Every three years, 60 participating countries in North and South America, Europe, and Asia are surveyed by The Programme for International Student Assessment (PISA). In this study, about 6,000 fifteen-year-old students from each country are given extensive tests to determine the country’s average mathematical aptitude. PISA not only gauges a student’s knowledge in a typical classroom setting, but also tests his or her mathematical aptitude in real-life situations.

The study’s latest results show the United States coming in at number 34 globally – slightly below the average among the group. Although the United States is the 5^{th} highest when it comes to spending per student, the average student tested almost two years behind the highest testing country, Singapore. Most of the weaknesses that were uncovered involved the student’s lack of understanding when using mathematical reasoning in real-world scenarios.

Although these results are not necessarily cause for dismay, there is certainly room for growth. According to the Common Core State Standards Initiative, the Common Core standards have been modified to remedy these mediocre test results in the following ways:

*Less Content, Greater Depth*

Instead of touching on many topics for short periods of time with little review, teachers are now encouraged to focus on fewer principles per year in order to cultivate a deeper focus in each topic. This enables students to practice a single lesson for a longer period of time and gives students a better chance at retaining mathematical knowledge.

*Building Blocks *

Under the old Common Core standards, subjects like algebra and geometry weren’t introduced until late junior high or high school. The changes in these standards now dictate that basic algebraic principles should be introduced earlier on in elementary school. This method allows teachers to use a student’s basic knowledge as a foundation and build upon the fundamentals that have already been learned.

*Understanding in Lieu of Memorization*

In the past, methods like memorizing multiplication tables and using shortcuts to solve equations have been utilized in order to make complex principles more manageable for students. However, the new standards recommend that teachers shy away from these methods. These habits may lead to correct answers, but students cannot learn the underlying principles of a topic when they rely on shortcut techniques completely.

These changes have been strategically implemented in order to equip students with a fuller understanding of mathematics, and they are expected to greatly improve the learning atmosphere for math students in the near future.