What is Mathematical Literacy
While literacy in mathematics may be different from the traditional literacy we find in an English classroom, it is just as critical. What counts as reading and writing looks very different in mathematics but communication is still a key part of the discipline. Mathematics has a very specific and precise language and in order for students to be mathematically literate they need to be able to communicate clearly in that language by understanding the vocabulary, symbols, and ways of formulating arguments.
Before students can engage in mathematics, they need to be to understand the vocabulary and be able to “read” and “write” using that vocabulary. Reading can take many forms as “reading in mathematics class can range from students ‘decoding’ an equation to reading paragraphs in a textbook to making sense of what a problem is asking” (Edelman & Hutchison, 2014, p. 83). Just as having a sizable English vocabulary is a prerequisite for being able to read a novel in English, having a mathematical vocabulary is necessary to proceed in the discipline. If students do not understand “the setting, the vocabulary, or meaning of the questions or tasks to be solved, they will not be able to continue the problem” (Koesling & Miller, 2009, p. 70). Students need to know what mathematical words mean when reading a paragraph but they also need to know how to read graphs and equations which involve symbols and visual representations of data. They also need to understand how to “write” using these forms to correctly convey their ideas. Once they have a vocabulary, they need to learn how to use it appropriately.
One of the defining characteristics of mathematics is its precision. In order to be understood by other mathematicians, students need to be taught to communicate using the correct mathematical terminology and syntax. I think the first step is to introduce vocabulary and different ways of representing ideas in mathematics and then, once the students feel comfortable with the language, we can focus on teaching them the nuances of the language that they need to be truly literate. When disciplinary experts were consulted about what it meant to be literate in their field “the mathematicians were 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” (Shanahan & Shanahan, 2008, p. 52). Students need to be taught exact notation, when to use it, and, most importantly, why they are using it the way they are. In my own experience tutoring students in college math classes, many of them would come to me to look over their exams and they would get half the points taken off problems solely for notation errors. They knew what the problem was asking and how to solve it but they did not know how to correctly and precisely express their answer. Often times their teachers had not taken the time to show them how to use notation correctly so I think that teachers should make a conscious effort to incorporate notational instruction along with their conceptual instruction. It was always heartbreaking for me to tell those students with notation errors that they had the right process and answer but their missing equal sign completely changed their argument. Students need to learn to communicate as professional mathematicians do and I do not think they should be able to get away with “the right gist of an answer” because “literacy implies an integrated ability to function seamlessly within a given community of practice” (De Lange, 2003, p. 72). We should want them to leave school with the ability to correctly communicate with professional mathematicians in college or in their careers. While learning the precise mathematical language is difficult, and sometimes tedious, it can be incredibly rewarding. To a student well versed in mathematical language the theorem shown in figure 1 is packed with meaning. Students can understand a lot from it without getting bogged down by paragraphs of words. Precision allows for succinct logical arguments that can be understood by everyone in the field.
Having a basis of knowledge about vocabulary and notation is important but if students do not know how to reason through problems, that knowledge is useless. The ultimate goal for literacy in mathematics is that students can use reasoning to solve complex problems and then present their answer using the correct language. In his TED talk Math Class Needs a Makeover, high school math teacher Dan Meyer (2010), laments that math education in American often skips over teaching students reasoning. It is much harder to teach than just plugging into formulas but it is infinitely more beneficial if we want students to retain what they learn in math class and actually be able to solve complex, real-world problems. He argues that the problem with mathematics education is that students are becoming literate in “decoding a textbook” but not in the discipline (Meyer, 2010). Textbooks and teachers give students that exact information they need, the steps needed to solve the problem, and the format to use when presenting the answer. We take inquiry and motivation for solving a problem away from the students because we “just give problems to students; we don’t involve them in the formulation of the problem” (Meyer, 2010). We need to give students a foundation of knowledge and help them know how to use it. When working on a problem “literacy becomes the tool that lets them access and assess math concepts, bringing together formerly disparate skills and approaches to solving problems into a coherent whole” (Koesling & Miller, 2009, p. 77). Mathematically literate students have the ability draw on their mathematical knowledge from different contexts to solve complex problems.
By the time they leave high school, mathematically literate students should be able understand how to “read” and “write” using mathematical vocabulary, notation, and ways of representing data appropriate to the context. They should be able to use mathematical reasoning and standard arguments to solve problems and present their solutions using precise language in a way that any mathematician could understand.
De Lange, J. (2003). Mathematic for Literacy. In B. L. Madison & L. A. Steen (Eds.), Quantitative Literacy: Why Numeracy Matters for Schools and Colleges (pp. 75–89). United States: Woodrow Wilson Natl Foundation.
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.
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.
Meyer, D. (2010, March). Math class needs a makeover [Video file]. Retrieved from https://www.ted.com/talks/dan_meyer_math_curriculum_makeover/transcript?language=en#t-450000
Peterson, J. (2017). Riemann Integral Properties [PowerPoint slides]. Retrieved from http://cecas.clemson.edu/~petersj/Courses/M454/Lectures/L12-RIProperties.pdf
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
