“You’ll need it to balance your checkbook” or “What if you wanted to re-paint a room of your house?” are phrases that we would often hear repeated to us when we asked “Why we will ever need any of this math?”. While these uses are just as relevant as ever, these answers not only leave today’s learners unsatisfied, but also do not address the essential needs of math in today’s working world. As parents and caretakers, we should be careful to not confuse arithmetic with Mathematics.

The way I see it, Mathematics is comprised of three essential elements: arithmetic, logic, and communication. The processes of balancing a checkbook, calculating surface area, or determining the sale price of an item are all simply arithmetic and, to today’s learner, arithmetic can be calculated faster and more accurately by a computer than he or she can compute by his or herself. We must challenge children with the deeper layers that lie within the field of Mathematics.

If we stray away from arithmetic for a moment we realize that very rarely in life are we given a clear-cut problem with a specific path to the solution. We need to aid today’s learners in becoming logical thinkers so that they can solve the problems that we cannot conceive of yet. To meet this daunting task of preparing someone for a world that has not yet been seen we must emphasize the importance of logic.

Logic is a systematic method of reasoning through any problem to make sense of it. In other words, logic is cause and effect, logic is “what else do you know”, and logic is “what does that mean?” Continue to ask your children these questions. Do not simply explain to them how to work that horrible monster of a fraction problem or how many places and in which direction to move that decimal; instead, ask them “What do you notice about this situation? What does that mean? What else do you know about the situation? How can we fix that? What else, what else, what else?”

The goal is to get the learner to break down the problem at hand into all of its smallest components, then rebuild the problem in a way that make sense to him or her. Through all of this the child gains ownership of the specific knowledge at hand, learns essential reasoning skills that will carry through to all parts of life, and, more importantly, will see that tasks are not insurmountable when broken down into their working pieces.

Knowing how to arrive at a solution for a problem does no good if you cannot communicate its importance to another person.

Once the child has the information broken down, what do they do with it? This is why I consider communication to be a key element in Mathematics. Knowing how to arrive at a solution for a problem does no good if you cannot communicate its importance to another person. If a scientist is attempting to justify his or her results, he or she must be able to establish that clear quantifiable link between hypothesis and conclusion. Revisiting the idea of the computers that can calculate arithmetic faster and more accurately than a human could, someone had to break down each of the arithmetic processes and communicate those ideas to a computer in a logical method so that a program could be usable by society.

To emphasize the importance of communication I always enjoy having students write algorithms for simple tasks, such as making a peanut butter and jelly sandwich, and then actually follow out their own instructions. This creates for great entertainment as they attempt to “spread the peanut butter” but have not yet opened the jar or have given the instruction to “pick up” several different items without ever having instructed to set one of the items back down. This, again, not only emphasizes logic and reasoning, but also the importance of communicating concisely and clearly to others the meaning of your work.

Equations, percents, statistics, fractions — these are all words that have been known conjure pure horror in the minds of many adults who are trying to help their child with his or her Mathematics education. I encourage these parents and caretakers to fear not and to remember that Mathematics is not purely about the calculations and arithmetic, but also about logic and communication. Just remember to talk and reason with your children often to strengthen the natural curiosities that are innate to them. You will not only strengthen their arithmetic skills, but will also strengthen the tools they need to succeed in any future role they may find themselves in.

As someone to whom words and art come like breathing but math is often more like pulling teeth, I personally really enjoyed this article; especially as I suspect part of my problem with numbers later in life has been caused by some kind of fundamental disconnect with the concepts as they relate to the “real” world around me.

Math is definitely one of those things that can “conjure pure horror” in my mind when even the though of being responsible to communicate such a vital concept to future generations is raised. So having it broken down in a simple and relatable way soothes my racing heart, and gives me hope for those little minds to come.

Emily, that was very well said. I appreciate the differentiation between arithmetic and mathematics — math is definitely a way of thinking, an approach to solving problems. I hope I can instill my love of math in my son.

If anyone wants to check out some really great math videos on youtube that make math fun, search for “vihart”, or go to her blog here: http://vihart.com/

She looks at the amazing stuff that math can be and it’s tons of fun.

What an awesome post!! I really appreciate the idea that learning math is not just about learning numbers, but about learning to apply logic and mental energy (and sometimes numbers)

to make things happen. This really made me think.

Someday, I hope to be a math teacher. You have put into words exactly what I try to teach my children about math and why I love it so much! I’m sharing this with everyone! 🙂

What’s interesting is that I’m not very good at arithmetic or doing calculations in my head, but as a scientist, I use math in my job all the time. I do everything from calculating the area of wetlands in acres to determining if a client would violate their stormwater permit if they release water from a certain pond with certain concentrations of permitted constituents at a certain flow rate over a certain period of time.