How to Help With Home Work

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math problem

As parents, we sometimes forget how confusing, frustrating and difficult middle school can be, and for some kids, math is especially confusing, frustrating and difficult. Being a middle school math teacher, I hear from many parents who want to help their children but aren’t sure how. Whether you identify with the Carla*, a mother who helps her son too much because she’s eager for him to get good grades or Todd*, a dad who doesn’t know how to help to his daughter because he “doesn’t understand the math” himself, every parent can benefit from these tips for supporting children who struggle with middle school math.

Before you can help your child, it’s important to understand what is happening (mathematically) to the adolescent brain. Middle school is an exciting time; adolescents’ brains are transitioning from reasoning in a concrete manner to understanding abstract concepts and ideas. According to the National Council of Teachers of Mathematics, middle school math typically begins with concepts such as fractions and decimals, and by the time students’ move on to high school, they have learned pre-algebra concepts, such as manipulating variables and solving or writing equations to find unknown values—ideas that cannot easily be visualized or explained with physical objects. Keep in mind that this is particularly hard for students stuck in a concrete state of mind; they tend to rely on memorizing steps or procedures to solve problems, which can lead to more difficulties later on.

Here are some useful tips on how you can support your child in math:

  • Always have notes from class, a textbook or other resources right next to a homework paper. If your child gets stuck, she is likely to find a similar problem in one of these resources that can help her move forward.
  • Ensure the student takes responsibility for her own learning by finding assistance independently; the ability to access help on your own is essential for student success in all areas of academics.
  • Never give children the answers to problems! By giving away answers, you’re depriving your child of the chance to develop the mental processes required to learn a new concept. No parent enjoys seeing their child struggle, but providing answers could set them up for frustration when they have to tackle more difficult problems and might even stunt their progress as classmates move to more advanced lessons. Furthermore, your child’s teacher will not be able to address the misconceptions or areas of weakness that should be targeted in school if homework assignments do not reflect the student’s level of understanding.
  • Encourage your child to underline or highlight key words or phrases in situational problems, as these often help students set up a solution.
  • Realize that your child may struggle with abstract concepts if his or her brain is not quite ready to reason at an abstract level. Your child’s brain will mature in time, and success in math class is likely to accompany this development.
  • If your child is frustrated by mathematics, show him how to focus on concepts rather than procedural knowledge. This might help some students approach and solve problems in a different way—one that makes more sense to them. For instance, ask your child to explain one problem in their assignment each night. If possible, choose one that incorporates both words and computation. If your child is simply reciting step-by-step instructions, encourage her to elaborate by asking questions focusing on the “why” of the problem:
    • What is the goal of the problem?
    • Why does that step work?
    • Why would we want to do that next?
    • What does this step in the process accomplish?
    • How do I know if my answer is reasonable?
    • Can I check my work to make sure it makes sense to me?
  • After your child has completed an assignment, ask her to share what she believes was the most important idea:
    • What is the goal of the problem?
    • What did these problems have in common?
    • Where would I use this in “real life”?
    • Why do you think your teacher gave you this assignment? What did he or she want you to learn?
    • How is this assignment related to the homework you had yesterday? In what ways is it similar or different?
    • Now that you can solve these problems, what do you think you might be able to do next?

    The most important thing to convey to your children is not to give up. Mathematical concepts are intricate and take time to fully grasp. Encouragement and patience go a long way. Read a book with your child while she works on homework or finish a Sudoku or crossword puzzle with her at the table while she studies to keep her company—just being in the same room and working on your own mind-stimulating puzzles might make them more comfortable with difficult homework. If your child continues to struggle and you’re becoming concerned, speak with the teacher or another administrative specialist.

By Diana Goldberg

Instill a Love of Math

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Family playing checkers

Parents are bombarded with messages to read with their children, but it’s rare to hear about the importance of doing math with them. Here are some helpful tips on why and how to instill a love of math in your children.

Early Math Matters
We may take for granted that our children will inevitably learn how to add, subtract, multiply and divide, but early math lessons establish the base for the rest of their thinking lives. “Mathematics that kids are doing in kindergarten, first, second and third grades lays the foundation for the work they are going to do beyond that,” says Linda Gojak, president of the National Council of Teachers of Mathematics (NCTM). “They are learning beyond just counting and numbers.” That’s why it’s so important to help children love math while they are still young. Parents can build on those first preschool lessons by counting with their children, asking them to look for patterns and recognize shapes, then moving on to numbers, Gojak says.

The goal should be to make math “real” and meaningful by pointing it out in the world around you. That could include checking and comparing prices at the grocery store, driving down the street counting mailboxes, reading recipes, calculating coupons, or even measuring food or drink at the dinner table. Kevin Mahoney, math curriculum coordinator at Pennacre Country Day School in Wellesley, Mass., says when his children were little, his wife kept a small measuring tape in her pocketbook. While they were waiting for their order at a restaurant, the children would measure different items on the table.

Just as you encourage your early reader to look for familiar letters, ask your child to watch for math, regarding math as highly as you do reading. “Every parent knows that it’s a good idea to read to your child every night, but they should also realize the importance of talking about mathematical situations with children every day,” says Mahoney.

So What If It’s Hard?
What if you hated math as a child? Parents should try to set aside their distaste for math and encourage their children as much as possible. Young children are eager to learn. “It’s hard to learn to talk or walk. But they don’t care,” says Sue VanHattum, a community college math teacher in Richmond, Ca., who blogs about math learning on www.mathmamawrites.blogspot.com. “They just push themselves over their limits. They are going to come at math with that same attitude.”

Avoid talking negatively about math, even if you have no need for trigonometry in your daily life. “A lot of people will only joke that they cannot do math or announce publicly, ‘I’m not a math person.’ When a parent does that in front of a child, it suggests that math’s not important,” says Char Forsten, education consultant and writer, who urges parents to create that desire to learn by constantly screening the environment for math. “Have you seen any good math lately?” she likes to ask students.

If your child believes that math doesn’t really matter, he’s not going to be as open to learn. “Attitude has everything to do with learning. You can’t make anyone learn. If a child has learned not to love math, if they don’t love math, and aren’t willing to learn, you have to deal with that first,” Forsten says.

If you are stuck on how to foster math enthusiasm, talk to your child’s teacher about some ways to support math learning at home. There may be a new game that you have never heard of, which both you and your child will love.

Play Games
With so many facts and figures to memorize and apply to math problems, children learn early that math is something that requires work. That doesn’t mean that it can’t be fun; keep the pleasure in math by playing games with your children. Many games, even the ones adults play, rely on math. With countless websites, computer games and phone apps, parents have endless options, but don’t forget about the nondigital games you loved as a child. The classics that require manipulating cards and game pieces, calculating along the way, may have the same appeal for your kids as they did for you. One game worth considering is Chutes and Ladders. A 2009 study conducted by Carnegie Mellon and the University of Maryland found that preschoolers who played the game improved math skills significantly compared to those in the study who played a different board game or did nonmath tasks.

As you play with your kids, try to tap into your own love for math. When you play Trivial Pursuit, you are using math to determine how many spaces you need to get to the next wedge or predict which category you can answer best. The game doesn’t have to be about math, but should involve it. If you have a good game store in your area, stop by and ask the salespeople for help. Some of VanHattum’s favorite games really push logic, which is the basis of math, and get children thinking visually. Check out Link, SET, Rush Hour, Blokus and Spot It, to name a few.

“Playing games is a great family activity,” VanHattum says. “The more you have a tradition of playing games, the easier it is to bring in other games you like.” So while you may not be passionate about your child’s latest board game, you can work up to another game you like. Try to make the game personal to your family by playing it in your own special way. “Mathematicians make up their own rules,” VanHattum says. “It’s really important to be open to making up your own games. Change the rules. ‘In our family, we play the game this way.’”

Flexing Math Muscles
Riding a bike, swimming in the deep end, and playing an instrument are just examples of our favorite childhood activities that require practice to master. So does math.

“Math is an intellectual muscle building; it’s crucial for fully developing a child’s potential,” Mahoney says. “Those muscles can atrophy. If school is the only place you do math, then it becomes something you only do at school. Then you don’t even think about using it in real life.” So brush off those negative feelings about math and instill enthusiasm. Math will play a role in your child’s life forever.

“It’s important to remember that those basics are essential for later learning. A lot of the stuff we learn in math we apply in different ways later,” says Gojak, who emphasizes the thinking skills that math provides. “I might not have to worry about what an isosceles triangle is, but it’s still an important part of education.”

As they grow, kids will learn that they are willing to work hard at something they love. It may just be math. Either way, remember that your child does not have to excel at math to enjoy it. “It doesn’t matter if they’re good, it matters whether they like it,” VanHattum says.

By Laura Lewis Brown

When is it Time to get My Child a Math Tutor

Leadership, Math, Math News 1 Comment »

As parents, we all want to see our children excel in school. Some children are great at motivating themselves, while others need a push to catch up or even a little help to accelerate beyond their current curriculum. When it comes to building math skills, there is no reason to postpone giving your child that push.

Signs Your Child May Need a Math Tutor
If your child is old enough to receive report cards, you can tell pretty quickly whether or not he might need help when you see his grades. “Always look at grades,” says Richard Bavaria, Senior Vice President for Sylvan Learning, who offers helpful tips and advice on DrRickblog.com. “Grades can indicate anything from a straight-A student getting her first B to a kid showing signs that he needs extra help.”

Beyond slipping grades, look out for a lack of enthusiasm for math. “Elementary school kids love to learn about new subjects, especially math. They like to learn about counting, money, telling time, all math-related subjects,” Bavaria says. “When you see enthusiasm slip, that definitely signals something.”

That loss in interest could signal that your child needs help, but it also may mean that he or she is bored. That’s where a tutor can come in. “Tutoring is good for children who are highly able, not just for children who need academic help,” Bavaria says. “If the math course is not challenging enough, that might mean that your child is pretty smart in math and in need of extra challenges.”

One of the best ways to get more insight on how your child is handling math is to talk to his or her teacher. It is important for the teacher to know your child’s relationship with math, especially if it has changed. If your child used to love math in second grade but suddenly dislikes it in third, let the teacher know. Since you cannot be in the classroom, starting a dialogue with the teacher will help you identify how best to help your child.

Get Help Sooner Rather Than Later
Whether you choose to hire a tutor or provide more games and learning opportunities at home, it’s important to identify your child’s signs of needing extra help early on, particularly in math, due to its linear nature.

“No subject is more important than math when it comes to vigilance,” Bavaria says. “Each new year, each new course builds on the previous lesson and course. Once you miss a lesson, once you don’t master a particular skill, it’s difficult to build something on top of it without it all falling down.”

By delaying the process of getting your child the help he needs, you risk letting him slip further behind as well as lose confidence, which is essential to continuing learning, Bavaria cautions.

Hiring a Tutor
By the time your child has reached second grade, it will be pretty clear whether a tutor would be helpful. Once you decide to find a tutor, take your search seriously. You want someone who is properly trained, will assess your child correctly, has a good reputation, and will provide lessons that are age appropriate. Stay away from tutors who rely mostly on technology, because the time spent tutoring should be focused on the child and tutor working together, Bavaria says. That being said, the tutor should attempt to make learning fun.

Above all, you want a tutor who will be a partner in your child’s education. This means that communication is key on many levels: between student and tutor, parent and tutor, and especially between tutor and teacher.

“For tutoring to be effective, the tutor needs to have contact with the classroom teacher in order to discuss the current curriculum and classroom goals, teaching styles and practices, and gaps the teacher is seeing in the school,” says Shannon Keeny, a private tutor in reading and math in Baltimore. “The tutor should support the learning in the classroom by reteaching or accelerating. The tutor becomes an advocate for the student’s learning for the school and a support for the parents.”

Setting Goals
When you select a tutor, make sure you explain to him or her what you (and your child) expect from the experience. To determine this, first sit down with your child and identify two to three goals you want the tutor to focus on, Bavaria suggests. Consider whether your child wants to catch up, keep up or get ahead. Does she want a higher grade? Does she want to study for tests better? Does she need help organizing? A good tutor should ask you some of these questions to help set goals.
When you establish the objectives, also determine how the tutor likes to work, so you can provide the best learning setting. “I like to have a quiet workspace. I don’t like the parent to be hovering, but it could be important for the parent to be in earshot to hear the language that is being used,” says Keeny, who tutors children in their homes. She also recommends parents explain to their children that tutoring is not a punishment, but rather is designed to help them succeed in the classroom.
“Half of my clients are tutoring for enrichment, not for remedial support,” Keeny says. “Tutoring is not looked at as something only for the kids who are behind and need a tutor; often they are at grade level, but parents want them to be challenged.”

Helping at Home
Math may not have been your best subject in school, but you can help your child by dusting off your math skills and knowing the lingo. If your child asks you to look at her geometry assignment, you want to be ready to relate as best you can.
“When you suspect that your child is having a little trouble in math, or any other subject, that may be a time to start boning up on stuff that you’ve forgotten since you were in a math class,” Bavaria says. “That doesn’t mean you have to be in expert in quadratic equations, but you should at least have the vocabulary to know what your child is talking about.”

You can ask your child’s teacher or tutor for ways to provide support. Another great way to keep in touch with your child’s schoolwork is by checking out the teacher’s web page, which many teachers maintain on the school’s site. Don’t let your child’s latest math challenge be a surprise to you.
Keep in mind, though, that you’re not required to be the teacher. If your child is struggling, let his teacher know that he needs more help and has been having a hard time with certain assignments. “Parents can encourage kids by giving them time to do their homework and by giving them a place to do their homework,” says Linda Gojak, president of the National Council of Teachers of Mathematics (NCTM). “It’s not their job to be the teacher.”

Free Resources
Tutoring, especially if you do it on a weekly basis, can be expensive. With sessions running $35 to $75 an hour in many places, you may be interested in other options. Luckily, there are numerous free math websites that offer lessons, games, or a combination of both. These include funbrain.com, which has tons of math games, and sylvanmathprep.com, which offers free instructor-led videos. Gojak recommends the Illuminations section of the NCTM website, which provides activities for different grade levels as well as a collection of more than 700 links to online math resources.

You can also work math into the regular day. Keeny recommends normalizing math language in the home and conjuring up real-life math problems throughout the day. On the way to the store, talk about how long it takes to get there, then ask your child what time you will arrive. When you set the dinner table, ask your child how many forks you need, including how many to take away if Dad won’t be home for dinner.
“Math is everywhere,” Keeny says. Use that to your advantage and give your child the best chance for math success.

By Laura Lewis Brown

There’s one key difference between kids who excel at math and those who don’t

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People in China, Japan, and Korea are more accustomed to criticism as a means to self-improvement, whereas Westerners avoid it or resent it. Reuters/Lee Jae Won

By Miles Kimball and Noah Smith

Miles Kimball is an economics professor at the University of Michigan. He blogs about economics, politics and religion.

Noah Smith is an assistant professor of finance at Stony Brook University. His blog is Noahpinion.

“I’m just not a math person.”

We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.

Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.

How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:

  1. Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
  2. On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
  3. The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
  4. The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.

Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic. Academic psychology journals are well stocked with papers studying the world view that lies behind the kind of self-fulfilling prophecy we just described. For example, Purdue University psychologist Patricia Linehan writes:

A body of research on conceptions of ability has shown two orientations toward ability. Students with an Incremental orientation believe ability (intelligence) to be malleable, a quality that increases with effort. Students with an Entity orientation believe ability to be nonmalleable, a fixed quality of self that does not increase with effort.

The “entity orientation” that says “You are smart or not, end of story,” leads to bad outcomes—a result that has been confirmed by many other studies. (The relevance for math is shown by researchers at Oklahoma City who recently found that belief in inborn math ability may be responsible for much of the gender gap in mathematics.)

Psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck presented these alternatives to determine people’s beliefs about intelligence:

  1. You have a certain amount of intelligence, and you really can’t do much to change it.
  2. You can always greatly change how intelligent you are.

They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades. But as Richard Nisbett recounts in his book Intelligence and How to Get It, they did something even more remarkable:

Dweck and her colleagues then tried to convince a group of poor minority junior high school students that intelligence is highly malleable and can be developed by hard work…that learning changes the brain by forming new…connections and that students are in charge of this change process.

The results? Convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic. (A control group, who were taught how memory works, showed no such gains.)

But improving grades was not the most dramatic effect, “Dweck reported that some of her tough junior high school boys were reduced to tears by the news that their intelligence was substantially under their control.” It is no picnic going through life believing you were born dumb—and are doomed to stay that way.

For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work. Because the truth may be hard to believe, here is a set of links about some excellent books to convince you that most people can become smart in many ways, if they work hard enough:

So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days—so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.

Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth and eighth graders score quite well in international math comparisons—beating countries like Germany, the UK and Sweden—our high-schoolers  underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work. In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math—for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.

We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hard-working foreigners. But even more importantly, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.

Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. We believe that this has to stop. Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz (here and here), that echo many of our views.

One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans.  In Intelligence and How to Get It, Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:

1. “Children in Japan go to school about 240 days a year, whereas children in the United States go to school about 180 days a year.”
2. “Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.”
3. “[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.”
4. “When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.”
5. “Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.”

We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well. In returning to an emphasis on effort, America would be returning to its roots, not just copying from successful foreigners.

Besides cribbing a few tricks from the Japanese, we also have at least one American-style idea for making kids smarter: treat people who work hard at learning as heroes and role models. We already venerate sports heroes who make up for lack of talent through persistence and grit; why should our educational culture be any different?

Math education, we believe, is just the most glaring area of a slow and worrying shift. We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism. In the debate between “nature vs. nurture,” a critical third element—personal perseverance and effort—seems to have been sidelined. We want to bring it back, and we think that math is the best place to start.

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