Playful Math Carnival 99 via Eat Play Math Blog

mtap99Check out the new playful math education carnival at eat play math blog. Math art, tessellations, review games, problem-solving challenges, and all sorts of mathy fun. Not to mention, Raspberry Tiramisu!

Welcome to the Math Teachers at Play #99 Blog Carnival, a monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math…
Click here to go read the carnival blog!


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.

10 Ways to Celebrate World Tessellation Day

Guest post by Emily Grosvenor.

June 17 marks the first-ever World Tessellation Day, a holiday I created to bring awareness to the fun of finding and making tessellations.

Will you celebrate with us?

Here are 10 great ways to play with tessellations, learn about them, and introduce your children to a math concept that opens a variety of creative learning opportunities.

1) Learn about tessellations with your kids.

A tessellation is a tiled mosaic pattern of the same shape laid out over and over again, repeating into infinity. Tessellations can be found in nature, or they can be created by people. Learn more at these websites:

1WorldTessellationDayExcept where otherwise noted, graphics and photos copyright ©2016 Emily Grosvenor. All rights reserved.

Continue reading 10 Ways to Celebrate World Tessellation Day

FAQ: He Won’t Stop Finger-Counting

“My oldest son has somehow developed the horrid habit of counting on his fingers. We worked on the math facts all summer. He knows the answers in simple form, such as 9 + 4, but if it’s in a bigger problem like 249 + 54, he counts up to add or counts down to subtract, all using fingers. My younger children have no problem with mental math, but he can’t seem to get it. Are there any tips or tricks to stop this?”

New Crutches

Counting on fingers is not a horrid habit, it is a crutch. Please think for a moment about the purpose of crutches. The blasted things are an uncomfortable nuisance, but there are times when you can’t get anywhere without them. And if you need them, it does you no good for a friend to insist you should crawl along on your own.

That is how your son feels right now about his fingers. He is struggling with something his younger siblings find easy, and he can tell that you are frustrated. His confidence is broken, in a cast, and needs time for healing. So he falls back on what he knows he can do, counting up the answer.

Think positive: this means he still believes that math ought to make sense — that to understand what he is doing is more important than to guess at an answer. You want him to value sense-making, because otherwise he will try to memorize his way through middle school and high school math. That is the road to disaster.

“Schools spend a lot of time working with young children to get these facts memorized, but many children aren’t ready for that task yet. They’ll count on their fingers, and may be reprimanded for it.
“What happens when a person becomes embarrassed about counting on their fingers? If they still want to think, they’ll hide it. That’s the better option. The worse option that way too many students choose? They start guessing. When math becomes too incomprehensible, or not living up to someone else’s expectations becomes too painful, many students give up on math, and then they just guess.
“We count on our fingers as part of a thinking process. Perhaps the thing I want to figure can be memorized. But if I haven’t memorized it yet myself, the most efficient way to figure it will likely involve fingers.

—Sue VanHattum
Philosophy

The Problem of Transfer

What you describe is called the problem of transfer, and it is one of the huge, unsolved problems of education.

We can train someone to do a simple, limited task such as answering flash cards. But how do we get that knowledge to sink in, to become part of the mind, so they can use it in all sorts of different situations?

No one has figured that out.

There is no easy solution. It requires patience, and providing a variety of experiences, and patience, and pointing out connections, and asking the student to think of connections, and lots more patience.

Some Things to Try

It might help to do fewer math problems in a day, so you can take time to work more deeply on each one. Talk together about the different ways you might solve it. Make it a challenge: “Can we think of three different ways to do it?”

In math, there is never just one way to get a solution. Thinking about alternatives will help your son develop that transfer of skills.

Or pick up some workbooks that target mental math methods. The Mental Math workbook series by Jack Hope and Barbara and Robert Reys will help him master the techniques your younger kids learned without effort. It may still take him longer to do a calculation than what you are used to with the other children, but these books will give him a boost in recognizing the types of mental tools he can use.

Here are a few of my previous blog posts that include mental math tips:

Or perhaps encourage him to keep using his fingers, but to switch to a more efficient system, such as Chisenbop. According to math education expert Jo Boaler, research shows that finger-counting supports mathematical understanding.

Mental Math: A Battle Worth Fighting

Jumping into mental math is hard for an older child who wasn’t taught that way. I believe it’s a battle worth fighting, because those mental math techniques build understanding of the fundamental properties of numbers.

But the main goal is for him to recognize his options and build flexibility, not to do each calculation as fast as possible.

And be sure he no longer needs those crutches before you try to take them away.

Mental-Math-Goal


Photo credits: “Stryde Walking To School on his New Crutches” by Jim Larrison and “Silhouette of a boy” by TimOve via Flickr. (CC BY 2.0)

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.

Dreams for our Children

Don’t you love this quotation?

For our children, we dream that mathematics…

… makes sense
… is more than just arithmetic
… is joyous
… makes them strong
… is meaningful
… is creative
… is full of fascinating questions
… opens up many paths to solutions
… is friendly
… solves big problems and makes the world better
… is a powerful tool they can master
… is beautiful
… lets them learn in their own ways
… is connected to their lives
… asks “why” and not just “how”
… opens the world

Avoid Hard WorkFrom the upcoming new book Avoid Hard Work by James Tanton and the Natural Math team.

Join the crowdfunding campaign and reserve your copy today!



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.


New Book: Avoid Hard Work

I’ve loved James Tanton’s How to Be a Math Genius videos for years. He offers great problem-solving tips like:

  • Visualize: think of a picture.
  • Use common sense to avoid grungy work.
  • Engage in intellectual play.
  • Think relationally: understanding trumps memorization.
  • Be clear on what you don’t know — and comfortable enough to admit it.

Seriously, those are wonderful videos. If you haven’t seen them before, go check them out. Be sure to come back, though, because I’ve just heard some great news.

Natural Problem-Solving Skills

Avoid Hard WorkTanton has joined up with the NaturalMath.com team of Maria Droujkova, Yelena McManaman, and Ever Salazar to put together a book for parents, teachers, math circle leaders, and anyone else who works with children ages 3–10.

It’s called Avoid Hard Work, and it takes a playful look at ten powerful problem-solving techniques.

Join the Crowdfunding Campaign

For more details about Avoid Hard Work, including a 7-page pdf sample with tips and puzzles to enjoy, check out the crowdfunding page at Natural Math:

Read the questions and answers. Try the activities with your children. And donate to support playful math education!


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.


FAQ: Trouble with Worksheets

“Worksheet problems make my daughter’s brain freeze. Even simple things such as “2 + ___ = 2″ confuse her. What can I do?”

Can your daughter do math if you put away the worksheet and ask her a real-life problem: “I have a lunch sack. I put two cookies into the sack, and then I give it to you. When you look into the sack, you see two cookies there. Can you tell me what was in the sack at the beginning, before I put my cookies in?”

Or can she solve problems when the answer isn’t zero? Could she figure out how many you started with if she saw four cookies when she looked in the sack?

The idea of having a number for “nothing” can seem strange to young children.

Worksheet Calculations Are Not Math

Can your daughter think mathematically, without calculations?

The symbols on the worksheet are not math. They are just one way of recording how we think about number relationships, and not a very natural way for children. Mathematics is a way of thinking — paying attention to the relationship between ideas and reasoning out connections between them. Encourage your daughter to notice these relationships and wonder about them.

Try watching Christopher Danielson’s video “One is one … or is it?” together, and then see how many different examples of “one” she can find around the house.

The Power of Story

Many kids at this age have a hard time with abstract number math — then their brains will grow up, and they’ll be able to do it. Development varies from one child to another.

When I do worksheets with young children, I turn each equation into a little story. Like the “cookies in a lunch sack” story above.

Sometimes we use blocks or other manipulatives to count on, but often the mental picture of a story is enough. Having something solid to imagine helps the child reason out the relationships between the numbers and symbols.

FAQworksheets


Quote photo: Carl Vilhelm Holsøe ‘Interior with a mother reading aloud to her daughter’ 19th Century. Image from Plum Leaves via Flickr. (CC BY 2.0)

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.