# Jing Liu: Show Kids that Solving Math Problems is Like Being a Detective

Noah and I have received a flood of overwhelmingly positive email about our Quartz column ”There’s One Key Difference between Kids Who Excel at Math and Those Who Don’t.” I am very gradually making my way through the electronic pile. I was delighted to read near the top of the pile this note from Jing Liu, which has an insight into math education that seems right on the mark to me. Jing kindly gave permission to reprint a slightly revised version of her note here.

I just read the article that you and Noah Smith wrote on Quartz,

“There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t.”

I’m writing to you because this is an issue that is close to my heart and I have been thinking about it for a long time. I have two kids in K-12 schools, both love math, and I have been worried about what they are learning at school for years. I have talked with teachers and school principles and, of course, many parents. A lot of the things that I’ve heard are concerning and reflect a general lack of understanding from the educators on what math really is and what math can do for students who will not be mathematicians. I finally started a math enrichment program at our neighborhood elementary school and have taught advanced 4th and 5th graders through that program for four years now (this is my main community volunteer work). So I’m sure you can tell why articles such as yours really strike a chord with me.

The issues that you raised in your article are all excellent and educators and parents should think hard about them. I’m also glad that you mentioned the starkly different attitudes toward sports and toward math. It’s not that Americans don’t understand the value of hard work and that effort can definitely make up (to a certain extent) for lack of talent, it’s just that this somehow gets lost in math education. But I also think that there are another couple of very important issues that contribute no less to the current state of math education:

- There is a tendency to treat math as a set of discrete skills, procedures and facts for students to learn each year, not as a coherent and logical way of thinking that students will develop continuously through the years. The amount of rote memorization is, honestly, overwhelming. It is also quite clear that some teachers think that solving math problems is to follow a series of set steps. They miss the point that solving math problems is actually a quite creative process, in which one assesses the situation, assesses the tools in his/her toolboxes and zeros in gradually on how to connect what one knows and what one needs to know. It’s a detective’s work. So the question is: even if we make the kids not fear math, even if they are willing to work hard on math, are they truly learning the essence of math in the classrooms?
- The strong tendency to protect kids from feeling deficient also affects those who are perceived to be capable math students. The math work tends to be very simple, kids are kept at a low level for a very long time until they are absolutely sure that they “have got it”. The slow pace and the lack of depth and challenge at each level can really turn kids off, even for those who are very capable. I’ve read that a whopping 60% of American students actually think that they are not challenged enough in math. In today’s high-stakes college entrance game, it is probably detrimental for a student to score a 70 on a math test. But in many other countries, East Asian or not, 70 is a perfectly OK score for good students. They know that they will apply a large set of math concepts and skills in various ways for a long time, and each time they apply these concepts and skills they have an opportunity to be better at it, and they know that it’s OK to make mistakes. After all, who is a good math student? Someone who only solves very simple problems and gets them all correct? Or someone who tackles very challenging problems but sometimes gets it wrong? In the US, the lack of challenge in the content, the lack of appreciation of math as a creative yet logical endeavor, and the high-stakes evaluation system together might just breed students who are risk-averse in their academic pursuit and who don’t get to see the true beauty of math. And this might be one reason why even the advanced students can be ill-prepared in math.