Ever since Massachusetts and Vermont began adopting the national Common Core standards in 2010, parents have found themselves baffled by math homework that looks nothing like what they learned in school.
"I hate it," said Cathy Georgi, a parent from Bennington, Vt.
"We owe it to our children to bring common sense back to the classroom," said William Celley, another Bennington parent.
However, many educators are encouraging parents to look past their initial shock, frustration and confusion and consider the reasoning behind the changes.
"We see people that have been brought up with the idea that math is a bunch of little tricks you learn, where we want them to view it as a body of knowledge," said Chantal Rhind, a professor of mathematics at Berkshire Community College in Pittsfield, Mass.
"When I was in school, it was 'This is the way you do it,'" said math teacher Rachel Kipp, who teaches at Mount Anthony Union Middle School in Bennington. "We were taught the algorithms, but we didn't really understand why we were doing things that way."
Process vs. procedure
Pat Conway, the Southwest Vermont Supervisory Union's math coach, tried to explain the disconnect between proponents and opponents of the new mathematics standards.
"The math standards are based on understanding the process rather than procedure," she said.
Conway said that Southwest Vermont Supervisory Union schools begin by teaching students to understand why they are doing things a certain way, and then eventually build up to the procedures or shortcuts.
Think like your kid
Adults, said Conway, often look at their children's homework through a high school or college mind, rather than through the mind of a second-grader. When parents explain how to do a method that they remember from their days in school, their student often responds that that isn't the way they were taught or that they were told not to do it that way. This frustrates parents, who know how to solve the problem and want to help, but can't according to the new curriculum.
"I understand that frustration," said Rhind, "I would try to understand what the teacher is trying to do, and try to not tell the children that there's only one way to learn something in life." She pointed out that the methods the students are now learning are designed to give them a larger toolkit that they can use to solve problems.
Conway used an example for first-grade level math: If Joe has five marbles, and grandma gave him some more for his birthday, and he now has 13 marbles, how many marbles did Joe's grandma give him?
A parent might see that problem and think to simply subtract five from 13, and get the answer, which is eight.
However, Conway said, under the new math standards, first-graders are taught several ways to think about the problem: They could think of it based around the number 10, for example. To get to 10 from five, Joe would need five more marbles. To get from 10 to 13 means three more marbles. Five plus three is eight.
The latter method may seem more complicated and less efficient to a parent that is focused on the solution rather than the process. But to the student, this approach is helping them learn to think about the relationships between the numbers in different ways.
Parent Adam Corrow, who lives in neighboring Hoosick Falls, N.Y., said he's been following the changes in instruction.
"Common core math is no different than the last method that was different from the norm. With change comes resistance. Adults are typically set in our ways, and mentally unable to learn like children," said Corrow. "I've seen the exams, I've tried the problems, and most of the arguments that I've seen against it is that the path to the answer is as important as the answer. This is not a new idea. Open your mind to new ways of thinking and you will see it's not so different."
The standards, said Conway, stress perseverance, and focus on problem solving, especially more complex problems that don't have obvious entry points. Gone are the days of looking for keywords such as "in total" or "all together" to tell students they will need to add. Instead, the problems are often designed so that they could be solved multiple ways, using the different methods students have learned.
Rhind said the reduced focus on calculators is another benefit of the new standards.
"Calculators have been introduced too early and been over-used," she said, "and have really got in the way of learning reasoning."
School administrators, like Principal Carolyn Boyce of Morris Elementary School in Lenox, Mass., say the new standards are proving to be effective.
"The program we use has been very successful for us over the past five years in regards to teaching students a deeper understanding of mathematical concepts as called for by the Common Core and building numeracy skills and math fact fluency," she said. "These skills have ultimately led to a steady improvement in our standardized test scores."
Figuring It Out
For parents who want to learn more about the so-called "new math" under the Common Core standards, Pat Conway, math coach for the Southwest Vermont Supervisory Union, said the best way to learn how to best help your student is to reach out to your child's math teacher or coach, or check to see if your school district hosts math nights for parents. While the standards are set by Common Core, each school develops its own curriculum.
The following websites also offer helpful tutorials and examples that parents and students can use to practice math together:
Khan Academy: khanacademy.org/commoncore
Achieve the Core: AchievetheCore.org
Common Core State Standards Initiative: corestandards.org/Math
National Council of Teachers of Mathematics: nctm.org/ccssm
Derek Carson can be reached at 802-447-7567, ext. 122.