Mathematical Literacy: A Necessary Skill
I regularly work with undergraduate and graduate students in statistics, and I notice that many of them, while they have all the skills to do math, are absolutely terrified of it. But you need it for daily life. Mathematical literacy is the knowledge and skills required to apply arithmetic operations, to numbers embedded in printed materials, such as balancing a checkbook, figuring out a tip, completing an order form or determining the amount of interest on a loan from an advertisement.
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My Grade 9 math teacher was a jolly British man, and probably taught me one of the most useful things I ever learned in high school:
how to do basic math in my head (or, since I was in the British educational system, it was Grammar School). Every so often we’d go into our math class and find little bits of paper on every desk. This was a harbinger of doom – it meant we were having a 20 question surprise quiz. And not just any quiz, a mental arithmetic quiz. He would read a question out loud twice, and then we’d have to do the math. He’d give us some leeway (you didn’t have to be exact), but man did I ever hate those quizzes. At the time, they seemed impractical and a colossal waste of time. In retrospect, they were incredibly useful.
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Now, being on the other side of the divide, I see something that concerns me. I regularly TA undergraduate and graduate students
in statistics, and I notice that many of them, while they have all the skills to do math, are absolutely terrified of it. And as soon as you fear a subject, or don’t want to learn it, you won’t. Your mind will shut down and every instinct you have will prevent you from engaging in the material.
As a result, I spend the first hour of any class I’m teaching talking to the students and determining what it is they don’t understand to tailor my sessions accordingly. But the comments generally involve variations on:
“I just don’t get math.”
“I’ve never been any good at math.”
“I don’t like it.”
Of these, the first two concern me. The third I can’t help – I don’t need my students to love math, but I do want them to understand
enough to pass the course and feel comfortable interpreting statistical analyses. There’s a culture among school kids to dislike math and the perception that it’s largely useless.
While in chemistry you can see stuff blow up, and in biology you can dissect animals, math is a largely abstract concept. That perception then manifests as a lack of interest, which results in poorer performance, and that puts people off math. This is further compounded by a phenomenon known as“Math Anxiety” or “Math Phobia.”
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Ashcraft and Kirk discuss this extensively in their 2001 paper, and suggest that much of the anxiety is a result of the fear
of getting the wrong answer in their tests. I’m not going to delve into it now as the whole area of math performance, both in terms of math anxiety and performance anxiety as well as cultural and gender differences in math warrant a dedicated post. For now, let’s just talk about what constitutes “mathematical literacy.”
The OECD released a report in 2000, where they defined literacy in three domains, and the way they defined numerical literacy was:
Quantitative literacy – the knowledge and skills required to apply arithmetic operations, either alone or sequentially, to numbers embedded in printed materials, such as balancing a chequebook, figuring out a tip, completing an order form or determining the amount of interest on a loan from an advertisement.
Identify and Understand
The OECD also conducts the Program for International Student Assessment (PISA) which evaluated the performance of 15-year olds
in math, science and reading. It defines mathematical literacy as:
Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen
Tips, Order Forms and Interest
As you can see, the idea of numerical or mathematical literacy, as defined above, isn’t advanced math like calculus
or algebraic manipulations. We’re talking about being to understand the order of operations and activities requiring that level of mathematical understanding.
Given that the world is moving towards a knowledge based economy, the lack of mathematical literacy is a big concern. Now more than ever the ability to critically evaluate information presented to us to draw our own conclusions, rather than have someone tell us what they mean, is of the utmost importance.
Challenges with Age
In Canada, this has particular relevance as we (like most of the Western world) are in the midst of an aging population.
This comes with its own set of challenges, but one is that as patients age, they suffer from illnesses, and if they are unable to interpret medical information or if doctors are unable to explain to patients in a way they’ll understand, then patients are unable to make informed decisions about their health.
I’m not implying that everyone needs to be able to advanced math and statistics. Given the advances in technology (see abacus app above), you can now use an app to calculate how to split the bill or calculate a tip
(iLounge reviews bit.ly/1xVArDC ).
You don’t need to be able to do hierarchical ordinal regression using bootstrapping, or factor analyses, or structural equation modelling.
But given how much data we are presented with on a regular basis, be that in the form of interest rates on a bank loan, discount on sale items or even polling numbers for political parties (the latter discussed by Swans on Tea bit.ly/1m11Pes), a basic level of numerical literacy is not only important, it’s necessary.
Ashcraft, Mark H.; Kirk, Elizabeth P., “The Relationships Among Working Memory, Math Anxiety, and Performance”, Journal of Experimental Psychology: General 2001 pp. 224-237
Ciampa PJ, Osborn CY, Peterson NB, Rothman RL., “Patient numeracy, perceptions of provider communication, and colorectal cancer screening utilization.” J Health Commun. 2010;15 Suppl 3:157-68. Available at: http://www.ncbi.nlm.nih.gov/pubmed/21154091
OECD. “Assessing Scientific, Reading and Mathematical Literacy: A Framework for PISA 2006? 2006. Available online at: http://www.oecd.org/pisa/pisaproducts/pisa2006/37464175.pdf
OECD. “Literacy in the Information Age: Final report of the International Adult Literacy Survey” 2000. Available online at: http://www.oecd.org/education/educationeconomyandsociety/39437980.pdf