Q: My kids love their teachers and want to give them each a holiday gift, even though the PTO discourages individual gifts because not all families give. What would be appropriate? For example, is it insulting to give a gift card to an office supply or discount store?

A: What to give or whether to give a gift to a teacher is a perennial parent puzzler prior to the holiday break.

Some schools issue guidelines, ranging from no gifts at all (or nothing more than a certain dollar amount) to encouraging a gift from the whole class, where one parent collects whatever each family wants to contribute toward it. That way, no child feels left out.

Other schools leave it to families. A recent survey of A-Plus Advice Teacher Advisers suggests that gift cards are the way to go. Teachers have more mugs, totes and apple paperweights than they'll ever use. Avoid books, candy, foodstuffs, beverages or personal items such as colognes, lotions and spa services. Also, don't re-gift something you'll think they'll just love.

Teachers value gestures of appreciation, from a handwritten note or a homemade greeting card to gift cards they can use easily, says Illinois elementary teacher Pam Evans.

"While gift cards may seem impersonal, teachers often use them to purchase supplies," she says.

Evans has also enjoyed gift cards to movies, local eateries and bookstores.

"Giving gift cards to a store like Target lets teachers decide whether to spend the gift on themselves, the classroom or both," says California teacher Bill Laraway. "Unless you know the teacher would enjoy it, a gift card to an office supply store may not be perceived as personal enough."

Virginia teacher Jill Warner says, "Any gesture that recognizes us is always greatly appreciated. A gift card to a local drive-through, coffee shop or favorite hangout says so much more than a travel mug."

Laraway adds, "What really matters to me is receiving a card with a handwritten personal message, whether or not there's a gift card inside. I really appreciate it when someone takes the time to write a note of thanks.

"If you choose to offer a gift card, don't just fill in the 'to' and 'from' lines. Include a note; it makes the gift more meaningful, rewarding and memorable. Teachers can re-read it and reflect upon it."

You don't have to spend money to show appreciation. "I teach in a low-income middle school, so rarely do I receive gifts, but I cherish the handwritten notes I get from students because I know they come from the heart. I read them over and over again after a tough day," admits Kansas teacher Valerie Snyder.

Artfully bundling together expressions of appreciation can touch a teacher's heart. "Last year, a parent asked families to submit things for a tribute book -- a letter, story, poem, photos or drawings," says Sally Hawks, a New York educator. "She created it online and then had it printed. It gave me a chance to reflect and share my joys and success with my family. I still look at it often."

(Do you have a question about your child's education? Email it to Leanna@aplusadvice.com. Leanna Landsmann is an education writer who began her career as a classroom teacher. She has served on education commissions, visited classrooms in 49 states to observe best practices, and founded Principal for a Day in New York City.)

Q: Often, my daughter Kristen, a third-grader, is taught math differently from the way I learned, so when she struggles, I show her my way. I never criticize her teacher's methods. I want her to love math, so I try to make sure that she understands what she's learning. Will I confuse her?

A: One of the beauties of math is that there's more than one way to approach a problem, and it's useful for kids to learn that early.

"Showing her another (way) will only enrich her learning," says Marilyn Burns, an author and one of the nation's top math educators.

You're wise not to criticize her teacher, says Burns.

"If your daughter ever seems confused about your approach, step back and confer with the teacher," she says. "Children do best when teachers and parents are partners. This doesn't happen enough with math."

How can you best support your daughter's math learning? Focus on mental math, says Burns, the founder of Math Solutions.

This refers to giving children exercises and problems to solve in their heads. Ideally, says Burns, "they are designed to review and advance essential basic skills. They help build number sense, convey the importance and relevance of math in our daily lives, and ground her learning."

Mental math is "a necessary skill," she adds, "but one teachers don't have enough class time to devote to."

Every day we add, subtract, multiply or divide mentally, notes Burns: "We figure how much time it takes to get to school, estimate the price of a sale item or double recipes by calculating in our heads."

With mental math, you put away the paper and pencil and present a problem. It might be an addition or multiplication problem presented as an estimation challenge.

"For example, give Kristen an addition problem with two two-digit numbers, say, 32 plus 54, and have her explain how she'll find the sum," says Burns. "To add challenge, have her figure out how much more is needed to make 100. This gives her practice manipulating numbers and develops her mathematical thinking to arrive at the answer in different ways."

Money presents great mental math opportunities, says Burns: "How can Kristen spend exactly $100 by buying two things with different prices? Three things with different prices? How could she spend exactly $100 by buying three things with different prices if one item costs $37?"

Always ask Kristen to explain her thinking, even when she gives correct answers.

"Explaining is important," says Burns. "Don't correct an incorrect answer immediately. Take time to question and let her explain. Kids often self-correct if given the chance. Never leave Kristen with a misconception, but don't rush to solve mental math problems for her."

Math play presents great opportunities to boost mental math skills, too.

"For example, building sophisticated structures with blocks promotes problem-solving and spatial skills," says Burns. "Math-related puzzles and riddles promote logic. KenKen puzzles get kids thinking about number relationships and using logic."

Everyday mental activities are extremely valuable, says Burns: "They boost skills and make classroom learning stick. They show Kristen how much math is a part of our lives."

(Do you have a question about your child's education? Email it to Leanna@aplusadvice.com. Leanna Landsmann is an education writer who began her career as a classroom teacher. She has served on education commissions, visited classrooms in 49 states to observe best practices, and founded Principal for a Day in New York City.)

Q: My two preteen daughters spend weekends with my new wife and me. While my wife loves the girls, she's quick to criticize them and corrects their mistakes immediately. My ex and I have our differences, but we think kids need room to make mistakes to become independent. My wife says that's asking for trouble as the girls head into their teenage years. Who's right?

A: Don't think of this as an either/or situation. There are times to correct a child on the spot, and there are times to allow the situation to play out.

"Effective parents vary their responses depending on the situation. Some poor decisions require immediate feedback; others present genuine learning opportunities that may allow the child to make a better decision the next time," says Dr. Jane Bluestein, a New Mexico-based educator and author who has advised thousands of parents, teachers and children over the past 40 years.

If one of your daughters makes a choice that puts her in danger, intervene right away.

"Discuss safer options and help her connect those choices to more positive outcomes," says Bluestein.

But if her science project fails, it's no biggie. Talk about how experimentation is part of the scientific process. Discuss how "mistakes" can lead to unexpected discoveries. Albert Einstein inspired students by telling them that "a person who never made a mistake never tried anything new."

Bluestein adds: "The most constructive way to help a child learn from mistakes is to shift your focus from what's wrong or undesired to the behavior you want."

For example, say your daughter uses a snarky or defiant tone with you. Telling her that she's being disrespectful is less effective than saying, "I want to hear what you have to say when you're willing to talk to me in a more respectful voice."

If your child's mistake is a result of a lack of understanding, explain what she needs to know. Don't play the blame game. If you say, "Too many sodas can cause an upset stomach," that's more validating than, "You're sick because you drank too many sodas, even though I said not to."

If your daughter makes a mistake while trying to achieve an unclear goal, help her focus on what she's trying to accomplish. Ask, "How did you want this to turn out? What was supposed to happen?"

Avoid expressing disapproval or disappointment. Instead, try, "That's interesting!" or, "That wasn't what you had in mind, was it?"

Get your daughters to reflect on their mistakes. Once the dust settles, ask them what they might do differently next time. Can they guess possible outcomes of a different approach?

Never shame kids or call them stupid.

"I disagree with 'tiger' parenting advice that condones humiliating children or calling them names in order to motivate desirable behaviors or academic achievement," says Bluestein. "There's a big difference between making a mistake and being one."

Encourage your wife to fight the temptation to fix the girls' every misstep. "It's always better to guide kids to a solution by helping them rethink their approach, strategy or goal," says Bluestein.

(For more advice, go to janebluestein.com.)

(Do you have a question about your child's education? Email it to Leanna@aplusadvice.com. Leanna Landsmann is an education writer who began her career as a classroom teacher. She has served on education commissions, visited classrooms in 49 states to observe best practices, and founded Principal for a Day in New York City.)