But most parent tip sites focus on the math activities themselves. I haven’t seen much that helps parents bring a gentle teaching mindset to math activities, or helps parents make the most of everyday math learning opportunities. Here are some suggestions for HOW to nurture a life-long interest in math and a sense that math can be fun.

1. Listen for and respond to your child’s innate curiosity –- build on what he’s already interested in and he’ll be motivated to learn.
2. Don’t try to turn every situation into a textbook math problem. Turning casual inquiries into a math drill is a quick way to turn curiosity off!
3. It’s OK to start without enough information and undefined terms. Learning to ask clarifying questions is the way kids learn how to solve problems.
4. It’s ok to begin with a problem that’s too complicated. Learning to pose a simpler question is also part of learning to solve problems.
5. Don’t be afraid to leave questions unanswered for another time -– let kids mull over their ideas, giving them time to marinate.

DreamBox counts many nurturing parents in our community! We’d love to hear your ideas on how best to foster curiosity and interest in math!

How do children learn through shapes, patterns, and numbers?

All those hours of fun your child spends playing with shape sorters, puzzles, and blocks, putting pennies into his piggy bank, and helping you make cupcakes. Guess what? He is absorbing early math skills all the while playing these games: geometry, measurement, even computation. Who knew? What we want to know now is: a) when will he be able to take over balancing the checkbook and b) when will the cupcakes be ready?

Here are some of the math skills that experts have identified as essential for preschoolers to learn, plus a few parent-created activities to help you help your children learn more about the world around them.

1. Try counting beans to help your child develop an understanding of addition and subtraction.
   Keep a plastic container filled with different beans—all colors and sizes. On a rainy afternoon, spread out a sheet or blanket on the floor and pour the beans out on a baking tray on the sheet. Give your toddler different cups, spoons, muffin tins to move, sort, count, and compare beans. You can make observations about numbers, sizes, textures, colors… the variations are endless!
2. To help your child recognize and compare written numerals, create a number line.
   Create a number line from 1 to 20 on the floor with masking tape and numbers that have been cut out of construction paper. Each number should be about a foot apart. Practice counting up or down, adding or subtracting by having the kids jump up and down the number line.
3. Play ‘The Change Game’ and learn to identify money.
   Teach your preschooler to distinguish between pennies, nickels, dime and quarters by emptying out some change from your wallet and having your child sort them and count them for you! As they become more advanced, they can count up the total amount of change you have. This is a great activity for when you have to wait and keep your little ones entertained.
4. Set up a pretend grocery store and teach adding and subtracting to ten using concrete objects.
   Set up a room in your house like a grocery store. Put some of your kids’ favorite foods on tables and chairs for the ‘aisles’ of the grocery store. Then give your kids something to use as a basket and some money—real or pretend—to ‘buy’ their food. It’s a fun activity that can teach young children colors, shapes, counting, and food names. Older children can learn about making a recipe and finding food from all the food groups. And, who knows, the next trip to the grocery store might be a little more fun for them!
5. Try ‘Sorting Shapes’ to help identify and sort basic figures: square, rectangle, triangle, circle.
   Find household objects that fall into 3 shape categories — circle, square, and triangle. For instance, you can use a wallet, a coin, a ball, a piece of bread cut into a triangle shape, a tomato. Once you have many objects, about 5 of each shape, put them on a table and ask your child to sort them by shape. This is great both for sorting and shape recognition!
6. Play ‘Measure with Me’ and practice simple measurement.
   Which things in the house are taller than your child and which are shorter? Help her find out by cutting a length of string to her height and then “measuring” furniture, large toys, etc. to see which are shorter than she is and which are taller. You can also write down several household items and have your child guess ahead of time whether they will be taller or shorter. Write down the guesses and see if they were right as she makes the measurements. Learning to measure is an important skill for older preschoolers and kindergartners.
7. Play ‘Bubble Count’ to practice counting from 1-31.
   My 4-year-old made up this game, and I thought it was rather clever! As I blow bubbles, she pops them with her finger as she says a number, counting on from number 1. As the bubbles float by, she pops and counts each one until she forgets what number she was on or can’t count any higher. Tagging bubbles as they’re popped teaches one-to-one correspondence, which is essential to understanding what numbers represent. It’s a fun way to reinforce sequencing, especially for those kinesthetic learners out there! Happy popping!

More from The Savvy Source on pre-school math:

• Browse our activity guides for even more ideas to help your child learn to count.
• Take a peek at our carefully selected books and toys, especially those that help make counting fun.
• For our children, every day is a learning day. Find even more great ideas at www.savvysource.com.

Not only is he absolutely amazing at mental math, he answered Colbert’s question “Why does math matter? Because Americans have a long tradition of believing that math is hard and boring.”

I imagine Arthur getting in a classroom with children classified at “the bottom of the educational system”. After taking his class those kids would blow away all state standards.

• Preschool: When sorting coins, start with pennies and dimes. Quarters and nickels can be confusing because they look alike. But when your children a’re ready, comparing quarters and nickels will help them learn to distinguish between 5 and 25 cents. Preschoolers can help make piles of ten if you give them a mat with a place for each coin. I prefer a mat with two rows of 5 each.
• Kindergarten: Sort coins and count piles of ten. Later combine the piles of ten to make groups of 40 (nickels and quarters) and groups of 50 (pennies and dimes).
• 1st grade and older: Sort coins, count piles of 40 and 50. Watch to see if your child uses a strategy such as stacking one pile of ten and making other stacks have the same height. Another of my favorite strategies is laying the coins in rows of ten and making additional rows.

This takes longer than Coinstar, but the time spent engaged with your kids is worth much more than the 9% you save by doing it yourself!

Looking for ways to motivate your dreamer in math? You can encourage your child by talking about how a [insert dream job here] needs math in their job. Here are a few ideas to get you started!

These 7 cool jobs all require math learning

1. Animator

When watching balloons whisk a house away in Pixar’s new summer movie Up, most of us weren’t thinking about math. But in animation, math and art go together like peanut butter and marshmallow fluff. Trigonometry helps rotate and move characters, while algebra creates the special effects to make images shine. Even artists have to pay attention in math class!

2. Game Designer

Designing board or video games is a cool job. Who wouldn’t want to playtest Candyland, Monopoly, or Clue? Every game designer needs to have a good grasp of game theory – a branch of applied mathematics. Aspiring video game programmers should also study trigonometry, physics, and calculus. Chances are, board game designers will need to know probability, even if they won’t be designing math games.

3. Robotics Engineer

Robotics engineers design, test, and maintain robots! It’s a growing industry and the employment outlook is sunny. Before you quit your day job and run off to design a house-cleaning robot, hit the math books. Most Robotics Engineers have a master’s or doctorate. According to the article, “Learn About Robots” robotics may be the most inter-disciplinary of engineering endeavors.

4. Roller Coaster Designer

As you ride a roller coaster through loops, dives, and dips, you’re busy wondering if you’re going to lose your lunch, not calculating velocity. But there are many different curves in a coaster and roller coaster engineers need to understand the mathematical properties of these curves, as well as physics, kinematics, and material strength. Like all cool jobs, roller coaster design is competitive — there are only 100 roller coaster design companies in the U.S.!

5. Jet Fighter Pilot

The thrilling life of a jet fighter pilot seems worlds away from the math classroom. Movies like “Top Gun,” show pilots streaking through the sky in futuristic birds, not calculating how much fuel they have left or figuring out the direction and speed of the wind. But pilots have to complete major math problems on the fly, and when they’re zipping through the air at 700 mph, math skills are life saving.

6. Sports Announcer

What is his batting average? How many bases has he stolen? When those sports personalities give the play-by-play, they have to pay attention to the numbers: percentages, player stats, the clock. And sports casting is done live, which means there’s no room for errors.

7. Professional Photographer

We think of shutterbugs as artists, not mathematicians. But professional photographers need mad math skills. They have to calculate depth of field, determine the correct film speed, shutter speed, aperture, and exposure — and more. And to capture the moment, they need to do it all in a matter of minutes. Who knew so much math went into one photograph?

So when I heard Robert Lang’s TED talk “Idea + Square = Origami” I found beauty in the way he uncovers the mathematical principles of this traditional art form and puts them to work. Origami is 1 uncut square and folding. He (and others) are modernizing the art, using math and engineering to fold intricate designs that are delightful, intriguing, and sometimes, as it turns out, very useful.

Robert Lang is a physicist, using the tools of physics and engineering to break down problems and study the underlying theory. Provocatively, he says the secret is letting dead people do your work for you. You take your problem, turn it into a problem that other people have solved before you, and let them solve it for you – you use their solution.

The 1st step to modernizing this art was the development, by a Japanese artist, of a language of dots, dashes and arrows that can be used to describe the design of a form. Traditionally a sheet is folded in half repeatedly to make a flap, to create the leg of a beetle for example. The crease patterns when it’s unfolded reveal a quarter circle – you need a quarter circle of paper to make a flap. You can also make flaps from other parts of the paper, but a flap needs some part of a circle. If you want to make a figure with a lot of flaps, you need a lot of circles. Origami artists discovered in the 90’s that they could make very complex designs by packing more circles into a single sheet of paper. The basic rules of origami are simple, but these artists were able to create intricate designs by understanding these rules and pushing them further.

Math learning and the rules of origami

As with so much else in our lives now, computers have extended what this art form can do. Lang developed a program, based on these simple rules, that can calculate the crease patterns and do the circle packing. Origami, once the preserve of a few select, skilled artists, was revolutionized by understanding the mathematical principles underlying it and writing software to do the number crunching.

Lang goes on to provide wonderful examples of how origami has now been made useful in the real world, with applications in medicine, science, space, consumer electronics, and more. It’s used to allow things that need to be big and sheet-like when they arrive at their destination to be folded down to a compact form to make their journey – like the lens for a hundred-meter telescope used in space.

Here’s a wonderful perspective on all of this. Robert Lang said, wrapping up his talk, “When you get math involved problems that you solve for aesthetic value only, or to create something beautiful… it may turn out to have an application in the real world. And as weird and surprising as it may sound, origami may someday even save a life.”

You can learn more about it in Lang’s book “Origami Design Secrets: Mathematical Methods for an Ancient Art.”

The trick is to teach your kids math by combining it with fun activities. DreamBox Learning has two new free summer math printables: our Super Fun Beach Day printable, which shows you how to plan educational beach activities and the DreamBox Read-and-Learn Math List, which lists great storybooks that also teach math. Both are free and no registration required, so please take advantage of these excellent parent resources.

Fun Summer Math Printables:

• DreamBox Read-and-Learn Math List
• DreamBox Beach Day Printable

Fun summer math activities:

• Bake cookies and let your kids help you measure ingredients
• Play a rainy day math game, such as Dominoes or Yahtzee
• Go on a scavenger hunt and teach your kids to count and sort objects

Comment below with tips on keeping your kids busy during summer vacation. Are there any travel math games you play or math stories you read with the little ones? Let us know!

Research shows avoiding the “summer slide” can have a profound effect on your child’s learning development. You may already know that DreamBox Learning is a wonderful source for engaging math activities for kindergarten, first grade and second grade students. You also know that the sun is out, the weather is great, and your kids shouldn’t spend their entire vacation in front of the computer. Don’t fret. There are so many summer math and science camp options that you’ll envy your kids’ learning possibilities this summer.

Out of this World Summer Math and Science Camps

Rocket at Space Camp

In 1977, while watching students study rockets at the U.S. Space & Rocket Center, Dr. Wernher von Braun commented “We have band camp, football, cheerleading; why don’t we have a science camp?” As the math camps pioneer, the United States Space Camps in Huntsville, AL brings space exploration alive with summer camps, day camps and year-round family oriented activities. My son still talks about Space Camp, even though he’s long outgrown his flight suit! If you’re looking for a space-related camp closer to home, here is a list of space camps throughout the country.

Down-to-Earth Summer Math and Science Camps

Giraffes at SeaWorld/Busch Gardens

If animals catch the eyes of your young ones, the SeaWorld and Busch Gardens Adventure Camps are sure to light the inspirational spark for biology. These resident camps, day camps, or group camps give children of all ages the opportunity to interact with land and sea animals from all over the world. These camps are offered at SeaWorld and Busch Gardens parks in Tampa Bay, Orlando, San Antonio, and San Diego, or here is a list of biological science summer camps throughout the country.

Budget-Friendly Educational Summer Camps

These science summer camps may be convenient, but they’re no less exciting. For math and science activities closer to home, look to your nearest children’s museums or science centers for summer camps. One example that we DreamBox Learning appreciate is the Pacific Science Center’s camp and workshop program, which offers overnight and day camps. This summer, campers of all ages will learn about candy chemistry, GPS adventures, and discover supervised experiments with unstable elements. And the Seattle Aquarium, where one of our own staffers volunteers every week, offers Marine Summer Camps, where kids can get face-to-face with underwater life.

Choosing a Summer Camp

Whatever activity you choose for your little campers this year, make sure the summer camp is connected with the American Camp Association (ACA) to ensure your children are cared for by trained professionals. For a complete list of summer camps of all kinds this summer, visit www.mysummercamps.com. When your summer is filled with DreamBox Learning and these great summer math and science camps, your children will learn and grow while having a blast this summer vacation.

If your child loved Finding Nemo or Toy Story, this Science Daily article might be a good read. Not all kids grow up with a love of math like Tony DeRose, a computer scientist at Pixar Animation Studios. He put the algebra and trigonometry he learned in high school to good use when he realized that “without mathematics, we wouldn’t have these visually rich environments, and visually rich characters.” The article includes a video clip of an interview with Tony talking about the connection between animation and math. You’ll also find a link to an article about the computer scientists who won an Oscar for developing the fluid simulation used in animated movies like Pirates of the Caribbean.

Or take a look at this PBS Teachers site that suggests ways to help students use measuring, multiplication, division, and fractions to understanding what motion picture film is and how it is used.

But we know that the best way to get kids interested in high school math is to make sure they’re engaged with math from the very beginning of school. And as a mother of an artist, in an environment where budget cuts have virtually eliminated art education from public school education, I was pleased to find someone like Wendy Jackson Hall. She was an animation artist and educator Seattle who used creative media like animation as a learning tool to help teach other subjects (and she introduced my son to stop-motion animation).

Relating Math Learning to Everyday Activities

In this terrific Stop Motion Works article, Wendy talks about teaching kids how to make flip books to relate math and aesthetics – with specifics for kids in grades 1 through 6. Helping children understand that 24 frames are combined to create one second of animation helps build comprehension of multiplication, division and fractions. And relating this to aesthetic principles of design, composition, contrast, and visual symbols, helps kids make the connection between the seemingly disparate worlds of math and art.

Turn down the heat and warm up for Math Awareness Month with a few thought-provoking activities your family can do together. Today’s topic: Reducing Carbon Dioxide.

Change a light. Replace one light bulb with a compact fluorescent bulb and you’ll save 150 pounds of carbon dioxide (Co2) per year. Math Practice: Count all the light bulbs in your home. Discuss how much energy you’ll save if you replaced each bulb with a compact fluorescent.

Recycle. If you recycle half your household waste, you can save 2,400 pounds of carbon dioxide per year. Math Practice: Separate all the aluminum cans, newspapers, and milk cartons in your home. Count how many items make up each pile and tally in a chart. Make pencil holders out of aluminum cans. Subtract the cans you’re reusing from the cans in the pile. Now how many cans will go into the recycle bin?

Every step you take. For every mile you travel by car, you let one pound of Co2 into the air. Math Practice: Take a family bike ride and count the blocks as you go along. How many blocks make up a mile in your town? Could you take more trips by bike or on foot? List the animals you see on your journey and collect fallen leaves.

Math Learning As A Way of Teaching Your Child About the Environment

It’s amazing how much a simple action, like changing a light bulb impacts our environment. While we talk with kids about climate change and conservation, math provides real values behind our decisions. When a child asks, “Mommy, why can’t we take the car?,” instead of using the old Mommy mantra “Because I said so,” say, “If we drive one mile, we’ll let one pound of carbon dioxide into the air. Let’s walk instead.”

Teach your kids about Math and the Climate with more fun Earth Day activities. Comment below and let us know if you’re participating in Math Awareness Month!

The Effects of Mandating Algebra in School Math Programs:

In 1997 the Chicago school district was one of the first to require that 9th graders take algebra to help ensure that its high school graduates would be ready for college. And many districts have followed—Minnesota and California even requiring it in 8th grade, assuming the California policy is implemented. However, researchers found rising failure rates, and the algebra mandate “did not seem to lead to any significant test-score gains for students in math or in sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school.” (You can read the Edweek article I’m quoting here.)

But isn’t it obvious that if algebra is the needed foundation for their future, kids need the right early foundation to be successful in algebra? All of which reinforces my belief in the importance of what we’re doing at DreamBox: helping more kids develop conceptual understanding and fluency with basics—like number sense and computation—and giving them engaging ways to develop problem solving skills. We’re helping kids to be confident and well prepared for success with algebra.

So I attacked Candy Land differently. I put aside the traditional cards with one or two colors indicating if one should move 1 red space or 2 yellow spaces, and introduced a squishy yellow die with dots representing the numbers 1 to 6. Elle thought the die was fun. Little did she know she was practicing the early math skill of recognizing dot patterns (or quick images) up to 6.

Try this with your own child. It’s truly surprising how quickly they roll and say, “five” or “four” without counting each dot on the die. With every roll, she also had to move that many spaces. This isn’t so easy for a 3-year old that doesn’t quite have one-to-one tagging down. She counts as she moves, but she doesn’t always move exactly one space for each number counted. So, when appropriate, I’d help her move or point to each space as we counted together. On my turns (when she wasn’t moving my piece for me), I’d model making my piece jump one space for each number counted. Elle absolutely loved playing the game this way, and I loved turning this into an opportunity to watch and learn from her. As a teacher, I was challenged to keep the experience light-hearted yet below her frustration level. As a mom, I just had fun teasing and laughing along with Elle.

The Challenges of Math Education for Your Child: Making Learning Fun

Other variations for using Candy Land with 3-6 year olds: I know Elle won’t be entertained by this forever, and I’ll want to challenge her more as she grows. Here are some twists I’ll use in the future. (Am I actually looking forward to playing more Candy Land?):

• Change the die used. Use a die with numerals 1-6; or better yet, 1-10, 1-12 or 1-20. As a teacher, I have a collection of these. Dice are cheap. Make the investment.
• Rotate picking a card with picking a die. The traditional cards make the game move a lot faster, unless you get sent back to the beginning!
• Roll two dice. Start with two dice, each using dot patterns. Then, combine one die with a dot pattern and one using numerals. Finally, use two dice with numerals. This introduces adding to the game.
• Roll two dice. Choose one to move. This adds strategy to this traditional game of chance.
• Pick a card and a die (for a slightly older child). Let your child decide if she should use the card first or the die first. Again, this adds strategy to the game.
• Let your child choose if she wants to use a die or the cards. Then, use the opposite. What happens? Does your child think one choice is better than the other? Why? Is one scarier or riskier? Why?

So I was fascinated by a radio interview I heard yesterday with a science writer named K.C. Cole, whose premise is that our brains simply aren’t built to comprehend numbers this large. She talked about our natural tendency to focus on the difference in the number of digits between 2 numbers instead of the effect of multiplication. (OK this was my takeaway—it’s not precisely what she said.) For example 1,000,000 has twice the number of zeroes1,000 has. So our brains might tend to understand it as twice as much, rather than the fact that those 3 extra zeroes multiply the number by 1,000, which makes it quite a bit larger number.

Metapohrs Help us with the Math in our Daily Lives

She also suggested that we can use metaphors to train our brains to better comprehend differences in scale like this. She referenced the old story about doubling the grain of rice on each square of a chessboard, and by the 64th square you’d need more rice than is grown in the whole world. (By the way, we highlighted a cool book to help kids get this idea in a post a while back: One Grain of Rice: A Mathematical Folktale).

When I got home I looked it up the interview so I could share it. You can read what she actually said on the Marketplace radio show website.

Everybody has a different take on what makes a good job. And we should be thankful for that. Down towards the bottom of the list are jobs society depends on such as firefighter, nurse, and child care worker. So the listing isn’t about importance or value, but rather more narrowly focused on pay, stress, and working conditions.

Math Education: A Pathway with Limitless Choices For a Child

That said, given the wide range of doors opened by a studying math, science, and engineering, you would think more parents would encourage their children to consider these areas. Not so, according to a second article publishing the results of a poll by Harris Interactive on behalf of the American Society for Quality.

A few highlights: 97% of parents “said they believe that knowledge of math and science will help their children have a successful career.” Yet, “only 20% of parents have encouraged/will encourage their child/children to consider an engineering career.” OK, so maybe it slipped parents’ minds to make the recommendation.

But the really disappointing results for me were: “More girls say their parents are likely to encourage them to become an actress (21%) than an engineer (10%).”And, “31% of boys vs. 10% of girls say their parents have encouraged them to think about an engineering career.”
So, with all due apologies to Willie Nelson:

Parents, don’t you let babies grow up to be actresses.

Let them be doctors, mathematicians, engineers, and such.

While I put out bird seed in my backyard feeder like many of you, I also have helped keep hummingbirds alive through five Seattle winters, traveled to Antarctica and the Canadian tundra to take photographs of birds, and help care for shorebirds and seabirds at a local aquarium.

The Christmas Bird Count is one of the big yearly bird events in North America. Counting birds in their winter territories establishes expected norms which helps private and public conservation groups develop appropriate species conservation plans.

When you see a large flock of birds, how do you count them? Usually, one estimates how much of the flock is occupied by 10 or 100 or 50 birds (a friendly number), then estimate how many of those chunks the flock occupies. Multiply the two numbers together and you have a reasonable estimate of the flock size.

How a Child’s Counting Explains The Ways In Which They Learn Math Skills

How would a small child count the birds in the flock? From watching preschoolers and kindergartner use our product during our school beta testing program — children use a variety of strategies.

The early learners try to count individual birds — 1, 2, 3, and so on. This is hard because the birds are moving around and it’s easy to lose track of which birds were counted, and which birds weren’t.

More advanced students use the subitizing skill; the ability to know at a glance how many objects are in a group. Developmental theory says that subitization is not quite the same as estimating large numbers on the order of 100, but large number estimation does build on this critical skill.

Our teachers strongly emphasize subitization in the K-level lessons. They started by using the standard-based curriculum underpinning all of our academic content. They then employed their own knowledge and experience working with children in the classroom.

Finally, they tested and refined their lessons during a year long beta program including in-school observation of children playing the lessons. After each school session the teachers would dive into an office and discuss in detail their observations of the kids and how lessons should be revised.

It’s this kind of passion for education, attention to detail, and refinement based on field observations that make me believe our teachers are great educators and experienced at turning dry academic standards into fun math games which really help children develop!