Mathematical Literacy: A necessary skill for the 21st century

Maths chocolate
Photo by Flick user s-guilana | CC BY 2.0

My Grade 9 math teacher was a jolly British man, and probably taught me one of the most useful things I ever learnt 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.

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 schoolkids 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 phenomena known as “Math Anxiety” or “Math Phobia.”  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.

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

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.

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 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.

Maths
Photo by Flickr user Minibe09 | CC BY-NC 2.0

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 30 (!!) apps here). 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), a basic level of numerical literacy is not only important, it’s necessary.

References
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

Facing the research-practice divide in science education

Science education researchers and science teachers have much to offer each other. In an ideal world, knowledge would flow freely between researchers and educators. Unfortunately, research and practice tend to exist in parallel universes. As long as this divide persists, classrooms will rarely benefit from research findings, and research studies will rarely be rooted in the realities of the classroom. If we care about science education, we have to face the research-practice divide.

How did it get this way?

When we talk about research and practice, we’re talking about academics and teachers. In the most typical case, we’re talking about professors of education working at universities, and teachers working at K-12 schools. The divide has its roots in historical and current differences between researchers and teachers in their training, methods, work environment, and career goals that have led to misunderstanding and mistrust. In a 2004 paper titled “Re-Visioning the academic–teacher divide: power and knowledge in the educational community” Jennifer Gore and Andrew Gitlin describe the state of the research-practice divide through the lens of the two groups of people involved, and the imbalance of power between them. Historically, they argue, the framework of science education research has been that researchers generate knowledge and materials that teachers need, but rarely recognize the need for teacher contributions. This assumed one-way flow of knowledge has certainly sparked animosity between the groups, deepened by cultural differences associated with differing career paths.

Of course, some people have been both K-12 teachers and academics in their careers. To get this perspective on the issue I reached out to a colleague, Assistant Professor of Science Education Ron Gray (Northern Arizona University). Ron has been a middle school science teacher, a teacher of science teachers, and is now a science education academic. When I asked him about the experience of transitioning from teacher to academic, he recalled:

“I don’t believe I had seen a single primary research document in education before earning my doctorate.”

Most K-12 science teachers are fairly disconnected from the research world once they leave universities and enter schools. They lack university library access, yet currently many of the best journals in the field, such as the Journal of Research in Science Teaching, Science Education, and the International Journal of Science Education are not open access, and require a per-article fee to read. So how does research reach most teachers? I talked to a few science teachers about where they encounter science education research studies — many used science and education pages on Facebook, one got papers sent from an administrator, and some read practitioner journals. Many science teachers are members of the National Science Teacher’s Association (NSTA), which publishes practitioner journals and holds national and area conferences where teachers can hear about research findings. NSTA plays an invaluable role in working to connect research and practice. However, for perspective, NSTA has about 55,000 members, most but not all of which are practicing science teachers, but there are currently about two million practicing science teachers in the U.S.

The disconnect also stems from unfortunate misperceptions of professors by teachers and teachers by professors. Both groups often discount each other’s knowledge bases and workloads. Professors can harbor elitist attitudes about teachers, discounting the value of practical classroom experience in determining what works in education. Teachers frequently claim that professors suffer from “Ivory Tower Syndrome” — the assumption here is that professors live cushy lives, sheltered from the realities of schools, and therefore can’t produce knowledge that is useful in today’s classrooms. A high school teacher quoted by Gore and Gitlin explained:

“A lot of what [researchers] think is based on the past and they are out of touch. And so we call it the Ivory Tower. Welcome to our world.”

When I asked high school science teacher Laurie Almeida how she perceived the credibility of science education research, she responded:

“Somewhat credible. I work at a difficult school, so I feel that some of the research is way too out of touch with the reality of my school.”

An ivory tower of sorts. Sather Tower, U.C. Berkeley. Photo by Bernt Rostad.
An ivory tower of sorts. Sather Tower, U.C. Berkeley. Photo by Bernt Rostad.

There is sometimes truth to the ivory tower criticisms; Gore and Gitlin noted that in some academic circles, the more closely research is associated with practice, the more devalued it is. Furthermore, science education research is far from perfect. Small-scale studies with limited applicability are published more frequently in science education than they are the natural sciences. This trend hasn’t escaped notice from teachers either. When I asked about the perceived credibility of science education research among teachers, science teacher Toni Taylor told me:

“Too often I see ‘research’ that includes only a small sample population which makes me question the validity of the research,” and “Sometimes I feel like science education simply tries to reinvent the wheel.”

However, a lot of the mistrust between the two groups is based on their misunderstanding of each other’s professions. Teachers do not always appreciate that many researchers are often in the classroom regularly, conducting classroom-based studies and collecting data. This “back of the class” view can be highly illuminating, and is a valid way to know classrooms. Some researchers got their start as K-12 teachers. And higher education is certainly not immune from classroom management issues or over-filled schedules. Professors have stress — just ask the #realForbesProfessors (this hashtag exploded on Twitter following the publication of a Forbes article claiming that professors have one of the least stressful jobs). Similarly, researchers can forget that experienced teachers have a wealth of knowledge about the specific interactions of classroom context, pedagogy, and subject matter.

 

What can be done?

My conversation with Professor Ron Gray about what academics can do to better connect with teachers aligned well with calls in the literature for more researcher-teacher partnerships. He said:

“The best way would be to get back in the classroom but the tenure process just doesn’t let that happen.”

His response highlights the rigidity of teacher and researcher career paths. Even a former teacher who switched to the researcher path can’t switch back again without ultimately losing “traction” in both careers. Perhaps we should question the wisdom of entrenching people interested in science education in one narrowly-defined career trajectory or another. Instead, career advancement could reward the accumulation of diverse but synergistic experiences. Science education is a multidisciplinary endeavor, involving science, social science, and communication skills — why shouldn’t our career options reflect this?

Similarly, certain aspects of teacher training might be due for a change. Teacher education could be a crucial time to break the mold  that has placed researchers as producers and teachers as consumers of research. Gore and Gitlin suggest that student-teachers at the undergraduate or master’s levels could be attached to ongoing education research projects as research assistants. They would become intimately familiar with the purpose and methods of educational research and could become significant contributors to it. This would take some restructuring, as many programs focus on more “immediate” concerns such as classroom management, but the benefit could be the production of teachers who recognize the value of research and feel capable of making contributions to it.

The open access movement in scholarly publishing could also have a crucial role in breaking down barriers. Toll-access journals can function as practically impenetrable “ivory fortresses” where valuable knowledge is locked away from practitioners. However, open access will likely prove necessary, but not sufficient in closing the research-practice gap. Teachers I’ve spoken to are very positive about open access but guarded about how much more time they’ll spend reading research articles. Time is a huge issue for teachers. But the alternative — locking up research findings in places where both time and money can be barrier for teachers — is certainly not helping to connect research with practice.

For the short-term, most education research articles are still in toll-access journals. For those without easy access to the primary literature in science, research blogs have become an incredible resource. However, the science education research blogging community pales in comparison to the science research blogging community. While teachers can find the latest science news and engaging resources to share with their students by following the science blogging community, they are not as likely to find quick-and-easy write-ups of science education research findings that are relevant to their pedagogy, curriculum development, assessment practices. As the Sci-Ed blog establishes itself, I hope that my fellow writers and I can attempt to partially fill this role. And I hope that many others in science education continue to follow the research blogging model.

 

Reference:
Jennifer M. Gore & Andrew D. Gitlin (2004): [RE]Visioning the academic–teacher divide: power and knowledge in the educational community, Teachers and Teaching: Theory and Practice, 10:1, 35-58.