Resources

General Guidance

Having started my own tutoring program since 2015, I would like to share some insights and tips from my 10-year experience interacting with hundreds of parents and students. As of today, I have 3 students winning Math League National champions, students qualified MATHCOUNTS national 16 times and over 40 students won AMC8 DHR roll.

1.1 Teamwork

The definition of team here includes the student, parent and teacher. In some cases, parents can serve as teachers as well. Teamwork is extremely important for students grade 5 and below.

1.1.1    The Roles and Responsibilities of Teachers:

— Evaluating the student’s level and finding the right class

— Preparing class materials (handouts, homework, solutions) which cover all the class material.  An experienced teacher should also adjust the difficulty level based on the student’s level.

— Explaining the class contests clearly and precisely. Focus on key concepts and different methods. Give examples followed by practice problems if time allows

— Inspiring students to ask questions and boost their interest

— Encourage students to think, such as giving hints instead of feeding them answers

— Adjusting class pace based on the student’s responses during class time and their progress for the semester

— Exploring various approaches if applicable

— Offering TA time for students who need help

— Providing additional consultation for individual students who have an interest in math contests

1.1.2    The Roles and Responsibilities of Parents:

— Finding the right tutoring program. The best one for your child is not necessarily the most famous one. The program that suits your child’s level and learning capability is the right one. Some factors to consider would be the syllabus of the course, the reputation of the program, past students’ performance, customer service, and referral from previous students.

— Arranging all after school activities wisely to leave at least 4 to 5 hours a week for math class and homework

— Setting up a realistic goal and check overall progress to adjust the goal if needed

— Ensuring that your child is not missing class or not doing homework

— Asking the instructor to provide additional books and practice based on your individual goal

— Discussing with the instructor on which math contests to join and finishing the registration process for them

— Forming a peer group to study together if possible

— Finding books or other means to encourage and inspire your child to success

1.1.3    The Roles and Responsibilities of Students:

— Learning by yourself or taking after school tutoring classes

— Avoiding missing class if possible

— Understanding all class materials and participating during class discussion

— Answering all homework problems seriously and as accurately as possible

— Asking questions during class time and about homework during TA time. Understanding and mastering what you learnt is as important as learning new things.

— Spending time to work on additional practice (past exams, AOPS Alumnus, etc.)

— Identifying your strengths and weaknesses. Overcome your weaknesses. For any bad habits, try to identify them and find a way to prevent any recurrence.

— Focusing on accuracy first, not speed. The goal is to get all problems correct the first time if you can.

— Learning to summarize and retain knowledge

1.2 When to Start

• For students whose goal is a good score on SAT/ACT, or a solid foundation in mathematics, or logic training; you do not need to start too early. Sometimes, it can take only 10 minutes to understand a new concept one year later compared to 30 minutes or more one year earlier. It also depends on each student. General recommendations will be to start Prealgebra at 6^th or 7^th grade, followed by Algebra 1, followed by Algebra 2 or SAT.

• For students with a goal of participating in math contests and getting a good score/ranking, we recommend that he/she starts early. It is a case-by-case situation and not the same for all students. Most students start AOPS Prealgebra class in the fourth grade. However, very few students start at even lower grades whenever he/she is ready. Most of the time, if a student is extremely interested in math or displays strong intuition with numbers or patterns, they can start early.

Besides when to start, there are other factors that could make an enormous difference eventually. Some students can catch up quickly even if they start a little late. Below are some important factors:

• The time he/she spends on doing math: Most students who win contest titles spend a minimum of 1 hour per day on math.
• The efficiency of learning: Just doing the same sets of problems will significantly improve test scores. Mastering all topics along the way is better than learning and forgetting.
• The persistence of learning and persisting when facing obstacles.

1.3 Formula for Success

1.3.1    Using the Right Materials (Books, Classes, Seminars, etc.)

The first critical step is to find the right materials for a student based on his/her current level. Too simple or too hard are both bad. By rule of thumb, if the probability of solving a problem (hints allowed) is between 20% to 85%, then it is a good learning zone. If the probability is lower than 20%, it is too challenging, and the student is not ready. Too difficult material will make students feel frustrated and is detrimental in the long run. If the probability of solving problems is over 85%, then it is too simple for the student. He/she can spend lots of time working on this kind of problem, but he/she won’t improve significantly.

1.3.2    Reviewing Old Knowledge Before Mastering New Material

An immensely popular misconception of students and parents is that learning a lot of new concepts and knowledge will help them win. This is true if and only if the students have mastered all the topics they have learnt. Most of the time, while students learn new topics, they forget older topics or perform worse on the old topics; they can perform less consistently well on older material. Mastering the material means that they can always use what they know consistently without any issue. It is as important to remember everything they’ve learnt as it is to learn new topics.

1.3.3    Focus on Accuracy First, then Speed

Another common mistake a lot of students have is focusing on speed first, not accuracy. They assume that they will have time left to come back and check. In reality, most students (over 95%) do not have enough time to finish the test, especially for MATHCOUNTS and middle school math league tests. So, the focus should be on accuracy first to make sure that you get all the points for the problems you solve. When you rush to solve the last 10 problems, the potential risk is that you have a high chance of missing the easy problems when you are rushing and a low chance of getting points for the last 10 problems since they are generally much harder than the first 20 problems.

To improve accuracy, here are several areas to pay attention to:

• Read problems carefully. According to some surveys, around a 1/3 of wrong answers are due to reading problems (overlooking, wrong understanding, etc.). It is wise to read a problem twice instead of rushing to solve it when you are not sure if you fully understand the problem. You could save about 15 seconds if you rush, but if you do not get the problems correctly, you can easily spend 1 to 3 minutes to get a wrong answer or get totally stuck.
• Prevent any calculation errors. Keeping your scratch paper neat and tidy can help you recall your thought process. Improving calculation speed with number sense training or mental math training will also improve accuracy.
• Overcome any bad habits. For the problems you can get correct the 2^nd time but get wrong answers the first time, please dig into the reason the error occurred to see if you have some unknown habits. Do not use “silly mistakes” to justify an error. The chance is that these repeatable mistakes will come back to hurt your scores if you do not fix them.

1.3.4    Improving Speed with Various Problem-Solving Skills.

For high level contests, the key for speed is not mental math. Mental math will help and can make a significant difference in the countdown round. However, using the best approach will be more impactful than raw calculation speed. You must be familiar with all available approaches and quickly determine the best one after you read the problems. It takes time to grow these skills, and reviewing the same types of problems is a way to build these skills. For example, in our topic lecture ‘Complementary Counting’, we teach students to think about this approach when you read several key words – one of them being “at least”.

1.3.5    Strategic Planning and Implementation

Good planning contributes to 50% of success.

Step 1: Set up your individual goal.

Step 2: Understand your current level to determine the gap.

Step 3: Put a plan to include all courses, books, practices to fill this gap.

Review these 3 steps based on the progress over the course.

If you are not familiar with this process, picking a tutoring program and sticking with it will likely also work.

1.3.6    Other Helpful Resources

• Forming or joining a peer study group. (2 to 5 students)
• Joining a local math club.
• Visiting math contest websites.
• Asking other students/parents to share their experiences.

1.3.7    Practicing and Summarizing

(There will be a separate detailed discussion on this topic)

1.3.8    Test Preparation and Strategy

(There will be a separate detailed discussion on this topic.)