How to teach your child math
Math education in the United States is abysmal. I say this as a math professor with a PhD in mathematics. To understand how I feel, take a look at Lockhart's Lament. Imagine that a child is studying music, say piano. However, for 13 years, all they do is practice scales, finger exercises, readning and writing notes---don't forget whether to draw the note with stem up or down! Imagine that they never hear a song, or get to play one. This is what society has done to math.
Basically this is how math education works, before the college level. The teacher shows the class how to solve a specific problem, like finding the equation of a line when you are giving two points on the line. Then the class does 20 exercises, just like the teacher's example and that is it, until the exam where the student repeats it. It is monkey see, monkey do. No creative thinking expected. Then came along Common Core, which is a tiny step in the correct direction. Common Core is supposed to force students to think a little more. It does, but not mathematically: it wraps up the math problem in complicated language so no one knows what the heck the problem is asking. However, Common Core is an improvement and when parents opt out, they are basically saying: I am afraid my kid will get a bad grade, so we are not taking the test. Or, the teacher is afraid that the students will do bad, so he/she tells the parents to opt out so he/she won't get fired.
The early years
Start with Dr. Wright's Kitchen Table Math: Book 1. This is the first book in the series, and there are two others (book 2, book 3). They also need to learn the very basic facts about numbers, and flash cards are good for this.
When they know all of their basic facts, make sure they can really do arithmetic. Now, we can start the fun books.
First there is the three volume set of Challenge Math by Edward Zaccaro (Primary Grade Challenge Math , Upper Elementary Challenge Math, Challenge Math For the Elementary and Middle School Student ). These books present problems that require a lot more mathematical thinking than the usual school curriculum. This is what Common Core math should be.
These days you can ask the simple artificial intelligences (Siri, Alexa,...) to work out simple math computations. There really isn't a good reason to be an expert in doing arithmetic on paper. However, being able to compute mentally is still important, especially to estimate because sometimes you make a mistake typing in a computation into your calculator and it is important to be able to catch errors, when they are off by a magnitude. A really good book is Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Arthur Benjamin. Check out his TED talk. Though we have calculators, mental math practice may increase a child's working memory (which is closely tied to IQ score and success in school. Look out for a future article on working memory). Also, check out the following book for teens and for parents: The Magic of Math: Solving for x and Figuring Out Why also by Arthur Benjamin.
The following two books are simple picture type books which present ideas that are extremely advanced, yet do so in as simple a way as possible. The first one Really Big Numbers by Richard Schwartz, helps us understand where really big numbers come from. For example, how many license plates numbers are possible? how many phone numbers can be made? Next, one big step from big isinfinity: Gallery of the Infinite also by Richard Schwartz.
Math books for the future math olympiad
The toughest and most advanced math books designed for school age children (mostly middle school through high school) are from the Art of Problem Solving series. If every school used these books, the US would produce 100 Bill Gates per year. If the you are not versed in math, you should purchase the full solution manuals that are available with each book. Start with Prealgebra and Solutions to Prealgebra for 7th grade.
Intro to Algebra + Solutions for 8th grade.
Intro to Geometry + Solutions for 9th grade.
Intermediate Algebra + Solutions for 10th grade.
How to study math
The best way to learn math is to struggle, trying to solve challenging problems. If a bright child comes home from school and says math is easy, then he/she is being short changed. If the parent is not good enough in math, you might want to hire a good tutor, perhaps a really good high school teacher (who teaches the BC Calculus course), a college professor, or a graduate student in mathematics (if you live near a major university). All I am saying is give math a chance. Real math, not the easy stuff they teach in school.