The online semi-finals will be held from January 12, 2025 to February 14, 2025. Students in grades 1 through 9 can download the semi-final test papers from the official website starting on January 12, 2025, and must log in to the system to submit their answers online by 23:59 on February 14, 2025.
Students in grades 3-9 who wish to participate in the Math League Finals and Summer Tournament held in the United States in the summer of 2025 must first take part in the semi-finals. Only those who earn an "Excellence" or "Outstanding" certificate in the semi-finals will be eligible to register for the finals and summer camp. (Grade 3 students who earn an "Excellence" or "Outstanding" certificate in the semi-finals are eligible to register for the Math League Finals and Summer Tournament held in the United States in 2026, or may choose to skip a grade to participate in the 2025 Math League Finals and Summer Tournament.)
However, participating in the semi-finals is not only a prerequisite for joining the Math League Finals and Summer Tournament.
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The Math League Semi-Finals are designed to cultivate students’ mathematical thinking, creative thinking, critical thinking, and problem-solving skills.
The ultimate goal of the Math League Committee in holding this activity is to encourage students who love science and excel in analytical thinking to engage with and better understand American approaches to mathematics and science. It aims to broaden students' global perspectives, promote mutual learning and inclusivity, and help students experience the joy of learning.
Many people believe that math education in American elementary and secondary schools is simple and that students elsewhere can easily outperform American students. In reality, American primary and secondary education—including mathematics—is not as simple as commonly imagined. The United States is home to many world-class universities, numerous Nobel Prize and Fields Medal winners, and countless innovations in science, technology, and the humanities.
While there is no Nobel Prize in mathematics, the highest honor in the field is the Fields Medal, awarded every four years to the world’s most outstanding mathematicians under the age of 40. Let’s take a look at the achievements of American mathematicians who have received the Fields Medal over the past 30 years.
Note: The above data comes from Wikipedia.Award year Winners The university or research institute where the winner worked when he/she won the award 2022 June Huh Princeton University (United States) 2018 Akshay Venkatesh Stanford University (United States) 2014 Maryam Mirzakhani Stanford University (United States) 2014 Manjul Bhargava Princeton Univeristy (United States) 2010 Ngô Bảo Châu Institute for Advanced Study (United States) 2010 Elon Lindenstrauss Princeton Univeristy (United States) 2006 Terence Tao University of California, Los Angeles (United States) 2006 Andrei Okounkov Princeton Univeristy (United States) 2002 Vladimir Voevodsky Institute for Advanced Study (United States) 1998 Maxim Kontsevich utgers University (United States) 1998 Curtis T. McMullen Harvard University (United States) 1998 Richard Borcherds University of California, Berkeley (United States) 1994 Efim Zelmanov University of Chicago (United States) 1990 Edward Witten Institute for Advanced Study (United States) 1990 Vaughan Jones University of California, Berkeley (United States)
Note: Professor June Huh of Princeton University, who won the Fields Medal in 2022, taught students participating in the Math League Finals and Summer Tournament in 2019.
The above data highlights the strength of mathematical research in the United States. Contrary to common belief, mathematics education in American elementary and middle schools is far from simple. For reference, consider the table of contents from a set of mathematics textbooks used in the U.S. Notably, the 6th-grade textbook has over 600 pages, the 7th-grade textbook also exceeds 600 pages, the geometry textbook has more than 900 pages, and the algebra textbook has over 800 pages. (Note: There is no unified national curriculum in the United States. Each school district designs its own instructional plan. The textbooks mentioned here are from a series commonly used in California.)
Mathematics Course 1: Numbers to Algebra (Grade 6)
Mathematics Course 2: Pre-Algebra (Grade 7)
Mathematics Geometry
Mathematics Algebra 1
For example, a math homework assignment for third graders in American elementary schools might be a small project totaling about 30 pages, to be completed within one month. Note that this is one question, and this question has a total of 30 pages, so this is a small project with a big question. This project trains students on how to run a project completely, from beginning to end, and systematically, and cultivates students' planning ability. At the same time, it provides students with space for self-design, allowing students to show their personality. The final result is not the most important. What is important is the experience and gains of students at each stage of the whole process. It can be seen that the amount of reading in mathematics in American primary and secondary schools is very large, which requires strong reading comprehension skills. American students have been doing various projects since childhood, so American students have relatively strong scientific research capabilities when they grow up, which can also be seen from the winners of the Fields Medal above.
“Primary and secondary education in the United States is not as simple as many might believe. The country is home to world-class universities, numerous Nobel Prize and Fields Medal winners (the Fields Medal being the highest honor in mathematics), and countless innovations in science, technology, and the humanities.” Let’s uncover the depth and rigor of American mathematics education by participating in the Math League Semi-Finals.
The purpose of the semi-finals is to allow students worldwide to experience the advantages and distinctive features of American mathematics education — namely, its heuristic, application-oriented, engaging, and exploratory approach that is closely connected to real life. The semi-finals are designed to inspire students to think mathematically and to cultivate their creative thinking, critical thinking, and problem-solving skills. By exploring how to apply mathematical concepts to real-world problems, students develop not only their creativity and analytical abilities but also their practical problem-solving capabilities.
What is “Thinking Mathematically?”- Many people associate mathematics with tedious computation, meaningless algebraic procedures, and intimidating sets of equations.
- The truth is that mathematics is the most powerful means we have of exploring our world and describing how it works.
- To be mathematical literally means to be inquisitive, open-minded, and interested in a lifetime of pursuing knowledge.
Creative Thinking, Critical Thinking, and Problem Solving Skills:- Creative thinking that focuses on the skills of fluency, flexibility, elaboration, and originality coupled with the affective characteristics associated with creativity such as curiosity and risk-taking.
- Critical thinking as the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and evaluating information to reach an answer or conclusion; a reasonable, reflective thinking focused on deciding what to believe or do.
- Inductive and deductive reasoning skills such as analysis, evaluation, and predicting.
- Problem-solving skills, using a math heuristic to outline the process.
Logic and Analytical Skills, Logic Relations, Inductive Reasoning, and Deductive Reasoning:Learning is an interactive process. The goal of education should be to provide the settings and opportunities for the student to become actively involved in the learning process. In a general sense, learning and intellectual development are not passive, sporadic activities, but dynamic, ongoing processes. The ability to acquire knowledge is built upon the capacity to organize and structure a concept’s key components. Furthermore, this process is based upon the development of logical relationships. Thus, it is necessary, first of all, to identify those logical relationships that serve as the foundation of intellectual development, then provide the settings within an academic discipline that will enable the student to acquire proficiency with these relationships.
The application of logic and analytical skills to numerical and spatial concepts is introduced in the questions through activities that are designed to focus student attention on the tasks of examining, discussing, and describing numerical and geometric relationships in terms of logical relations.
These logic relations include:- analyzing similarities and differences
- recognizing sequences and patterns
- using numerical and spatial concepts and functions
- applying the concept of analogies to relations and functions
In addition, many of the activities stress using inductive reasoning to extend patterns, make predictions based upon available data, and formulate inferences. The role of deductive reasoning is introduced to students through the use of logical connectives, counterexamples, and the application of the process of elimination to derive solutions to numerical and geometric problems. Students should realize that mathematics does not necessarily restrict itself to a single simple solution or a single strategy to arrive at a solution. Such analysis and verbalizing results in students developing an appreciation that mathematics is indeed a logical discipline with recognizable patterns, order, and structure.
“Tell me, I will forget. Teach me, I will remember. Involve me, I will learn.” - Benjamin Franklin
Our understanding is that a defining characteristic of Western education — including American education — is not about how much "knowledge" is "poured" into students or how many "difficult problems" they can solve. Rather, it emphasizes cultivating the ability to observe, identify root causes, discover problems, solve them, and develop practical skills. At the same time, students are encouraged to continue exploring and researching according to their own interests.
Education is not about filling the mind, but about allowing it to soar. It is a process of observation, discovery, reflection, debate, hands-on experience, and deep understanding. Through this process, students gradually master the skills needed to discover problems, ask questions, think critically, find information, and draw conclusions. Once students truly understand a concept on their own, it not only stays with them for life, but also enables them to apply it flexibly in different contexts.
Of course, simply participating in the Math League’s activities is not enough to fully grasp the essence and depth of American education. We encourage and advocate for students to learn, compare, and experience a variety of advanced teaching methods and practices — to truly "embrace all rivers" and broaden their horizons.
- What is a "good" math problem?
Ideal problems are low-threshold, high-ceiling; they offer a variety of entry points and can be approached with minimal mathematical background, but lead to deep mathematical concepts and can be connected to advanced mathematics.
Problems considered "good" are easy to pose, challenging to solve, require connections among several concepts and techniques, and lead to significant math ideas. They offer opportunities for intellectual satisfaction and learning experiences, as well as provoking curiosity and creative thinking.
You don't have to be a mathematician to enjoy mathematics. It is just another language, the language of creative thinking and problem-solving, which will enrich your life.
Many people seem convinced that it is possible to get along nicely without any mathematical knowledge once you finish school. This not so: Mathematics is the basis of all knowledge and the bearer of all high culture. it is never too late to start enjoying and learning the basics of math, which will furnish our all-too sluggish brains with solid mental exercise and provide us with a variety of pleasures to which we may be entirely unaccustomed. - Students in grades 1 to 9 who receive an "Honor Roll of Distinction Certificate (Top 8%)," "Honor Roll Certificate (Top 25%)," or "Certificate of Achievement (Top 50%)" in the preliminary round are eligible to participate in the semi-final.
- Reflections and feedback from the semi-finals (selected)
- Students in grades 1 to 9 who have received an "Honor Roll of Distinction Certificate (Top 8%)," "Honor Roll Certificate (Top 25%)," or "Certificate of Achievement (Top 50%)" in the preliminary round are eligible to participate in the semi-finals. The purpose of the semi-finals is to allow students to experience the advantages and distinctive characteristics of American mathematics teaching — including heuristic, application-oriented, relaxed, engaging, real-life-connected, research-based, and exploratory approaches. This is different from most current Chinese Mathematical Olympiads, which often focus on difficult, tricky, or unusual problems designed to frustrate students and make them experience failure.
- Students in grades 3 to 9 who plan to participate in the Math League Finals and Summer Tournament in the summer of 2025 must take part in the semi-finals. Only those who receive an "Outstanding" or "Excellence" certificate in the semi-finals will be eligible to register for the Finals and the Summer Tournament.
- All students who participate in the semi-finals will receive a semi-final score report and a set of test question solutions.
The semi-finals are divided into five grade groups:
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Grades 1–2.
The questions and format for this group are novel, interesting, entertaining, and well-illustrated,
providing a great opportunity for students to experience American-style math teaching.
[Click here to view the sample questions for the Grade 1–2 semi-finals.]
(Note: The sample questions are for reference only and do not indicate that this year's questions will have the same difficulty, types, or formats.)
- Grades 3-4. The questions are not necessarily difficult but require careful and
in-depth thinking — the more you think, the more interesting they become.
The simplicity of these questions does not mean they are unimportant or meaningless.
Real inventions and creations in the world are often simple, easy to understand,
and closely connected to life.
The Grade 3–4 semi-final questions are novel, interesting,
and entertaining, while being compactly arranged, logically rigorous, and
self-contained. They include a large amount of reading and are richly illustrated,
providing an excellent opportunity for students to experience American math teaching.
These questions not only test and develop students' math skills but also
challenge and improve their English reading comprehension. Students
often spend years studying English in school — how effective is it?
Participating in the semi-finals offers a rare chance to truly test and strengthen this skill.
- Grades 5-6. The questions are not necessarily difficult but require careful and
in-depth thinking — the more you think, the more interesting they become.
The simplicity of these questions does not mean they are unimportant or meaningless.
Real inventions and creations in the world are often simple, easy to understand,
and closely connected to life.
The Grade 3–4 semi-final questions are novel, interesting,
and entertaining, while being compactly arranged, logically rigorous, and
self-contained. They include a large amount of reading and are richly illustrated,
providing an excellent opportunity for students to experience American math teaching.
These questions not only test and develop students' math skills but also
challenge and improve their English reading comprehension. Students
often spend years studying English in school — how effective is it?
Participating in the semi-finals offers a rare chance to truly test and strengthen this skill.
- Grades 7-9. Students in this group need to read a math topic written in English
— for example, number theory (this is just an example; the actual topic may vary) —
and then solve about 25 questions related to this topic.
The questions range in difficulty from simple to complex. Students are allowed to
search for information (including online) and consult experts, but they cannot ask
others to do the work for them. They must complete the questions independently and genuinely understand the content.
This group provides a special opportunity to test and improve English reading comprehension skills learned in school.
- Students in grades 3–9 who receive a certificate of excellence or higher in the semi-finals will be eligible to register for the Math League Finals and Summer Tournament in the summer of 2025.
The semi-finals will be conducted as an open-book exam. Students log
in to the official website of the Math League, download the semi-final questions, complete them, and then upload their answers.
Students may search for information (including on the Internet) and consult experts,
but they cannot ask others to do the work for them. They must complete
the questions independently and genuinely understand the content.
Participants are not allowed to communicate with each other during the exam.
After submitting their answers, students will be required to explain
their solutions to five questions (selected by the system) in a voice recording.
Students can learn mathematics and solve problems without strict time constraints and are allowed to consult reference materials. This approach helps them relax, appreciate mathematics, enjoy the process, and truly experience the beauty of the subject.
The fundamental purpose of learning mathematics is not to tackle difficult, obscure, or tricky problems, but to develop the ability to solve real-life problems. On a higher level, mathematics cultivates one’s character, enriches the soul, and enhances personal growth and quality.
Learning mathematics encourages creativity and inspiration, fosters logical reasoning, promotes rational thinking, and helps individuals live, work, and make decisions with greater flexibility and joy. Ultimately, learning mathematics should be an enjoyable and fulfilling journey.
The organizing committee allows students to search for information
(including on the internet) and consult experts; however,
they must not ask others to complete the questions for them.
Students must solve the problems on their own and truly
understand their solutions. But what if a student cheats and has someone else do the work for them?
After students log in to the system,
enter their semi-final answers, and submit them,
the system will select approximately five questions based
on the answers submitted and require students to explain
their solution ideas in a recorded voice response.
Each question must be answered within six minutes,
which includes reading time, thinking time, and recording time.
Among these five questions, some will be ones the student answered correctly,
and some will be ones they answered incorrectly.
The explanation may include (but is not limited to) the following aspects:
- How did you understand this question?
- How did you analyze and approach solving it?
- What do you think is the key point of this question? How many steps can it be broken into?
- Have you seen this or a similar question before?
- How difficult do you think this question is?
The five questions are unique for each student and generated based on their individual responses. Teachers from the organizing committee will carefully review each student’s explanations.
In addition, for award-winning students, the organizing committee may also conduct random follow-up phone interviews to verify the authenticity of the results. Please keep your phone accessible after submitting your semi-final answers.
The organizing committee of the Math League will award "Excellence Certificates"
and "Outstanding Certificates" to students with exceptional results in the semi-finals.
(All other participants will receive a "Certificate of Participation"
issued by the organizing committee.)
The list of award-winning students will be announced on the official website of the Math League in the United States (www.mathleague.com).
Students who receive an Excellence Certificate or Outstanding Certificate in the
semi-finals are eligible to register for the 2025 Math League Finals and Summer Tournament.
Step 1: Check the preliminary results.
Step 2: Register for the semi-finals.
Step 3: Download the semi-final test paper (available on the official website starting January 12, 2025).
Step 4: Complete the test questions.
Step 5: Submit your answers online (including explanations for five selected questions and the recorded English essay) before 23:59 on February 14, 2025.
Step 6: The organizing committee will grade, verify, and conduct spot checks on the submissions.
Step 7: Check and download your semi-final results, analysis report, and reference answers.