# The early years: teaching young children math concepts

byCaralee Adams March 19, 2021April 8, 2021

Student work posted in an elementary school before the pandemic shows the “partial product” method of solving a multiplication problem, one of many methods students have learned with Common Core. Credit: Jackie Mader/The Hechinger Report

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Mathew Felton-Koestler, known as “Mathy Matt” on his YouTube channel, makes videos for parents that explain why and how young kids are learning math these days. He has two sets of videos specifically on the Common Core, in which he talks about the kindergarten and the third grade standards.Allonda Hawkins said the way her children are expected to do math is “100 percent different” from the way she learned.

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This story also appeared in The Washington Post

“There are terms that I’ve never heard before, like arrays. It’s very foreign to me and it’s hard to teach,” said the 38-year-old real estate agent from Winston-Salem, North Carolina.

The mother of four children, ages 5 to 11, often turns to YouTube for explanations and recruits her fifth grader, Zoe, to help her younger siblings. Hawkins said she’s catching on more now that she can eavesdrop on her kids’ online classes, but still is frustrated that she doesn’t have more guidance.

“There are a lot of teachers that lack grace with parents who don’t understand,” Hawkins said of the new approach to math. “We end up teaching

With virtual learning, parents across the country are getting an up-close look at math instruction — and, like Hawkins, they don’t always know what to make of it. But with more than half of American kids still learning at home as of Feb. 21 (either all virtually or in hybrid programs), it’s time for parents to get up to speed.

Sylvia Majdoch, 9, pictured here during a remote school day at her home in Florida, is the fourth in her family to take on math using the principles of Common Core. Her older sisters have already moved on to Algebra 2 and pre-calculus. Credit: Michelle Majdoch

Experts say it’s important for parents to know the basic ideas behind the current methods if they are going to help their kids. Positive parental help could make the difference between students being excited about math or falling behind during the pandemic, said Jennifer Bay-Williams, co-author of “Elementary and Middle School Mathematics: Teaching Developmentally” and professor of education at the University of Louisville.

The new approach is actually not all that new. It’s grounded in research going back more than 30 years and is reflected in the Common Core State Standards, which are used in 41 states. (And most states now follow standards with the same principles, whether or not they call them Common Core.) Instead of memorizing procedures to solve problems, kids are now asked to think through various ways to arrive at an answer and then explain their strategies. While some parents believe these methods are just a more complicated way of teaching math, they are designed to promote a deeper understanding of the subject and help students make lasting connections.

“There’s not just one way to solve a problem,” said Megan Burton, president of the Association of Mathematics Teacher Educators and associate professor of elementary education at Auburn University in Alabama. To fully grasp deeper mathematical concepts, “students need to think about what makes sense and build on what they learn.”

“There are a lot of teachers that lack grace with parents who don’t understand.”

Allonda Hawkins, parentEducators and mathematicians pushed for states to adopt Common Core math in hopes of moving away from a curriculum that was “a mile wide and an inch deep” and focusing more on big ideas, said Bay-Williams. When the Obama administration offered benefits to states that adopted the Core, the standards took on a partisan edge. But they were not meant to be political, Bay-Williams said. They were meant as simply a short list of concepts that would prompt teachers to spend more time on core mathematical ideas and would be common across states. In addition to a brief outline of what kids should learn in each grade, they include eight standards for mathematical practice that frame how to do math.

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The first practice standard, to make sense of problems and persevere in solving them, is the top priority, said Bay-Williams. A focus on understanding problems and working to solve them should shift the pressure away from just getting homework done correctly and encourage parents to ask how their children are thinking.

“It creates in kids this identity that they can do math” when they are asked to explain their thought processes, Bay-Williams said. “Just memorizing something their parents show them and then practice, practice, practice, leads to a different emotional reaction and a different way they think about themselves as a math doer.”

Research is clear that allowing kids to experience a “productive struggle” pays off in children’s math ability. “Productive struggle” is merely wrestling with an idea or pondering a new concept, which is when teachers say learning occurs.

127 = 12 tens and 7 ones

“Kids need to know math may be a little challenging, but it’s going to make sense” eventually, said Burton. When watching a kid struggle to complete a math problem, “it’s very tempting for a parent to want to get in there and rescue the child, which doesn’t always help in the long run,” she said.

One of the key concepts in Common Core math is that students are asked to look at numbers and think about the amounts they represent. For instance, 100 can be thought of as 100 ones, or a bundle of 10 units of 10, or “10 tens.” And 127 can be thought of as a bundle of 12 units of 10 and seven ones, or “12 tens and 7 ones,” or even “10 tens and 27 ones.”

Students are asked to use the idea that numbers can be represented differently when problem solving, too.

Take 4 x 27.

Traditionally, a student would line up the numbers vertically, multiply 4 x 7, carry the 2, then multiply … well, most adults remember the procedure. (The answer is 108.)

Now, kids are encouraged to think: Wait a minute, that’s really just 4 x 25, which is 100, plus 4 x 2, which is 8. If I add the two products together, I get 108.

4 x 27 = (4 x 25) + (4 x 2)

“That works pretty slick and makes more sense,” said DeAnn Huinker, professor of mathematics education at University of Wisconsin-Milwaukee and director of the university’s Center for Mathematics and Science Education Research. “I can do that in my head, write down a couple of partial products and add it up.”

Isabel Majdoch, 17, is enrolled in pre-calculus as a high school senior and is headed to Florida Polytechnic University next year. Her mother said the grounding in math reasoning that Isabel got in elementary school has helped. Credit: Michelle Majdoch

Huinker advocates redefining math success: “It’s not being able to tell me the answer to three times five within a heartbeat. Rather, being successful means: ‘I understand what three times five is.’ ” (For those following along at home, it’s three groups of five.)

Math practices today emphasize reasoning, being able to make a viable argument and critiquing others. Teachers have students pause and think before diving in to learn a standard algorithm, said Bay-Williams. In a classroom, students might pair off and share their math strategies with a partner. With remote learning, teachers may ask students to turn to an online interactive whiteboard or record a short video.

For some students, it might help to use a number line to see the relationship between numbers. If a student is given the problem 12 minus 7, the student can start at 7, jump to 10 (that’s 3), and then jump to 12 (that’s 2), so the difference is 3 plus 2, or 5. Ten in this example is known as a “benchmark number,” said Huinker, and students are encouraged to use benchmarks to move toward more efficient and meaningful computation strategies.

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3 x 5 = three groups of five

An array, which flummoxed Hawkins, is a model that students can use to master multiplication. It’s essentially a grid. Students can plot out 5 x 6 by coloring in five rows of six or six columns of five. Count the total number of squares and you’ve got the answer: 30. Break the grid apart into sections, and you can see three sets of 10. The visual representation can also help kids understand area and measurement and can plant the seed for connections that will help in later math. Parents may think it’s tedious, but when students use visual models and explain their thinking, it also helps teachers make sure students truly understand a concept and haven’t just memorized a formula, said Burton.

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In China Grove, North Carolina, Abby Covington, a mathematics instructional coach at Millbridge Elementary School, hosted a webinar last fall for parents to explain teachers’ math expectations and tamp down pressure for perfection with homework. The school typically holds similar events in person each year, but tailored this year’s online content in response to parents’ questions that arose with virtual learning.

“We honor and value mistakes, because mistakes are how we learn,” Covington said. “We want to be celebrating the different types of math strategies

“Yes, we want future citizens who can add and subtract, but we also need citizens who can reason and talk about their thinking — skills that humans can bring to the table that my calculator can’t.”

Mathew Felton-Koestler, Ohio UniversityIn time, students will learn to do the traditional step-by-step approaches to solving problems, which are faster and more efficient, but Covington said the idea is to build a proper foundation: “I tell parents we are going to get there … that’s our ultimate goal, we’re just not in a race.”

To help demonstrate the value of the new flexible approach to teaching math, Mathew Felton-Koestler, associate professor in the department of teacher education at Ohio University, produces videos for parents such as “What’s Wrong With Carrying the One?”

The Majdoch kids, pictured here at their Florida home during the holidays, have all learned math using Common Core principles; their mother said seeing how well the older girls have done in advanced high school math has made her more patient with her younger kids’ math experiences. Credit: Michelle Majdoch

“Yes, we want future citizens who can add and subtract, but we also need citizens who can reason and talk about their thinking — skills that humans can bring to the table that my calculator can’t,” said Felton-Koestler. “People worry that if we are focused on these different strategies, kids aren’t going to be good at doing computations. That doesn’t turn out to be true. They end up being just as good — and much better at higher-order type tasks.”

And critical thinking skills are what employers are asking for in the workplace, he said.

Some parents of older kids are finally seeing the long-term benefits of all that early focus on how to think about math. Despite having an MBA, Michelle Majdoch, 46, of Coral Springs, Florida, said she was initially confused by her kids’ math homework with the story problems and drawing to show their work.

But now that her children are in fourth, fifth, 10th and 12th grades, she gets it. Having to learn three ways to do a problem in the early grades made each of her kids discover the methods that made the most sense to them. These days, her high school daughters are doing well in Algebra 2 and pre-calculus. Now “I can see the progression of what’s going to happen,” she said of watching her kids as they move through the math curriculum, which she was pleased to find was similar to what her older kids had learned when the family lived in Ohio.

With school instruction spilling over to the home, it’s fair for parents to say to their kids: “Wow, that’s so interesting. Here’s how I learned it,” said Huinker of the different math methods. Then they can ask the child how the “old” way is similar to or different from what is being taught in school now.

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Michele Alley said she and her third grade daughter, Cora, often disagree about how to do math homework. In a spare bedroom converted to an office/school, Alley works full time while Cora and her first grade son, Carter, do their distance learning at home in Monticello, Kentucky.

If it’s something Cora understands, she follows her teacher’s directions. But, if her daughter gets stuck, Alley said, she doesn’t know how to help other than to demonstrate the way she learned it in the 1990s — working through the problem by writing out the equation on paper. “Whatever the teacher says is the gospel, which is a good thing. They should listen. But they need to know there is more than one way to do things, too,” said Alley, 36, a re-entry coordinator for the state department of corrections. Alley said she would welcome more information about Common Core math. “I know very little about it. I can say I don’t like it, because I don’t know how to do it.”

“It’s very tempting for a parent to want to get in there and rescue the child, which doesn’t always help in the long run.”

Megan Burton, Association of Mathematics Teacher EducatorsSome schools are doing what they can to fill parents in on the whys behind the new ways of teaching math.

In Alley’s district, Bell Elementary hosts math nights for families twice a year to help bridge the home-school divide, and in October pivoted to a drive-through “Family Learning Night” on a Saturday morning. The fall event drew 300 people — one of the best-ever turnouts — perhaps because it was held on a weekend and reading materials were also distributed, said Jamie Reagan, a first grade math intervention teacher at Bell.

Jamie Reagan presides over a table of math “goodies” during a socially distant Family Learning Night for students of Bell Elementary in Monticello, Ky., where she is a first grade math intervention teacher. Credit: Jamie Reagan

Teachers gave out goodie bags with math games and information on math standards in “layman’s terms” so parents would know what kids needed to learn by the end of first and second grades, said Reagan.

“Kids can learn while they are playing — it doesn’t have to be a worksheet,” said Reagan, who also regularly provides math packets with cards, counters and other materials in tubs in front of the school for families to pick up. Teachers have had to adapt their instruction as they go back and forth from in-person to virtual learning, she said, and have come to realize they will have to make adjustments next year, as many students will likely not meet grade-level expectations when they are assessed later this spring.

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On the upside, said Burton, of the math teacher educators association, the pandemic gives parents time to help children see the usefulness of math outside of school.

“When you are setting places at the table, ordering things online to be delivered, rearranging furniture and measuring, have your child be with you,” said Burton. “We need to recognize that math is important. Math is fun. It’s like a puzzle, and it’s understanding the world around us. If parents can convey that enthusiasm, it has a huge potential for impacting their child’s success in the future.”

Also, there’s a pandemic on, and parenting has never been so hard. Bay-Williams, the author of a book on teaching math to kids, said parents should trust their intuition about what ends up being important.

“Take a deep breath,” she advised parents supervising online math learning right now. “Kids are resilient, they are learning things at home — baking with you and doing things that are going to serve them in other ways.”

*This story about teaching math was produced by *The Hechinger Report*, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the **Hechinger newsletter**.*