"Mathematization" was the ladder to upgrade "life math" into "formal math".
“数学化”是“生活数学”提升为“形式数学”的阶梯。
Previously thought to be the result of different teaching styles, this relationship seems to already exist before kids start formal math education in school.
之前的观念则认为是不同的教学方式导致了这一结果，而这种联系似乎在孩子去学校开始接受正式的数学教育之前就存在了。
A: Yes, but more often, prodigies excel in fields with formal rules, like math, music, art or chess. The children master the rules and become early experts in the field.
答：是，相当经常，小天才在数学，音乐，艺术或是象棋等领域里有过人之处，孩子们在他们的学习领域里掌握了规律并能在早期成为该领域的专家或能手。
Often unschoolers with no formal training in math acquire mathematics through real world applications or can catch up with formally instructed peers easily.
其实，接受非学校教育的孩子即使没有经过正规的数学课训练，也很容易通过现实生活知识来培养其数学能力，或者很容易赶上那些接受正规培养的同龄人的数学水平。
Food service majors prepare to serve food in both informal and formal environments. They learn about food, customer service, business math, and more.
餐饮服务专业学习在正式和不正式的场合供应食物。课课程包括食品，客户服务，商业数学等。
The next area had to do with the more formal areas of MATH and LANGUAGE.
下一个领域是更正式的数学和语言领域。
Yes, but more often, prodigies excel in fields with formal rules, like math, music, art or chess. The children master the rules and become early experts in the field.
是，相当经常，小天才在数学，音乐，艺术或是象棋等领域里有过人之处，孩子们在他们的学习领域里掌握了规律并能在早期成为该领域的专家或能手。
Yes, but more often, prodigies excel in fields with formal rules, like math, music, art or chess. The children master the rules and become early experts in the field.
是，相当经常，小天才在数学，音乐，艺术或是象棋等领域里有过人之处，孩子们在他们的学习领域里掌握了规律并能在早期成为该领域的专家或能手。
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