1. Find a teacher that is knowledgeable and passionate about math. Grad students might fit the bill. Engineering grad students also. Low level math (e.g. calculus, differential equations and below) can be taught by anyone in STEM, it doesn't need to be a trained math teacher. Engineers, physicists, or chemists often do a better job and passionate ones might be easier to find. Passion is important, because a good teacher will be a window onto another world, that you are invited to explore. A bad teacher is a window onto a brick wall. I used to tutor undergrads in math and the worst students were the math education people. I was often told "I hate math" by these students. I would even plead with them to find another subject, that it was unfair that someone who hates math becomes a math teacher, but they insisted that they love "teaching", they just hate math. Welcome to the US Public school system.

2. Include history in the math education. This depends on the personality of the student, but for me, I loved learning about the lives of the people who made mathematical discoveries, and the circumstances of those discoveries. To this end, I recommend books by George F. Simmons, for example:

3. Look at the Russians. The Soviet Union had an amazing pedagogical program in math education, with fantastic books, puzzles, newsletters, etc. Some of that survived the turn to capitalism, and today they still punch above their weight. Some resources:

4. Interdisciplinary approach. A great way of studying math is to present some problem in physics or engineering and develop the mathematical techniques to solve it. This is how much great math was discovered.

5. Ask questions. Rather than telling students techniques and then watching them use those techniques, you can create a dialogue where you start by asking specific questions and guiding the student to discover the math on their own. This of course requires a smart student and a smart teacher, but it's a very effective way to really learn a topic. This was famously done by the Texas Topology department in the mid 20th Century.

6. Teach concepts. If you cannot get the student to discover concepts, you can still emphasize the teaching of concepts. For example, there is no reason why a 5th grade math class can't begin to cover concepts such as simply connectedness, or Euler characteristic, or hamiltonian circuits. These can be done with simple pictures, yarn, paper and scissors. Then encourage the student to generalize to other shapes. Similarly in geometry classes, working with a ruler and compass creates a more memorable hands on experience for young students and can be a technique to introduce them to early theorem proving, for example bisecting a chord.

1. Find a teacher that is knowledgeable and passionate about math. Grad students might fit the bill. Engineering grad students also. Low level math (e.g. calculus, differential equations and below) can be taught by anyone in STEM, it doesn't need to be a trained math teacher. Engineers, physicists, or chemists often do a better job and passionate ones might be easier to find. Passion is important, because a good teacher will be a window onto another world, that you are invited to explore. A bad teacher is a window onto a brick wall. I used to tutor undergrads in math and the worst students were the math education people. I was often told "I hate math" by these students. I would even plead with them to find another subject, that it was unfair that someone who hates math becomes a math teacher, but they insisted that they love "teaching", they just hate math. Welcome to the US Public school system.

2. Include history in the math education. This depends on the personality of the student, but for me, I loved learning about the lives of the people who made mathematical discoveries, and the circumstances of those discoveries. To this end, I recommend books by George F. Simmons, for example:

* https://www.amazon.com/Differential-Applications-Historical-...

* https://www.amazon.com/Calculus-Gems-Memorable-Moments-Spect...

3. Look at the Russians. The Soviet Union had an amazing pedagogical program in math education, with fantastic books, puzzles, newsletters, etc. Some of that survived the turn to capitalism, and today they still punch above their weight. Some resources:

* http://www.ascd.org/ASCD/pdf/journals/ed_lead/el_198102_bran...

* https://www.amazon.com/Moscow-Puzzles-Mathematical-Recreatio...

* http://docshare02.docshare.tips/files/17782/177829869.pdf

4. Interdisciplinary approach. A great way of studying math is to present some problem in physics or engineering and develop the mathematical techniques to solve it. This is how much great math was discovered.

5. Ask questions. Rather than telling students techniques and then watching them use those techniques, you can create a dialogue where you start by asking specific questions and guiding the student to discover the math on their own. This of course requires a smart student and a smart teacher, but it's a very effective way to really learn a topic. This was famously done by the Texas Topology department in the mid 20th Century.

6. Teach concepts. If you cannot get the student to discover concepts, you can still emphasize the teaching of concepts. For example, there is no reason why a 5th grade math class can't begin to cover concepts such as simply connectedness, or Euler characteristic, or hamiltonian circuits. These can be done with simple pictures, yarn, paper and scissors. Then encourage the student to generalize to other shapes. Similarly in geometry classes, working with a ruler and compass creates a more memorable hands on experience for young students and can be a technique to introduce them to early theorem proving, for example bisecting a chord.