When my children were young, I worked hard to give them all the things I thought they needed to be eager learners. I took them to museums. I planned trips to the library. I read to them every day. (Heck, I put board books in their cribs long before they could read.) They had educational games on our computer, and we watched lots of shows on PBS. I also prioritized doing math at home.
As I was preparing to write this article, I started thinking specifically about how I engaged with them around math. Early on, we did a lot of counting. Later (and for many years), we made recipes together, giving us opportunities to work with fractions and, if we needed more or less of a recipe, scaling. Across all ages we did a lot of comparisons of how much ice cream cost at the local ice cream stand versus the supermarket. We had conversations about math and, unfortunately, some tears over homework.
Now that my girls are grown and I have been in education for over 25 years, I find myself wondering: knowing what I know now, what might I have done differently?
Why engagement with math at home is important
As a parent, I didn’t consult research on how to support my child at home, but my instinct was that doing so had to have a positive impact. Thankfully, research has shown that parental engagement does indeed have a positive impact on student outcomes. On John Hattie’s Visible Learning Metax database, the results of 33 metanalyses and 2,970 studies involving over 4.5 million students indicate that parental involvement has a potential to accelerate student learning. Furthermore, the analysis has a robustness index of five, meaning that the average effect size is considered highly stable and that the researchers have high confidence the average effect size is not likely to change even if new metanalyses are added.
Parental involvement can mean a lot of things, from attending school events to helping with homework, so let’s zoom in a little more on the research. A 2019 metanalysis of the impact of parents’ involvement on children’s academic adjustment distinguished between school-based involvement, which includes things like joining the PTA or attending parent conferences, and home-based involvement. They further divide home-based involvement into three types:
- Discussion and encouragement: This involves engaging with children about school, what they are learning, and encouraging them in their academics
- Cognitive intellectual involvement: This involves providing cognitively enriching activities and environments
- Involvement in homework: This involves both engaging with children about their homework and creating spaces to support focus
I want to pause for a moment to talk about language. Although this metanalysis and many other studies refer to parental support or involvement, because home-based support can come from many people beyond the biological, nuclear family and can include community members, caregivers, extended family, and others, I will use the terms “home-based engagement” or “home-based support” for the rest of this article.
Getting back to the research, the 2019 metanalysis showed that in general, home-based support “was significantly associated with positive adjustment” relative to the areas of achievement, engagement, motivation, social-emotional adjustment, and delinquency. Digging further, both discussion and encouragement and cognitive intellectual involvement showed similar positive impacts on achievement and motivation, with discussion and encouragement resulting in greater positive impacts on engagement. The study also found that discussion and encouragement have positive effects from elementary through high school and that cognitive-intellectual involvement has positive effects from preschool through high school.
You may be surprised (or possibly happy) to learn that this and other studies show there is a small negative association between homework support and children’s achievement; however, homework support does have some positive impact on engagement. Don’t get too excited just yet; you’re not totally off the hook on homework. We’ll talk more about that later.
Molding mindsets
Engaging in math at home has another potentially critical impact. It is estimated that over 90% of US adults experience some amount of math anxiety. Data from the 2022 PISA shows that nearly 40% of US students said they get very nervous when doing math problems. While some of this could be attributed to the impact of COVID on learning and mental health, ten years prior, nearly a third of US students expressed the same anxiety.
While this may seem disheartening, engaging with math at home can give you an opportunity to shift children’s attitudes toward math. Interestingly, research has shown that what parents or caregivers convey about failure has the greatest impact on whether children have a growth mindset and a more positive attitude toward math. When a child is struggling to understand a concept or doesn’t do well on a test, you can see this as an opportunity for learning or as a sign of failure. If you take it as a sign of failure, you are expressing a fixed mindset, thinking that the child “just can’t get it” or “just isn’t a math person.” Maybe you instinctively want to add “…just like me” after that last phrase.
Parents and caregivers who position failure as a positive opportunity to learn, rather than as either a debilitating experience or as a measure of ability, help children develop a growth mindset. Your response can change a child’s thinking from, “I just can’t do this,” which has an implicit sense of finality, to, “I can’t do this just yet,” which has an implicit sense of possibility.
Studies by researcher Carol Dweck have shown that students with growth mindsets perform better than those who believe ability is fixed. Furthermore, other research shows that positive, high parental support can even mitigate the negative effects experienced by high schoolers who perceive they are not getting enough support from their math teacher. Parents and caregivers have a powerful role to play in shaping a child’s attitude toward math and their ability to engage with it.
Homework headaches
Now that we see the benefits of home-based support on children’s achievement, engagement, motivation, and attitude, let’s deal with the elephant in the room: homework. Homework is often a cause of frustration and stress for families and caregivers. And as I mentioned previously, caregiver involvement can actually have a small negative impact on achievement. That said, whether you are checking in on a child’s progress or they come to you for help, there are ways to approach homework that better support the child’s learning, reducing stress for everyone. At a high level, the best way to support a child when it comes to homework is to encourage them, make clear that you trust their ability to wrestle with a problem, ask open-ended questions, and avoid jumping in to show them how to do it.
If that last statement sounded like a needle being pulled across a record, you are not alone. As a parent, I was guilty of this too. When a child is confused or frustrated it may be natural to want to step in to try to “fix” the issue by showing them what to do. Taking on the role of coach instead does two things. First, it helps you avoid any math anxiety you may have and don’t want to convey to the child. Second, it signals to the child that you believe in their ability to persist and work through the problem.
Two recent metanalyses, one focused on homework in general and one focused specifically on math homework, confirmed what the previously referenced study found: overall, parental homework support had a weak negative correlation to student achievement. However, both studies found a positive relationship between a sub-type of homework support designed to reinforce the child’s autonomy. What does this mean? A third study defines environments that support autonomy as ones characterized by “acknowledgement of children’s perspectives, encouragement of children to experiment, provision of opportunity to make choices, and minimal use of controlling language and contingencies.… In an interaction about homework, for example, an autonomy supportive parent might ask for the child’s input, try to understand their child’s perspective on approaches for solving the homework assignment, and encourage their child to work in their own way.”
So, what does this mean when a child is standing there asking you for help with their math homework? Instead of showing them what to do, you can try these approaches:
- Have the child read the question they are having difficulty with and then write down what mathematical ideas, strategies, or steps they think might be important for solving this problem. Researchers Joseph DiNapoli and Emily Miller found that prompting students to conceptualize the math involved in a problem before solving it could help them get re-engaged if they got stuck.
- Ask the child to do a brain dump and tell you everything they know about the topic. Retrieving previously learned knowledge can both support learning and activate knowledge that will help them get unstuck. It also reinforces the idea that the child is a possessor of knowledge.
- Ask the child questions about process. Questions like “What is this problem about?” “Could you act out the problem with objects?” and “Have you worked on other problems that could help you with this one?” help children develop a repertoire of strategies for any problem. Having a toolbox to help get unstuck can promote resilience and perseverance. You can find a longer list of questions in my article “That’s not how I learned it! 4 ways to help your child with ‘new math.’”
In general, the goal is to help the child access the knowledge they need while demonstrating your belief that they are capable of persisting and tackling the problem. As much as jumping in to help them solve feels like the right thing to do, in the long term it may inadvertently erode the child’s confidence in themselves.
Engaging with math at home at various ages and stages
Supportive conversations about math that promote children’s autonomy and help them see themselves as capable problem-solvers is a wonderful way to engage with math at home at any age. Parents and other caregivers can also provide examples and experiences of math in the real world, helping students see both the joy and relevance of math.
Let’s dive deeper into some specific ways you can engage at each level.
Preschool
Research has shown that developing concepts of numbers, number relations, and number operations is an important foundation for later achievement in math. You can learn more about these three concepts in “Everything you ever wanted to know about early numeracy but didn’t know to ask.” Spatial reasoning and measurement are also critical for early math understanding. Supporting preschoolers in these areas is as simple as looking for opportunities to introduce mathematical language and concepts into daily activities. Highlights has a great site called Talking is Teaching that shows you how to do just that.
While you may naturally be engaging in math-supporting conversations, there are ways that you can deepen what you are currently doing. Take counting, for example. Most people naturally engage in counting activities with children, but you can deepen a child’s sense of number by modeling other counting concepts.
Let’s say you are reading a book and there are five ducks in a picture. You can say, “Look at the ducks! I see one, two, three, four, five ducks. There are five ducks in the picture.” This last sentence helps children understand cardinality, which is the idea that the last number word said is the number of objects counted. You can count the ducks in different orders to show that that doesn’t impact the amount. If more ducks appear on the next page, you can model counting on: “Here are the five ducks from the other page. Now there are six, seven, eight ducks in the picture!”
With older preschoolers, this can lead into the idea of composing and decomposing numbers, which supports understanding of addition and subtraction. You can count the total number of a type of object and then look at different ways to break them into groups, always returning to the idea that the total never changes.
Check out “Building strong foundations for early math skills at home” for even more ideas and resources for engaging with math with preschoolers.
Elementary school
Once your child enters school, be sure to give them plenty of opportunities to explain what they are learning in math at home. Recalling information can help cement it into memory.
You can also leverage the idea that they are learning different ways to do math than you were taught. Ask them to teach you how to do long division or multiply fractions. Just be sure not to impose your approach; this is all about them and their knowledge. I encourage you to ask open-ended or clarifying questions, but avoid pushing them to do it the way you learned or introducing shortcuts. Current approaches to teaching math often focus on developing conceptual understanding before teaching the algorithm so that once children learn the algorithm, they understand how it works. So, while using the partial products method to multiply multidigit numbers may take longer, it helps children understand what they are doing once they learn the traditional algorithm.
You should continue to look for math in your everyday life. Here are just a few examples of what you can ask a child to do:
- Measure when you are doing DIY projects
- Read and manipulate recipes
- Compare unit prices, read nutrition labels, and calculate totals and change when shopping
- Estimate and weigh produce at the store
- Figure out what time to leave based on the time you need to be someplace and the estimated time to get there
- Use a calendar to figure out how long it is until an upcoming event
Books are also a great way to engage with math with elementary school–aged children. Mathical is a wonderful site where you can search for math-related books for various age groups. On this site, you’ll find books that directly engage with math concepts, like Greg Tang’s The Grapes of Math, and books like Madeleine L’Engle’s A Wrinkle in Time, which contain math but don’t make math the focus. Age-appropriate biographies and stories about mathematicians and engineers are excellent choices as well.
Finally, playing math games can be a fun way to engage with a variety of math concepts. Regular playing cards can be used to play games that reinforce place value, estimation, operations with whole numbers, and fraction concepts. There are plenty of commercial board and card games that involve math as well. One of my younger daughter’s favorite games growing up was Zeus on the Loose. It’s a card game that involves adding and subtracting within 100 and rounding to the nearest ten. As with books, the explicitness of the math varies across games. But remember, even non-math games offer opportunities to reinforce mathematical ideas. For kindergarteners and first-graders, counting steps along a game board is math; for second- and third-graders, games with play money offer opportunities to find totals and equivalent amounts and make change.
The site Artful Math offers suggestions for fun and engaging math games by grade for K–5. My former colleague Kara Bobowski’s article “Parent strategies for improving their child’s math” has many other great suggestions for engaging with math at home.
Middle school
Middle school is a time of huge change and insecurity for many young adolescents. They may be questioning their strengths and abilities in many areas while simultaneously beginning to internalize beliefs and motivations. It is also a time when they are becoming more independent, so the way you interact with them may be changing.
As researchers Nancy Hill and Diana Tyson state, “Early adolescence is often marked by changes in school context, family relationships, and developmental processes. In the context of these changes, academic performance often declines, while at the same time the long-term implications of academic performance increase.” Their research talks about the important role parents and caregivers play in academic socialization, that is, “communication of their expectations for achievement and value for education, fostering educational and occupational aspirations in their adolescents, discussing learning strategies with children, and making preparations and plans for the future, including linking material discussed in school with students’ interests and goals.” Their review of 50 studies found that engaging in academic socialization conversations and activities had the greatest impact on middle schoolers’ achievement compared to both school-based and other home-based involvement activities.
Your most critical role at this stage is as a coach. Here are ways to support academic socialization with young adolescents:
- Listen to what interests them and look for ways to connect that to math, future goals, and possible career options.
- Pay attention to how they talk about their own mathematical abilities. Push back on negative self-talk with real examples of times they struggled and persisted in taking on a challenge.
- Continue to support their autonomy as mathematical problem-solvers and help them develop strategies to deal with frustration rather than showing them what to do.
- Talk about the role of education in your life, or the lives of family and friends. How did parts of your education help you achieve your goals? What new things would you personally like to learn? This conversation can be delicate, as you want to convey high expectations without prescribing a particular life path or career.
While academic socialization is most critical at this point, you can continue the home-based math activities that you started in elementary school. Just be careful to read the child’s cues on what they do and don’t want to engage in. For example, if they are still interested in playing math games, this can be a great time to introduce puzzle-based games like Sodoku, Ken Ken, Str8ts, or toothpick puzzles. These types of puzzles support perseverance, trial and error, and patience in problem-solving. Or, when it’s your turn to pick the movie on a family movie night, consider movies like Hidden Figures or documentaries like Underwater Dreams that show math in action. Again, let your middle schooler take the lead, but be ready to engage when they show interest!
High school
As high schoolers move closer to life after K–12 education, the academic socialization that was so important in middle school takes on more specificity and urgency.
Older adolescents are increasingly thinking about the big “What next?” question. As they express their interests, make sure high schoolers are on the right path, mathematically, to pursue their long-term goals, whether they be college or career. If you aren’t sure what type of math is needed for a particular path, AI can be a great tool for exploring this. You can also check out career sites together to see what basic requirements are listed for various jobs.
Keep in contact with guidance counselors to make sure the child is on the right path of courses for whatever they hope to pursue next. If your child takes MAP® Growth™ at school, our interactive College Explorer tool allows you to enter MAP Growth scores and see what schools or majors might be a good fit.
Igniting a love for math
Engaging with math at home is important across all ages. It supports academic achievement, fosters a critical—and often lacking—positive attitude toward math, and helps reveal the day-to-day relevance of math. By creating a math-supportive home environment, parents and other caregivers are ensuring children develop the skills they need to succeed in whatever path they choose.
