NCTM President Diane J. Briars
time. As you plan for the new school year, don’t forget to make explicit plans
for engaging parents and families. As you well know, parents can be invaluable
supports for their children’s mathematics learning. While it’s helpful to send
parents basic information about their children’s mathematics class, such as
course outlines, assignments, and descriptions of teacher expectations, they typically
need much more than that to be prepared to support their children’s mathematics
learning, as the following examples illustrate:
- The father of a third-grader who says, “Every
night, my son and I fight about math! Like last night. I told him you have to
start adding from the right; he says ‘No, you don’t. That’s not the way we do
it. I can start adding at the left—or anywhere.’ He gets the right answers—and
explains to me what he’s doing. But it’s not the way I learned it! Is that
okay? I’m very frustrated!”
- The mother of a seventh grader who calls the
principal, complaining that her daughter’s mathematics teacher is not teaching;
she’s just asking students questions instead of showing students “the steps.”
- The mother of a high school student who
complains, “Ms. Smith is not a good teacher. When my son does his homework,
there are problems that he struggles to solve. If she were a good teacher, he
would be able to work all the problems easily.”
Sound familiar? As recent media
postings and comments about mathematics instruction and homework illustrate,
many parents have beliefs about mathematics learning and instruction that are
at odds with current content expectations and the effective teaching practices
identified in Principles to Actions: Ensuring
Mathematical Success for All. If we want parents to support—rather than
hinder—their children’s learning, we need to actively help them to update their
knowledge and beliefs. And this needs to be done at the very start of the
school year—before they become confused and frustrated!
What mathematics should my child be learning?
First and foremost, parents need to know that being prepared
for the 21st-century workforce requires being able to do more than simply
compute or carry out procedures. Children need conceptual understanding as well
as procedural fluency, and they need to know how, why, and when to apply this
knowledge to answer questions and solve problems. They need to be able to reason
mathematically and communicate their reasoning effectively to others. In short,
students need the habits of mind described in the Standards for Mathematical
Practice in the Common Core State Standards and the NCTM Process Standards, as
well as in the process standards of other college- and career-readiness
Clearly communicating these overarching outcomes to parents
is essential if we want them to understand and accept the teaching practices
that promote them. It might also be helpful for parents to know that this
description of 21st-century competencies is coming from business and industry
leaders and the broader research community, as well as from mathematics
educators. They should also know that similar expectations exist for
English/language arts and science as well as mathematics. The National Research
for Life and Work: Guide for Practitioners is a useful resource
regarding 21st-century competencies and instruction to develop them. The Hunt
Institute and the National PTA have produced a series
of videos for parents that describe these increased expectations.
And, of course, parents want to know the specific
mathematics that their children will be learning. This involves more than
providing a list of content standards or objectives, such as that students in
grade 2 are expected to become able to add and subtract two three-digit numbers
within 1,000. Parents need to know how
children are expected to solve these problems, especially when the methods may
be different from the ones they learned as students. For adding and
subtracting, for example, they need to understand that students may use
strategies based on place value or properties of operation, explaining their
strategies, or using drawings to support their explanations. It is also helpful
to explain to parents how these approaches benefit children and to set the
approaches in the context of what their children will be learning over the next
several years. For multi-digit addition and subtraction, children eventually will learn standard paper-and-pencil
procedures; however, first using a variety of strategies helps children
understand and more easily learn the standard procedures. These same
recommendations apply to all grades. For example, in grade 6, students will use
unit rates or equivalent ratios to solve proportion problems instead of
cross-multiplication; in high school, students may solve quadratic function
problems presented in real-world contexts using tables and graphs, before
solving quadratic equations. My experience has been that parents are very
receptive to these “new” approaches when they clearly understand what is
expected and how these approaches help their children learn mathematics.
What will my child’s mathematics class look like?
Second, parents need to know that developing the
mathematical knowledge described above requires instruction that actively
engages their children in doing
mathematics—solving unfamiliar problems alone and collaboratively, analyzing
alternate solutions, and generalizing those solutions to methods and procedures
that apply to classes of similar problems—rather than listening to the teacher
show and tell them which procedures to apply and how to carry them out. Because
of their own school experiences, many parents hold beliefs about teaching and
learning that Principles to Actions describes
as “unproductive.” Helping parents understand the shifts in students’ and
teachers’ roles and actions in effective mathematics classrooms is a critical
priority for your beginning-of-the-year parent engagement efforts.
How can I help my child?
Most parents want to help their children learn mathematics.
However, traditional ways of helping, such as showing children the steps to get
answers, are at odds with our efforts to engage students in solving high-level
tasks and developing conceptual understanding, thinking, and reasoning. Parents
need specific suggestions about productive ways to help their children and how
to implement them.
A key shift is for parents to ask questions to help their children solve unfamiliar
problems rather than to show them how to solve them. Explicitly tell parents
that when their children are struggling with a problem, their role is to help them solve it by asking questions such
as the following:
- What are you being asked to find out?
- What does the problem tell you? Can you describe
it in your own words? Have you seen a problem like this before?
- Is there any part of the problem that you
already know how to do?
- Is there anything you don’t understand? Where
can you find the answers to your questions?
- Will it help to make a list, a chart, a table, a
drawing, a diagram? Can you act out the problem?
- What do you estimate your answer will be? Why?
- Is your strategy working? Why or why not?
- Is there another way to check your answer?
- How do you know if your answer is right or
wrong? (From A Parent’s
Handbook, Grade K–5, Allegheny
Intermediate Unit, p. 2; similar questions appear in the Grades
6–8 and Grades
9–12 Parent Handbooks.)
Parents can support their children’s learning in other ways:
- Practicing basic facts. Children are expected to develop
immediate fact recall as well as understand the meaning for operations.
Immediate recall requires practice, in addition to understanding—and time for
practice in the school day is limited. Parents can help in a variety of ways,
especially since orally presenting facts promotes immediate recall more
effectively than worksheets. Perfect times to practice are while driving,
walking, waiting, and so on. Just be sure that parents understand that this
practice should build on understanding of operations, not occur in isolation.
- Playing games. Games are a great way for parents to give their children practice
with mathematics concepts and skills and develop strategic thinking, while also
promoting positive parent-child relationships.
- Posing contextual problems. Mathematics problems are part of
everyday life. Parents help children see that math is all around them when they
pose problems that arise in everyday situations.
A variety of useful resources support these activities:
Finally, schedule your parent engagement activities to begin
as close to the beginning of the school year as possible to get parents, along
with their children, off to a good start. The sooner you involve and inform
parents, the better partners they can be in helping their children learn