Category Archives: Elementary

Recreational math

A few weeks ago I saw an article in the New York Times, “How to Fix Our Math Education.” The authors suggest replacing the theoretical teaching of math with applicable math. “The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact,” mathematicians Sol Garfunkel and David Mumford wrote in their op-ed piece.

Most people never need to solve the quadratic formula or use complex numbers, so why do we spend so much time teaching so many children math skills they will never use? Sounds rational.

The authors suggest “teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.” Again, entirely rational and reasonable. Perhaps if people understood math better on a relevant, everyday basis, fewer people would have signed mortgages they could never pay. (I have no proof of this, but I can’t help fantasizing about a couple ridiculing a mortgage broker proposing ludicrous terms.)

Kari Kling teaching a Math Mania class in her home.

I started teaching in 1993 at Aztec Elementary School in Scottsdale. One of the lead teachers responsible for designing the school, Kari Kling, is an expert at making curriculum relevant to students based on how their brains develop. She understands that awareness of the brain development in children should be driving what is presented in the classroom.

In 1997 she published a book called It’s Not About Math, It’s About Life. It relates math to the real world, where it belongs. The authors of the Times article would probably approve of her approach.

Kling says, “We use the language of math to communicate about something in real life. Numbers aren’t just random, they stand for things.” She teaches a class called Math Mania “to teach kids about numbers as a foundational piece so they understand math when it gets more complicated. Kids need to have real experiences with numbers. If they hear something weighs 14 pounds they need to know what 14 pounds feels like.”

When I taught third and fourth graders, we were learning about the Titanic. They read that the doomed ship was 882 feet long. I asked if that was bigger than a football field. Some said yes, some said no. I told them a football field was 300 feet, goal line to goal line. Silence. One kid who understood numbers said, “The Titanic is almost three times the size of a football field?” He was stunned. I asked if they thought the Titanic would fit on our playground. Some said yes, some said no.

Dice for generating sums.

The next day I brought my 100-foot extension cord to measure the playground. By the time we had got to 882 feet, they had a clear sense of how big the Titanic was. Teachers call this number sense and it is what Kling focused her second and third graders on. What good is manipulating numbers in an algorithm if there is no understanding what those numbers mean?

I went to Kling’s house a few weeks ago to watch her teach a Math Mania class for second and third graders. She had the kids come up with as many ways as they could to add two numbers to make 10 as a short cut to adding large columns of numbers. She calls this “bridging to 10.” It yielded a pattern as pictured in the photo at left. Hopefully the student will see the numbers on the left go from 1 to 9 and the numbers in the middle are 9 to 1 and apply this pattern for any sum.

Then they rolled two or three dice and added the numbers to discover what combinations the dice yielded. They kept track of the sums on a chart. In a subsequent class they would analyze which sums came up the most often, which pairs of numbers came up and why.

The kids were all doing math but they were playing with numbers and playing with dice and writing about the activities in their journals. It wasn’t more “kill and drill” of worksheets or page after page of problem sets. They were playing with numbers in their heads, on paper and with other kids.

There are parents who think math doesn’t need to be fun, it has to be learned. But these are kids, and kids — and adults, really — remember things that are fun because so many parts of their brains is being stimulated all at once.

Plus, it’s better to think of math as fun than as a chore.

Story and photos by Daniel Friedman

Students keep track of what number combinations and sums they roll.



Numbers, sensibly

10 CheeriosTeaching new skills and concepts depends on understanding what the student already knows. This applies to adults as well as children. When kids enter school and learn to read they need to know their alphabet and have an inkling that letters correspond to sounds. Most kids learn the alphabet by singing the ABC song as well as seeing letters in books, on signs, on television, etc.

Math is the same way. Before kids learn 1+1=2, they need to know what numbers are and what they represent. They must develop number sense, which is the understanding that numbers relate to the real world. Young children have number sense when they know that three people can fit in their family car, but 30 could not.

A study by David Geary at the University of Missouri confirms scientifically what parents and teachers know: that number sense is as essential to learning math as the alphabet is to learning reading. The study followed 177 elementary school kids for five years to track the differences in progress amongst the group of elementary school aged kids.

press release about the study reports, “A long-term psychology study indicates that beginning first graders that understand numbers, the quantities those numbers represent and low-level arithmetic will have better success in learning mathematics through the end of fifth grade, and other studies suggest throughout the rest of their lives.”

Number sense is part of the standards as set by the Arizona Department of Education for first grade but number sense is part of a youngster’s life when parents count things and play games with quantities.

When I taught third, fourth and fifth graders, I still taught number sense, though with a more advanced perspective than one would for a preschool student. When teaching multiplication, I needed to make sure my students understood that multiplying two numbers in the hundreds would necessarily be in the tens of thousands or in the millions — not just thousands. Number sense bolsters estimation skills also.

From the National Council for the Teaching of Mathematics: “Researchers note that number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts and relating them in ways that are not limited by traditional algorithms (Howden, 1989).”broccoli5

Hmmm. That’s a complicated way of saying kids should know that the five pieces of broccoli they don’t want to eat is four pieces of broccoli after they manage to choke down one piece of broccoli. 5-1=4 means very little to children without number sense, even though they may be able to count on their fingers and get the answer right on a worksheet. Kids understand math when they have number sense.broccoli4

Before you rush out to find a cool number sense smartphone app, remember, number sense is a real-world, three dimension experience, not the flat screen of a smart phone or computer. Numbers count things. With your child, count the number of Cheerios that fit on a spoon or in a cereal bowl, or discover what 100 Cheerios looks like. Or count all the socks that have no mates. In the car count the number of orange cars compared to the number of white cars.spoon full of cheerios

“Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study,” will be published in the journal Developmental Psychology. But really, you don’t need to read it. — Dan Friedman

Summer reading, turned adventure

Linda McFayden, reading director at New Vistas School, helps a young reader meet her summer reading goal.

Encouraging your kids to keep reading over the summer is so important for maintaining their reading proficiency, and it doesn’t have to be a struggle. With a little creativity, it can even be fun!

New Vistas Center for Education, a Chandler private school for children from preschool through high school,  has developed a special program that turns summer reading from a chore into a game, complete with a theme, goals and rewards.

Linda McFadyen, reading director at New Vistas, developed the “Book a Trip – Ticket to Read” program to engage preschool through grade school readers by encouraging them to log their reading hours and achieve their goals.

Preschool through second grade students strive to log 300 hours of reading over the course of the summer, while third through sixth grade students must reach or exceed 600 hours. At the start of the school year, McFayden plans to distribute awards to recognize students who complete their reading goals.

McFayden also organized an accountability system called “Check and Chat,” through which students have the opportunity to come in to three sessions throughout the summer, which serve as check points to keep students on track.

The program at New Vistas is inspired by the Johns Hopkins Center for Talented Youth, which provided the reading list from which New Vistas students have made their summer selections in subjects ranging from mystery to mathematics.

McFayden says parents have been instrumental in facilitating the reading program, coming up with creative ways to keep books accessible and fun for their young readers. Some have begun to keep books in the family car, developed their own special incentives for meeting reading goals and organized neighborhood book clubs.

You can inspire your own young reader in similar ways, developing curiosity, vocabulary and confidence. Just get creative, and read for fun with your child this summer! — Sadie Smeck

RAK Archives
Find links to summer reading programs at Valley libraries.

Caring for students, all year round

You’ve heard the saying, “There’s nothing like a good breakfast to start the day right.” The same goes for a healthy lunch, which children need to maintain energy and alertness throughout the afternoon. However, many children across our nation and state don’t have access to the nutrition they need to stay healthy and active, both physically and mentally, throughout the summer months.

To combat this heartbreaking reality, public schools across the state have joined the USDA’s nationally funded Summer Food Service Program. Free breakfasts and lunches are provided to local children who may not otherwise have access to regular meals. The meals, provided at times and locations that vary by school district, are not district-specific; they are available to any child in need who is 18 or younger.

Summer Food Programs across the state are growing their capacity serve, and new districts have begun their own programs this year. Glendale Elementary School District’s Summer Food Program expects to serve more than 50,000 balanced meals this summer. Roosevelt School District anticipates another 25,000. Other districts involved include Coolidge Unified School District, Safford Unified School District, Gilbert Public Schools and Willcox Unified School District.

For more information on times, dates, and locations of Summer Food Programs, visit — Sadie Smeck

Library clerk’s Millionaires Club promotes reading

Members of the Millionaire's Club. Photo courtesy of GESD.

Last week, the Glendale Elementary School District‘s Discovery Elementary School welcomed 27 new members to the prestigious Millionaires Club, where the criteria are not about dollars earned, but words absorbed.

Created by library clerk Michele Beney, the club issues a challenge to students and staff at the school: Read as many books as it takes to reach the mark of one million words or more.

The new members, along with the top five readers from every grade, were rewarded with an ice cream party put on by the school’s Parent Teacher Organization.

This year, 267 students and a few staff members accepted the challenge. Beney tallied their progress on a board in the school library. With the help of websites and some counting on her own, Beney totaled up the word counts of every book in the school library. The students and staff had until May 25, the last day of school, to break the one million-word mark. One student was admitted to the club way back in November!

Open to all ages—two second-graders were recently inducted—the challenge is a school-wide endeavor. Because lower-level books often have small word counts, Beney instituted an alternate counting system for grades K-3. “I didn’t want anyone to be discouraged, she said.

Since the October founding of the Millionaires Club, Discovery Elementary has seen a boost in library attendance, even among students whose primary interest beforehand was not reading.

“It does take extra time,” Beney says, “but if I can get one student to read more then it’s worth it.”

With luck, Beney hopes, the club’s success will translate into more books for the library. Tight education budgets make the purchasing of new books difficult, so the school is taking donated books, which Beney can exchange with local bookstores to secure what the library needs. The program is also giving the clerk an idea of what students’ favorites are. So far the leaders are the Harry Potter and Diary of a Wimpy Kid series, as well as the creepy books of R.L. Stine.

“I’m enjoying seeing what they’re reading,” says Benney. “I’m getting to know what they enjoy and like, and that gives me plenty of ideas on what new books, if any, I can order.” – Robert T. Balint

Young artists debut at Phoenix Art Museum

Desert Palms Elementary fourth graders on a field trip at the Phoenix Art Museum. Photo courtesy of Peoria Unified School District.

If you are proud to display your child’s artwork behind a magnet on the refrigerator, just imagine it hanging in a real art museum! For some Valley parents and kids, this dream came true.

Amidst of the exhibitions of work by famous artists and designers, 60 young students of Desert Palms Elementary School in Peoria had the chance this month to see their original artwork on display at the Phoenix Art Museum.

A donation of exhibit space from the Phoenix Art Museum made this unique opportunity possible for the lucky students. The museum also held a reception for the students and their parents, who were able to experience the student exhibition, as well as others in the museum.

The art teacher at Desert Palms, Marian Meadows, has collaborated with the museum in a year-long initiative to bring art into classrooms and students on field trips to see art on display at the museum.

Desert Palms is scheduled to display again at the Phoenix Art Museum in May 2013, the museum’s soonest available opening for exhibit space!

The student exhibition will be on display only through Memorial Day, so if you would like to see it, May 29 is your last chance.

Inspire your fledgling artist this weekend with a trip to the art museum to see what their young peers have been able to accomplish! — Sadie Smeck

Online tool prevents summer “brain drain”

We all know that when school lets out and there’s no more homework or class time, kids are at higher risk for losing what they learned during the school year. So don’t let your kids’ brains melt in the summer heat!

The Scholastic Summer Challenge is an interactive, online summer reading program that allows kids to track their progress with an online reading log, win prizes for reaching their reading goals and even compete as a school to reach a summer reading World Record.

Parents and educators are encouraged to get involved too – you can register online to receive updates on your young reader’s progress, search and share summer reading lists and get tips and activity ideas to engage your child or student.

The Summer Challenge is totally free, and program resources are available in both English and Spanish. It is easy to register any time at — Sadie Smeck