My wife and I recently hired a math tutor for my first-grade son.
This might not surprise you, until you learn that I am actually a professional math tutor myself.
Many of the students whom I work with have parents who are perfectly capable of teaching math, but when it comes to helping our own children understand even the simplest math concepts, we math tutor parents can find ourselves at a loss. The relationship between child and parent is so complex that I rarely see great success when adding "math tutor" to the mix.
In more than 20 years tutoring, I have seen many students fall behind in math for a variety of reasons.
Often it's because weak foundations make subsequent topics a struggle.
Just like learning a foreign language, math builds on foundations.
Languages come with vocabulary. Math comes with its own vocabulary —"math facts"— such as times tables and certain key formulas, like $C=2\pi (r).
Math also has sets of rules that must always be at the forefront of students' minds, such as fraction and exponent rules. If a student is weak on foundations, that is where the time must be spent. In a language, there's no sense learning how to speak in advanced tenses until one can speak in the present tense. The same is true of attempting advanced math concepts without having the basics down.
Calculators: tool or crutch?
Calculator overuse often has a damaging effect on students' abilities to manipulate numbers, especially fractions. This leads to a weakness in manipulating equations with variables in later classes. I constantly see students using calculators to multiply 30 x 40 or 1/2 x 8. Many teachers realize that students are weak with numbers, but few seem to take appropriate steps to correct this.
Nearly every high school student in Washington owns a TI-83 or TI-84 graphing calculator that is, arguably, harder to pry from their hands than a smartphone. It should be noted that, although these calculators are allowed in AP Calculus, the University of Washington does not allow graphing calculators in its first year calculus series.
What about test stress?
I've heard many parents complain that their son or daughter lacks test-taking skills. My answer is to have students practice solving problems (like the ones on review sheets or in the textbook chapter tests) with a timer, as part of at-home exam preparation. To me, good test-taking skills means good problem-solving skills. Studying for a math test simply means practicing problems.
Advanced math is not always a good thing
Sometimes math difficulty is a result of an advanced class gone bad.
Educators seem quick to push kids succeeding in math into more advanced classes. This can very often have a lasting negative impact if done hastily.
Students used to working moderately and getting A's are sure to rebel when they have to work harder to get B's or C's. What's worse than the how a C looks on a transcript is that C students are not mastering the material and are on a poor trajectory for their next class. Students are often over-confident in their abilities and are willing to take on that AP class, especially if all their friends are taking it.
The danger is that when a class teaching rate outpaces student learning rate, almost nothing is retained, as kids tend to shut down. Students then fall further and further behind and start to dislike a subject that might have once been their favorite.
Everyone eventually reaches a place in their education where math stops coming easily to them.
Math had always come pretty easily to me until 11th grade, when I fell behind in an advanced class. My dad and I decided I would switch to the regular 11th grade math class. After doing so, I started to do well again and went on to succeed in "regular" 12th grade math, and earned an A on British Columbia's Comprehensive Final Exam.
What do math and skiing have in common?
What I want parents to know is that it's OK for kids to struggle in math.
It's actually a good thing, to a point.
However, it is imperative for kids and parents to seek help when the struggle turns to frustration.
The harder the struggle in learning mathematics, the stronger the foundation when the light finally comes on. I'm an effective math tutor because I struggled immensely with the topics I now thoroughly understand.
Because I'm a math tutor, people naturally assume I never struggled in math or certainly ever failed a math class. This is quite far from the truth. Part of what makes me a good math tutor is the experience of the struggle and the success of hard work.
For me, the real moment of truth came in first year college math at the University of British Columbia (UBC). I took two years off after high school to ski race, and when I entered college, the math was like nothing I'd ever seen before. I was completely unprepared for this jump in the level of difficulty.
I failed a math class for the first time in my life, and then it "snowballed" for several years until I found myself picking up the pieces at a community college. Three years later, I completed a Civil Engineering degree at Seattle University, eight years after I had begun at UBC. After that I was accepted to MIT and finished my Master's Degree in Civil Engineering.
The road was long and winding for me, although it didn't have to be.
It doesn't have to be for your child, either.