebra, others in college calculus.

Continue reading How Can I Teach Math If I Don’t Understand It?