Wow, that's amazing—why did I never realize that before?" commented the parent of a 5th grader. I had just explained that 9 is a "square number" because you can make a square pattern from nine objects, just as you can from 16, 25, or any other square number.

The conversation, which took place on the sideline of a middle school soccer game, was the initial impetus for a series of workshops I conducted with parents at the Richmond Elementary School in Richmond, Vermont, during the spring semester of 1997. Having taught elementary school math to children, preservice college students, and practicing teachers, I realized that a series of workshops in elementary school mathematics might help parents to develop a better understanding of their children's math skills. Although not part of the National Network of Partnership 2000 Schools, Richmond Elementary has been exploring ways of diversifying the involvement of parents in their children's school experiences. We designed the workshops to enhance "Student Learning at Home," the fourth category of parental involvement identified in the Partnership 2000 project (Sanders 1996).

## Workshops for Parents

The series of seven, hour-long workshops, which met every two weeks throughout the semester, was designed to help parents develop relational understanding (Skemp 1978) of the mathematics typically encountered by elementary schoolchildren (see fig. 1). Although we engaged in many different activities, the workshops were not meant to give parents a grab bag of projects to complete with their children at home. Rather, they focused on the development of parents' conceptual knowledge (Hiebert and Lefevre 1986) to complement the procedural knowledge they had learned when they were in elementary school.

#### Figure 1. Richmond Elementary School's Workshops

#### Number Sense and Counting Skills

#### Place Value and Base Ten

#### Addition and Subtraction

#### Multiplication and Division

#### Common Fractions

#### Decimal Fractions

#### Problem Solving

- When dividing fractions, change the sign to multiplication and invert the second fraction.
- When adding, carry the one.
- Pi is 3.14.

I developed topics for each workshop by consulting with the school principal, Jim Massingham; the National Council of Teachers of Mathematics Standards; and the Vermont Framework for mathematics in grades pre-K through 4. Each workshop included a series of activities designed to deepen parents' conceptual knowledge and relational understanding of the mathematics their children would encounter during their elementary school years. Above all, parents felt free to share personal experiences and ask questions in a relaxed atmosphere. Out of 18 parents taking part in the workshops, all but 2 were moms; and sessions contained 6 to 12 parents each. Parents agreed to abide by one ground rule: I would not discuss anything related to specific teachers, especially their teaching styles or treatment of students. I was happy to discuss individual students' experiences with math as long as it did not detract from the mission of the workshop.

At the conclusion of each workshop, I gave parents a handout entitled "Math at Home," which listed ideas for putting into practice the topic of discussion. For example, after the workshop on decimal fractions, I suggested parents take their children to the ATM machine so they could press the decimal-point key. These activities helped to reinforce the content of the workshops with everyday tasks that parents and children could do together.

## The Language of Math

Most parents wanted to focus on upper elementary mathematics, such as common fractions, decimals fractions, and problem solving. Parents frequently perceive mathematics as being not quite as important at the preschool/kindergarten levels, or they believe that mathematics for younger children is easy. However, this was not always the case; in one session, we had a dynamic discussion involving the differentiation between "simple number naming" and "rational counting."

The changing use of language in teaching mathematics was an issue parents consistently raised. "Why do teachers use the word 'regroup,' when 'borrow' and 'carry' worked so well for us?" Such questions gave rise to productive discussions. For example, the method of subtraction has changed—from "equal addition" to "decomposition"—requiring a change in language to maintain a conceptual basis for the operation. In the older procedure, "equal addition," 10 ones were added to the ones place in the top number of the equation, and one ten was added to the tens place in the bottom number. The act of adding the one ten in the tens place of the lower number provided a chance to "pay back" the ten that had been previously "borrowed" in the ones place. The words bore no conceptual relationship to the procedure. In the current "decomposition" method, however, the top number is actually "regrouped" to complete the subtraction.

The language of mathematics also became an issue as parents explored their understanding of procedures learned many years ago by rote memorization. They found they could not use words such as

*reduce*when computing with fractions because the meaning of such words had been derived instrumentally and not relationally. The word*reduce*, for example, means to make smaller. When taught to*reduce*the fraction, children tend to think three-fourths is smaller than six-eighths. Several parents admitted that three-fourths "felt" smaller than six-eighths, until they began to*rename*rather than reduce the fraction.## Problem Solved

Many parents said they had been held hostage by their elementary school experiences in mathematics, experiences that were almost exclusively characterized by instrumental understanding and rote learning. They were unable to help their children with problem solving because they did not understand the math concepts involved or the current approaches to problem solving, such as drawing pictures, making charts, and guessing and checking. Several parents had difficulty helping their children to select an appropriate process for solving a problem because they had been taught only to get the right answer.

After the workshops, parents felt more confident helping their children. They responded positively to the workshops in a final assessment form, supporting both the concept of reteaching parents elementary school mathematics and the style and format of the workshops. Many parents requested to repeat the series in the coming year. They also wanted to expand the workshops to include additional elementary topics, such as measurement and geometry, and middle school topics, such as algebra.

As public schools work toward enhancing their partnerships with parents, informed and knowledgeable parents become important allies. Parents who have a conceptual understanding of elementary school mathematics will be stronger advocates for effective teaching strategies and more active teaching partners in their children's education.