"New Math" refers to the way basic number concepts and strategies in grades 1-5 are currently taught in schools. It gets a bad reputation, and for an unsurprising reason. Here's how it usually plays out... Young students sit down to complete homework, but they can't remember how to use the strategy that's written in the directions. The helpful parent or caregiver sits down and explains how to solve the problem the way they were taught it. The student insists, "That's not how my teacher showed me!", but the parent is sure that the way just explained is easier than whatever strategy the child was trying to do. More often then not, everyone ends up frustrated and homework becomes a battle.*
*As an aside... any elementary school teacher would rather have homework sent back with a note explaining why it couldn't be completed, rather than having fights break out at home.
The "new" way of doing math is different, and at first glance seems so much more difficult and confusing. HOWEVER (and bear with me here), there are very compelling reasons why math is taught using these different strategies. You can Google to read articles explaining the reasoning behind New Math, but here's my quick perspective.
MOVING FROM MEMORIZATION TO UNDERSTANDING
"Old Math" just taught us to memorize steps. Phrases like, "carry the one" in addition, and "divide, multiply, subtract, bring down" in division aren't used anymore. "New Math" helps students understand math in a way where they can fully grasp what they are doing and why. When young students are given the opportunity to explore how the number system works, they are able to move forward with a solid math foundation.
INDIVIDUALIZED INSTRUCTION
"New Math" teaches students multiple strategies for solving basic problems. We know now that teaching is not "one size fits all". Students are exposed to various strategies, and are encouraged to use the one they likes best moving forward. This is a great example of individualized instruction in the classroom.
IMPROVED VISUALIZATION
Many "New Math" strategies are rooted in visualization. Students can see the breakdown of problems in a variety of ways. At first, this seems like so much more work and written explanation. But, once students are confident with a specific strategy, they can simplify the steps and use mental math to solve problems more quickly.