What does it mean to be mathematically literate?
Literacy is quite the term. When I started my teaching career as an English educator, I assumed that literacy was my domain. As I continued teaching and studying education, it became clear that literacy is all encompassing. I learned about the ways students could become literate in science, social studies, and more recently, racially literate. For some reason, none of these literacies seemed out of my reach, and then entered math. Math has always been a tough subject for me, and in this conversation, I was able to again sit down with Bob Janes, Secondary Supervisor of Mathematics for East Hartford Public Schools (revisit our first conversation, on equitable assessment, here), and talk about what literacy in math looks like.
How would you define literacy as a math teacher?
Literacy in math is the ability to understand and communicate mathematics in a variety of forms. I typically use the following definition from the The Connecticut Common Core of Teaching (CCT) Rubric for Effective Teaching 2017:
Thinking about the definition as conveying meaning and understanding meaning in a variety of forms, how does that show up in the math classroom?
It shows up in a variety of ways. I’ll go through a few different modalities.
Students should be able to read about a scenario or context and apply mathematical understanding to it, often called mathematizing, decontextualizing, or modeling. Students should also be able to read a mathematical text and understand common notations and representations. This includes algebraic notation, tables, charts, and graphs. We call these processes decontextualizing and contextualizing.
Students should also be able to justify their ideas in text using the same notations and representations that they are able to read (e.g. sentences, algebraic notation, tables, charts, and graphs).
Speaking and listening
Students should be able to listen, interpret, and critique their peer’s ideas. They should also be able to share and support their own ideas.
Students should be able to recognize and use both Tier II and Tier III vocabulary with precision while reading, writing, speaking, and listening.
This one is more math specific than the others. Students should be able to draw connections between different representations and understand when one representation is more advantageous than another. For example, suppose students were analyzing the freefall motion of a skydiver. A paragraph, an algebraic function, and a graph would all reveal different information about the scenario, and taken together, they provide a more complete understanding.
Unfortunately, I’ve seen the opposite of this in many math classrooms, what some might call “plug and chug”. If teachers are stuck providing worksheets and asking students to fill them out to “demonstrate mastery”, how can they change their classroom practices to ensure students are literate in mathematics?
We often shy away from giving our students tasks that ask them to read, write, speak, and listen in math class because we think that they will struggle. We also think that students who already find math content difficult will be completely exasperated by integrating literacy skills. Unfortunately, it is nearly impossible to build literacy skills in a vacuum. We must start by exposing our students to high-quality, standards-aligned tasks that promote the use of literacy skills. Then, we use literacy strategies to support students within the context of these tasks.
There are a number of great resources out there to choose from when selecting tasks. Curriculums that are aligned with the Common Core State Standards (CCSS) for Mathematical Practice (MP) typically include opportunities for students to read, write, speak, listen, work with vocabulary, and draw connections between representations. My favorite curriculum to pull from is Illustrative Mathematics, and my two favorite instructional routines are Three Act Tasks and Which One Doesn’t Belong.
A distinguishing feature of the tasks and routines linked above is that they all give students something to discuss or think about. This includes tasks that give students different starting information, tasks that have multiple solution methods, and tasks that have multiple answers. Robert Kaplinsky calls these approaches “Open Beginning”, “Open Middle”, and “Open Ended” and even has a website dedicated to these types of tasks.
This all sounds fantastic, but what if a high school student was not exposed to this kind of literacy in previous grades? What are some strategies teachers can use to help students develop math literacy?
I’ll talk through a few of my favorites, although there are a number of strategies and routines that are great for supporting student’s literacy skills. It’s important to understand that none of these strategies will cause immediate success. Students who are not accustomed to literacy in math class may struggle at first, but over time they will begin to use these strategies on their own.
I like to use the three reads protocol when reading word problems. Different groups have their own tweaks on the protocol (e.g. LAUSD, SFUSD, Kelemanik & Lucenta), but the structure is generally the same. Students read the first time to understand the context, a second time to identify important quantities, and a third time to interpret the problem.
Students can also use annotations or highlights as they are reading to identify important information. When working on an interdisciplinary team, I like to use common annotations for text so that students can see the connections between subject areas; however, we can annotate more than text in math class. Tables, graphs, and even visual patterns are great places to make meaning through annotation.
Other disciplines have their own response structures such as RACE or CER. Just as with annotations, I prefer to use a common response structure with other disciplines.
Speaking and listening
I’ve found that talk moves can help students get started when they don’t know what to say. Talk moves can be prompts from the teacher, visuals for students to see, or both. Other educators use similar techniques such as sentence frames or discourse cards, and have created extensive lists of prompts and stems to get students talking. I think it’s up to the teacher to choose what works best for their students.
I would be remiss not to talk about Building Thinking Classrooms by Peter Liljedahl. While not technically literacy strategies, I have observed the 14 practices in this book promote more student to student discourse than I have ever seen in a math classroom. It’s worth a read!
Many students find active listening and comprehension in real-time challenging. While this is the ultimate goal, technology such as EdPuzzle can be used to slow down videos and provide frequent comprehension checks.
Vocabulary is one that I still personally struggle with. The traditional approach is to front-load vocabulary instruction, where a teacher explicitly teaches new vocabulary terms before they are used in context with the thought that students will not be able to understand the subsequent lessons without the vocabulary.
However, I have found that many students do not need front-loaded instruction. Instead, many students learn vocabulary terms best when they are introduced only when needed, and when instruction is embedded within the context of the lesson. For example, students are asked to describe different parts of a graph and begin to use informal language. They might quickly discover that their informal language is imprecise and has limits. At this point, the teacher would step in to support students either with formal vocabulary or with an instructional routine that allows students to build their own vocabulary (e.g. Stronger and Clearer Each Time). In my experience, more students are able to attach meaning to the vocabulary using this approach than using the front-loading approach, but it will be up to the teacher to meet the needs of their students.
Teachers should spend substantial instructional time for students to use, discuss, and connect representations. In the book Routines for Reasoning, Grace Kelemanik and Amy Lucenta suggest using an instructional routine to allow students to make connections and share them with their peers. Teachers can also be explicit about connections by using annotations to connect specific parts of each representation with arrows.
Is that it? Tasks and strategies?
All of this falls apart unless the teacher gives students specific and actionable feedback. It’s not enough for students to simply complete the tasks and apply the strategies we’ve talked about. Students need to know when they’re communicating effectively, and what they can do to improve. Error analysis routines and exemplars can be helpful in this regard.
What if teachers want to learn more?
There are a few places to visit if you want a deeper dive. The work done by Stanford University’s Center for Understanding Language (UL) is particularly helpful. They have developed a series of design principles and math language routines to support language and content development. Jeff Zwiers is the director of professional development for UL, and his website has even more tools to support authentic communication across the disciplines. More recently, The New Teacher Project (TNTP) created a Student Experience Toolkit for Math Instruction for Multilingual Learners that builds on the work of UL. These resources provide a great next step to learn more about literacy in math education.