Learning Math with Puzzles

Posted on by Denise Gaskins
Mother and daughter homeschooling math

Learning mathematics begins with puzzles. As stories are to history or science, puzzles are to math.

In ancient times, math began with puzzles like:

• How can we keep track of our herds, or predict the cycles of the moon, or figure out how much to pay for taxes?

• How can we draw perfect right angles, or make beautifully symmetric designs?

• What are the ratios of harp strings that create the most beautiful sounds?

Math puzzles touch every area of life. Puzzles inspire curiosity and solving them brings joy.

And we can enrich any homeschool math program with puzzles that invite children to think about mathematical concepts.

Even those monster topics that often bring homeschooling families to tears, such as fractions.

Continue reading Learning Math with Puzzles

Homeschooling: The Rhythm of a Math Lesson

Posted on by Denise Gaskins
Mother and son homeschooling math

If there’s one thing common to all new homeschoolers, it’s a feeling of being overwhelmed. One solution is to develop a basic homeschooling rhythm, a daily routine of what you do first, and then next, and then next.

Most new home schoolers try to adopt the rhythm they remember from their own school days, their own classroom experience. But our home is not a classroom, and that pattern can lead to burn-out.

The secret to successful homeschooling is to find a natural rhythm that fits your family. Even in math.

Continue reading Homeschooling: The Rhythm of a Math Lesson

Podcast: From Right Answers to Adventure

Posted on by Denise Gaskins
Notice and Wonder podcast logo with quote by Denise Gaskins

If you find a free hour this week, you may enjoy listening to my latest Notice & Wonder podcast discussion with Sonya and Della about the power of playful math:

We share plenty of tips, stories, and practical advice for bringing a sense of curiosity and exploration into your math lessons.

Plus, the Best Math Game Ever!

I love this podcast, because it always feels like sitting down to chat over coffee with good friends who love kids and love teaching.

Taking our focus off answer-getting can be hard for the adult, because that right answer gives us security that we know what we’re doing. It’s hard to give ourselves the freedom of saying, “I’m going to go into this lesson, and I have no idea where it’s going to go. I have this puzzle, I have this problem, but I don’t know where it will lead.’’

    That’s a scary situation to be in as the adult who’s used to being in control of everything.

      But we’re exploring this landscape of math. There are a lot of cool things to discover, and we’ll find something. We may not find the answer, but we’ll find something interesting, if we just explore it.

      — Denise Gaskins,
      “From Right Answers to Adventure”

       
      * * *

      If you enjoy listening to podcasts, check out my other interviews here.

      Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store.

      This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

      If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

      “Podcast: From Right Answers to Adventure” copyright © 2024 by Denise Gaskins. Podcast logo copyright © 2024 Sonya Post.

      New Podcast: Notice and Wonder

      Posted on by Denise Gaskins
      Quotation from Notice and Wonder podcast

      When I was a novice homeschooler, our local Moms’ Night Out provided mentoring and kept me sane. We’d leave the children home with their dads and meet up at a local restaurant for a cup of coffee, a slice of pecan pie, and a robust discussion of educational philosophy.

      This spring, my friend Sonya Post launched a new podcast called “Notice & Wonder” — and it captures that same feeling perfectly.

      Sonya explains: “What is Notice, Wonder, Discover? It’s the development of cognitive skills, without which you have never learned anything in your life. We are developing the underlying skills that will make anyone more proficient at learning anything.”

      I’ve had the privilege to join Sonya for three episodes of the podcast so far, and I’ve thoroughly enjoyed our conversations.

      Here’s a taste…

      Continue reading New Podcast: Notice and Wonder

      If Not Methods: Fraction Multiplication

      Posted on by Denise Gaskins
      Father and son doing math homework together

      This is the last post (for now, at least) in our If Not Methods series about how to help children figure out tough calculations.

      By the time students reach the topic of multiplying fractions, they have become well-practiced at following rules. After some of the complex procedures they’ve learned, a simple rule like “tops times tops, and bottoms times bottoms” comes as a relief.

      But we know that relying on rules like that weakens understanding, just as relying on crutches weakens physical muscles.

      If we want our students to think, to make sense of math, to figure things out, what can we do with a problem like 5/6 × 21 ?

      Continue reading If Not Methods: Fraction Multiplication

      If Not Methods: Mixed Numbers

      Posted on by Denise Gaskins
      A family doing math homework together

      Continuing our series on teaching the tough topics of arithmetic…

      Our own school math experiences led many of us to think that math is all about memorizing and following specific procedures to get right answers. But that kind of math is obsolete in our modern world.

      The math that matters today is our ability to recognize and reason about numbers, shapes, and patterns, and to use the relationships we know to figure out something new.

      But what if our children get stumped on a mixed-number calculation like 2 5/12 + 1 3/4?

      Continue reading If Not Methods: Mixed Numbers

      If Not Methods – Subtracting Fractions

      Posted on by Denise Gaskins
      Father and daughter doing math homework

      We’re continuing our series of posts on how to build robust thinking skills instead of forcing our children to walk with crutches.

      When we say, “Use this method, follow these steps,” we teach kids to be mathematical cripples.

      If your student’s reasoning is, “I followed the teacher’s or textbook’s steps and out popped this answer,” then they’re not doing real math. Real mathematical thinking says, “I know this and that are both true, and when I put them together, I can figure out the answer.”

      But what if our kids get stumped on a fraction calculation like 7/8 − 1/6?

      Continue reading If Not Methods – Subtracting Fractions

      If Not Methods: Scary Division

      Posted on by Denise Gaskins
      Father and son working on math homework

      We’ve been exploring the many ways to help children reason about tough math problems, without giving them rules to follow.

      As always, real math is not about the answers but the thinking.

      But what about division with scary, big numbers? What if our kids get stumped on a calculation like 3840 ÷ 16?

      When kids say, “I don’t know how”

      We can teach without crippling children’s understanding if we follow the Notice-Wonder-Create cycle:

      • Notice everything about the problem.
      • Wonder about the possibilities.
      • Create something new: perhaps a solution or a math journal entry, or perhaps just a deeper level of understanding.

      “Notice, Wonder, Create” is not a three-step method for solving math problems. It’s the natural, spiraling cycle by which our minds learn anything.

      Continue reading If Not Methods: Scary Division

      If Not Methods: Multi-Digit Multiplication

      Posted on by Denise Gaskins
      Mother helping her daughter with math homework

      As we’ve seen in earlier posts, there are more ways to solve any math problem than most people realize. Teaching children to follow memorized steps and procedures actually cripples their understanding of number relationships and patterns.

      But what if our children get stumped on a multi-digit multiplication calculation like 36 × 15?

      Continue reading If Not Methods: Multi-Digit Multiplication

      If Not Methods: Dividing Fractions

      Posted on by Denise Gaskins
      Mother and daughter working together on math homewrok

      As I said in an earlier post, we don’t want to give our children a method because that acts as a crutch to keep them from making sense of math.

      But what if our children get stumped on a tough fraction calculation like 1 1/2 ÷ 3/8?

      Continue reading If Not Methods: Dividing Fractions