MET:Numerical Literacy
This page was originally authored by Denise Flick (2010).
This page has been revised by Janet Barker (2011).
The stop-motion animation video was added by Meril Rasmussen (2016).
Numerical literacy, or numeracy, is currently a topic of great educational concern. Provincial curriculum developers across the country, and throughout the world, are working to address the issue of numeracy. In general, the term numeracy can be used to describe two different, but related, areas of ability:
- The ability to use basic math skills and interpret data in daily life and work.
- The ability to engage in mathematical discussion and knowledge building at a higher level.
The first issue is of immediate concern to educators while the second issue has a more limited scope within the mathematical community.
Numeracy
What, might you ask, is the difference between numerical literacy (numeracy) and mathematics? Dave Vanbergyk 2009-2010 president of the British Columbia Association of Mathemtatics Teachers, BCAMT, spoke to the difference. "Mathematics is body of knowledge that if not used can be lost. Numeracy is a set if proficiencies that once gained are forever with you”. (D. Vanbergyk, personal communication, October 1, 2009)
The United Kingdom's Department for Children, Schools and Families defines numeracy in their National Strategy documents as follows:
"Numeracy is a proficiency which is developed mainly in mathematics, but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables." Department for Education and Skills (UK)
Just as literacy is much more than decoding, spelling, and grammar so too is numeracy much more than math facts and computation. Just as we wish to immerse our children in a world of literacy in which they can develop skills and attitudes that enable them to understand, learn, appreciate, and communicate so too do we want to have the attitudes and skills that enable them to make sense of, feel successful in, see the beauty in, and pursue opportunities in the world of numeracy. - D. Flick [1]
Why is Numeracy Important?
- Proficiency in numeracy is related to successful completion of high school and successful transition to post-secondary education and the work force.[2][3]
- Numeracy is necessary to be able to interpret and verify information in the media: Results from political polls, survey data, and statistical "facts" cited in commercial advertisements are just a few examples.File:Wiztees 2162 34728005.gifPopular T-Shirt
- Numeracy is imporant in making educated choices in health care - for example, understanding the probabilities behind false positive or false negative test results. A study published in Annals of Internal Medicine reported that "Numeracy was strongly related to gauging the benefit of mammography" and that "Higher numeracy scores were associated with greater accuracy in applying risk reduction information" as it applied to mammography.[4]
- Numeracy is important for understanding mortgage rates, investments and loans.
- Numeracy is found in the skills needed to make measurements for home repair or renovation, such as determining how much paint to buy to paint a room.
- Numeracy is a requirement in a wide variety of employment opportunities.
Attention to numeracy is well-documented throughout curriculum in Canada and globally. In British Columbia, the Premier’s Technology Council addresses numeracy in its publication A Vision for 21st Century Education. Queensland, Australia, addresses numeracy in Numeracy – Lifelong Confidence with Mathematics. Many other provinces and jurisdictions around the world have similar documents available online to indicate how they are dealing with the issues surrounding numeracy in their educational systems. In their plan for improving literacy and numeracy in Ireland, the Department of Education and Skills states that "The skills of literacy and numeracy equip young people to make the most of learning opportunities, to take up satisfying careers and to contribute to and participate fully in all aspects of our culture and society". [5]
Innumeracy
Innumeracy was a term developed to convey a person's inability to make sense of numbers. Basically innumeracy refers to a lack of numeracy. Innumeracy was coined by cognitive scientist Douglas R Hofstadter in the early nineteen eightees. Dr. Hofstader wrote several Metamagical Thema columns for Scientific American.
Later that decade mathematician John Allen Paulos published his book Innumeracy: Mathematical Illiteracy and Its Consequences.[6] In this book, many numeracy concepts were explored and explained in an entertaining and meaningful manner. The book was written with the hope of drawing attention and creating action to address the issue. David Letterman, who himself has self confessed difficulty with numbers, interviewed John Allen Paulos. Innumeracy interestingly, was a national best seller.
Causes of Innumeracy
Innumeracy, like illiteracy, has many causes. As with all types of learning, culture plays a pivotal role in innumeracy. In his book, Mindstorms, Seymour Papert refers to the concept of “mathophobia”. Papert states that, “The mathophobia endemic in contemporary culture blocks many people from learning anything they recognize as “math,” although they have no trouble with mathematical knowledge they do not perceive as such."[7] He goes on to state that difficulty with mathematics in school is often the first step in perceiving oneself as either mathematically capable or not. What may have started as a lack of understanding, opportunity or experience may become internalized as a personality characteristic and becomes a block to future learning. In essence, students have difficulty learning math simply because they think they cannot.
In his article, Counting Past 10: Numeracy versus Literacy, Drew Cayman sums up North American society's attitude towards mathematics. He states that:
"Numeracy, at heart, is a cultural value. As Americans, we do not typically pride ourselves on understanding our mortgage contracts or multiplying in our heads, and this is not a source of shame. We readily admit “I’m not very good at math,” but would be silent if we had similar troubles with reading. There are late night infomercials for “Hooked on Phonics,” but not “Hooked on Fractions.” We feed children alphabet soup.",[8]
Math Anxiety
A concept related to mathophobia is “math anxiety”. Math anxiety differs from mathophobia in that it is not a result of inability with numbers but is a result of emotional distress when working with numbers. The anxiety may then lead to innumeracy. The problem of math anxiety "becomes acute when the person most afraid of numbers and equations is standing in front of the classroom trying to teach the subject."[9](Campbell, 2006) If a teacher suffers from math anxiety, the teacher's fears affect how math is approached in the classroom, which in turns affects the students in the classroom. This issue is addressed in the article, How Does the Notion of Numeracy Affect Teaching?[10]
A High School Student's Math Anxiety Success Story:"Hi. My name is Carly. And I have math anxiety."]
Improving Numeracy from an Educational Perspective
Many of the proposed new curricula guidelines and online resources dedicated to improving numeracy share two common themes. First, in order for numeracy to improve, mathematics education needs to move away from isolated, rote learning to problem-based learning where problems are situated in realistic scenarios. That is not to say that there is no place for mastery or rote learning of certain topics to facilitate the problem solving, just that mastery of individual topics out of context leads to concepts that are learned and then lost or that students are unable to transfer to real life situations. In The Common Curriculum Framework for Grades 10 – 12 Mathematics, problem-solving based learning requires students to encounter problems that they do not know how to solve. Valuable problem-solving “requires students to use prior learnings in new ways and contexts.”[11] These problems must also be presented so that they are culturally relevant and of inherent interest to the students.
Along with the other Western provinces, Alberta has adopted the Western and Northern Canadian Protocol curriculum for mathematics. Alberta Education states that, “Students ...come to classrooms with varying knowledge, life experiences and backgrounds. A key component in successfully developing numeracy is making connections to these backgrounds and experiences.”[12]
The second common theme appearing in curriculum around the world is that numeracy is an issue that crosses all curriculum areas. The Premier’s Technology Council states that, “In some jurisdictions, numeracy discussions have previously focused on computational skills, but it is increasingly believed that if numeracy is to improve student’s use of mathematics in life, numeracy education cannot be restricted to math classes but should be implemented across the overall curriculum.” [13]
Here are just a few examples of how numeracy is important and can be integrated throughout many branches of the curriculum:
| Subject | Examples of Numeracy Skills |
|---|---|
| Social Studies | Reading graphs and maps, understanding population trends |
| Science | Interpeting graphs, manipulating formulae |
| Home Economics | Budgets, altering recipes, altering patterns, dress designing |
| Trades | Fractions in measurement, angles for building stairs |
| Accounting | Creating spreadsheets, manipulating data, balancing accounts |
| Physical Education | Laying out playing fields (measurements), using angles of incidence and reflection for making shots in hockey and billiards, laying out play patterns in football, keeping score |
When designing educational media related to numeracy, designers should consider how aspects of problem-based learning and cross-curriculum activities could be incorporated into their designs. Problem-based learning generally requires collaboration and working in groups which would create a need for specific interaction affordances within the design medium.
Numeracy and Upper Level Mathematics
While numeracy is important for every member of society across all jobs and lifestyles, numeracy is particularly important for that much smaller segment of the population that goes on to study formal, post-secondary mathematics. The Western and Northern Canadian Protocol states that there are two types of problem solving in mathematics – contextual problems and mathematical problems. A contextual problem is based on a real-life problem, such as determining the volume of paint required to paint a room. A mathematical problem is purely mathematical, for example proving the Pythagorean Theorem. While the techniques arising from a mathematical problem may be used in a contextual problem, the goals are quite different. A contextual problem needs a practical answer, a mathematical problem is purely theoretical and these types problems form the basis of much of higher mathematics.
Great Math Reads
Burns, M. (1998). Math: Facing an American Phobia. Sausalito CA: Math Solutions Publications.
Ma, L. (1999). Knowing and Teaching Elementary Mathematics. Mahaw NJ: Lawrence Erlbaum Associates.
Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.
Sousa, D. A. (2008). How the Brain Learns Mathematics. Thousand Oaks CA: Corwin Press.
Tobias, S. (1993). Overcoming Math Anxiety. New York NY: Norton Publications.
Lockhart, P. (date unknown). A Mathematician's Lament
Additional Information and Related Sites
BBC - Schools Ages 4-11 - Numeracy
BBC - Schools Ages 11-16 - Maths
Numeracy - a list of sites from Grande Prairie School District
Trends in International Mathematics and Science Study
British Columbia Association of Mathematics Teachers - Numeracy
Sir Ken Robinson on Education (TED Video)
Problem-Based Learning and Math Education - ETEC 510 Design Wiki
Stop Motion Animation Video
Number Sense (2016) by Meril Rasmussen. Duration: 2:26. On the importance of number sense at the elementary level.
References
- ↑ Flick, D. E. (2010). Numeracy Success Begins at Home. West Kootenay Family Magazine, Winter, 26
- ↑ National Numeracy Review Report, (2008). Commissioned by the Human Capital Working Group, Council of Australian Governments.
- ↑ Human Resources and Skills Development Canada, 2011. Indicators of Well-Being in Canada: Learning - Student Numeracy
- ↑ Black, W., Schwartz,L., Welch, H. G., & Woloshin, S. (1997). The role of numeracy in understanding the benefit of screening mammography. Annals of Internal Medicine, 127(11), 966 - 972
- ↑ Department of Education and Skills (2010). Better Literacy and Numeracy for Children and Young People: A Draft Plan to Improve Literacy and Numeracy in Schools
- ↑ Paulos, J. A. (1988). Mathematical Illiteracy and its Consequences. New York NY: Hill and Wang
- ↑ Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
- ↑ Cayman, D. (2011) Counting past 10: Numeracy versus literacy. The Alternative Press.com Retrieved online from [1]
- ↑ Campbell, G. (2006). Popping math anxiety. Retrieved October 8, 2006, from ASU Research http://researchmag.asu.edu/stories/cresmet.html
- ↑ Flick, D. E. (2008). Teacher Math Anxiety. Vector, Spring, 19 - 24.
- ↑ The Common Curriculum Framework for Grades 10 – 12 Mathematics, Western and Northern Canadian Protocol, (2008).
- ↑ Alberta Education, (2007). The Alberta K-9 Mathematics Program of Studies with Achievement Indicators. Retrieved online from: http://education.alberta.ca/media/645598/kto9math_ind.pdf
- ↑ Premier's Technology Council, 2011. A Vision for 21st Century Education