- Associated Press - Saturday, January 23, 2016

DUBUQUE, Iowa (AP) - Ann Johnson encouraged students to explore math concepts with a real-world problem.

The Sageville Elementary School teacher guided her second-graders through a visualization exercise before they solved a problem that featured a classmate and snacks.

The problem: Ethan has 30 candy canes to put in boxes. Each box only can hold two candy canes. How many boxes does he need?

“Close your eyes,” Johnson told her students. “Can you see Ethan? Ethan has 30 candy canes to put in boxes. Do you see all those candy canes? Think about how you might represent those. Each box can hold only two candy canes. How many boxes does he need to make sure all the candy canes go in a box? Open your eyes.”

After a brief discussion, students used various strategies — from tallies to number sentences (i.e., 2 + 2 = 4) — to solve the problem.

“We don’t usually tell kids what the answer is anymore,” said Johnson, a math content leader at Sageville. “We are asking them questions so we lead them to the answer.”

Common Core standards for mathematics expect students to conceptually understand math. Multiple strategies, versus a single algorithm, are taught.

Forty-two states, including Iowa, Wisconsin and Illinois, have adopted the standards designed to prepare K-12 students for higher education and the professional world.

“(Critics) keep saying “new math.” It’s not new math. Math is math,” said Bridget Hamilton, preK-12 mathematics coordinator for Dubuque Community Schools.

Back in Johnson’s classroom, students answered variations of the candy cane problem. For instance, they found six strategies to determine how many boxes were required for 40 candy canes with five in each box.

“We’re celebrating all strategies,” Johnson said. “Kids who are direct-modeling and drawing every single one of those candy canes. We’re also celebrating the kids who can multiply and the kids who can divide.

“We’re just making connections, and we’re forcing them to talk about math so they can’t forget anything that they’re doing.”

The Telegraph Herald (https://bit.ly/1P877AM ) reports that Common Core is not a curriculum. Rather, it provides benchmarks that students should be able to reach.

“The Common Core encourages a greater depth of instruction on fewer topics within a school year,” said East Dubuque (Illinois) Elementary School Principal Michelle Till.

Math standards were developed in an attempt to lay the foundation and prevent misconceptions that older students seemed to possess, officials said.

“The whole purpose was to roll all the way back and make sure we’ve got these foundational skills solidified and then we can build,” Johnson said.

A criticism of the standards is they are not the way parents were taught. In the past, students learned specific procedures to solve equations.

“One of the biggest ‘ah-ha’s was that we used to teach so many procedures and rules for how you do math,” Johnson said. “Now, there is no one way to do math. What we hope happens is that we give kids enough exposure to different types of problem-solving and different types of strategies that kids figure out how math works for them.”

While students are expected to know facts from memory, Hamilton said, rote memorization as the way of teaching those facts is de-emphasized.

“Once students are taught to use reasoning strategies based on known facts to derive answers, then expected fluency would follow,” she said. “The reason for this is research will tell us when students learn facts through reasoning, not just memorization, they are better able to regenerate a fact if they have forgotten it.”

Students, for instance, are not taught rote memorization of multiplication tables. Hamilton said students instead are taught reasoning and conceptual understanding to be fluent in multiplication facts.

Dubuque Community Schools was aligned to Common Core math standards long before the standards were required to be in place in Iowa for kindergarten through eighth grade in 2014-15.

“With the adoption of the Common Core standards at the elementary, our life didn’t change much,” Hamilton said.

For more than 10 years, Dubuque’s public elementary schools have used Math Trailblazers curriculum that supports conceptual thinking. Students are encouraged to collaborate to create methodologies, draw conclusions and share results, according to www.mathtrailblazers.com. The curriculum is aligned to Common Core standards.

“We want kids to be 21st-century learners, problem-solving thinkers,” Hamilton said.

It’s difficult to compare student scores from before Math Trailblazers started in 2003 to now. Associate Superintendent Lynne Devaney said data prior to 2005 is not comparable due to changes in data collection and reporting methods.

In 2005-06, 68.3 percent of students in grades three, four and five combined were proficient in math based on Iowa Tests. That percentage grew to 76.6 percent in 2014-15.

At East Dubuque Elementary School in Illinois, teachers continue to analyze Common Core math standards and improve classroom lessons.

“We are definitely in a transition period,” Till said.

Debra Stork, University of Dubuque professor of education and head of the Teacher Education Department, said she believes the standards work.

“Sometimes we get hung up with not memorizing or, ‘Kids aren’t learning how I learned,’” she said. “We have to go beyond what we did 35 or 40 years ago.”

Molly Burrows Schumacher recalls the days of asking her parents for help with math homework.

Now the Marshall Elementary School parent-teacher organization president turns to Google and her children to help them with their homework.

“I was really surprised (with all the strategies). I had no idea where to start,” Burrows Schumacher said.

An often-cited criticism is that parents are confused and flustered by multiple strategies versus a standard procedure.

Jennifer Benson, a teaching specialist faculty member at the University of Dubuque, said it can be difficult for parents who were taught one way to solve an equation to grasp the concept of numerous ways.

Roxane Tharp, who has a second- and fifth-grader at Sageville, overcame frustrations.

“Initially, I had to wrap my head around it a little bit. We’re so used to the typical lining up the columns and adding and subtracting,” she said. “It was kind of difficult at first. We have to almost retrain our brains as parents.”

But Tharp watched her children’s confidence grow. Her own confidence in the strategies did the same.

“I do think it’s beneficial because kids are learning at different paces and it takes the pressure off having to memorize,” she said.

Jason Neises does not have a problem with how math is taught to his second-grader at Sageville.

“I’m encouraged by the way (the curriculum is) using critical thinking to solve problems rather than just memorization,” he said.

Burrows Schumacher understands that things change over time, and she said parents need to learn to adapt. She said her younger children — a kindergartner and a second-grader at Marshall — enjoy math. She also has an eighth-grader at Thomas Jefferson Middle School.

“They love it. They don’t know anything different. For them, this is math,” she said.

Southwestern Elementary School in Hazel Green, Wisconsin, implemented a new math curriculum last school year amid widespread parent concerns.

“There were some huge struggles when we first rolled out the curriculum,” said Superintendent John Costello.

He said Math Expressions Common Core was a “huge shift for parents” since it was not what they viewed as the traditional way to teach math. Like Dubuque schools had done for years, students were taught multiple strategies.

The Southwestern parent-teacher organization voiced its fears about the change.

“We were concerned about how well the kids were going to do with the change,” said Sarah Rouse, president of the organization.

The mother of a preschooler, sixth-grader and seventh-grader said it became difficult to correct her older children’s math mistakes at home.

“The first year was very hard, especially with my older two,” Rouse said.

Storey Dreessens, an organization member with a kindergartner, fourth-grader and seventh-grader, said the curriculum also impacted her ability to help her children with their math homework.

“Last year was a tough year. It was a transition year,” she said.

Concerns quieted down now that Southwestern is in its second year of the curriculum.

“I have not heard much more negativity with the curriculum this year,” Rouse said. “I kind of feel like parents, as a whole, are getting used to it.”

Dreessens agreed. She said math strategy samples are sent home now and she is able to work through those with her children.

“We can learn right along with them,” Dreessens said. “My fourth-grader has taught me.”

Costello added that the district has experienced some strong gains with students grasping math concepts and completing mental math, among other items.

Dreessens said just because it’s difficult for her to grasp the concepts, it does not mean math is difficult for her children.

“I personally think it’s great. They’re able to comprehend it more than either it’s right or wrong and this is the way to solve it,” she said.

Jakob Sand, a second-grader at Sageville, enjoys math class.

“When I think about math, I think about plus signs, minus signs and number sentences,” he said. “Sometimes it’s hard, sometimes it’s easy.”

Jakob recently joined his classmates on the floor near an easel in Johnson’s classroom to solve warm-up equations. Students then direct-modeled, counted by numbers or used known facts to solve facts they don’t know at their desks while trying to answer real-world problems.

Eventually, Johnson paired the students with someone who used a similar strategy. The two students compared and contrasted their work.

“It’s fun,” said Natalee Koopman, a second-grader. “When you can’t find the numbers and then you get to the right number, it feels good.”

Selected students meticulously wrote their solutions on a white board and then explained to the class why the strategy worked.

“We’re moving kids by having them talk about what somebody else did,” Johnson said. “We want those kids to be moving. That’s why we can justify celebrating everybody and not worrying about efficiency right now.”

Sometimes, students might struggle with which strategy to choose. “It gets crazy,” Jakob said. “I get too much stuff in my brain.”

Shelton Splinter, a second-grader who likes multiplication and number sentences, agreed. “It’s hard to decide what strategy to use.”

Johnson said she hopes students will work through the problems to become 21st-century thinkers.

“We want them to be able to go into the grocery store and do math without pen and paper,” Johnson said.

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Information from: Telegraph Herald, https://www.thonline.com