Mathematical Journeys

Mapping Your Child’s “Number Sense” to Make Math Make Sense

The ability to understand math and its underlying concepts is key to developing a deeper understanding of the world around us. Yet, how many of us, or our children, throw up our hands in frustration or groan when we encounter a math problem? Or maybe your child easily navigates basic arithmetic only to stumble with fractions, algebra, geometry or other more advanced topics. We all can get lost in unfamiliar territory. Some of us have a better direction sense than others, and then again, sometimes our assumptions about how things should be laid out get in the way of our figuring out where they actually are!

For example, when our family moved to New Jersey from the Midwest four years ago, finding our way around town was challenging. Having never visited the state previously, New Jersey was strange and unfamiliar territory.

Even our first trip to the grocery store felt like an adventure as we were unfamiliar with one-lane underpasses, traffic circles, and jug handles. To further complicate things, having only experienced grocery stores with the word "FOOD" in their names, we didn’t know ShopRite and Stop&Shop were actually grocery stores, so we weren’t even sure where to go to stock our pantry. With help from new neighbors and directions from MapQuest, we located a nearby A&P. Unfortunately we took a wrong turn following the directions and found it quite difficult to get back on track – although we did eventually make it to the grocery store that day.

Since then, we have purchased a GPS navigator for our vehicle and have found it to be very useful when journeying in new territory. If we make a wrong turn, a kind calm voice from the GPS simply states new directions. Large parts of New Jersey are now familiar enough to us that we no longer need directions or a GPS system there. In these areas, we travel with confidence knowing that we are heading the right direction. Our growing knowledge of how things are laid out in and around New Jersey makes finding our way to new destinations easier and more fun.

Intended Destinations

As math teachers, we have often thought of this experience as analogous to how children learn mathematics. Simply memorizing a mathematical procedure, without understanding key concepts underlying it, is similar to having a specific set of directions from point A to point B without any other knowledge of the surrounding landscape or key landmarks. Without knowing the lay of the land, a child that unwittingly makes a wrong turn, will likely find it difficult to get back on track and arrive at the intended destination.

Just as our unfamiliarity with local grocery store names left us clueless as where to head, children may not even know what direction to take without some basic understanding of math’s nuanced vocabulary. To aid this understanding, the language of math must be presented in a way that makes sense to children.

For example, if you asked your child, "what is 7% of 250 (or what is the sales tax on a $250 item)," would you get a blank stare? What if your child understood that "percent" actually means "for each [per] hundred [cent]"? Your child might then understand that 7% means "7 for each 100" and could then count 7 for the first 100, 7 for the second 100, and half of 7 for the last 50 (i.e., 7+7+3½) to give 17½ (or $17.50) as the answer. Being familiar with mathematical vocabulary such as percent helps us navigate to our desired destination (the correct answer).

Our goal as math educators is to enable each student to understand and solve problems independently. However, when assisting a child who is navigating unfamiliar mathematical territory, we try to act as a GPS, guiding the child to the answer. Beyond mere memorization, when children truly understand a mathematical concept, they have it as a map for future reference.

As each child’s conceptual set of maps grows, so does the child’s ability to see, understand and navigate an ever broadening picture of the mathematical world. Such children can more easily navigate to any selected destination through a wide range of alternate pathways. These children understand why mathematical procedures and formulae work and, given the opportunity to practice mathematical thinking, develop true “number sense”. In doing so, they become both familiar and comfortable with the lay of the mathematical landscape. At this level, a GPS is no longer needed; these children venture with confidence knowing that they are heading the right direction soon to arrive at their intended destination.
________________________
(c) 2009 Jodi & James Ralston who together own and operate MATHNASIUM - The Math Learning Center in Chatham and Summit, New Jersey. Their individualized math enrichment and tutoring programs are tailored to the needs of each student and offered in a relaxed, enjoyable atmosphere. Jodi and James may be reached by phone at (973) 377-MATH or by the Internet at www.mathnasium.com.