FAQ: Forgetting What They Learned

“As we go through each lesson, it seems like my daughter has a good handle on the concepts, but when we get to the test she forgets everything. When I ask her about it, she shrugs and says, ‘I don’t know.’ What do you do when your child completely loses what she has learned?”

Forgetting is the human brain’s natural defense mechanism. It keeps us from being overwhelmed by the abundance of sensory data that bombards us each moment of every day.

Our children’s minds will never work like a computer that can store a program and recall it flawlessly months later.

Sometimes, for my children, a gentle reminder is enough to drag the forgotten concept back out of the dust-bunnies of memory.

Other times, I find that they answer “I don’t know” out of habit, because it’s easier than thinking about the question. And because they’d prefer to be doing something else.

And still other times, I find out they didn’t understand the topic as well as I thought they did when we went through it before.

No matter how we adults try to explain the concepts, some kids want to be answer-getters. They don’t want to do the hard work of thinking a concept through until it makes a connection in their minds. They want to memorize a few steps and crank through the lesson to get it over with.

In all these cases, what helps me the most is conversation.

My children and I always talk about our math. I ask questions like “What do you think? What do you remember? Can you explain the question to me? What are they asking for?”

And, whether the child’s answer is right or wrong, I practice my poker face. Trying not to give anything away, I ask, “How did you figure it out? Can you think of a way to confirm your answer?”

Talking Math with Your Kids

Danielson-Talking Math

Not sure how to talk about math with your children?

If you have preschool and elementary-age kids, read Christopher Danielson’s inspiring book and blog:

For middle school and older students, check out Fawn Nguyen’s wonderful collection of Math Talks. Be sure to read the “Teachers” page for tips and talking points:

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.”

— Christopher Danielson
Talking Math with Your Kids

Playful Ways to Learn or Review Math

Games are a great way to practice math. Check out these (free!) math games for all ages:

And if you have elementary-age children, here are a few grade-level tips to help them learn (and remember) math concepts:


Credits: Girl in field photo by SOURCE Hydration Systems and Sandals technology via Flickr. (CC BY 2.0) Nigerian classroom photo by Doug Linstedt and young girl studying by pan xiaozhen on Unsplash.

Click for details about Let's Play Math bookThis post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Math Debate: Adding Fractions

Cover image by Thor/ geishaboy500 via Flickr (CC BY 2.0)

I’ve been working on my next Playful Math Singles book, based on the popular Things to Do with a Hundred Chart post.

My hundred chart list began many years ago as seven ideas for playing with numbers. Over the years, it grew to its current 30+ activities.

Now, in preparing the new book, my list has become a monster. I’ve collected almost 70 ways to play with numbers, shapes, and logic from preschool to middle school. Just yesterday I added activities for fraction and decimal multiplication, and also tips for naming complex fractions. Wow!

Gonna have to edit that cover file…

In the “Advanced Patterns” chapter, I have a section on math debates. The point of a math debate isn’t that one answer is “right” while the other is “wrong.” You can choose either side of the question — the important thing is how well you support your argument.

Here’s activity #69 in the current book draft.

Have a Math Debate: Adding Fractions

When you add fractions, you face a problem that most people never think of. Namely, you have to decide exactly what you are talking about.

For instance, what is one-tenth plus one-tenth?

1/10 of 100

Well, you might say that:

\frac{1}{10}  of one hundred chart
+ \frac{1}{10}  of the same chart
= \frac{2}{10}  of that hundred chart

But, you might also say that:

\frac{1}{10}  of one chart
+ \frac{1}{10}  of another chart
= \frac{2}{20}  of the pair of charts

So what happens if you see this question on a math test:

\frac{1}{10}  + \frac{1}{10}  = ?

If you write the answer “\frac{2}{20}”, you know the teacher will mark it wrong.

Is that fair? Why, or why not?


CREDITS: Feature photo (above) by Thor/geishaboy500 via Flickr (CC BY 2.0). “One is one … or is it?” video by Christopher Danielson via TED-Ed. This math debate was suggested by Marilyn Burns’s blog post Can 1/3 + 1/3 = 2/6? It seemed so!

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

A Beautiful Puzzle

This lovely puzzle (for upper-elementary and beyond) is from Nikolay Bogdanov-Belsky’s 1895 painting “Mental Calculation. In Public School of S. A. Rachinsky.” Pat Ballew posted it on his blog On This Day in Math, in honor of the 365th day of the year.

I love the expressions on the boys’ faces. So many different ways to manifest hard thinking!

Here’s the question:

No calculator allowed. But you can talk it over with a friend, as the boys on the right are doing.

You can even use scratch paper, if you like.

Thinking About Square Numbers

And if you’d like a hint, you can figure out square numbers using this trick. Think of a square number made from rows of pennies.

Can you see how to make the next-bigger square?

Any square number, plus one more row and one more column, plus a penny for the corner, makes the next-bigger square.

So if you know that ten squared is one hundred, then:

… and so onward to your answer. If the Russian schoolboys could figure it out, then you can, too!

Update

Simon Gregg (@Simon_Gregg) added this wonderful related puzzle for the new year:


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Advent Math Activity Calendars

Once again, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the run-up to Christmas.

Including an especially-tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar home pages.

For Primary Students

Easier activities for elementary and middle school.

Math puzzle fun, plus a printable coloring page.

2017 Primary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Secondary Students

Activities for middle and high school.

Each day features a challenge from the Short Problems Collection.

2017 Secondary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Teens and Adults

“This year we’ve decided to bring you some of our favourite Plus videos. There’s nothing more soothing that a bit of fascinating maths, explained by a fascinating mathematician, that doesn’t even require you to read stuff. Happy watching!”

When you get to the +Plus Magazine website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

Plus Advent Calendar 2017

One link becomes live each day — so come back tomorrow and discover something new!

Christmas Meta-Puzzle

Or try your hand at the biggest mathematical mystery of them all — and save Christmas for Alex, Ben, and Carol!

Santa’s lost his memory, and the elves are cursed to alternate between lying and truth-telling. It’s up to you to piece together the clues and figure out which presents go where.

Christmas Logic Puzzle

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.


“Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Check Out These Cool Math Sales

I’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math.

You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

Sale price is $30 from December 2-15.

Cuisenaire Rod Activities Blowout Bundle

But Wait, There’s More

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

Their newest book is just off the presses — Funville Adventures, a math adventure chapter book.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

Natural Math Book Sale

Stock Up on My Playful Math Books

Finally, if you’ve been wanting to pick up a paperback copy of Let’s Play Math or some of my game books, or maybe a set of dot-grid math journals, I’m currently offering a discount on bulk orders.

Bundle ANY assortment of titles. Stock up on books for your family, friends, or homeschool group.

  • 2–4 books: 15% discount off retail prices
  • 5–9 books: 25% discount
  • 10–19 books: 35% discount
  • 20+ books: 35% discount, and free Continental U.S. standard shipping or the equivalent discount off other shipping options

Bulk Order Playful Math Paperbacks

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

Do You Know of Any Math Deals?

Apollonian greetings from my homeschool co-op kids, and best wishes for a grace-filled holiday season.

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Playful Math Education Carnival 106

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

Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 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 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

  • How many times would you have to slice the pizza to get 106 pieces?

Click here for all the mathy goodness!