Resources >> Browse Articles >> Curriculum & Instruction


Improving Math Instruction: New Techniques to Solve Problems

Improving Math Instruction: New Techniques to Solve Problems

First-grader Shayley Groff, right, figures out how to solve a math problem. (Katherine Jones)

BY BILL ROBERTS, Idaho Stateman

IDAHO-Deborah Whitaker doesn’t spoonfeed math to her first- graders. Rather than tell them 1+1=2, she takes them on a math journey, explaining the concepts of addition. She shows that numbers are symbols for real things in life, like the number of legs on a cow.

If she’s successful, her students understand not only how to add, but when, why and what it means.

Whitaker’s style of instruction — combining math concepts with computation — is at the heart of a $4 million math improvement proposal state schools Superintendent Tom Luna wants lawmakers to approve.

Luna’s Idaho Math Initiative aims to beef up student arithmetic skills and reverse a longstanding slip in math proficiency that occurs between third and 10th grades in Idaho.

If it is backed by lawmakers, Luna’s plan could affect 268,000 students, the 8,600 instructors who teach math from kindergarten through 12th grade and the colleges and universities that prepare teachers for the classroom.

But first, Luna needs to get the money — and Gov. Butch Otter’s top budget adviser has already branded the program “very expensive.”

Luna has crafted a multi-front assault on math patterned after the decade-old Idaho Reading Initiative for students in kindergarten through third grade.

The math initiative tries to boost student performance by:

• Showing teachers better ways to be math instructors.

• Testing students regularly to assess their math abilities.

• Providing remediation focused on student weaknesses through computer-based programs and special instructors for students who fall behind.


Luna’s plan faced its first challenge in the Legislature last week when Otter’s budget director, Wayne Hammon, told the budget committee that the math initiative is among the costliest of new proposals this year that would require funding year after year.

Additional Information
  • Math initiative highlights

    Here are some of Superintendent Tom Luna’s math initiative proposals. Not all details are worked out yet.

    Establish classes on teaching math concepts for Idaho’s 8,600 math instructors.

    Offer remediation – some through computer programs – to help kids who fall behind in math skills.

    Provide math coaches to help classroom teachers be better math instructors.

    Assess students regularly to see how they are performing. Assessments could combine existing tests and some new ones. You can spend time with your kids helping them get better at math.

    Here are some ideas:

    Hand out some numbers: Give your kids numbers and let them create a word problem. For example, tell them they have $212 saved toward purchasing a mountain bike. Then ask how much more they would need to buy the bike. Kids will likely have to look at ads to find out how much a bike costs and then do some math to figure out how much more they will need.

    Make a budget: Ask your kids what they would like to do if they could go downtown and buy things. Or ask them how much food they should buy for a Halloween party.

    Quick math quizzes for fun: Check to see what your kids know about money, or the calendar. Lots of kids come into class not knowing how many days are in a year. Make sure your child knows there are 365 days in a year or that a quarter is 25 percent of a dollar. Try the same for months.

    Get cooking: Turn your children into chefs. Ask them to make cookies by doubling a recipe. Learning to convert a half cup instead of a quarter cup, or two tablespoons instead of one is a great way to learn math.

    Play with fractions: Say you and your children are standing in the grocery line. Ask them if they know what fraction of people in the line are male and what fraction are female.

    Toss the dice: Another way to learn fractions is to throw a pair of dice and ask kids to create fractions by making the small number the numerator and the large number the denominator. If the dice show a three and a six, then the fraction would be 3/6. Ask your kids if they can simplify the fraction down to 1/2.

    Measure: If you are buying new carpet for your house, ask the kids to measure the area of the room in feet or even inches, Merkley said.

    Play math games: Dominos, Monopoly and chess are great math games.

    Go online:

    Math is Fun Go now.

  • Need a scholarship to make your degree a reality? Connect with millions and get started.

Luna doesn’t dodge the cost.

“It is expensive,” Luna said. “But in my opinion it is … an investment into getting children better prepared for the math they will need when they get to middle school and to high school. I think we will spend less money on remediation once we have the math initiative.”

He’s got a supporter in Rep. Bob Nonini, the Coeur d’Alene Republican who chairs the House Education Committee.

“I would hope we could look deeper into certain programs to see sometimes that what appears to be expensive on the surface returns good dividends,” Nonini said.

Last year, the Legislature approved a plan to increase math graduation requirements for high school students because of concern about students’ ability to compete in college and the workplace.

Beginning with the class of 2013, students will have to take three math classes, not two, before they graduate.


Idaho isn’t alone in toiling at math. Across the country, students do well in early grades, but their skills fall off as they move through school.

National math education experts see a lot of problems in math education:

• Math doesn’t get the same attention as reading in many schools.

• Reliance on calculators is replacing a basic understanding of some math concepts.

• Parents freely admit to their kids and teachers that they were never good at math.

• Kids don’t get a thorough understanding that numbers aren’t simply scribblings on a page meant to be solved to please the teacher. They stand for real things in the world.

“That whole business of ‘number sense,’ they need to know,” said Francis “Skip” Fennell, president of the National Council of Teachers of Mathematics.


Jonathan Brendefur, a Boise State University education professor, is carrying the banner for changing math instruction in Idaho.

His work with teachers in schools such as Boise’s Taft Elementary is behind much of the math initiative Luna supports.

Teachers — especially in primary grades — have relied heavily on teaching kids how to add, subtract, multiply and divide. But not when and why, he said.

So when students enter the fifth grade — where they are expected to apply math to problem solving — many of them falter.

David Lorenzo sees it year after year as students enter his fifth grade at Linder Elementary School in Meridian School District.

“Students are able to compute the math problem but many times they don’t know what that means,” he said. “They don’t understand what information that gives them.”

Lorenzo offers an example:

Suppose a train is traveling 300 miles at an average of 60 miles per hour and it has a two-hour layover. How long will it take for the train to complete the trip?

In such a problem, Lorenzo said, students struggle with knowing when to divide or when to add. (However you calculate it, you should get to seven hours, by the way.)

“Students find it very difficult to extract the information from the problem they need to solve it,” he said.

That’s what Whitaker works toward with her students, well before they reach fifth grade.

“They are not afraid to think,” she said. “They are not afraid to solve a problem, and what we want to raise in our public schools are children who are able to go out and solve problems.”

Turning math instruction around is a big task. Luna’s plan envisions professional development and classes to teach thousands of Idaho teachers to be better math instructors. He also wants coaches to help math teachers be more effective.

Brendefur would like to see prospective teachers take more than the three semesters of math BSU requires for a general credential to teach in kindergarten through eighth grade. But BSU’s education course load is already full with all the other subjects that school districts say they want would-be teachers to know.

BSU would like to provide more professional development for math teachers and more sections in regular classes on math instruction. But it would require about two additional faculty, at a cost of about $150,000, said Diane Boothe, dean of the BSU college of education.

This money wouldn’t be included in Luna’s plan — though similar dollars for higher ed teachers were included in the Reading Initiative about a decade ago.

Still, Luna said the $4 million would put Idaho on the road to helping teachers be better math instructors and put instruction about math concepts in the early elementary grades like Whitaker does at Taft.

To make sure her students were getting these new ideas, Whitaker abandoned the textbooks and helped write her own curriculum for her class.

“My math books, I am proud to tell you, are on the shelf,” Whitaker said. “This is the second year they have not been used. They are dusty and they have not been opened.”

© 2008 YellowBrix, Inc.

Teaching School Finder

Save time in your search for a degree program. Use Teaching's School Finder to locate schools online and in your area.

* In the event that we cannot find a program from one of our partner schools that matches your specific area of interest, we may show schools with similar or unrelated programs.