Mathematical Literacy?  Disciplinary Literacy?  We Need and Want Both.

By Kathy Berry, Monroe County ISD; Cherron Ramsey, Wayne RESA; Marcus Deja, Kent ISD; Brad Thornburg, Gratiot-Isabella RESD; and Karen Reister, Traverse Bay Area ISD

Think for a moment about literacy in the mathematics classroom.  What comes to mind? Do you immediately see word walls of mathematics vocabulary?  Writing in math journals?  Vocabulary strategies?  Or do you think of students connecting ideas from geometry and algebra together to solve and model problems?  Maybe you envision students individually and collaboratively analyzing a problem situation and determining multiple possible solution paths.  For each of us, our own past learning and experiences influence our reactions to “literacy.” It may be helpful to pause and seek clarity around the ideas of students becoming mathematically literate while using the tools of disciplinary literacy. 

We want all students to be both critical thinkers and problem solvers. We and our students cannot dig deeply into mathematics nor make connections across topics and grades/courses without communicating our mathematical thinking. We want each learner to be able to access, use, and produce all types of mathematical text. Mathematics as a discipline includes a rich, and at times bewildering, collection of text types, including (and certainly not limited to):

• viewing, manipulating, and making mathematical models; 

• writing and using expressions, inequalities, equations and functions; 

• problem scenarios stated in words, as well as combinations of words and other text;

• diagrams, tables, graphs, sketches, and physical models;

• analyzing and constructing explanations, justifications, arguments, and proofs - expressed verbally, visually, and demonstratively;

• using a variety of tools from low-tech (paper folding, number lines) to high-tech (Desmos, Excel) to justify, model, and share their ideas; 

• photos and video, audio recordings, demonstrations, and presentations; and,

• prose, from students’ written work peppered with many of the above items to recreational mathematics, articles, and books (including mathematical novels!).
  
  

As students use, create, and share mathematical ideas using these and other kinds of mathematical text, they are learning and using disciplinary literacy. Simultaneously, they gradually become mathematically literate, able to think about and use mathematical ideas, skills, and habits of mind. Disciplinary literacy provides the language through which mathematical literacy grows, is used, and is shared. When we equip every student to use a full range of communication strategies and tools - including those particular to the discipline of mathematics - we also enable them to identify themselves as knowers and doers of mathematics. With these strong mathematical identities, they can comfortably and ably apply mathematical thinking and tools in a wide variety of abstract and real-world situations, which may be the most practical outcome of being literate in mathematics.

Mathematical literacy doesn’t just happen on its own for our students; we educators set the environment, resources, tasks, and supports to grow this in our students.  In the same way, disciplinary literacy doesn’t just happen either. We intentionally select and use disciplinary literacy practices to engage students in learning mathematics, to process and apply and connect that learning, and to seek evidence of their understanding.

In the glossary of the Essential Instructional Practices for Disciplinary Literacy in the Secondary Classroom (the Disciplinary Literacy Essentials, or DLEs), we find a definition of literacy (p. 33) which was informed by prior literacy theory and scholarship. This definition states that

literacy is framed as a set of socially constructed (developed by people through interaction) practices that use some form of a symbol system to communicate meaning, along with a technology to produce and share it. Therefore, literacy is more than just the skill sets of reading and producing different forms of texts; it also includes the application of these skills "for specific purposes in specific contexts of use" (Scribner & Cole, 1981). Literacy then provides the means to access, process, and communicate information. It is central to all academic disciplines and should thus be included as an important component in disciplinary instruction.

So let’s peel this apart a bit.  We might notice key phrases and think about how they might relate to what we know about high-quality mathematics teaching and learning:

Literacy Characteristics	High-Quality Mathematics Teaching & Learning Characteristics
Socially constructed	Include partner, small group, whole class interaction and collaboration
Uses a symbol system to communicate meaning	No shortage of symbol systems here!  Numerals, equations, diagrams, graphs, tables, matrices, words, labels...and mathematical symbols (%, !, ∠, ⟂… )
Uses a technology to produce and share	Writing, drawing, graphing, video and audio recordings, manipulatives, technology tools…
Reading different forms of texts	Symbolic forms, graphs, diagrams, sentences, paragraphs, arguments, prose, drawings…
Producing different forms of texts	Produce all types of mathematical text for a variety of audiences and purposes
Applying all of the above in context	Solve problems; reason; make and critique arguments; model; use tools; be precise; find, recognize, and generalize patterns
Access information	Obtain mathematical and other needed information from a wide variety of sources
Process information	Comprehend, apply, analyze, synthesize, evaluate; connect, calculate, reflect, use tools
Communicate information	Share thinking using a variety of techniques and tools appropriate to the task, audience, purpose, and desired effect (explain, argue, inform, persuade, etc.)

Thinking about this exploded form of the definition, we readily see how disciplinary literacy is inextricably interwoven into teaching and learning mathematics.  Only by engaging in disciplinary literacy for mathematics can any of us communicate mathematically and make meaning. Through this meaning-making and communicating of mathematical ideas with others, we become knowers and doers of mathematics; we add “mathematician” to our identity.

We encourage you to read the mathematics DLEs.  From the bulleted items you will likely recognize strategies you are already intentionally incorporating into your planning, instruction, and assessment.  You may also find you have a number of questions.  You’re in good company!  Colleagues across the state are asking: What exactly is “text” in mathematics?  Where is the disciplinary literacy in my Geometry class/unit? What is “problem based” (DLE 1) for my mathematics courses?  And of course, “How might I even begin???”

Future blog posts will tackle these and other questions.  We encourage you to submit your questions to our team via the contact link for Cherron Ramsey on the MAISA GELN home page for Disciplinary Literacy.  On that same page, sign up for the mailing list, check out the professional learning opportunities, and follow us at #disciplinaryliteracy.