Popsicles and Numeracy

Popsicles and number sense

One of my projects this summer has been to put together a short course on calculating medications for care givers. This on-line course is meant to help prepare pre-nursing students and others to safely prepare medication doses based on prescribed amounts and drug labels. Why is this needed? I hear repeatedly how anxious nursing  students are about the math  component of pharmacology and medication administration. I also hear from parents, adult-children, and other family care givers that there are often moments of confusion and concern when preparing doses for their family members. Many very capable people experience moments of anxiety or self-doubt when required to use math. 

I have had my own angst about math that began during those dreaded classroom drills in grade six and seven pushing mental calculations and memorized times tables. All done from a well-meaning teaching perspective, but to me, mentally paralyzing!  By high school, I was identifying myself to others as ‘hating math,’ or, ‘not a math person,’ but to myself as, ‘not smart enough to do math.’

Reflecting on earlier moments with math, I did not have that dread or negative reaction as a kid. I remember how amazing Arithmetic was in grade one. How the ‘aha’ light bulb went on while playing with Popsicle sticks at the big Arithmetic table. Heaps of single Popsicle sticks, rubber-banded bundles of ten Popsicle sticks, counting ten of those bundles out and stacking them in a pile: 100 Popsicle sticks!

One bundle of ten and three singles: 13 Popsicle sticks! Okay, so I admit to this very day that I love Popsicle. Especially the orange ones. Maybe that is because of the big, round, orange sticker I got from Miss Mudry for my good work at the Arithmetic table.

It is true though, that after the dreaded mental math drills, it took a while until I had another math-related Popsicle moment. One lazy summer afternoon, eating Popsicle, I was idly throwing dice up in the air and catching them after playing a table game on a blanket in the backyard with my brother and sisters. A lovely breeze played through the hazel nut trees and the dappled sun through branches sifted and shifted light as leaves fluttered. My mind went back to

those dreaded mental math drills and before the walls of shame had time to rise, the light and shadow, playing on those dice showed me how the whole was made up of parts … how 5 was made up of 2 and 3 and if I recognized the patterns of the dots—each dot a part of the whole—I could more quickly arrive at an answer. Simply by visualizing patterns in the parts making up a whole I could visualize the whole. Extrapolating from that popsicle moment, I realized that I could ‘think in 10’s.’  I could move parts in and out to add in fives and tens to estimate and calculate bigger numbers that were more difficult to add, such as 27 and 58. I realized by adding 30 and 60, which was easy, and then taking away 3 and 2, or five, was easy too. Suddenly grouping, or what I recognized as seeing patterns of the parts making up the whole, made sense. Number sense! Yeah for Arithmetic! Miss Mudry would have given me another orange sticker.

Preparing to write the Calculations for Care givers course, I went on a hunt and scanned educational studies on developing number sense, or numeracy, in the era of math anxiety. I came across Dorothea Steinke’s work. Steinke understands the foundation of numeracy to "be part-whole thinking, which she defines as the ability to deconstruct quantities, keep track of the parts, put the parts back together in a different way to solve a math problem, and know that the answer makes sense" (Steinke, 3). Whatever numeracy was, I seemed to at least have an A, B, C understanding of it, thanks to a lazy afternoon throwing dice on a blanket in a nut orchard.

Numeracy, I learned, was a different way of looking at numbers from the math my high school and college profs represented. Their approach was to do their utmost to prepare me to understand higher levels of math thinking—abstract conceptual math. Utterly beautiful but requiring a discipline and passion that I was not able to give to it. Instead, numeracy is the ability to work with numbers in the context of their purpose and use. Numeracy focuses on a working relationship with numbers that are allies and colleagues in providing what you need to know to do your job or live your life successfully. For nurses, this would be the ability to calculate dosing safely and accurately. For my other life with the horses and goats on Fox Song Farm, it is the ability to figure out how much hay I need to get through the winter and determine if my barn has space enough to hold that number of bales. It is also figuring out if I can find

the money in my skinny bank account to pay for it. By the way, the magic hay number is 10 tons, and yes, full up to the top, we have just enough room to store the equivalent amount of  small bales that make up 10 tons of breakfast and dinner for our horses and goats (for 120 lb bales: 167 bales, rounded to 170 bales because I like round numbers). I'm still working on the bank account numbers.

Although I admire the mental athletics of mathematicians, I am a lazy-pants math person and prefer playing in the shallow end of the pool, yes, with popsicle sticks at the Arithmetic table. Numeracy—number sense—is how I approach problems requiring calculation. And, instead of seeing numbers as alien species with inscrutable habits, I now greet them as representatives of a specific quantity of something tangible. Counters. Containers of the ‘thing’ I am trying to calculate.

A light-bulb moment I have witnessed in students is when they recognize the simple truth that ‘1’ is made up of all the points on the ruler from 0 to 1. ‘One’ becomes substance, not mere label. For in numeracy, we are concerned with the amount of something very real and meaningful. If I can reframe a person’s understanding of number from an abstract non-entity to the thing being measured itself, that person’s math anxiety greatly diminishes.

For example, I met with a student who was having difficulty recognizing when a calculation in pharmacology (medication dosage) was incorrect. The usual teachings about estimating an answer first and comparing this to the solution, or double-checking her answer by using the ‘is this reasonable?’ question, or backwards solving the question was not working for her. Without thinking, I said, “Okay, from the label know that you have 4000 mg in the bottle total. Let’s say instead that it’s 4000 beans you have in

there. Given the drug prescription you have been given, how many beans are you going to administer to your patient?” 

This time, she was able to recognize that with her wrong answer, she was going to be giving WAY too many beans! That student later soared through her calculations final, getting the required 100% of questions right in record time. “It’s all about the beans,” she said to me. “When I begin to get anxious, I ask myself, ‘how many beans!’”

Many of us with math-terror need a new way of visualizing numbers. If thinking of beans helps, so be it. In Stanislas Dehaene’s book, The Number Sense, he mentions that many

people often attribute a sense of personality, or identity, to specific numbers, especially the integers. For example, many people see a specific color when thinking about a specific number. Dehaene cites studies demonstrating associations between numbers and colors: “most people associate black and white with either 0 and 1, or 8and 9; yellow, red, and blue with small numbers such as 2, 3, 4; and brown, purple, and gray with larger numbers such as 6, 7, and 8” (Dehaene, loc 1646). What a rainbow an intricate calculus problem would be! 

Other than ‘4’, which I do see as a pale red rather shy fellow beside the flashier ‘5’ who wears a herringbone suit with a wide tie, I don’t see colors when I work with numbers. I do, however, in solidarity with many primary school children, see the shape of numbers as demonstrating a sense of personality. For example, ‘8’ is clearly googly-eyes set sidewise, an obvious snoop who is trying to be sneaky about it, and ‘0’ definitely looks like the Kool-Aid man who similarly intrudes into most large numbers that are just standing there minding their own business.

I think I may include time in the course for students to air their feelings about numbers. It will probably therapeutic for me, too. I might have some unspoken animosity toward ‘O.’ On the other hand, I quite like ‘3,’ who is peaceable and always open to things.

When it comes down to it, although math can be intimidating to many, numeracy—numbers—are etched in the gray matter of our fingertips. They are a part of how we order our daily lives, but more, they are intimately connected with the way we think. We are, ultimately, bean counters in the nicest possible way. We measure things: with our tools, our hands, our eyes. We count on our fingers and on each other. We weigh broccoli in the grocery store as well as the worth of a politician’s words. Number sense lies in uncovering the reason behind our search for the representative set of numerals, reasoning out what we need to know, and allowing our words and numbers to slide together.

I guess that is the starting point—as well as the final anticipated outcome—of my little course. For students to uncover their own natural number sense so they recognize what makes sense number-wise, and are thus safe, safe, safe when calculating medication doses.

Beans. Popsicles. Dice. The Kool-Aid man. Here’s to our collective movement from math terrors to visualizing a rainbow of happy integers.

References

Dehaene, S. (2011) The Number Sense: How the mind creates mathematics, 2nd ed. 

Steinke, D. (May, 2008) Part-Whole thinking. World Education. http://www.ncsall.net/fileadmin/resources/fob/2008/fob_9a.pdf

Milestones and wellbeing

Milestones and Wellbeing

There’s nothing like a school-age kid daydreaming in class to the droning of a teacher, seeing in her dreams sun-drenched beach days, or snow-deep toboggan days, or lazy sleep-in mornings. We learn, from early on to measure our work time with fun time; that the cycle of days includes periods where fortitude means constrained effort toward goals that aren’t necessarily our own, as well as cycles of days where our inner and outer beings are more aligned to the whim and whisper of our own heart-minds. Summer vacation, Christmas holidays, Spring break: don’t they still strike a feeling of bliss in you when you say them? Each one like an island sanctuary beckoning to us during those long school days when the effort of structured learning seemed interminable. They functioned as milestones all along our 12-year journey. “The summer I first went to camp and had a huge fight with my best friend.” “The spring break we went to Disneyland.” “The Christmas we were snowed in and I broke up with my first boyfriend.”  School: our first community journey that culminated 12 years later in that final milestone recorded by family photos of you in a gown with a funny hat.

Our first ‘real’ jobs that paid by the hour or that first pitiful

salary perhaps did not have the length and breadth of those school-year vacations, but they did have a rhythm that marked work and rest, too. Coffee breaks, lunch breaks, birthday celebrations, all helped to create a pattern demarking the periods of time that belonged to another and that belonged to ourselves. Throughout the year, springing up like jewels released only by time, stat holidays and vacation days gleamed on our calendar. Although many of us greedily grasped stat holidays to work and earn double-pay, and vacations days were meager, they still stood as days that were different and distinct from the days making up the weeks that marched on in uniform consistency. Milestones, perhaps smaller than our school year events, rippled the surface on that stream of days giving us a sense of cycle and a turning of seasons.

College-years had their own distinct pattern. Milestones were not only winter and spring breaks and semester or year ends, rather they were midterms and finals and summer jobs and internships and clinicals with specific start and end dates. They were research projects tied into budget funding that began with proposals that included deadlines. And, of course, there was that final graduation week that culminated in more family photos of you in a

gown with yet another funny hat.

Our first career jobs began the process, for many of us, that eroded the healthy, refreshing cycle of milestones as cyclical seasons signifying a beginning and an end. Career jobs demanded that sacrifices be made. If our careers were in an office, coffee breaks and lunches were often taken at desks while work went on with a minor interruption for chewing and swallowing. If our careers were in retail or service industries, coffee breaks and lunches meant quickly attending your own shopping or banking or dashing out to ferry kids. For healthcare providers, breaks were skipped altogether on short-staffed shifts, or became time to catch up on charting, collaborate quickly with colleagues, or, on night shifts, to catch a few Zzz. And not in a relaxing way but a grim “Must sleep as I only have 20 minutes” kind of desperation.  During 12-hour nights that were, likely, about to be stretched into 16-hour shifts, a 20-minute nap became a dead-serious task to be accomplished.

Career jobs, including self-employment, blur the landscape of milestones and as a result these rarely become moments of pause, reflection, change of pace or refreshment. Instead they are seen as tiny islands that can be plundered for extra time to catch up on the many tasks that the river of enterprise continues to demand. Vacations become stolen time that must, somehow, be made up on your return. The frantic efforts to clear tasks away before vacations, knowing the pile of work that will continue to grow when you are away can make any plans for vacation a herculean effort. We say we do it for the family, for the

kids to experience the pause, refreshment, change of pace. But we are exhausted. It is not unusual to witness eager rising stars turn into cynics and energetic care givers burn out and exit their profession.

Milestones are important to well-being. Not simply those event-moments of graduation, big birthdays and anniversaries and christenings. Rather, the rhythm of events that break up our flow of work; that separates for us time-that-belongs-to-others and time where our bodies, minds, hearts can listen, align, become coherent again. Where purpose and personal mission can bubble up once again to provide us with a lifeboat on the relentless river of industry and career. Sometimes we need to stop; more often, we need to re-establish a synergy with nature and ourselves that follow seasonal change, beginnings and endings, fall deluge and spring run-off, times of surge and times of withdrawal. We need cycles with milestones that signal to us that the pause button is on its way as reliable as summer vacation was to us sitting in the February classroom in Grade three.