Mathematical Literacy

Imagine looking at this as a 9th or 10th grade student. How do you interpret what has been given. Is is certainly not just reading text. There are arrows and equations and graphs, each of which must be decoded in a different way. The ability to understand the graph for instance, requires a set of skills that have hopefully been developed over a period of years. A basic understanding of the analytic geometry of lines and curves is essential to

understanding the nature of the conic section. Understanding the graph goes far deeper than just knowing what each piece is. It is the ability to see how the various pieces, both of the graph, the equations, and the words interact with each other. Showing an understanding of the concept would require literacy in reading (understanding the question itself), arithmetic (understanding the numbers and basic operations), art (drawing the diagram of the hyperbola), and algebra of course. Being mathematically literate requires an ability to integrate several literacies in a logical way.

In order to be mathematically literate, one must have the essential basic and intermediate literacies (Shanahan & Shanahan, 2008, pg. 44). These basic skills include basic reading and writing and ability to read context and comprehend structure. Once these literacies are learned, one has the grounding to begin learning in the mathematics discipline. This could make things difficult for whom english is not a native language. In Miller and Koesling’s Mathematics Teaching for Understanding: Reasoning, Reading, and Formative Assessment they reference Charlie, an ESL student, and have him read problems twice to give him a better chance to translate the question into his native tongue (Miller & Koesling, 2009, pg. 74).

Once the foundations are well established, we can begin building mathematical literacy. The Program for International Student Assessment (PISA) defines mathematical literacy as: “Mathematical literacy is an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to recognise the role that mathematics plays in the
world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens (“PISA 2012 Mathematics Framework”, 2013, p. 25).” In this definition you can see the emphasis on using the concepts of theoretical mathematics to solve real world problems. The ability to solve problems generally using logic is perhaps the most important piece of mathematical literacy. As a teacher, it is often easy to just give the students a simple worksheet, and have the student do the same type of problem over and over again. While this can help ground the student in the basic elements of the theory, it gives the student no help in the application. I remember learning systems of equations in Algebra I, but remained completely unable to solve a problem using the skill. Learning theory without the practice can also distance the student from the work. Many students cannot see how the work could ever apply to them. This can make the student less interested in the material. By giving interesting, real world problems, students are able to apply the theory to practice, and perhaps become more interested the subject.

In addition to the problem solving element is the idea of rigor (or rigour). The word itself is hard to define. It is often compared and contrasted with mathematical intuition (Tao, 2009; Curry, 1941). I believe that the major emphasis should be on the process of logically working through the proof, and on the precision required to be correct in the solution. In most high school math courses, proofs are unemphasized, if taught at all. In fact, one author states: “a glaring defect in the present-day mathematics education in high school, namely, the fact that outside geometry there are essentially no proofs. Even as anomalies in education go, this is certainly more anomalous than others inasmuch as it presents a totally falsified picture of mathematics itself (Knuth, 2002, pp. 379).” Further, Edelman and Hutchison state: “Proof is a central focus for demonstrating an understanding of the logic of an idea in mathematics and how it fits into an established system (Edelman & Hutchison, 2014, pp. 90) Proof remains the basis of all mathematics, and it is a great disservice that the students are denied a presentation of the most foundational concept of the subject.

There are many aspects to mathematical literacy, in this paper we looked at what are the two most important. It is the ability to translate a real world problem into a mathematically solvable problem and the ability to use current theory to create new theory that makes one mathematically literate.

Bibliography

Curry, H. B. (1941). Some aspects of the problem of mathematical rigor. Bulletin of the American Mathematical Society, 47(4), 221–242. doi:10.1090/s0002–9904–1941–07414–8

Hutchison, L., & Edelman, J. (2014). Literacy in the Mathematics Classroom. In Teaching Dilemmas and Solutions in Content-Area Literacy, Grades 6–12 (pp. 81–102). Thousand Oaks, CA: Corwin.

Knuth, E. (2002). Secondary School Mathematics Teachers’ Conceptions of Proof. Journal for Research in Mathematics Education, 33(5), 379–405. doi:10.2307/4149959

Miller, P., & Koesling, D. (2009). Mathematics Teaching for Understanding: Reasoning, Reading, and Formative Assessment. In The Right to Literacy in Secondary Schools: Creating a Culture of Thinking (pp. 65–80). New York, NY: Teachers College Press.

PISA 2012 Mathematics Framework. (2013). In PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy (pp. 23–58). Paris, France: OECD Publishing.

Shanahan, T., & Shanahan, C. (2008). Teaching Disciplinary Literacy to Adolescents: Rethinking Content- Area Literacy. Harvard Educational Review, 78(1), 40–59. doi:10.17763/haer.78.1.v62444321p602101

Tao, T. (2009, February 29). There’s More to Mathematics than Rigour and Proofs [Web log post]. Retrieved June 8, 2017, from https://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/