What do We Know About “Mathephobia”
Mathematician Mary de Lellis Gough, who often observed her struggling students fail to work out mathematical problems, coined the term ‘mathephobia’ in 1953. She described it as “a disease that proves fatal before its presence is detected”. Other experts have defined it as “the panic, helplessness and mental disorganization that arises among some people when they are required to solve a mathematical problem” and “a general fear of contact with mathematics”.
Sian Beilock, a cognitive scientist and her colleagues of Barnard College in New York have shown that math anxiety can start as soon as we enter formal schooling. “Math is one of the first places in school in western cultures where we really learn about whether we got something right or wrong, and are exposed to being evaluated in timed tests.”
Girls may be more prone to it than boys. Primary school teachers often have high levels of math anxiety, says Beilock, and in the US and elsewhere, they are mostly female. Since young children tend to identify with adults of the same gender, this means girls are more likely to pick up math anxiety from their female teachers. Having a female teacher with math anxiety makes girls more likely to believe gendered stereotypes about math, leading to poorer achievement.
“Once you have it, it can be self-lasting. Worrying about it can make it worse.” says Beilock, whose study of children between the ages of five and eight suggests math anxiety might weaken performance by burdening working memory. “As our ability to focus limited, our attention gets divided when we do more than one task at a time.” she says. “If you’re worried about having to do math, you may have an internal monologue saying you can’t do this and at the same time you’re trying to calculate numbers.”
When people have math anxiety, they tend to avoid the subject, as researchers from 2019 show. But since math builds on itself, avoiding it makes it harder to catch up. “Math is foundational. If you miss a certain idea, it’s harder to learn the next one.” says Darcy Hallett. “And then you can fall behind, which might make math more of a targeted anxiety compared to other topics.”
Taylor opened her sleepy eyes and looked out the window at the foggy field below. “NO!” she cried, now fully awake. Buttermilk, the cow, was in Mama’s daisy(雏菊) field.
I must have forgotten to fasten the gate last night, Taylor thought as she pulled a sweatshirt over her head. Mama was planning to sell daisy bouquets at the fair next week. But Buttermilk was eating the flowers.
Taylor hurried outside and grabbed the lead rope hanging on the porch. “Why can’t you stay in the field?” she shouted at Buttermilk as she headed across the yard to the daisy field.
Buttermilk stood nipping (啃咬) tender flowers off their stems. Taylor leaped to her feet and rushed to the cow. Angry and anxious, she thought to herself: “When I grow up, I’ll be an artist and paint pictures all day. I’ll never own a cow. Too much trouble.”
Just as Taylor was about to snap the lead rope onto Buttermilk’s collar, the family dog, Red, rounded the corner of the house. The cow couldn’t stand Red.
Buttermilk took off, tearing through the daisies and across the yard. She finally ran through the open gate and into the field.
“Thank goodness!” Taylor said as she closed the gate and secured the latch (门栓).
She turned to look at the flower garden. Most of the daisies were either eaten or crushed.
Mama came out of the house. “What’s going on?” she asked. She looked sadly at her garden.
“I forgot to latch the gate,” Taylor said.“ I’m so sorry.”
“I know you are.” Mama sighed and gave Taylor a hug. “You learned an important lesson today.”
Taylor’s heart was heavy as she went back into the house. She had to think of a way to make it up to her mother.
Notice
Students’ Union
| A．Because he thought smoking would do good to his heart. |
| B．Because he didn’t believe smoking would be that harmful. |
| C．Because he thought smoking could help him feel relaxed. |
| D．Because he believed smoking could make him feel excited. |
| A．Air pollution. | B．Smoke. |
| C．Secondhand smoke. | D．Thirdhand smoke. |
| A．Because the government hasn’t taken any effective measures to stop smoking. |
| B．Because each year many children’s death is connected with secondhand smoke. |
| C．Because smoking and secondhand smoke do more harm to children than adults. |
| D．Because the government has passed the relevant law to prevent from smoking. |
| A．The smell of tobacco smoke left on things such as clothes, furniture and so on. |
| B．The tobacco smoke accidentally caused by the third person who smokes nearby. |
| C．The poisonous chemicals released from things like clothes, furniture and so on. |
| D．The poisonous chemicals from tobacco smoke left on things like clothes etc. |
| A．that what | B．what that | C．that which | D．what |
When it comes to black holes, we are caught between a rock and a hard place. In the 1970s, Stephen Hawking showed that all black holes give off thermal radiation(热辐射)and eventually evaporate(蒸发). In doing so, they seemed to be destroying information contained in the matter that fell into them, therefore going against a rule of quantum mechanics(量子力学): information cannot be created or destroyed.
Some argued that the outgoing “Hawking radiation” preserved the information. However, if this were the case, then given certain assumptions, the event horizon(视界)—— the black hole’s boundary of no return—— would become intensely energetic, forming a firewall. But such firewalls go against the theory of general relativity, which says that space-time near the event horizon should be smooth. The black hole firewall paradox was thus born.
Now, Sean Carroll at the California Institute of Technology and his colleagues have shown that the paradox disappears when the evolution of black holes is understood in the context of the many-worlds interpretation of quantum mechanics.
The quantum state of the universe is described by something called the global wave function(全局波函数). According to traditional quantum mechanics, whenever there are many possible outcomes for physical process, this wave function ”collapses“ to represent one outcome. But in the many-worlds Interpretation, the wave function doesn’t collapse-rather, it branches, with one branch for each outcome. The branches evolve independently of each other, as separate worlds.
In this way of thinking, the formation of a black hole and its evaporation due to Hawking radiation lead to multiple branches of the wave function. An observer monitoring a black hole also splits into multiple observers, one in each branch.
The new work shows that from the perspective of an observer in a given branch, space-time behaves as described by general relativity and the black hole has no firewall.
But does that imply loss of information? No, says team member Aidan Chatwin-Davies, also of Caltech. That is because the principle of preservation of information applies to the global wave function and not to its individual branches, he says. Information is preserved across all branches of the global wave function, but not necessarily in any one branch. Given this case, a black hole that doesn’t lose information and yet has a smooth, uneventful event horizon without a fire wall isn’t a contradiction.
Yasunori Nomura at the University of California at Berkeleyy has independently arrived at some similar conclusions in his work. He agrees that the many-worlds approach resolves the paradox around information loss from black holes. “Many worlds should be taken seriously,” he says.
1．Which word in the article is similar in meaning to the underlined word in Paragraph 2?| A．Assumption (Paragraph 2) | B．Interpretation (Paragraph 4) |
| C．Evaporation (Paragraph 5) | D．Contradiction (Paragraph 7) |
| A．There is a firewall. | B．No observer will split. |
| C．No information is lost. | D．The wave function collapses. |
| A．introduce an independent scientist |
| B．support the many-worlds interpretation |
| C．question whether many worlds really exist |
| D．argue against the information loss from black holes |
| A．Rules of quantum mechanics. |
| B．A new understanding of the black hole. |
| C．Hawking’s interpretation of the black hole. |
| D．The development of the global wave function. |
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