Remember the days when working a math problem resulted in a right or wrong answer, and parents had a basic grasp of how to help their children with math homework? Those days predated the Common Core math standards, which arrived in 2010 and put forward a central idea: Students should know why they arrived at an answer, and that is just as important as getting it right.
Thus “new math” was born, and teachers nationwide modified their methods in order to apply the federal standards to traditional mathematical practices, says Lynette Washington, a senior lead educator at Olney Charter High School in Philadelphia.
“What we expected then and now are different,” she says. “A traditional classroom was very procedure-based, where the teacher did all the lecturing and explaining in front of the class. The students took notes and followed procedures and routines. The students didn’t have a voice, and the math was very abstract.”
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Common Core math procedures are much different because the teacher has become a facilitator. For example, there are eight mathematical practices, such as analyzing, approximating and grouping, embedded in lessons that help students gain a sense of the problems and then solve them, according to TeacherStep, an organization that provides education for teachers.
“Students are now asked to reason, quantify and give input about how they think,” Washington says. “We are asking students to collaborate, work with their peers and discuss situations. So, it’s no longer a scenario of ‘This is the answer and that’s it, let’s move on to the next section.'”
Common Core Math
Common Core math moves into educational lanes of literacy and visual cues, allowing students to read the problems and then make sense of them.
Jen Gleason, a senior educational consultant and associate director of service design for Teaching Matters, a New York-based professional development organization for teachers, says her organization has been helping educators implement Common Core standards since 2011.
Gleason says the new way of teaching math is not an either/or situation, but rather a balance of understanding mathematical concepts and developing students’ ability to apply math procedures.
“The new way of teaching math focuses on building students’ conceptual understanding so that they understand the ‘why’ of math, and what the underlying concepts are about the procedures they are learning,” she wrote in an email.
“Kids are now working toward using this deep, conceptual understanding to then apply the knowledge,” she says. “But this doesn’t mean there is no emphasis on fluency. There is still a heavy emphasis on kids being able to fluently apply algorithms.”
A New Math Language
Common Core puts an emphasis on how to solve problems, and experts say that comes with a new math language. “Friendly numbers,” “making 10s” and “landmark numbers” are just some of the new phrases students learn to dissect math problems.
Visuals can also help students understand a problem, show their thinking, reason with other students and grapple with more difficult concepts. At the elementary level, that can include math manipulatives, number lines, area models and math clipart.
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Here are some examples of concepts that children are taught under Common Core standards, provided by Caroline Farkas, a former elementary school teacher and founder of Doodles and Digits, which provides online educational resources to make math more accessible.
— Landmark Numbers. These are numbers that students are familiar with, such as 10, 25, 50 and 100. Students will change a number into a landmark number in order to solve a problem. For example, to add 123 and 50, students would turn the 123 into the “landmark number” 125 and then add 50 to get 175. They would then subtract 2 to make 173.
— Friendly Numbers. These are similar to landmark numbers, but are numbers that end in zero, such as 10, 20, 50 and 100. The concept works much the same way. To add 18 and 25, for example, students would change the 18 to the “friendly number” 20. They would add 20 and 25 to get 45 and then subtract 2 to get 43.
— Making 10s. This is a strategy typically used in lower elementary school. It can help students see the relationship between numbers and reinforce our base-10 number system. It is often accompanied by blocks or 10 frames on a grid to help students visualize the regrouping of numbers. The goal is to have students make a group of 10 in order to solve a problem. For example, to add 8 and 5, students would turn the 8 into a 10 by taking 2 from the 5. They could then easily see that 10 plus 3 (like 8 plus 5) equals 13.
— Decomposing. Decomposing a number is breaking it down into parts (typically by place value in elementary school) in order to solve a problem. Decomposing can also be called “expanded form.” For example, the number 1,245 decomposed is 1000 + 200 + 40 + 5.
Of course, these are just examples. There are more concepts, from box multiplication to mental math. One that Farkas says is important for parents to remember as they navigate the world of new math with their children is known as a “growth mindset.”
“This is huge in math education,” she says. “It’s the idea that students believe they are able to develop good math skills through learning and growing. Many teachers teach it by telling students to add the word ‘yet’ at the end of the sentence. For example, instead of saying, ‘I don’t know how to solve this problem,’ change it into ‘I don’t know how to solve this problem — yet.'”
Five Resources for Parents
— TeacherStep’s guide breaks down the Common Core’s eight mathematical practice standards.
— Khan Academy offers free math classes in grades PK-12, as well as college-level courses.
— Cuemath offers live online math classes.
— Parents.com’s “new math” explainer offers video and visuals.
— Understood offers nine “new math” problems and the methods to solve them.
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Understanding the ‘New Math’ Your Children Are Learning originally appeared on usnews.com