What It Means to be Literate in Mathematics?
I’ve always been good in math, in school and as an Engineer. Maybe because it came easy, plus I enjoyed getting to an answer, but was I really literate in math?
I remember the movie, “Good Will Hunting”, with Matt Damon as a blue-collar math genius and how he dazzled a Harvard mathematician with his ability to develop and solve complicated proofs. Was this really possible for an untrained person to be able to speak the language of sophisticated mathematics?
So how is literacy in mathematics different from other disciplines? In Teaching Disciplinary Literacy to Adolescents: Rethinking Content-Area Literacy, Timothy & Cynthia Shanahan, (2008), Harvard Educational Review stated that, “The end result is that the literacy demands on students are unique, depending on the discipline they are studying” (p.48) and that math reading requires a precision of meaning, and each word must be understood specifically in service to that particular meaning” (p.49). Mathematicians are typically adamant that the precise\mathematical definition needed to be learned — memorized, as it were — in order to obtain true understanding of the mathematical meaning in contrast to its more general meaning. For example, a student must know that prime refers to a positive integer not divisible by another positive integer (without a remainder) except by itself and by 1. Prime also means perfect, chief, or of the highest grade, but none of these non mathematical meanings aids in understanding the mathematical meaning. (p.52)
In What Is Disciplinary Literacy and Why Does It Matter, Timothy & Cynthia Shanahan, (2012), Top Lang Disorders, make a strong distinct in the difference between content- area versus disciplinary literacy, “Content area literacy focuses on study skills that can be used to help students learn from subject matter specific texts. Disciplinary literacy, in contrast, is an emphasis on the knowledge and abilities possessed by those who create, communicate, and use knowledge within the disciplines” (p.8). The difference is that content literacy emphasizes techniques that a novice might use to make sense of a disciplinary text (such as how to study a history book for an examination), whereas disciplinary literacy emphasizes the unique tools that the experts in a discipline use to engage in the work of that discipline (p.8). As a true “math person”, I am beginning to understand that all my successful studies of math were truly a result of my teachers using the specific math discipline text i.e. algebra, geometry, calculus, etc. It was always a little easier to read in math class than say English for me. I would memorize the math specific symbols like π, ≠, ∞, f, ≤, ˃, and they would become my “new” vocabulary for solving problems.
Peter Smagorinsky, In Teaching Dilemmas & Solutions in Content-Area Literacy (2014), notes that there are unique forms of text found in mathematics classrooms including,
· Symbols
· Drawings
· Verbal explanations
· Formal proofs, and
· Diagrams among others (p.82)
Writing in mathematics provides students an opportunity to reflect on their work and consolidate their thinking about mathematical concepts. Teachers and students communicate their mathematical thoughts using mutually defined symbols.
As a future Math teacher I believe in the following: “The aim of disciplinary literacy (mathematics) is to identify all such reading- and writing-relevant distinctions among the disciplines and to find ways of teaching students to negotiate successfully these literacy aspects of the disciplines. It is an effort, ultimately, to transform students into disciplinary insiders who are able to approach literacy tasks with some sense of agency and with a set of responses and moves that are appropriate to the specialized purposes, demands, and mores of the disciplines (p.11).”
In The right to Literacy in Secondary School, Suzanne Plaut, (2009), International Reading Association, points out that, “Teachers can marry the mathematical reasoning process with a reading process that helps students understand the real-world context and mathematical concepts of a problem (p.65). I particularly like Suzanne Plaut’s assessment of, “Reasoning and Reading like a Mathematician in the classroom”,
1. Have students read the problem twice before they actually try to solve it
2. Ask open-ended questions to further understanding and uncover conceptual misunderstandings
3. “It’s not here’s how you do it”. “It comes from breaking the problem-solving process into small pieces that the student is able to successfully negotiate.”(p.68)
These basic teaching approaches support math literacy by thinking like a mathematician.
In Teaching Dilemmas & Solutions in Content-Area Literacy, Peter Smagorinsky (2009), Corwin, provides a process of Problem Solving literacy that I thought truly represents Math Literacy.
Problem-Solving is an integral literacy in learning mathematics in that it is central to thinking within and about mathematics. (p.85).
George Polya’s problem-solving heuristic routine includes: (Each step has a series of questions that students may ask of themselves to arrive at a solution)
1. UNDERSTANDING THE PROBLEM
2. DEVISING A PLAN
3. CARRYING OUT THE PLAN
4. LOOKING BACK
After reviewing Poyla’s Problem Solving process, I found that I have been following this for years. “IT REALLY WORKS”.
In closing, math literacy is an integral part of learning and applying mathematics. As a future Math teacher I plan to teach like a thinking mathematician.
Shanahan, Timothy & Cynthia, (2008). Harvard Educational Review, Vol 78, No.1, Teaching Disciplinary Literacy to Adolescents: Rethinking Content-Area Literacy
Shanahan, Timothy & Cynthia, (2012). Top Lang Disorders, Vol 32, No.1, What is Disciplinary Literacy and Why Does it Matter
Plaut, Suzanne, (2009). Teaching College Press: The Right to Literacy in Secondary Schools
Smagorinsky, Peter, (2014). Corwin: Teaching Dilemmas & Solutions in Content-Area Literacy
