Growing up, I thought math class was something to be endured, not enjoyed. I disliked memorizing formulas and taking tests, all for the dull goal of getting a good grade. In elementary school, my mind wandered so much during class that I sometimes didn’t respond when I was called on, and I resisted using the rote techniques we were taught to use to solve problems. One of my teachers told my mother that I was “slow” and should repeat a grade.

But my problem wasn’t with math itself. In fact, I spent countless hours as a child doing logic and math puzzles on my own, and as a teenager, when a topic seemed particularly interesting, I would go to the library and read more about it.

By high school, none of my teachers questioned my mathematical talent, but none of them really encouraged it, either. No one told me that I could become a professional mathematician. And frankly, that was fine with me. I had no desire to spend my life doing exercises out of a textbook, which is what I assumed mathematicians did — if I even thought about what they did.

What I wanted to do was play college football. I was an offensive lineman. My hero was Jake Long, the starting left tackle for the University of Michigan who would later be selected first in the N.F.L. draft. My ambition was to get an athletic scholarship to attend a Big Ten school.

The chances of that happening were very low. In high school, I weighed “only” 220 pounds — about 80 pounds less than a big-time college tackle. I was an above-average athlete, but not a freak of nature. And my high school in Buffalo was an academic powerhouse, not a “feeder” school for college sports programs.

That didn’t stop me from dreaming, though. And it didn’t stop my coaches from encouraging me to believe I could reach my goal, and preparing and pushing me to work for it. When they told me I had potential but would have to work hard, I listened. I heard their voices in my ear when I dragged myself out of bed for predawn weightlifting sessions. They made videotapes of my performances and sent them to college coaches around the country. It didn’t matter that I didn’t initially attract much interest from the big schools. My coaches kept picking up the phone, and kept convincing me to try to prove myself.

In the end, a Big Ten school, Penn State, did offer me a scholarship. I was the 26th of 27 recruits. After college, I was even drafted by the Baltimore Ravens. I played for the Ravens from 2014 until my retirement in 2017.

Football coaches can be easy to caricature: all that intensity, all those pep talks, all those promises to build character. I certainly don’t romanticize them. I don’t believe that they make better young men, just better football players.

But I wish math teachers were more like football coaches.

Don’t get me wrong: I don’t blame my math teachers. They taught me well. When I got to Penn State, where I majored in mathematics, I was prepared to do the subject at an advanced level.

No one expects a math teacher to tell a talented student that he or she could become the next John von Neumann. (No one expects math teachers to tell students about von Neumann — perhaps the greatest mathematician of the 20th century — at all.) And no one expects math teachers to talk with the kind of fire, or to demand the kind of commitment and accountability, that football coaches do. But I wish they did.

A growing body of research shows that students are affected by more than just the quality of a lesson plan. They also respond to the passion of their teachers and the engagement of their peers, and they seek a sense of purpose. They benefit from specific instructions, constant feedback and a culture of learning that encourages resilience in the face of failure — not unlike a football practice. There are many ways to be an effective teacher, just as there are many ways to be an effective coach. But all good teachers, like good coaches, communicate that they care about your goals.

Until I got to college, I didn’t really know what mathematics was. I still thought of it as problem sets and laborious computations. Then one day, one of my professors summoned me to his office, handed me a book and suggested that I think about a particular problem. Understanding it, I realized, required reading other, more elementary books. I would make my way down one path only to hit a dead end. It wasn’t easy, but it was fascinating.

My professor kept giving me problems, and I kept pursuing them, even though I couldn’t always solve them immediately. Before long, he was introducing me to problems that had never been solved before, and urging me to find new techniques to help crack them.

The mathematical research I was doing had little in common with what I did in my high school classrooms. Instead, it was closer to the math and logic puzzles I did on my own as a boy. It gave me that same sense of wonder and curiosity, and it rewarded creativity.

I am now a Ph.D. candidate in mathematics at the Massachusetts Institute of Technology, and I have published several papers in mathematical journals. I still feel that childlike excitement every time I complete a proof.

I wish I’d known this was possible when I was a kid.

John Urschel (@JohnCUrschel) is the author, with Louisa Thomas, of the forthcoming book “Mind and Matter: A Life in Math and Football.”

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B:

2015年马会开开奖结果查询【圣】【灵】【教】【的】【警】【告】，【钟】【离】【的】【警】【告】，【镜】【红】【尘】【在】【乎】【吗】？ 【呵】【呵】…… 【他】【丝】【毫】【不】【在】【乎】，【因】【为】【他】【是】【镜】【红】【尘】，【是】【整】【个】【日】【月】【帝】【国】【之】【内】【最】【重】【要】【的】【人】【之】【一】！ 【而】【明】【德】【堂】【呢】？【怕】【圣】【灵】【教】【吗】？ 【呵】【呵】…… 【不】【怕】！ 【明】【德】【堂】【在】【日】【月】【帝】【国】【的】【地】【位】，【无】【论】【圣】【灵】【教】【在】【怎】【么】【对】【日】【月】【帝】【国】【今】【后】【的】【战】【争】【作】【用】【非】【凡】，【那】【也】【比】【不】【上】【明】【德】【堂】【在】【日】【月】【帝】【国】【的】【地】

【那】【条】【大】【蛇】【竟】【然】【能】【跟】【苏】【抚】【月】【默】【契】【沟】【通】【似】【的】…… 【魏】【然】【心】【里】【都】【差】【点】【冒】【出】【一】【个】……【大】【胆】【的】【想】【法】…… 【苏】【抚】【月】【莫】【不】【是】【条】【蛇】【精】……？ 【他】【很】【快】【便】【在】【心】【里】【摇】【头】【了】…… 【队】【友】【不】【禁】【开】【口】，“【一】【定】【是】【一】【条】【聪】【明】【的】【高】【阶】【野】【兽】【了】！【这】【么】【有】【灵】【智】！” “【对】【啊】，【没】【想】【到】【看】【起】【来】【这】【么】【凶】【的】【东】【西】……【竟】【然】【这】【么】【听】【话】！” “【那】【个】【苏】【小】【姐】，

【第】【二】【百】【八】【十】【一】【章】【机】【甲】【出】【动】！（【上】） “【滋】【滋】！” 【一】【道】【声】【波】【再】【次】【从】【山】【谷】【深】【处】【传】【来】，【这】【次】【孙】【金】【宝】【扶】【着】【树】【干】【没】【有】【栽】【倒】。 【声】【音】【响】【起】【一】【瞬】【间】，【其】【他】【冲】【撞】【别】【处】【的】【蚂】【蚁】【纷】【纷】【调】【头】，【开】【始】【冲】【撞】【这】【处】【豁】【口】，【仿】【佛】【这】【些】【蚂】【蚁】【有】【智】【慧】【一】【般】。 【而】【随】【着】【蚂】【蚁】【怪】【物】【接】【二】【连】【三】【地】【冲】【撞】【着】【突】【破】【口】，【孙】【金】【宝】【的】【脸】【色】【变】【得】【越】【来】【越】【难】【看】。 【长】【安】【新】

【相】【较】【之】【下】，【星】【域】【是】【由】【各】【个】【神】【自】【己】【率】【兵】【前】【来】，【因】【此】【虽】【然】【由】【神】【王】【担】【任】【总】【指】【挥】【官】，【各】【个】【部】【队】【却】【是】【照】【自】【己】【或】【派】【系】【的】【想】【法】【在】【动】。 【讲】【明】【了】，【就】【是】【支】【缺】【乏】【统】【率】【的】【军】【队】。 【即】【使】【是】【身】【为】【前】【锋】【长】【的】【胡】【克】【神】，【也】【不】【过】【是】【受】【命】【率】【领】【神】【王】【直】【属】【的】【战】【士】【团】【部】【队】，【并】【不】【能】【命】【令】【各】【个】【神】。【的】【确】，【如】【果】【经】【由】【神】【王】【发】【出】【命】【令】【或】【许】【可】【行】，

“【巴】【别】【塔】，【巴】【别】【塔】，【所】【以】，【高】【梵】【你】【就】【是】【想】【造】【一】【个】【魔】【法】【世】【界】【的】【巴】【别】【塔】【出】【来】【向】【着】【神】【的】【空】【间】【进】【发】？【上】【一】【次】【人】【类】【制】【造】【建】【造】【巴】【别】【塔】【换】【来】【的】【是】【一】【场】【大】【洪】【水】，【莫】【非】，【你】【想】【再】【次】【引】【发】【一】【场】【大】【洪】【水】【吗】？【如】【果】【是】【经】【由】【你】【引】【发】【大】【洪】【水】，【我】【们】【基】【于】【这】【个】【担】【心】【已】【经】【可】【以】【对】【你】【出】【手】【了】。” “【上】【一】【次】【我】【们】【人】【类】【面】【临】【大】【洪】【水】，【几】【乎】【是】【处】【于】【一】【个】【任】【人】【鱼】【肉】【的】2015年马会开开奖结果查询【赵】【挺】【之】【拜】【相】，【张】【子】【文】【复】【出】【主】【政】【的】【短】【短】【时】【期】，【是】【海】【军】【真】【正】【的】【黄】【金】【蜜】【月】【期】。 【依】【托】【原】【苏】【州】【和】【上】【海】【之】【辖】【区】，【犹】【如】【一】【头】【吞】【金】【巨】【兽】，【吸】【引】【半】【个】【大】【宋】【资】【金】【进】【入】【投】【资】，【工】【厂】【作】【坊】【短】【时】【间】【内】【遍】【地】【开】【花】。 【海】【军】【集】【博】【览】【会】【远】【近】【闻】【名】，【致】【使】【了】【越】【多】【越】【多】【的】【宋】【国】【和】【异】【国】【船】【只】【靠】【上】【海】【港】，【相】【比】【以】【前】【翻】【七】【倍】【量】【的】【贸】【易】【走】【货】【需】【求】，【极】【端】【刺】【激】【了】【江】【阴】【造】

【半】【个】【月】【后】，“【黑】【血】【谷】”【深】【处】【一】【道】【黑】【影】【正】【于】【遮】【天】【避】【日】【的】【黑】【霾】【雾】【气】【中】【快】【速】【穿】【梭】，【正】【是】【身】【着】“【天】【鹰】【墨】【染】【袍】”【的】【刘】【玉】，“【黑】【血】【谷】”【深】【处】【地】【貌】【与】【外】【围】【毒】【林】【完】【全】【不】【同】，【没】【有】【树】【木】，【光】【秃】【秃】【一】【片】，【连】【绵】【凸】【起】【的】【丘】【陵】，【形】【成】【连】【片】【大】【小】【不】【一】【的】【凹】【谷】。 【刘】【玉】【施】【展】【御】【风】【术】【踩】【着】【凸】【起】【的】【怪】【石】，【快】【速】【向】【前】【飞】【奔】，【四】【周】【冒】【着】【缕】【缕】【黑】【烟】【的】【泥】【土】【不】【时】【翻】【动】

【从】【沃】【野】【镇】【回】【到】【小】【孤】【山】，【大】【概】【又】【过】【了】【两】【三】【日】，【魏】【焘】【还】【没】【有】【回】【来】。【贺】【小】【安】【不】【由】【得】【又】【有】【些】【担】【心】，【阿】【骆】【与】【里】【娜】【两】【人】【轮】【换】【着】【每】【日】【都】【会】【去】【一】【趟】【沃】【野】【的】【军】【营】【打】【探】【消】【息】。 【有】【时】【候】【也】【许】【没】【有】【消】【息】【也】【是】【要】【学】【着】【起】【接】【受】【的】【消】【息】，【因】【为】【日】【子】【依】【旧】【在】【继】【续】。【家】【里】【水】【缸】【里】【的】【水】，【终】【于】【用】【尽】【了】，【虽】【然】【她】【们】【很】【节】【约】，【毕】【竟】【三】【口】【活】【人】，【每】【天】【要】【吃】【饭】【喝】【水】。【许】

【大】【长】【老】【环】【视】【大】【厅】【一】【周】，【叶】【家】【子】【弟】【就】【算】【是】【着】【急】【测】【试】，【却】【也】【怕】【真】【的】【和】【大】【长】【老】【说】【的】【那】【样】。【万】【一】【自】【己】【是】【有】【缘】【人】，【那】【因】【为】【灵】【盘】【反】【应】【的】【慢】，【反】【而】【让】【别】【人】【成】【为】【有】【缘】【人】，【那】【岂】【不】【是】【亏】【死】【了】。 【关】【乎】【着】【下】【任】【家】【主】【的】【人】【选】，【甚】【至】【成】【神】，【他】【们】【宁】【愿】【谨】【慎】【一】【些】，【也】【不】【愿】【为】【他】【人】【做】【了】【嫁】【衣】。 【他】【们】【眼】【中】【的】【不】【甘】【自】【是】【被】【大】【长】【老】【扑】【捉】【到】【了】，【几】【个】【没】【有】【叶】

“【前】【边】【就】【是】【火】【烈】【宫】【了】！” 【穆】【极】【自】【然】【是】【不】【知】【道】【云】【笑】【曾】【经】【来】【过】【火】【烈】【宫】，【见】【得】【他】【指】【着】【前】【边】【的】【一】**【火】【红】【色】【建】【筑】【开】【口】【出】【声】，【口】【气】【之】【中】，【有】【着】【一】【种】【隐】【晦】【的】【傲】【意】。 【火】【烈】【圣】【鼠】【一】【族】【族】【人】【不】【多】，【但】【每】【一】【个】【成】【年】【的】【火】【烈】【圣】【鼠】，【都】【是】【可】【以】【独】【挡】【一】【面】【的】【强】【者】，【尤】【其】【是】【那】【些】【达】【到】【至】【圣】【境】【层】【次】【的】【族】【人】，【走】【在】【外】【间】【更】【是】【无】【人】【敢】【惹】。 【这】【火】【烈】【宫】

[责任编辑:余丹丹]

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