Overview
       In 2021, the state of California's average SAT score was exactly average and was ranked 30th out of the 50 states. That's a big miss. A state that is home to some of the largest companies and industries in the world still seems to fail at a proper education system, especially in the math department. Currently, many students have no motivation to learn math. To quote a younger brother, “Math stinks!” Many would rather play video games than solve simple problems which, in their eyes, foster no possible gain in the future. It is unlikely that the current system will be able to get students interested and excited about math—especially in this materialistic world we live in today. The branch of most state governments whose job is to put curricula and learning systems into place seem to be dismissing the problem and pretending like it doesn’t exist. Due to the plummeting of student interest, engagement, and proficiency, we need to reform and refresh the current mathematical education system. 

Note: All goals and issues presented are regarding standard K-12 mathematics education in public and private schools. Colleges and extracurricular programs for math are not discussed, except where mentioned. 

Goals
Goal 1: To incorporate more practical concepts into the revised curriculum

Goal 2: Integrate a proof-based curriculum into mathematics education

Goal 3:  Revise the system of learning to provide to more proficient students

1. Integration of practical concepts
    Problems:  Lessons taught in Common Core are often of the theoretical, pass-to-move-on type. Examples of these topics include statistics (MAD, box plots, standard deviation, etc.), algebra (systems of equations, systems of inequalities, modular equations), and geometry (area of polygons, trigonometry, etc.). However, very few of these topics are of any value to a standard person, and furthermore, many students are not motivated to complete the lessons and put in the effort of learning because they see no practical application. While curricula such as CPM have tried to remedy this by attempting to include potentially real-world problems in their books, these curricula just aren’t able to provide a true sense for how mathematics is used in the real world.  

    Suggested Solutions: By completing the basics of mathematical skill quickly (arithmetic, simple algebra, simple geometry, etc.) students can focus on more relevant mathematical applications such as personal finance. These courses would effectively kill two birds with one stone: they would exercise students’ mathematical analysis skills while also teaching them useful 21st century skills such as tax calculation, money management, and more.

    In later years, extra courses could be offered that teach advanced concepts such as trigonometry and calculus in settings where those concepts are properly applicable, for example, statistics in a data analysis career course. These extra courses cover mathematical concepts in an environment where students can immediately observe their practical applications and also gain insights into future careers for college and future preparation.  

2. Proof-based curriculum
    Problems:  While the Common Core Standards may claim to foster reasoning skills for a problem rather than just blindly applying a formula (by asking students to prove their answers or show their steps), the actual steps of the students’ “solutions” are no more than applying formulas and describing the numbers to input into them. Especially in geometry, these curricula give no insight whatsoever into the meaning, origin, or derivations of area and volume formulas. In my experience, I was punching numbers in a calculator with no explanation as to why the answer is what it is. Such mindless computations are another reason students get bored in class. In their view, mathematics is just a series of things to punch into a calculator, when in reality it is so much more than that. Unfortunately, many programs hide these deep theorems, insights, and concepts from students, claiming them to be “too advanced”. 

    In addition, many problems given to students are of the form “Solve this problem; give me a specific answer; show your calculations” type. Because of the vast majority of problems being of this kind, the student does not learn how to make deductions and use logical reasoning to verify a statement. Students are often irritated by the constant “How did you get that?” to a seemingly obvious fact, and rarely approach proper proofs. 

    Suggested Solutions: There are curricula that solve these problems and are already adapted in some schools. For example, the Bulgarian math curriculum and other math programs around the world provide either full proofs or partial ones for the student to complete on their own (this is also a great strategy to engage the student), while also incorporating proofs into homework problems. 

3. More flexible learning options
    Problems: Currently, the mathematics department of California's education is based on a one-size-fits-all precedent. In practice, this means that almost all students are required to take the same math courses as everyone else, regardless of ability. Some schools do offer “advanced” courses, but such courses aren’t much more advanced than the traditional learning path (especially in middle school). This causes students who are already familiar with the material to get bored and lose focus in class. In addition, the environment in which students learn is not conducive to more advanced students. Whenever a question is slightly outside the realm of the current lesson, the teacher remarks that the question is outside the lesson, instead of attempting to provide an answer. 
    Suggested Solutions: As mentioned before, the AoPS (Art of Problem Solving) and the Bulgarian curricula both contain many challenging topics suitable for advanced students. For deeper topics and an even bigger challenge for exceptional students, the Decade of the Berkeley Math Circle series or any other math circle books are viable options, as they contain topics that go much deeper into the universe of mathematics.