Passage 2 Math The Key to a More Equitable Society

Math: The Key to a More Equitable Society

John Mighton

A

Over the past few years I’ve asked hundreds of people why, when dividing by

a fraction, you can invert the fraction and multiply. Only a few have been able

to give me a simple explanation. The vast majority will admit they learned this

procedure as a rule that they never understood.

B

It usually takes just 20 minutes for me to teach even the most math-phobic(数学恐惧症的) child or adult why this mysterious procedure works. I don’t have

to explain much—I can usually guide the learner to figure out the math for

themselves by drawing a diagram and asking a few questions about the

picture.

C

Most people believe that math is an inherently difficult subject—accessible

only to people who are born with a “gift” for numbers or who display

mathematical ability at an early age. They assume that topics such as the

division of fractions are too complex for ordinary minds and that the majority

of brains are not suited for solving problems in math. But imagine how

backward our society will appear to be if one day people discover that math is

actually the subject in which learners of all ages can most easily unlock their

true intellectual potential.

D

If it turns out that everyone can learn math, we may have trouble explaining—to our children, for example—why we let so many students struggle in the

subject. We already know that for young children, success in math is the

strongest predictor of success at school and that the abilities and perspectives

students develop in math can be applied in all areas of life.

E

Not knowing how to think mathematically makes people, on average, less

healthy, less financially secure, less innovative and less productive.

Innumeracy damages the economy and degrades the environment. All of

these facts are well established by a large body of scientific research that we

have inexplicably ignored. And there are other benefits of numeracy, including

an appreciation of the beauty of math, which are harder to quantify.

F

For young children, the strongest predictors of later achievement in math

involve very simple skills and concepts—such as counting or associating a

numeral with a quantity—that every person will almost certainly develop. And

brain scans of mathematicians have revealed that expert problem solvers

activate the same neural networks (and rely on the same primitive sense of

space and number) that young children use when they think about math. As

well, logicians have shown that even the most complex mathematical

concepts can be unravelled(拆散) into extremely simple conceptual threads.

All of these results suggest that math should be accessible to every brain.

G

Research in cognitive science also suggests there are more and less efficient

ways to learn math. Lessons that cause “cognitive overload” by pushing

learners too far outside of their comfort zone, or that fail to provide consistent

feedback and support [called “scaffolding(支架式教学法)”] for learners, can be

highly inefficient.

H

Teachers are sometimes blamed for poor results in math, but in my opinion

they are not ultimately responsible for these problems. I believe teachers

should be commended(表扬) for helping their students as much as they do,

especially when the resources and methods of instruction that they are

required to use are not typically designed to close the gap between students.

If teachers had more authority to test approaches that have produced positive

results in rigorous(严酷的) studies, I expect they would help even more

students.

I

Methods of teaching that guide student learning shouldn’t be confused with

rote learning(死记硬背式的学习). When a teacher helps her students to see

connections and make discoveries using well-structured questions, activities

and exercises, the students do the thinking, not the teacher. As students

develop the confidence and conceptual knowledge they need to do more

challenging work, the teacher can let them struggle more (and direct their own

learning more).

J

Several years ago, Jump Math, which uses a form of guided instruction called

“structured inquiry,” participated in a large randomized controlled trial in

Ontario. Oddly, the U.S. Department of Education provided funding for the

study. U.S. scientists believed there was enough evidence behind the

methods of teaching used in Jump to justify a rigorous study—in another

country. In the second year of the study, in Grade 3, students in Jump classes

made significantly more progress in solving the kinds of problems that appear

on the Ontario provincial exams than students in the control group. The study,

which was published in the scientific journal PLOS One, provides more

evidence for the view that the best way to help students become strong

problem solvers is to rigorously guide their learning.

K

One reason teachers should look for ways to help all students learn math is

because students learn more efficiently in classrooms where there are fewer

visible academic hierarchies. As early as kindergarten, children start to

compare themselves with their peers and to identify some as talented or

“smart” in various subjects. Children who decide they are not talented will

often stop paying attention or making an effort to do well. The cycle is vicious:

The more people fail, the more their negative view of their abilities is

reinforced and the less efficiently they learn.

L

Psychologist Carol Dweck, who has drawn attention to the role that attitudes

play in learning, once watched me teach a problem-solving lesson on

perimeter(周长). She observed that “the kids all have the feeling of progress

and they all get the feeling that, ‘I can be good at this.’ ”

M

In the first few minutes of the lesson, I realized that 20% of the Grade 6

students couldn’t find the perimeter of a simple L shape. But after 45 minutes,

they were all enthusiastically solving problems at grade level and could even

explain how they found their answers.

N

If I had been teaching a different subject, especially one that required strong

reading skills or extensive background knowledge, I might have had trouble

getting all of the students doing the same work, even if I had many lessons to

work with them. But in math, there are usually only a small number of skills or

concepts that I need to review, or misconceptions that I need to catch, in order

to include everyone in the lesson.

O

Rather than thinking of math as a subject that is accessible only to the brilliant

few, we need to recognize it as a powerful educational tool for creating a more

equitable society. Everyone should have a right to fulfill their intellectual

potential. The research suggests that math is the subject in which the vast

majority of people could enjoy that right today.

Each of the following statements contains information given in one of

the paragraphs in this passage. Identify the paragraph from which the

information is derived. You may choose a paragraph more than once.

Each paragraph is marked with a letter. Answer the questions by filling

the blanks with the corresponding letter.

1. Not being able to think numerically generally makes people less

healthy.

2. Most people think that math is an inherently difficult subject.

3. People learn less efficiently, the more often they fail and the more their

negative view of their abilities is reinforced.

4. Lessons that cause cognitive overload can be inefficient in teaching

students math.

5. For young children, the strongest predictors of later success in math

involve very simple skills and concepts.

6. Math can be used to create a more equitable society.

7. Innumeracy damages the environment.

8. Jump Math uses a form of guided instruction called “structured inquiry”.

9. Mathematicians activate the same neural networks that young children

use when they participate in math.

10. Teachers are sometimes blamed for poor math results among students.