By: Jeff Heyck-Williams
Math can be one of the most challenging areas of school for children, and many parents don’t have an idea about where to begin to help their kids be successful within the discipline. A lot of websites, video games, and materials are produced that are designed to help kids develop procedural fluency with computation, but they sap the pleasure out of a subject that can be as fun as it is difficult. Helping our children be successful in math we need to recognize the full breadth and depth of mathematics learning. This means we need to take into account what kids understand about all of the domains of math, how they problem solve, their attitudes towards the subject, and of course their ability to calculate accurately as well. So what could this look like for a parent working and playing with their child at home. Here are five things that I share with parents that can have a huge positive impact on their child’s mathematical life.
Some of us had awesome experiences with school mathematics or despite our experience with school mathematics have come to love the subject anyway. Unfortunately that isn’t the norm. Most adults (parents and teachers included) are indifferent to mathematics at best if they don’t downright despise the subject. These attitudes have been passed down from generation to generation both through the way that we talk about math with friends and family as well as math programs in school that emphasize a lock-step algorithmic approach to mathematics. These programs place computational fluency above any other form of mathematical proficiency. Math is portrayed as a subject in which you must follow these exact steps and your answer is always right or wrong. There is little room for creativity or fun. Thus math becomes the required hoop to jump through and not a joyful end in and of itself. This is a distorted view of a vibrant exciting subject with a rich history.
For our children to reach their potential, we must break a cycle of negativity. If we truly are dedicated to providing rich and varied options for our children’s futures, we must give our students a positive disposition towards this amazing subject. This means never saying “I hate math” or “I don’t like math,” phrases which are unfortunately all too common. When applied to other core skills like reading and writing, these phrases would be considered taboo. For some reason they are expected in regards to math.
So even if math is not your favorite subject (and everyone has a least favorite subject), don’t make it out to be a distasteful requirement by the way you talk about it. There are plenty of nasty things to be negative about doing and that you want your children to think of in a negative light. However school subjects and math in particular shouldn’t be one of them.
2. Have High Expectations and Communicate Effort Matters
All students can develop a conceptual understanding of mathematics and solve complex problems using math. However, not all students learn in the same way or at the same rate. With this in mind, it is worth acknowledging that math can be difficult. However, it is this very nature that makes, mathematics so enjoyable. After all, consider the level of satisfaction one achieves when accomplishing a task that initially seems impossible.
Thus we need to expect our children to work difficult problems without giving them the answers or insisting on a single particular path to a solution. This means allowing them to use the mathematics that they do know to solve problems, and allowing them to make sense of the solution paths that we might show them. It also means we need to show them that we will support them and that they will be successful as they take classes that require high levels of mathematical proficiency. Ultimately, we expect them to take statistics and calculus whether in high school or college and that they will understand it.
Connecting this idea to the previous one, we shouldn’t ever tell our children “I can’t do math” or “I can’t do this or that problem.” Instead we should communicate to them honestly that a problem may be difficult and we might not find an answer immediately, however with effort, support, and persistence then we can succeed. Carol Dweck outlines the research that supports this point of view in her work Mindset: The New Psychology of Success. She argues that with effort and a growth mindset we can improve our performance. It is when we have a fixed mindset and are convinced that we won’t succeed that we don’t.
All of our children can learn to love mathematics, enrich their understanding of the world through a greater appreciation of the mathematical structures in everything around them, and can ultimately be successful in doing high-level mathematical work. Few of us as parents have all the tools to help our children reach their full mathematical potential. However, we have one of the most powerful tools available for setting them on the right path. That is we can help shape our children’s attitudes and beliefs about math. Help them to see it in a positive light and that with persistence, effort, and support they will reach the high expectations we set for them.
3. Recognize the Math Around You
Mathematics is all around us. We just need to stop to recognize it and point it out tour children. Whether it is having young children sort the laundry, or helping an older child create and maintain a budget, we are showing our children that there is mathematics all around them. From measuring for cooking to statistics in sports, mathematics permeates our lives.
Building off of my previous two recommendations seeing the mathematics around us, provides for students an opportunity to see the importance of understanding concepts that are formalized in their mathematics classrooms. It provides for them a motivation to understand this math and to use it to help explain the world around them.
4. Play with Math
Math is fun. To really believe this, we need to play with math. This can include tons of things you already do like building with blocks, stringing beads to make jewelry, completing jigsaw puzzles, or playing board games. It means looking for the math imbedded in each of these activities. Look for opportunities for counting, making patterns, sorting, and problem solving. All of these illustrate mathematical concepts that provide real world experience for how math is fun.
Another amazing way to play with math, is to work math puzzles or solve math riddles like the Mathemagical Wizardry Prize at Two Rivers. Each week I provide a problem for the whole school to work. A couple of features about these problems make them ideal for playing with math. First, questions typically have lots of different pathways to solutions and occasionally they have multiple solutions. This allows for a wide variety of children and adults to engage in the problems. In addition, it reinforces the conceptual understanding of the problem as it can be approached from multiple perspectives. Second, they are designed to allow for children to work on with their families, with their classmates, or alone. So they can become a regular tradition that allows everyone an opportunity to dig into the problems.
Regardless of how we approach it, we need to learn to find pleasure in math, and help our children enjoy it as well.
5. Support Math Homework through Engagement with Your Child and the Math
Last, but not least, I would be remiss if I didn’t make a recommendation about the one area of school mathematics that parents have some hand in: homework. The purpose of math homework at Two Rivers is twofold. First, homework is a mechanism for teaching children skills of independence. Specifically, homework teaches students responsibility for their work, perseverance when the work is challenging, and self-advocacy skills in the upper grades as they talk to their teachers about the level of difficulty of the work: whether it was too easy or too difficult. Secondly, we intend for math homework to provide an opportunity for students to reinforce procedural fluency. In other words, homework is a place to practice the foundational basic skills and knowledge of mathematics.
With all of that said, homework, does not communicate the whole of our curriculum. Students are not tackling the most challenging open-ended tasks that we give to them while in school through homework. More importantly, homework addresses two goals that are important for mathematical proficiency, namely independence and procedural fluency. However, as outlined the National Research Council’s 2001 report, Adding it Up, they recognize that proficiency is not defined solely by procedural fluency, but also by strategic competence, adaptive reasoning, conceptual understanding, and productive disposition as well. Goals that are not well suited for homework assignments. That is to say we believe that mathematics is more then developing efficient methods of computation, but also include understanding the mathematical structure behind problems, solving problems, reasoning effectively about problems, and having a positive outlook towards math in general. Keeping in mind that homework only addresses two of our larger goals for mathematical proficiency, there are several considerations that go into homework. The first one is around the level of difficulty. If the homework is very easy for your child, that isn’t necessarily a bad thing. It is an opportunity for them to practice independence. If it is too difficult for them, similarly you should encourage them to work the problems the best they can, and for your child talk to the teacher the next day to gain understanding.
Secondly, consider the amount of time homework takes. Homework shouldn’t be a battle that ruins an entire evening at home. We use the national PTA’s recommendations for the amount of time a child should spend on homework each night which amount to 10 minutes per grade level. So a 1st grader should have about 10 minutes of homework and a 6th grader should have about an hour of homework each night. For families where homework becomes a nightly fight to get done and it seems to stretch on forever, I recommend setting a timer for the number of minutes that is appropriate for the grade level, and then having the parent write a note at the top of the assignment saying the child took that amount of time to work on their homework to whatever degree of completion.
Finally, in considering homework, many parents worry that their children are working problems in ways that are totally unfamiliar to them. Many parents say to me that they don’t understand how their child is working a problem and thus don’t know how to help them. This simply reflects that children are learning different algorithms or steps to solving problems, and shouldn’t be viewed as a roadblock but as opportunity. When a child comes home with a solution method to a problem that you haven’t seen before, use this as a place to have a discussion. If you have a different solution method that you learned in school, use that method and see if you get the same answer as your child. You should. If you don’t, then there is probably something faulty with one of the methods. Regardless if you get the same or different answers, explore how your child is working the problem. Have them explain it to you. Explain your method to you. Find similarities and differences. All of this will build both you and your child’s understanding.
Regardless of how you engage in math homework with your child, there are a couple of key points to keep in mind. First, homework is intended to foster independence. So don’t do the homework for your child. They should be able to accomplish the homework on their own. If they can't complete it independently, this is an important piece of data for the teacher. Also, only engage in a conversation about the work if you have the time, energy, and a positive outlook on it. Otherwise you may both go away from the experience frustrated and it undermines the goals of the homework. Second, always communicate with the classroom teacher about homework. If you have questions about time. level of difficulty, or solution methods, he or she is the best person to answer those questions.
We have an amazing opportunity to broaden the opportunities for our children. Mathematics is a brilliant subject that can open doors for both you and your child. Supporting them with a positive attitude towards math, high expectations, pointing out the math around us, time to play with math, and supportive engagement around homework can make the difference.
For additional resources check out the family resources page at the National Council of Teachers of Mathematics at: http://www.nctm.org/resources/families.aspx.