I have a confession to make. When I was in fifth grade, I was kicked out of the gifted program at school because I wasn’t very good at complex multiplication and long division problems. Oh, I could tell you how to solve them. I could even teach my friends. But I could work one of those problems five times and come up with five different answers, not a single one correct.

You see, careless errors were the bane of my existence. They still are. They always will be.

Last week, my husband, daughter and I attended Family Math Night for parents of first-graders at my daughter’s elementary school. I attended with some trepidation, remembering some of my early math experiences and knowing some of the homework horror stories I have heard from parents of students in other school systems.

The first thing we did at Family Math Night was calculus. My husband and I were thrilled. We started out with an example of shapes with increasing numbers of sides—triangle (three sides), square (four), hexagon, octagon, dodecagon (12), etc. The question asked was, “as you add more sides, what shape are you approaching?” The answer: “circle”. Next question: “Do you ever get to a circle by adding more sides?” Answer: “No.” This is an example of limits in calculus. And it’s also very similar to a question my daughter asked me a couple of weeks ago, “Mom, does a circle have lots and lots of little tiny sides or no sides?”

My daughter has showed a propensity to “play” with numbers and shapes in her mind and to ask these kinds of questions for several years now: “What’s the largest number?” “Did you know if you cut a circle into pieces it has all kinds of lines inside?” I have two concerns about this. The first is quite simple: I often don’t know how to answer these questions. I am math competent, not math confident. With the notable exception of fifth grade I performed well in math, even excelling in high school and college when the quality of the instruction improved. However I think I missed out on developing a genuine understanding for math. My husband, however, is math savvy, and I really wish our daughter would ask him these questions. He could take that statement about lines inside circles and lead her to the circumference of a circle. I fear that I could only lead her to pumpkin pie.My second concern is more complex: I want the experiences she has in elementary school to encourage the exploration of those deep math thoughts, not quash them. That takes a brave teacher, one willing to let students learn things for themselves and a curriculum that actually accommodates the rather messy process of student learning.

I became very interested in STEM education when started college teaching. My first semester I taught clinical microbiology to nursing students, and one of the concepts we covered was serial dilutions. I mistakenly assumed that my students left high school understanding that 1/10, 0.1 and 10–1 all represented the same thing mathematically, but about half of the class had never encountered negative exponents and was very uncomfortable with the concept of diluting molecules that they could not see. I spent a lot of time working with the math specialist in the college learning center figuring out how to help my students wrap their minds around this concept. Since then I have spent a lot of time learning about learning, and it has informed my casual observations of my daughter’s development.

I like what I have seen so far in the math curriculum. It strives for a genuine understanding of math as the language that describes what we see in the world around us, and it supports the teacher in the classroom by providing concrete, practical suggestions for supporting students every day. All students need support; one day a student may need support by way of extra assistance; the next day that same student may need support by way of extra challenge. The curriculum is flexible enough to accommodate that.Additionally, it is clear that our school’s math specialist is passionate about math, that she sees the incredible beauty in it. That passion and excitement is contagious, and that alone can make math a better experience for my daughter than it was for me. So, I am much relieved after family math night, and I’m excited to see what I will be learning alongside my daughter.

And, one more question (asked by the child of a friend): if you keep dividing a number by two…do you ever get to zero?

©2013 Michele Arduengo. All rights reserved.

When answering questions of how many sides a circle has or how many times 1 can be halved before the result becomes zero, it is helpful to understand the concept of the Planck length, ℓP. There is a point in the physical Universe in which we now exist when and were it becomes meaningless to seek finer detail or understanding for there can be none for those of us confined here. Nonetheless, it’s also important to recognize were this limit lies so that one does not abandon that grand quest too soon. Speaking of time, it’s similarly useful to know how long one should ponder a difficult question before further effort could be labeled “pointless.” Enter the Planck Time, tP. One should never abandon an important quest until one has spent 1/tP, asked a more informed source and obtained an answer, or solved the problem oneself.

Sometimes the smallest things matter, but nothing smaller than that does.

There’s probably a very good reason why π is an irrational number.