Parents and Teachers Pass On Math Anxiety to Kids Like a Virus, Especially to Girls

“Why do smart people enjoy saying that they are bad at math?” laments Petra Bonfert-Taylor, a professor of engineering at Dartmouth College. “Few people would consider proudly announcing that they are bad at writing or reading.” After seeing one too many examples of adults “passing on [mathematical anxiety] like a virus,” Bonfert-Taylor has an important message for math-phobic parents and educators: “We are passing on from generation to generation the phobia for mathematics… [and] as a result, too many of us have lost the ability to examine a real-world problem, translate it into numbers, solve the problem and interpret the solution.”

Many people will recognize what Bonfert-Taylor calls “damaging myths” that adults perpetuate when they call themselves bad at math: “math is inherently hard, only geniuses understand it, we never liked math in the first place and nobody needs math anyway.” And while well-meaning adults may think they’re encouraging kids by sharing their own math fears, research has shown the opposite — “Anxiety over mathematics has been recognized as a grade killer.” Research has found that the problem is particularly significant for girls, who “are especially affected when a teacher publicly announces math hatred before she picks up the chalk.” Moreover, as Bonfert-Taylor explains in a Washington Post article: “A study published in the Proceedings of the National Academy of Sciences reported that female — but not male — mathematical achievement was diminished in response to a female teacher’s mathematical anxiety. The effect was correlated: the higher a teacher’s anxiety, the lower the scores.”

Parents’ anxiety about math can have a similar effect on kids’ achievement and their attitude toward the subject. According to Bonfert-Taylor, “children who received math homework help from mathematically fearful parents showed weaker math achievements than their peers, which in turn resulted in increased math anxiety for the children themselves.” New research on math anxiety confirms that these parents unintentionally teach kids to expect that math will be beyond their capabilities. As Sian Beilock, a cognitive scientist and president of Barnard College, explains in an NPR piece, “A parent might say, ‘oh I’m not a math person, it’s okay if you’re not good at math either’… [which] can send a signal to kids about whether they can succeed.”

Fortunately, Beilock’s research has found a surprisingly easy way for parents to stop passing on math anxiety and build their children’s math confidence — and it doesn’t require overcoming their own fear of the subject. For the study, researchers gave Chicago-area families an iPad filled with math-themed stories for parents and children to read together. From first to third grade — the years when children tend to solidify their fear of math — the families read stories that included fun math facts, like the size of the world’s largest cupcake or information about walking frogs, and then kids would answer simple questions about the content. By the end of the first year, parents didn’t feel more confident in their own abilities with math, but they did feel more confident in their kids’ math potential — and equally importantly, they valued math skills more. This had a direct effect on their children’s achievement: when the kids’ math skills were tested at the end of the study, children of math-anxious parents who had participated in the program performed just as well as the kids of math-confident parents.

The most important finding from the study for parents is the importance of normalizing math at home in a way that’s relaxed and playful. While Beilock’s research used math-themed books and stories, there are many other ways to do it, from playing with math games and toys to cooking together. Bonfert-Taylor agrees, arguing that we need to teach kids that “working on mathematical skills is not unlike practicing a sport. Neither can be learned by watching others perform the activity and both require encouragement and effort… You do not need an innate mathematical ability in order to solve mathematical problems. Rather, what is required is perseverance, a willingness to take risks and feeling safe to make mistakes.” So the next time you’re sitting down to talk math with a Mighty Girl in your life, Bonfert-Taylor urges you to “try to have fun and give reassurance that perseverance will yield results. Numbers are always simple, clean and beautiful — and nothing to be afraid of.”

Study finds that mastering prerequisites—not taking calculus in high school—better predicts success in college

Phys Org 

July 10, 2018, Harvard University
calculus
Credit: CC0 Public Domain

The word alone is enough strike terror into the hearts of even the most accomplished students, but for those who break out in cold sweats at the thought of differentiation rules and integral tables, Philip Sadler and Gerhard Sonnert are here to offer some hope.

Contrary to widely-held opinion, taking high school calculus isn’t necessary for success later in college calculus—what’s more important is mastering the prerequisites, algebra, geometry, and trigonometry—that lead to calculus. That’s according to a study of more than 6,000 college freshmen at 133 colleges carried out by the Science Education Department of the Harvard Smithsonian Center for Astrophysics, led by Sadler, the Frances W. Wright Senior Lecturer on Astronomy, and by Sonnert, a Research Associate.In addition, the survey finds that weaker math students who choose to take calculus in high school actually get the most benefit from the class. The study is described in a May 2018 paper published in the Journal for Research in Mathematics Education.

“We study the transition from high school to college, and on one side of that there are college professors who say calculus is really a college subject, but on the other side there are  who say calculus is really helpful for their students, and the ones who want to be scientists and engineers get a lot out of it,” Sadler said. “We wanted to see if we could settle that argument—which is more important, the math that prepares you for calculus or a first run-through when you’re in high school followed by a more serious course in college?”

The study’s results, Sadler said, provided a clear answer -a firmer grip on the subjects that led up to calculus had twice the impact of taking the subject in high school. And of those who did take calculus in high school, it was the weakest students who got the most from the class.

To get those findings, Sadler and Sonnert, designed a study that asked thousands of college freshmen to report not only demographic information, but their educational history, background and mathematics training.

“They fill out the detailed survey at the beginning of the semester…and there’s a field on the last page where the faculty member can put their grade,” Sonnert said. “Then the professors remove the first page with the ‘s name and we get their final grade and all the self-reported information.”

“We looked at how students did in college calculus…and tried to figure out what the predictive influence of taking a calculus course in high school was versus mastering those pre-calculus subjects,” Sadler said. “So, we looked at how those students did in algebra, geometry, and pre-calculus subjects like trigonometry, as well as their SAT and ACT scores, and we combined those into one factor.

That gave us a composite measure of how much they know of the math that’s preparatory for calculus,” he continued. “Then we looked at the students who had taken the subject in high school and built a statistical model to separate the two.”

While it’s difficult to pin down an exact reason for why weaker students who took calculus in high school get the most out of it, Sadler suggested that part of the difference may be chalked up to the educational environment of high school calculus.

A high school class, he said, might have just 15 or 20 students, each of whom likely receives constant support from their teacher and homework assignments are turned in daily.

“In some ways, the high school class is probably better supported,” Sadler said. “In high school, if you are not doing your work, there is an interim grade that goes home to your parents (so intervention happens when you need it.)”

By the time they arrive in college, however, students might be one of several hundred in a lecture hall, and their only opportunity for one-on-one contact with the professor comes during office hours. In some cases, attending sections and even completing problem sets is optional, so unless students make an effort to seek out tutoring help, it’s easy to fall behind.

“Even Harvard students run into this—they have trouble with learning how to be an independent learner,” Sadler said. “But one other difference is that in college the professor just assumes you know all the prerequisites, and if you don’t, or you’re not really solid in them, then what do you do? They won’t go back and cover the things that you may be missing like a teacher can do in high school.”

Another reason weaker math students take more from a high school calculus class, Sadler and Sonnert suggested, may be similar—though they may not receive top marks, the high school class gives them a chance to bone up on the basics, so by the time they get to college those students have a stronger mathematical foundation on which to build.

“To some extent, it’s like learning a foreign language,” Sonnert said. “The more you’re exposed to it, the more you do it every day, the more sentences you say, the better your sentences are. So, there may be this practice effect and facility with it that only comes in a college class.”

Ultimately, Sadler said, the study’s findings don’t suggest that students should drop high school calculus altogether, but rather shows that success in the subject—whether in high school or college—comes more from having a strong foundation. That foundation starts early and every year of great math teaching, even as far back as Algebra I in eighth grade, contributes to math proficiency that pays off in college.

“The one thing the paper says is if your background is strong, if you really know your algebra, geometry and pre-calculus, you’re going to do well in college calculus,” Sadler said. “You don’t need a high school calculus course. That was a surprise. There is no reason that those new to calculus should not take the course in college, in spite of half the students in class having taken it in high .”

“There are always these kinds of arguments in education, where people have very strong views based primarily on personal experience, and we specialize in investigating those views,” Sadler said. “As it turns out, in this case, the professors are more right than  teachers, because how well students did in courses before calculus makes the biggest difference in their   grade. But, the heavy-lifting is done by those math teachers whose efforts lay the foundation for later student success.”

Read more at: https://phys.org/news/2018-07-mastering-prerequisitesnot-calculus-high-schoolbetter.html#jCp

Tell Your Kids: Math Makes Money

Published: Jan 28, 2017

Why learning more high school math now could make kids richer later

20th Century Fox Film Corp. All rights reserved. / Courtesy Everett Collection

By

JILLIAN BERMAN

REPORTER

Parents and math teachers regularly asked by their school-aged charges whether math matters in real life may now have an answer.

In a study published by the National Bureau of Economic Research this week, Harvard Kennedy School Policy Professor Joshua Goodman took a look at what happened to students whose high schools were required in the 1980s to increase the minimum level of coursework required to graduate. What he found is that black students were more likely to increase the number of math courses they took as a result of the change in standards and that translated into higher earnings down the line.

Put simply: About 15 years after they graduated, African-American high school graduates who went to school when these changes took effect saw their average earnings increase about 10% for every extra year of math coursework. The findings may add fuel to the steady drum of education experts, policy makers and others calling for an increased focus on science and math education. “Our efforts to increase access to high-quality science and math education likely do matter for people’s life outcomes,” Goodman said.

The increase in required math courses didn’t necessarily produce rocket scientists, Goodman notes, because the extra coursework wasn’t at a particularly high level. But becoming familiar with and practicing relatively basic math skills allowed high school graduates to pursue and excel at jobs that required some level of computational knowledge, he said.

A burgeoning industry of tech companies is enabling employers to make contributions toward their employees’ student loans.

There’s other evidence indicating that having a comfort level with basic math principles can go a long way. Requiring students to take an extra math course increases the likelihood that they’ll build wealth through real estate and other assets and decreases the likelihood that they’ll experience foreclosure or become delinquent on credit card debt. “It just seems like a lot of things that many of us take for granted in life depend on being able to do some pretty basic computation,” Goodman said.

This study indicates that local policy makers can play a role in ensuring students acquire those skills, he said. White high school graduates didn’t see much of a boost in earnings as a result of the increased math requirements and Goodman speculates that’s because they were more likely to be in better-funded schools that were already going beyond their state’s updated requirements.

Still, Goodman acknowledges that the earnings boost for black students correlated with the uptick in math education may be dependent on the state of the economy. When Goodman checked in in the late 1990s and early 2000s on the earnings of black students who graduated in the late 1980s, he found that their earnings increased significantly if they took more math. But when he looked at their earnings again after the Great Recession, he saw the earnings effect disappear.

He posits two possible explanations for this. Firstly, as high school graduates get further away from their high school career, students with fewer math skills ultimately catch up. Secondly, math skills may be more desirable during different periods. The tech boom of the late 1990s and early 2000s may have meant that math skills were particularly valuable. Whereas, the more service-oriented economy of the late 2000s may put more of an emphasis on softer skills. “Some of these results may be dependent on what the labor market looks like at any moment in time,” Goodman said.

Stop telling kids you’re bad at math. You are spreading math anxiety ‘like a virus.’

The Washington Post

April 25

When I read the following post, I was chagrined to see myself in it. Are you? Here’s why you need to change your tune. This was written by Petra Bonfert-Taylor, a professor of engineering at Dartmouth College and a 2016 Public Voices Fellow of the OpEd Project, a non-profit working to increase the range of public voices and ideas.

By Petra Bonfert-Taylor

“How was skiing?” I asked my 14-year old daughter as she hauled her boot bag into the car. “Well, the ratio of snow to ground was definitely low,” she replied, adding that she had tried to figure the ratio of snow-to-ground during practice but had received only mystified looks. “Stop the math!” demanded a coach. “You are confusing us!”

Why do smart people enjoy saying that they are bad at math? Few people would consider proudly announcing that they are bad at writing or reading. Our country’s communal math hatred may seem rather innocuous, but a more critical factor is at stake: we are passing on from generation to generation the phobia for mathematics and with that are priming our children for mathematical anxiety. As a result, too many of us have lost the ability to examine a real-world problem, translate it into numbers, solve the problem and interpret the solution.

Mathematics surrounds us, yet we have become accustomed to avoiding numerical thinking at all costs. There is no doubt that bad high school teaching and confusing textbooks are partly to blame. But a more pernicious habit does the most damage. We are perpetuating damaging myths by telling ourselves a few untruths: math is inherently hard, only geniuses understand it, we never liked math in the first place and nobody needs math anyway.

Often adults are well-meaning when telling children about their own math phobia: after all, won’t it make the children feel better if they know that others feel that way as well? Research shows the answer is a resounding “no.”

Anxiety over mathematics has been recognized as a grade killer. The National Mathematics Advisory Panel of the U.S. Department of Education has found that anxious students perform lower than their abilities. What’s more, there is growing evidence that mathematical anxiety can be passed on like a virus from teachers to students as well as from parents to children.

Girls are especially affected when a teacher publicly announces math hatred before she picks up the chalk. A study published in the Proceedings of the National Academy of Sciences reported that female — but not male — mathematical achievement was diminished in response to a female teacher’s mathematical anxiety. The effect was correlated: the higher a teacher’s anxiety, the lower the scores.

Parents’ mathematical anxiety can have a similar effect on their children. Researchers observed that children who received math homework help from mathematically fearful parents showed weaker math achievements than their peers, which in turn resulted in increased math anxiety for the children themselves.

 What we need to do instead is encourage our children to persevere. In France, for example, math skills are appreciated and it is quite cool to be good at math. Teaching — especially math teaching — is a highly respected and well-paid profession, even at the preschool level and children there are trained early to appreciate the art of mathematics.

Working on mathematical skills is not unlike practicing a sport: neither can be learned by watching others perform the activity and both require encouragement and effort. In the words of Michael Jordan: “I’ve missed 3,000 shots. Twenty-six times the game-winning shot has been trusted to me, and I’ve missed. I’ve lost over 300 games. I’ve failed over and over and over again, and that is why I’ve succeeded.” (Notice the math in that statement?)

You do not need an innate mathematical ability in order to solve mathematical problems. Rather, what is required is perseverance, a willingness to take risks and feeling safe to make mistakes. The next time you help a student with homework, try to repress the “I hate math” instinct, which is even worse than making a few flubs.

Instead try to have fun and give reassurance that perseverance will yield results. Numbers are always simple, clean and beautiful — and nothing to be afraid of.

The Family Roots of Math Anxiety

EdWeek

By Sarah D. Sparks on August 10, 2015 

In general, parents’ help with homework can be a major support for students. But if parents shudder at the thought of algebra or arithmetic, they can pass that math dread on to their children.

So finds the latest in a series of studies by University of Chicago psychologists including Erin MaloneySian Beilock, and Susan Levine, who study the causes and effects of performance anxiety. The new research, in the journal Psychological Science, finds that parents with math anxiety can hinder their students’ progress in math.

The researchers tracked more than 400 1st and 2nd grade students whose parents provided different levels of help with their homework. They also assessed both parents’ and kids’ attitudes toward math at the beginning and end of the school year.

Students whose parents reported high math anxiety made significantly less progress in math over the course of a year, and they were more likely to become anxious themselves—but only if their anxious parents sweated through helping them with homework.

By contrast, students with math-anxious parents who helped with homework showed no similar problems when it came to reading. While there may also be some genetic influence on math anxiety, that did not seem to be a factor here. Students whose anxious parents did not help with math homework did not show similar difficulties or fear when it came to math.  

Parent Attitudes Shape Children

Even if a parent understands how to do a problem, his or her underlying dread of math could hinder students’ enjoyment of solving problems, particularly if it plays into broader stereotypes about who should like or be good at math.

“Our work suggests that if a parent is walking around saying ‘Oh, I don’t like math,’ or ‘This stuff makes me nervous,’ kids pick up on this messaging and it affects their success,” Beilock said in a statement.

That’s in line with prior research that found girls whose female elementary teachers were anxious about their own math competence showed bigger gender gaps in math performance by the end of the year, even if they had started on par with boys. Maloney told me that because nearly 9 out of 10 parents who responded in this study were women, they were unable to look at parent gender differences, but they found no differences in the effects of parent anxiety on boys versus girls. 

Overcoming Dread of Numbers

Even if parents try to control how they talk about math, fear may hinder how they help their children, the researchers found. Anxious parents may have trouble explaining math concepts, Levine noted in a statement. They may react badly when their children make mistakes while solving a problem. 

“We can’t just tell parents—especially those who are anxious about math—’Get involved,'” Maloney said in a statement on the study. “We need to develop better tools to teach parents how to most effectively help their children with math.”

We already see this for teachers. One school in New York, for example, offers weekly training to help math-anxious teachers brush up on skills and gain confidence with numbers. Another works with teachers to understand the theory of growth mindset—that math performance is not a fixed innate skill, but one that can be improved through effort.

Could it be that the teaching profession isn’t pink enough?

US News & World Report

Two studies say more women would study math and science in college if there were more female math and science teachers in high school

Photo of Jill Barshay

Education by the Numbers

More girls might pursue science fields if they had more female teachers in middle and high school, two studies suggest (AP image of a middle school student, learning computer programing in Pennsylvania)

More than three-quarters of U.S. public school teachers are female. So it’s a bit surprising to hear an argument that there aren’t enough women in the profession. It’s kind of like saying there aren’t enough lawyers in Washington. But that’s exactly the case that two new research studies make for what’s needed to produce more women scientists and engineers in this country.

The studies suggest that if there were more female math and science teachers in middle and high school, more girls would study these subjects in college, and that providing female role models earlier in life — before students get to college — might be one of the more effective ways to encourage more girls to pursue higher level math and science. (“Science” broadly refers to all the hard sciences from computer science and physics to chemistry and engineering).

“A lot of the talk has been about trying to promote more female faculty in college. Maybe that’s misdirected,” said Tim Sass, an author of one of the studies and an economist at Georgia State University. “Maybe there should be more emphasis in hiring qualified faculty in the middle and high school level.”

While women dominate the teaching profession, they are somewhat less numerous among middle and high school math and science faculty. According to the Schools and Staffing Survey, conducted by the Department of Education, female teachers make up between 44 and 65 percent of middle and high school math and science faculty, depending upon the subject and the grade. Eighth-grade math teachers are 65 percent female, for example, but only 44 percent of 12th-grade science teachers are female.

The first study, “Growing the roots of STEM majors: Female math and science high school faculty and the participation of students in STEM” (referring to Science, Technology, Engineering and Math), published Jan. 31, 2015 in the Economics of Education Review, looked at every student in North Carolina who graduated from a public high school in 2004 and continued on to a public college or university in the state. Researchers from the University of North Carolina-Charlotte and Duke University had access to a trove of data, from the students’ middle school grades and high school transcripts to family income and school characteristics.

The researchers found that girls who went to high schools where at least 72 percent of the math and science teachers were female were 19 percent more likely to graduate from college with a science or math major than similar students whose only difference was that they went to a high school where only 54 percent of the math and science teachers were female.

The influence of female teachers was even stronger for high achieving girls — the ones who are most likely to have the preparation and ability to complete the demanding coursework of a science major. Among girls who scored at least 580 on the math section of the SATs, there was a 44 percent increase in the likelihood of graduating from college with a science or math degree if they had attended a high school where 72 percent of the math and science teachers were women, compared to a school where just 54 percent of the math and science teachers were women.

Boys, by contrast, were unaffected by the gender mix of their high school teachers.

Martha Bottia, the lead author of the study at U.N.C.-Charlotte, has also conducted interviews with dozens of science students, and said the high school experience is “what matters most” for pursuing higher-level science. “More than half of them make the decision (to major in a science or math subject) before they enter college,” said Bottia, explaining that science majors require more planning and preparation and a commitment to hard work. “It’s not like STEM majors go to college their first year with no idea what they’re going to major in and then decide to do physics.”

In humanities subjects, by contrast, freshman-year professors might be more influential than high school teachers in the selection of a major.

A second study looked at four years’ worth (or cohorts) of students in Florida from fifth grade through college graduation, and found that female math and science teachers as early as middle school make a difference in how many women pursue math and science in college. A still-unpublished working paper from this study, “Understanding the STEM Pipeline,” was delivered on Feb. 20, 2015, at a conference of the National Center for Analysis of Longitudinal Data in Education Research (CALDER), a research consortium of six universities.

This data analysis showed that girls who had higher proportions of female math and science teachers in middle and high school were more likely to take one or more science or math courses during their first year in college. The author, Professor Sass, found that the probability of a young woman taking a math or science course in her freshman year of college increased by 3.3 percentage points as the proportion of female middle and high school teachers went from zero to half. To put that in perspective, that 3.3 percentage-point increase nearly eliminates the gender gap between men and women in the likelihood of taking at least one science or math course in the first year of college, according to Sass.

That’s important because young women in Florida perform nearly as well as young men in math achievement tests. But once they get to college, women are much less likely to take courses in the physical sciences in their first year, and less likely to earn a degree in physics or engineering, even after adjusting for pre-college test scores.

By contrast, Sass found that in college, women were just as likely to complete a major in a hard science whether they had been taught by male professors or female professors.

It does sound crazy, when a majority of K-12 math and science teachers are already women, that the solution to gender inequity in STEM fields might be to create an even more female-heavy teaching profession.  If you followed these studies to their logical extremes, we’d make all high school math and science teachers women.  Personally, I would still prefer to see more male K-12 teachers — because it might increase the prestige of the profession overall.

5 Ways To Help Your Kid Not Stink At Math

Photo

CreditPhoto illustration by Andrew B. Myers. Prop stylist: Randi Brookman Harris.

In “Why Do Americans Stink at Math” for this week’s edition of the magazine, I wrote about the latest wave of math reforms, which are both the best chance we have of curing our national “innumeracy” (the mathematical equivalent of not being able to read), and a near guarantee at driving children and their parents understandably insane. As I write in the story, the problem is not the new approach itself. The problem is our widespread failure to help teachers figure out how to teach in the new way.

While we wait for teachers to get the help they need, though, families will still be left with the frustrating task of monitoring homework time. What can parents do to help their children extract all the best from the new math — and minimize suffering from the worst? With the right attitude, and these tips, it might just be possible for you and your children to not only survive, but thrive.

1. Listen to What’s Going Wrong

Teaching children math requires first figuring out what they don’t understand. Instead of getting to the heart of a misunderstanding, we are far more likely to tell children something like, “No, that’s not right, try it this way instead.” The better response to a wrong answer begins with asking the child to explain her thinking.

For example, take a simple problem like 49 x 5. Many children will incorrectly write the answer as 405, and great math teachers know why. They have used the correct algorithm, lining up the numbers, carrying the 4, etc. But they have them in the wrong order, first adding 4 to 4 to get 8 and then multiplying the product by 5 to get 40, instead of multiplying 5 x 4 to get 20 and then adding 4 to get 24. Seeing this deeper misunderstanding in a child’s wrong answer allows you to combat it, showing the child not only the right steps, but why the wrong ones don’t make sense.

2. Do Everyday Math Out Loud

Many people use math in their jobs without realizing it. Dairy factory workers use it to figure out how to pack quarts of milk efficiently onto trucks; cashiers use it to make change and calculate prices; even those of us who are customers have to think about how to calculate a tip, compare prices and confirm we’ve gotten the right amount of change.

Math is not a disconnected process but a manipulation of real numbers that exist in the real world and make real sense. If you open up these everyday problems for your kids to think through with you, you won’t just be helping them to see how math makes sense in the real world. You can also get some help figuring out the tip.

3. Reclaim the Dreaded Dots.

One of the math exercises giving parents indigestion these days is the idea of asking children to draw and count dots in order to solve addition and multiplication problems. Motoko Rich recently reported for the Times on a couple vexed by “the pictures, dots and sheer number of steps needed to solve some problems.” Without any sense of why these exercises matter, they can be tedious.

But drawing dots can also help children think more deeply about math. The trick is not just to have them draw, but to think. In aresponse to Ms. Rich’s piece, Christopher Danielson, a math teacher as well as a parent, described how he used “arrays,” the structure the dots are supposed to get kids thinking about, to help his 7-year-old daughter understand multiplication.

First he asked her to draw three rows of five dots, paying attention to how she counted out the total — probably counting by fives, he realized. Then he asked, “What if it had been 3 rows of 6?” After what Mr. Danielson described as a “long, thoughtful pause,” his daughter announced her answer: “Eighteen!” He followed up with the key question parents should marshal as much as possible: “How did you know that?” As Mr. Danielson describes, the resulting conversation took only a minute, but helped his daughter see some key ideas about multiplication and math in general:

The three rows of five she drew gave us a jumping off point for imagining the three rows of six we discussed. Three groups of five now has a relationship for her to three groups of six.

More importantly, the strategy of finding new facts based on old facts (here that 3 groups of 6 is 18 based on knowing that 3 groups of 5 is 15), has been introduced explicitly. It is something we will talk about in the future, and something she will know to consider.

4. Combine Memorization With Understanding

When I was in 3rd grade, my father was horrified to go to a meeting with my elementary school’s new principal and hear her announce that our school would no longer be teaching “math facts.” To promote understanding, my dad recalls the principal saying, she’d ask teachers to focus only on concepts, not memorization.

My old principal’s idea is a common misunderstanding of math reforms. Back then, in the early 1990s, just as today with the Common Core, the idea is not to replace memorization with “understanding” but to make each one stronger by teaching both at once. (In addition to arrays, the Common Core mandates that students demonstrate fluency with basic times tables and addition facts.)

My dad’s response to my principal was good, but could have been even better. He decided that if the school wasn’t going to teach me math facts, he was. As a result, we spent our car trips with my dad grilling me on times tables. 3 x 3? 6 x 7? Like many children, I didn’t hate this exercise; I liked memorizing, and I liked the rock-music math-for-kids audiotapes my mom bought to supplement our drills.

But my math facts knowledge only took me so far. I still mostly think about multiplication as pure memorization, rather than an operation on numbers that really makes sense. Magdalene Lampert, a former math teacher who now teaches educators how to train teachers, taught me an activity my dad might have added to his repertoire to combat this phenomenon: choral counting — that is, counting by 3s, 4s, 3/4s, (think Schoolhouse Rock) or even larger numbers, or getting more complicated by going backward instead of forward, for example. The exercise helps children see that multiplication is truly only repeated addition, and it also helps them see patterns in numbers, making multiplication something to memorize and to understand.

5. Introduce Big Ideas Early

After coming across so many great ideas about math teaching in research papers, I started to wonder whether parents could take them up on their own with their kids. So I decided to give one set of books — including “Children’s Mathematics” by the education professor Thomas Carpenter — to a friend with a young son.

I wasn’t sure how useful the books would be; they are written more for teachers than for parents. Also, the books aim to do something very ambitious: help elementary school children begin to learn algebra’s building blocks, starting with addition and multiplication problems. For example, instead of simply asking a child what 3 + 4 equals, Carpenter encourages teachers to ask them 3 + what number equals 7. “What number,” of course, is the first step to imagining variables like “x.”

The same idea exists in the Common Core, which replaces “what number” with empty boxes that children are supposed to fill in.

It’s a great idea, but hard to carry out in practice. So I wasn’t sure what my friend would make of it, not to mention what his 4-year-old would think. Then he sent me this email:

I tried the first lesson in the book out on him tonight at dinner: combining arithmetic with algebra. I said, OK, 2 plus 2 equals 1 plus what? At first he got confused, like what does *what* mean? But then he got it and thought for a while and said, 3! (Actually, “free.” He has trouble pronouncing “th.”) We got all the way up to 3 plus 3 equals 2 plus what. Nailed that one too. So proud.

Taking that next step deeper into understanding is one of the most underappreciated goals of the Common Core. When that kind of teaching becomes standard in the classroom, we’ll see real gains in math understanding. In the meantime, parents will have to do our best to embrace the best of the “new math” at home.

Read more about math and education on Motherlode: Goodnight, Moon. Goodnight, Math Problem., and In Defense of Algebra.

When Advanced Math Placement Is a Struggle

The New York Times Motherlode Blog

By JESSICA LAHEY

This week’s question is an amalgam of two questions, but because I have received quite a few inquiries about ability grouping, I thought I’d do a mash-up in order to cover all the issues surrounding the challenge of academic placement.

Algebra homework, the second time around.Jessica LaheyMrs. Lahey’s own algebra homework, when she retook the course last year.

Dear Mrs. Lahey,

We pushed really hard last year in order to get our daughter placed in above-level math. She claimed she was up for the challenge at the time (she’s in seventh grade now) and while her teachers were worried about her skills and her ability to rise to the challenge, we promised we’d get her tutored over the summer to shore up her skills in preparation for the more challenging math class. Now, two months into the new school year, we fear we may have made a mistake. Despite tutoring over the summer and help from both of her parents every night during math homework, she’s hovering around a C-. In order to keep her on the accelerated math track in her school, she needs to maintain a B- or better in math, and I know the subject of math placement will come up at our next parent-teacher conference. We are all exhausted by her nightly struggle with the material but feel we are stuck because we pushed for the placement in the first place. What should we do?

Thank you, M.A. (and M.G.)

Dear M.A. (and M.G.),

As with any complicated math problem, the first thing we need to do is look over all of the factors involved and figure out the order of operations we need to employ in order to make some sense of it all.

The first place to start is with your daughter, as she’s clearly the most important factor in this equation. I’d be honest: Admit that you are unsure of how you handled the issue of math placement, and ask what she would do if she were in charge. After all, she is in middle school, and it’s important to allow adolescents to have a say in the trajectory of their education. She should be taking on an increasing degree of autonomy and choice when it comes to her courses, so give her a taste of this responsibility now. She’s the one who is going to have to shoulder the consequences of this decision, after all. If she really wants to stick out the harder math level, that should count for a lot in the finally tally. If she wants to move down to the lower ability grouping, if she reacts with relief that you have finally asked her opinion in the matter, that would be the end of it for me. I’d have the class change arranged the following day.

Your next step should be to talk to the teacher, particularly if your daughter really wants to stick out the above-grade class. Find out how the teacher perceives your daughter’s progress, and if both the teacher and your daughter are game to stick it out, then see how things go for a while longer. You can always revisit this decision in a month or two.

I will warn you, however, that if her teacher is anything like me, he or she will ask you one simple question: What is your goal? If your goal is for your daughter to be enrolled in above-grade-level math, then mission accomplished. Stick with the strategy you have committed to so far and tough it out. Your daughter might be in a rough patch, she might kick into high gear and find her way through the material, she might find her passion for math – we simply can’t know what the future holds. Given enough tutoring and support from you, she might limp through the year and remain in the above-grade math track, particularly if she’s invested.

If, however, your goal is for your daughter to learn math, and feel competent in her abilities, I’d recommend that you demote her to grade-level math.From what you have described, above-grade-level math has been challenging for everyone, and if your daughter’s grade is any indication, she’s not achieving mastery in what she needs to know in order to be fluent and confident in her math skills. Middle school is challenging enough without being pushed into an ability grouping she’s not ready for. Math skills are cumulative, and if your daughter does not achieve mastery this year, she will be at a real disadvantage as she moves forward.

I hope this is helpful, and I wish your daughter luck with math. If she’s interested in a fun read about math (no, really), I’d recommend Danica McKellar’s smart and funny books on math, written specifically for adolescent girls.

Good luck to all of you, and keep me posted!

Mrs. Lahey


 

Jessica Lahey is an educator, writer and speaker. She writes about parenting and education for The New York Times, The AtlanticVermont Public Radio and her own blog, Coming of Age in the Middle. Her book, about why and how parents need to let their children fail, will be published by HarperCollins in 2014.

Can Playing Video Games Give Girls an Edge In Math?

MindShift

 | July 24, 2013

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Girls should play more video games. That’s one of the unexpected lessons I take away from a rash of recent studies on the importance of—and the malleability of—spatial skills.

First, why spatial skills matter: The ability to mentally manipulate shapes and otherwise understand how the three-dimensional world works turns out to be an important predictor of creative and scholarly achievements, according to research published this month in the journalPsychological Science. The long-term study found that 13-year-olds’ scores on traditional measures of mathematical and verbal reasoning predicted the number of scholarly papers and patents these individuals produced three decades later.

But high scores on tests of spatial ability taken at age 13 predicted something more surprising: the likelihood that the individual would develop new knowledge and produce innovation in science, technology, engineering and mathematics, the domains collectively known as STEM.

The good news is that spatial abilities can get better with practice. A meta-analysis of 217 research studies, published in the journal Psychological Science last year, concluded that “spatial skills are malleable, durable and transferable”: that is, spatial skills can be improved by training; these improvements persist over time; and they “transfer” to tasks that are different from the tasks used in the training.

This last point is supported by a study published just last month in the Journal of Cognition and Development, which reported that training children in spatial reasoning can improve their performance in math. A single twenty-minute training session in spatial skills enhanced participants’ ability to solve math problems, suggesting that the training “primes” the brain to tackle arithmetic, says study author and Michigan State University education professor Kelly Mix.

Playing an action video game “can virtually eliminate” the gender difference in a basic capacity they call spatial attention.

Findings like these have led some researchers to advocate for the addition of spatial-skills training to the school curriculum. That’s not a bad idea, but here’s another way to think about it: the informal education children receive can be just as important as what they learn in the classroom. We need to think more carefully about how kids’ formal and informal educational experiences fit together, and how one can fill gaps left by the other.

If traditional math and reading skills are emphasized at school, for example, parents can make sure that spatial skills are accentuated at home—starting early on, with activities as simple as talking about the spatial properties of the world around us. A 2011 study from researchers at the University of Chicago reported that the number of spatial terms (like “circle,” “curvy,” and “edge”) parents used while interacting with their toddlers predicted how many of these kinds of words children themselves produced, and how well they performed on spatial problem-solving tasks at a later age.

[RELATED: How Thinking in 3D Can Improve Math and Science Skills]

As kids grow older, much of the experience they get in manipulating three-dimensional objects comes from playing video games—which brings us back to the contention at the start of this article. Males have historically held the advantage over females in spatial ability, and this advantage has often been attributed to genetic differences. But males’ spatial edge may also reflect, in part, differences in the leisure-time activities of boys and girls, activities that add up to a kind of daily drill in spatial skills for boys.

If that’s the case, then offering girls more opportunities to practice their spatial skills may begin to close the spatial-skills gender gap—and produce more female scientists, engineers and mathematicians in the bargain. So suggests a study by University of Toronto researchers, published in the journal Psychological Science. They found that playing an action video game “can virtually eliminate” the gender difference in a basic capacity they call spatial attention, while at the same time reducing the gender difference in the ability to mentally rotate objects, a higher-level spatial skill.

Exposure to video games, the authors conclude, “could play a significant role as part of a larger strategy designed to interest women in science and engineering careers.” Participants with little prior video-game exposure “realized large gains after only ten hours of training,” they note, adding that “we can only imagine the benefits that might be realized after weeks, months, or even years of action-video-gaming experience.”

Parents of daughters may blanch at the idea of actually encouraging “years” of action video game play. These moms and dads should tell themselves that their daughters aren’t wasting their time—they’re readying themselves for brilliant careers as scientists and engineers.

If You’ve Got the Skills, She’s Got the Job

The New York Times, OP-ED COLUMNIST

If You’ve Got the Skills, She’s Got the Job

By 
Josh Haner/The New York Times

Thomas L. Friedman

TRACI TAPANI is not your usual C.E.O. For the last 19 years, she and her sister have been co-presidents of Wyoming Machine, a sheet metal company they inherited from their father in Stacy, Minn. I met Tapani at a meeting convened by the Minnesota Department of Employment and Economic Development to discuss one of its biggest challenges today: finding the skilled workers that employers need to run local businesses. I’ll let Tapani take it from here:

“About 2009,” she explained, “when the economy was collapsing and there was a lot of unemployment, we were working with a company that got a contract to armor Humvees,” so her 55-person company “had to hire a lot of people. I was in the market looking for 10 welders. I had lots and lots of applicants, but they did not have enough skill to meet the standard for armoring Humvees. Many years ago, people learned to weld in a high school shop class or in a family business or farm, and they came up through the ranks and capped out at a certain skill level. They did not know the science behind welding,” so could not meet the new standards of the U.S. military and aerospace industry.

“They could make beautiful welds,” she said, “but they did not understand metallurgy, modern cleaning and brushing techniques” and how different metals and gases, pressures and temperatures had to be combined. Moreover, in small manufacturing businesses like hers, explained Tapani, “unlike a Chinese firm that does high-volume, low-tech jobs, we do a lot of low-volume, high-tech jobs, and each one has its own design drawings. So a welder has to be able to read and understand five different design drawings in a single day.”

Tapani eventually found a welder from another firm who had passed the American Welding Society Certified Welding Inspector exam, the industry’s gold standard, and he trained her welders — some of whom took several tries to pass the exam — so she could finish the job. Since then, Tapani trained a woman from Stacy, who had originally learned welding to make ends meet as a single mom. She took on the challenge of becoming a certified welding inspector, passed the exam and Tapani made her the company’s own in-house instructor, no longer relying on the local schools.

“She knows how to read a weld code. She can write work instructions and make sure that the people on the floor can weld to that instruction,” so “we solved the problem by training our own people,” said Tapani, adding that while schools are trying hard, training your own workers is often the only way for many employers to adapt to “the quick response time” demanded for “changing skills.” But even getting the right raw recruits is not easy. Welding “is a $20-an-hour job with health care, paid vacations and full benefits,” said Tapani, but “you have to have science and math. I can’t think of any job in my sheet metal fabrication company where math is not important. If you work in a manufacturing facility, you use math every day; you need to compute angles and understand what happens to a piece of metal when it’s bent to a certain angle.”

Who knew? Welding is now a STEM job — that is, a job that requires knowledge of science, technology, engineering and math.

Employers across America will tell you similar stories. It’s one reason we have three million open jobs around the country but 8 percent unemployment. We’re in the midst of a perfect storm: a Great Recession that has caused a sharp increase in unemployment and a Great Inflection — a merger of the information technology revolution and globalization that is simultaneously wiping out many decent-wage, middle-skilled jobs, which were the foundation of our middle class, and replacing them with decent-wage, high-skilled jobs. Every decent-paying job today takes more skill and more education, but too many Americans aren’t ready. This problem awaits us after the “fiscal cliff.”

“We need to be honest; there is a big case for Keynesian-style stimulus today, but that is not going to solve all our problems,” said the Harvard University labor economist Lawrence Katz. “The main reason the unemployment rate is higher today than it was in 2007, before the Great Recession, is because we have an ongoing cyclical unemployment problem — a lack of aggregate demand for labor — initiated by the financial crisis and persisting with continued housing market problems, consumers still deleveraging, the early cessation of fiscal stimulus compounded by cutbacks by state and local governments.” This is the main reason we went from around 5 percent to 8 percent unemployment.

But what is also true, says Katz, was that even before the Great Recession we had a mounting skills problem as a result of 25 years of U.S. education failing to keep up with rising skills demands, and it’s getting worse. There was almost a doubling of the college wage premium from 1980 to 2007 — that is, the extra income you earn from getting a two- or four-year degree. This was because there was a surge in demand for higher skills, as globalization and the I.T. revolution intensified, combined with a slowdown in the growth of supply of higher skills.

Many community colleges and universities simply can’t keep pace and teach to the new skill requirements, especially with their budgets being cut. We need a new “Race to the Top” that will hugely incentivize businesses to embed workers in universities to teach — and universities to embed professors inside businesses to learn — so we get a much better match between schooling and the job markets.

“The world no longer cares about what you know; the world only cares about what you can do with what you know,” explains Tony Wagner of Harvard, the author of “Creating Innovators: The Making of Young People Who Will Change the World.”

Eduardo Padrón, the president of Miami Dade College, the acclaimed pioneer in education-for-work, put it this way: “The skill shortage is real. Years ago, we started working with over 100 companies to meet their needs. Every program that we offer has an industry advisory committee that helps us with curriculum, mentorship, internships and scholarships. … Spanish-speaking immigrants used to be able to come here and get a decent job doing repetitive tasks in an office or factory and earn enough to buy a home and car and put their kids through school and enjoy middle-class status. That is no longer possible. … The big issue in America is not the fiscal deficit, but the deficit in understanding about education and the role it plays in the knowledge economy.”

The time when education — particularly the right kind of education — “could be a luxury for the few is long gone,” Padrón added.