A Math Tutor’s Guide To Doing Well In Math

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As a (former) mathematics tutor and teaching assistant in mathematics courses, I have seen many ways in how students learn mathematics. I have seen successes and not so great work while marking assignments. Mathematics is a subject that many love to hate and most likely want to forget about. Hey, there are some parts of (higher level) mathematics that I don’t like nor understand!

I’m not sure about you, I think there is strategy in learning technical subjects like mathematics, physics, computer science and so on.

Do note that the numbers of students I have dealt with is still a “small” sample size of less than 1000. I will give advice on how to do well in math in different sections. These sections will be:

  1. Toddlers Starting Early
  2. Advice for Elementary Students (Grades 1 to 8 or Age 6 to 13)
  3. For the High-School Crowd (Grades 9 to 12 or Age 14 to 18)
  4. At the University Level (Age 18+)

It is important to note that I am referring to the Canadian School system as I have been under this system since Kindergarten. The school system in Canada is different from Germany and other places. Also, I have not mention colleges in Canada as I am not familiar with them. Colleges in Canada offer education in the skilled trades while colleges mean something else in the United States.


1) Toddlers Starting Early

It is somewhat hard to give advice on how a toddler can do well in math. Some of them are naturally good at abstract concepts/mathematics at a young age.

In Cal Newport’s Blog Study Hacks, I believe there was an article with a reference of a parent who taught his\her child to play and count with food (macaroni I think). The child was already ahead in the class when the actual formal lesson of counting came around. This children knew how to count already and gave him\her confidence to do more in mathematics. The child eventually turned into a math whiz.

With me, I think playing Sonic 2 on the Sega Genesis at the age of 4 kickstarted my problem solving skills and counting skills. In addition, I think my parents gave me some self-study mathematics book. This book had worked out examples of how to add, subtract, multiply three digit numbers. There was also division by two digit numbers and a bunch of Kumon-style problem sets.

When I hit grade 5 or age 10 or 11, the math classes was teaching multiplying 2 digit numbers and I already knew how to do it. This confidence carried through for a while to university. More importantly, I built the habit of doing work at an early age.

Tips for Toddlers:

  • Let your child play and count with food.
  • Teach your child counting or how to spend money when doing shopping or groceries. This is a good lesson in early mathematics and in personal finance!
  • Kumon programs are an option.
  • Teach your child a new language. Languages like French, German or Mandarin Chinese are good. For example the French word quatre-vingt means 4 twentys which is 80. The German word einundsiebzig is one and seventy which is 70. And with Mandarin Chinese, er shi is 2 tens which is 20.


2) Advice for Elementary Students (Grades 1 to 8 or Age 6 to 13)
My advice for students is similar to the above. With those nearing high school, their lives start to get more complicated with extra-curriculars, TV shows, distractions, sports, etc.

Tips

  • DO YOUR MATH HOMEWORK REGULARLY! Never do it the day before. I doubt top athletes or dancers put all their training in one go.
  • Start to maintain balance in your schedule. Balance homework, family time, personal time, exercise, leisure early. It makes things easier for you when things get REALLY BUSY.


3) For the High-School Crowd (Grades 9 to 12 or Age 14 to 18)

Sometimes homework is not important for the high-schooler as there are much more attractive options such as going out to concerts, hanging out with friends, video games, social media, etc.

Math lessons are more formal and gets complex. Independence is expected. Being lazy with work hurts you on a test.

Tips

  • Think of doing homework as an investment to your future.
  • Math homework takes a while. Practice often.
  • If the teacher has office hours, use them and ask good questions.
  • Understand the bigger picture and how math can help you.
  • Learn to write notes fast and practice shorthand writing. It can help.


4) At the University Level (Age 18+)

The transition from high school mathematics to university mathematics is a big one. You are responsible for your own work and your own learning. Self-discipline, time management and focus are really important here.

Tips

  • Don’t skip lectures unless there is a very good reason.
  • Start earlier than you think. You never know when things pile up. Things come at you randomly.
  • Cramming is super dangerous here.
  • Use the math help centre (or similar) and/or office hours often.
  • Try working out examples from class. The detailed answers are in your notes.
  • Minimize distractions like Facebook, etc.
  • Consider a planner or a schedule planner like this.

Summary

Technical subjects like math requires a lot of time, focus, and determination. There is no room for laziness. The advice given here by me may seem generic or common sense. A lot of this advice is easier said than done so discipline is really necessary.

Treat learning mathematics as mental exercises. The more work you put into it, the more you get better. Like any exercise, you need rest. No rest leads to burnout which leads to people cursing about math.

A good reference that I used as an undergraduate student was Cal Newport’s Study Hacks blog. Look into his archives and there are some insightful articles for students. His book How To Become a Straight A Student is good too. The book covers is also for non-math majors.

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