The Problem with Socratic Questions

Statue of Socrates.

“I cannot teach anybody anything, I can only make them think.”

—Socrates

“There is no education but self-education and only as the young student works with his own mind is anything effected.”

—Charlotte Mason

Two great teachers of the past agree that a child’s mind is no bucket. We cannot shovel in whatever information we please and call that “learning.”

So how can we get children to think, to work with their own minds, to build their own relationships with knowledge?

Charlotte Mason's Living Math book by Denise Gaskins, hardcoverI try to answer that question, at least for math, in my new book Charlotte Mason’s Living Math, which is now available exclusively on my Playful Math Store.

As I was finishing up the final bits of indexing and formatting the book for publication, I continued to tweak the manuscript. This ability to tinker endlessly is both a benefit and curse of indie publishing. For example, I added four new pages to explain my quibble with Socrates.

You see, Socratic questions are very much a case of “Do what I say, not what I do.”

Continue reading The Problem with Socratic Questions

Four Stages of Learning Math (or Anything Else)

young girl doing math homework

Book, Charlotte Mason's Living MathThe following is an excerpt from Charlotte Mason’s Living Math, coming to your favorite bookstore or library this November.

But if you’re impatient—or if you want the exclusive, deluxe, full-color paperback or hardcover edition—you can order your copy now on my Playful Math Store.

This section comes from the chapter called “How Shall We Teach?” which also includes tips about textbooks, a little-known truth about the math facts, and what to do if you never understood math yourself.

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Dragons, Gryphons, and Math Mistakes

statue of a gryphon

Let's Play Math by Denise GaskinsThis post is adapted from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It.

Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.

Even teachers are human.

Continue reading Dragons, Gryphons, and Math Mistakes

Conversion Factors: How Old Are You in Nanoseconds?

birthday cupcake with sparkler

Homeschool Memories

[Based on a problem I made up for my co-op students, once upon a time…]

Conversion factors are special fractions that contain problem-solving information. Why are they called conversion factors?

  • “Conversion” means change, and conversion factors help you change the numbers and units in your problem.
  • “Factors” are things you multiply with. So to use a conversion factor, you will multiply it by something.

Continue reading Conversion Factors: How Old Are You in Nanoseconds?

Podcast: Charlotte Mason’s Living Math

family doing math together

Cindy Rollins, Dawn Duran, and I had a delightful chat about my new book, Charlotte Mason’s Living Math, which is now available in ebook (print editions coming soon!) at my Playful Math Store.

We talked about how math is a whole world full of big, living ideas that we can explore with our children. What it means to have a living education in math, opening our children’s minds to big ideas about the relationships of numbers, shapes, and patterns. And how to tell if our kids really understand what they are doing, or if they’re just parroting back the steps we taught them.

And lots more — listen for yourself…

Continue reading Podcast: Charlotte Mason’s Living Math

Make Your Own Nim Games

tower of rocks on a beach

Nim is a pure strategy game for two players. On each turn, players remove an option until finally no choice remains.

Game options might include:

  • How many stones to take from a pile.
  • Which position to claim on a gameboard.
  • How far to count in a given sequence.

The rules can vary at the players’ whim (as long as both players agree). How many possibilities do you start with, what are the rules for removing options, and how do you win or lose the game? Everything is open to change. And with every tweak, players must reanalyze their strategy.

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FAQ: Doing Math His Own Way

FAQ learning subtraction math

Isn’t it fun when children surprise us with their understanding?

All my children have figured out ways to do things in math that I would never have expected, and I’ve learned quite a bit from listening to their explanations.

But what if the child’s creative method makes it hard for them to learn what our textbook wants to teach?

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Puzzle: Random Blocks

colorful wooden blocks

In the first section of George Lenchner’s Creative Problem Solving in School Mathematics, Lechner poses this problem. If you have seen it before, be patient — his point was much more than simply counting blocks.

A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1-cm cubes as shown below. How many of the 1-cm cubes do not have red paint on any face?

red cude cut into smaller blocks

Create Your Own Math

And then he challenges us as teachers:

  • Do you have any ideas for extending the problem?
  • If so, then jot them down.

Continue reading Puzzle: Random Blocks

FAQ: Remembering What We Learn

Mother and son working on math homework

“When we do our daily lessons, my son does great. Everything seems to click. But when he sees the same topic later, in a review or on a test, it’s like he’s never heard of it before. How can I help him pull math up from the dregs of lost memory?”

This is a common problem, and there’s no easy answer.

You see, it’s easy for humans to convince ourselves we understand something when someone else explains it. It seems to make sense, but it doesn’t stick in our minds.

If you think of times when you’ve tried to learn something new, you can probably remember the feeling—you thought you had it, but then when you tried to do it yourself, your mind went blank.

So how can we help our kids when they can’t remember what to do?

Continue reading FAQ: Remembering What We Learn

Mental Math: Advanced Division

Father and daughter working mental math

The farther we go in math, the more division disappears. It ceases to exist as a separate concept.

Instead, we learn to see division as:

  • an inverse multiplication
  • a fraction (ratio)
  • a proportional relationship

Each of these perspectives offers us a new way to think about and make sense of our calculations.

Continue reading Mental Math: Advanced Division