The Methodology of Japan Math

Try, Understand, Apply and Master 

When Japan Math’s learning methodology was created, it was designed with the values and beliefs of the Japanese educational system in mind. For us, the most important thought was the idea that through their lessons and curriculum, students should be discovering concepts and skills for themselves.

Why does Japanese education place such importance on the idea of the self-possessed student? ? This specific educational approach fosters a sense of ownership in students as they move through their learning journey. Japan Math’s program heavily emphasizes the idea of students thinking for themselves and strengthening their own problem-solving skills, rather than teachers giving students the solutions too quickly.

What other Japanese education values can you see in our curriculum? Here are just a few:

  1. Nurturing a sense of joy in students at the prospect of math and problem-solving to create a positive attitude toward learning.
  2. Encouraging the ability to think independently and outside the box.
  3. Strengthening problem-solving skills to the point that students can attempt more difficult problems using the skills and concepts they have previously learned.

Japan Math curriculum is designed to get your students excited about learning and problem-solving. We’re not concerned as to whether a student solves a problem correctly on their first try. Instead, our program focuses on encouraging positive attitudes while tackling new, harder problems.

The Japan Math Process

So, what is the Japan Math learning process? It’s a series of steps that your students will go through for each new concept and skill, for every unit. The steps are as follows:

  • Try
  • Understand
  • Apply
  • Master

Let’s take a look at each step individually.


The very first step is “Try,” where your student will be given a problem that they may not necessarily have the skills to solve yet. Even though this problem is slightly difficult, it will usually be based on real-world circumstances that are easy for your student to understand.

In this step, your student is encouraged to think back on the skills they have previously learned and see if those concepts can aid them to solve new problems. They are also asked to brainstorm and work together with their fellow classmates. We even provide them with a place to write their ideas and the ideas of their friends in their workbook! 

Check out our piece on “Try and the Role of the Teacher” for more information on “Try”


After the students have tried the new problem for the unit, the teacher will review the answers from the class, encouraging discussion of different tactics and approaches. Once this discussion is complete, it’s time for the “Understand” step.

To achieve a solid understanding of a new concept, students must reflect upon the problem-solving process of the “Try” step. This may include reviewing and discussing questions like this:

  • What did the problem ask them to find?
  • What were the differences between this problem and the problems they’ve worked on previously?
  • What concepts or skills did they need to know to solve the problem?
  • What kinds of operations were necessary or helpful to solve the problem?
  • Why were those operations effective?

The teacher’s role during the “Understand” step is to encourage deeper thinking by the students as they reflect on these questions. Then, they will come together as a class and decide which concepts were most important as they solved the “Try” problem and what part of the problem required new skills.

During the “Understand” step, students will solidify their understanding of the newly introduced concepts, with guidance from their teacher. 


The ability to choose a helpful, appropriate method for solving a problem, and to be able to execute this with speed and accuracy, are important skills in mathematics. After gaining a thorough understanding of a new concept, the next step in Japan Math’s process, students proceed to “Apply” to refine these skills.

In the “Apply” step, there are several different configurations of problems where students can use the knowledge learned in the “Understand” step. These include problems similar to those seen in the “Try” step, helping students understand that the same concepts and operations can be applied even if the problems seem different. Solving these problems improve students’ speed, accuracy, and confidence.

Sometimes, students get stuck on a particular problem. That’s okay! When this happens, it’s important to take a step back and review the foundation of the new concept. If they’re still stuck, they can return to previous pages in their workbooks to look for clues, to show students that they can apply previously acquired knowledge to almost every problem. They’ll also be able to learn that when they are having trouble with a particular problem, the key to the answer can be found by returning to the basics of their newly-learned concept.


Ideally, once a student has a firm grasp on the new concept, every problem in the “Apply” step will be solved by each student alone, without the help of their teacher or their fellow students. Once this is completed, your students have reached the final and most exciting step of the Japan Math process - “Master!” This should be celebrated before moving on to the next unit, in order to continue fostering a joy for learning and a passion for problem-solving.

The Complete Process

This process will be repeated for each lesson, allowing your students to progressively build on the concepts and skills they learned previously, while still tackling new problems with the help of their problem-solving skills and their classmates. By completing these steps in each unit, the curriculum helps your students develop an internal process for problem-solving that will be a foundation for all future mathematic endeavors. 

If you’re interested in adding the Japan Math curriculum, contact us here to request a free sample.