Videogames are better than teachers
This is a short story of a sad preschooler subjected to early academic instructions. It demonstrates the dangers of coercive teaching.
Kid that can't get his numbers straight
Tobias is 6 years old and he told me he was crying. He is just about to go to school. His pro-active mom considered his counting skills well behind the curve "These days, 4 year olds can count up to 100". Tobias can only count up to 13. From then on, it goes on like this 15, 17, 14, 18, 19, 15, and so on. The sequence is different at each try. Tobias is very smart. He can tell me things about car engines I have never heard of. I would not worry about his counting. This is not dyscalculia. This is just his brain not being ready. I can confirm this easily. When I try to teach him to count 3, 4, 5, 6, 7, 8, and 9, he is fluent and automatic. However, when I disrupt his sequence by adding "teen" after each digit, he gets confused easily. It is again 3-teen, 4-teen, 7-teen, 9-teen, and back to 5-teen. He clearly developed an automatic sequence memory and that sequence gets easily killed by any form of disruption. This is a type of early fluency that is not as universal as that of an adult who may think 3-teen, 4-teen trick is easy to do.
Empathy for a crying kid
I asked Tobias why he was crying. He said, his mom took away his computer because he could not count. She claimed he refused to cooperate. It is easy to think the kid is uncooperative if the job is just beyond his brain's capacity. It is awfully hard for an adult to think that the sequence 13, 14, 15, etc. is difficult, and failure must be kid's fault. For a bit of empathy, I suggest the parent try to learn the same sequence in Chinese. Even then, it is easy to fall back on English names and the student only needs to link English numbers with Chinese numbers. She does not need to produce a fluent Chinese sequence. Most adults are pretty confident they can learn to count up to 20 in Chinese in 20 minutes. Indeed, some can do it. Once they do, they boast with a big smile. Again, good learning is pleasurable. For those who find Chinese easy, another test is to remember a simple poem and then recite it by inserting drake- before each syllable. For example, try this text, if you know it well:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness
Convert it fast to we-drake, hold-drake, these-drake, truths-drake, to-drake, be-drake, self-drake, evi-drake, dent-drake ..., etc. Easy? If you struggle, you feel the child's pain with 4-teen, 5-teen, 6-teen. Parents keep forgetting that a child's brain is different, and is not ready for such rote feats. Kids get their learning rewards differently.
Happiness of math discovery
I had a short chat with Tobias about numbers. I wanted to confirm what I suspected is likely to be true. He admitted that he needs his computer for playing computer games. He also admitted that some games include virtual monetary rewards. It is impossible to play some of those games effectively without having a good number sense. I would write numbers in sand and ask Tobias to name them. Exactly as expected, he struggled with 17, 28, 53, etc. He reads 23 as two-thirteen. However, I also predicted correctly he would know 100 and 1000. Even better, he knew them all 200, 300, ... 900, and 2000, 3000, ... 9000. He also knows that millions and billions are very big and very good. Tobias knows that the more digits there are to the number, the better the reward. He also knows that numbers that begin with 9 are better than numbers that begin with 1 as long as they are of the same length in digits. Using computer games that his mom has just banned, Tobias developed a good sense of numbers. He cannot put them well in a sequence, but he can look at a number and guess how "good" it is. This is how little brains work. They do not employ rote memorization to cram a sequence (in 20 rules we call it a list). They employ neural network generalization to figure out the rules. The rules that govern the world of numbers. This can be counterintuitive to a parent, but those rules are far more useful in understanding the world of numbers than a dry sequence 13..19.
I got my final reassurance when I asked Tobias "How much is 2*2?". He perked up and said "Four!" with a big smile. "And 2*3?". "Six!". Multiplication is no big deal for a six year old except ... nobody has ever taught multiplication table to Tobias. This "teaching omission" resulted from the assumption that there is no need to move to "advanced" concepts such as the multiplication table if the kid struggles with counting.
Hating school in advance
My last question was about schools. Most kids are pretty happy to go to school. However, when I asked Tobias, he resolutely said he already hates school. Kids have poor memory. In a week, he may change his mind and the damage will be negligible as long as he is not getting hammered for confusing 15 with 18 over and over again. He might fear those numbers and develop acquired dyscalculia or math anxiety or general hate of academic instruction. Luckily, Tobias is not a cry baby that would easily get damaged. On a football field he is tough. It was the stress of learning or mom's harshness that cracked his shell.
Advice to parents
I know I cannot tell parents what to do. Like kids at school, parents hate to be given instructions, esp. by strangers. I only mentioned to Tobias's mom that I am writing a book about schooling and that the overarching principle is that without pleasure there is no good learning. She agreed! I can only hope that next time, she will notice that putting her kid to tears over numbers is a blatant violation of that principle. Letting him play those money games on the computer, on the other hand, would be learning with pleasure. A bit of supervision would be necessary to see if the kid does not slide down a gambling path. However, Gabor Mate says that for a happy kid there is little need to compensate with addictions. Gaming may take longer to get the kid to the goal of number sense, but those math generalizations can last for life. Good coherent and mnemonic numerical framework is a capital that delivers interest throughout lifetime. With that capital calculations are easier, learning math is easier, logical reasoning improves, and the ultimate hallmark of intelligence, problem solving capacity is the most precious beneficiary.
See also: Abandon early math instruction!
Summary: Math in videogames
- children learn math best via generalization (i.e. extracting rules from examples)
- early academic instruction in math is dangerous (see: Abandon early math instruction!)
- early math instruction can lead to toxic memory that may result in math anxiety
- videogames can be a great introduction to the world of numbers
- due to its abstract nature, math is the area most sensitive to the violations of the Fundamental law of learning