## Reading & Writing in the Disciplines

# Reading in Mathematics

### THE READING DEMANDS OF MATHEMATICS CLASSROOMS

In mathematics classrooms, students encounter many different kinds of texts. There are likely to be textbooks or other instructional resources that are used to support student learning of the mathematics content of the grade level or course. There are problem sets or tasks that students are asked to solve during class time or for homework. There is material associated with mathematics assessments that students are asked to complete, usually independently and often under timed conditions, including some of the new assessment material associated with the Common Core State Standards for Mathematics (CCSSM).

Take a few minutes to look at the textbook you are currently using, the additional resources you draw on, and any assessments you are using with your students. Try to find examples of these mathematics materials:

- Explanations of mathematics content that include narrative text, mathematical expressions or equations, and representations such as tables, graphs or other images
- Sets of mathematics problems or tasks that students are to engage in and solve
- Lists of mathematics vocabulary that students are expected to know and use as they communicate their mathematical thinking
- Mathematical notation that students are expected to understand and be able to use in their mathematical work
- Samples of student work displaying a range of strategies for solving particular mathematics problems, some correct and some incorrect, for analysis and discussion

**Reflect: **What are the literacy demands associated with reading and making sense of the range of mathematics materials that students are likely to encounter in your classroom?

What do you think would be challenging for students as they read and try to make sense of this range of mathematics material? What strategies might you use to help students understand and engage in the range of mathematics material they are likely to encounter over the course of the year? In what ways does this mathematics material itself offer support for student sense making? These are all important questions to consider in relation to the literacy demands associated with the discipline of mathematics and what it takes to be successful in this field.

### INSTRUCTIONAL STRATEGIES THAT SUPPORT SENSE MAKING

The next set of videos highlights instructional strategies that teachers are using to support student engagement in making sense of a range of mathematics texts and other instructional resources. Each video highlights specific strategies designed to effectively engage students in becoming effective readers of a range of mathematics material.

**Video and Reflection: **Watch *Collaborative Talk About Mathematics*, which revisits the classroom where students work on exponential and logarithmic functions using a real-world context of earthquakes. You may want to take notes on the questions below.

**Before you watch:**How do you support student engagement in making sense of mathematics texts and other instructional resources? What indicators do you use to monitor whether these supports work?**Watch the video:**As you watch, pay attention to the reading demands in this high school mathematics classroom. Note the different ways Ms. Burow supports student engagement in making sense of the mathematics text.**Reflect:**In what ways does working collaboratively support student sense-making of mathematics text? What strategies do you see used in this classroom that might work in your own classroom?

**Video and Reflection: **Now watch *Deconstructing Word Problems*, in which students are working together in structured small groups to solve problems that involve representing situations algebraically and then finding a solution. Each small group includes a reader, translator, annotator, and double-checker. Each group also has a graphic organizer on which they capture their thinking. You may want to take notes on the questions below.

**Before you watch:**How do you support student engagement in making sense of mathematics texts and other instructional resources? What indicators do you use to monitor whether these supports work?**Watch the video:**As you watch, pay attention to the different roles students take on and the purpose of each role. Note the different ways Ms. Gay supports student engagement in making sense of the mathematical text as they enact these roles.**Reflect:**How do the assigned roles and the graphic organizer support student sense making of the mathematics text? What strategies do you see used in this classroom that might also work in your own classroom?

What if student collaboration to make sense of mathematics text is not a possibility? Sometimes it is important to see how well students can make sense of text as they solve mathematics problems on their own, particularly as you prepare students to engage in the rich non-routine mathematics tasks that are likely to be included in many assessments that reflect the expectations of the CCSSM. How might students learn to make sense of mathematics materials when they are working alone?

### EXPLORING SENSE-MAKING PROTOCOLS

Now that you have had the opportunity to view and reflect on videos of teachers engaging students in reading and making sense of mathematics material, you will experience a protocol designed to support your *own* reading and mathematical sense-making and consider how it might be used to support the reading and mathematical sense-making of your students.

**3 Read Strategy Activity**

In this activity, you will play the role of reader, translator, annotator, *and *double-checker to read, make sense of, and solve a rich mathematics task. As you work through the various parts of this protocol, reflect on how it supports your engagement with this mathematics material and how it helps you reach a solution to the problem that is posed. Also consider how this protocol might be used to support the engagement of individual students, students working with partners, or students working together in small groups. Click here to begin.

**Reflect: **How did the protocol support your engagement with the mathematics material? How might the protocol be used to support the engagement of individual students in your classroom? How might this protocol also be used to support the engagement of students working with partners or in small groups?

**Video and Reflection: **Watch *Annotating Word Problems* in which a high school teacher is working with students to make sense of a mathematics task. The problem has several parts and involves representing a range of situations with several inequalities. Students explore this task in their small groups, using a sense-making protocol, while the teacher circulates to observe their work and ask them about their thinking.

**Before you watch:**Think about what it would look like when students use a familiar sense-making protocol to support their mathematics reading and sense-making. What would it take to help students internalize a protocol so they begin to use it whenever they feel they need support reading and making sense of problems?**Watch the video:**As you watch, notice and take notes on how students use the protocol when working collaboratively, how students listen and respond to each other as they go through the protocol, and how students comment on what they learn as a result of using a protocol to support mathematics reading and sense-making.**Reflect:**What is Mr. Dinh’s role as students collaborate using their sense-making protocol? How does he support discussions that deepen students’ understanding of the mathematics in the task? What did you find new or interesting in this video that you might use in your classroom?

**Making Sense of Mathematics Text Activity**

The mathematics education literature includes a range of protocols designed to support student reading and sense-making of mathematics problems and tasks; some of these also build mathematical vocabulary. In the following activity, you will have the opportunity to explore several of these protocols and think about which ones might best serve the needs of your students. Please select one protocol to try in your own classroom. Click here to begin.

**Handouts referenced in the activity:**

Reading and Understanding a Mathematics Problem [PDF]

Mathematically Speaking [PDF]

Although there are a number of protocols designed to support student sense-making of mathematics problems and tasks, what is it these protocols offer students, and to what extent do they actually work? As Chapin, O’Conner, and Anderson (2013) point out, being able to read and make sense of mathematical problems is key to becoming a successful mathematics student and mathematician, so thinking about the role and effectiveness of sense-making protocols is an important question.

In order to be able to solve a mathematics problem, students need to be able to carefully read the problem, identify the important information in the problem, and devise a plan for solving the problem. Chapin et al. (2013) note that many “novice” problem solvers spend little time reading and making sense of the problem and, instead, jump right into finding a solution. They note the following:

Discussions about the givens in a problem can be extremely effective in developing students’ abilities to read carefully, to identify the important information in the problem, and to formulate a plan for solving [the problem]. . . . Good problem solvers ask themselves key questions about the given and unknown information in the problem. Talking about the facts in a problem broadens students’ knowledge base, helps them recognize the important information, and is a form of scaffolding for problem solving. Many students give up early in the problem-solving process because they do not understand the mathematical relationships inherent in the words. (p. 154)

In other words, protocols can help students “slow down” in their rush to find a solution to a mathematical problem so more time is spent on actually *understanding *the problem before finding a solution. All the protocols you have explored thus far provide these kinds of opportunities for students to read and make sense of a problem before beginning to work on a solution.

### WHAT DOES THE RESEARCH LITERATURE SAY?

What does the research literature say about the impact of these kinds of protocols on mathematics reading and sense making? Can these kinds of protocols help students make sense of a broad range of mathematics materials, including mathematics texts and other resources? Several researchers (Borasi, Seigel, Fonzi, & Smith, 1998) pursued this question by examining the use of “transactional reading strategies” in high school mathematics classrooms—meaning strategies designed to help students actively negotiate interpretations of text using their knowledge of language and their knowledge of the world.

The researchers explored the use of several protocols that high school mathematics teachers used to support student reading and sense making of a variety of mathematics texts. One important feature of the use of these protocols was that students were expected to stop and share questions and interpretations with a partner as they made their way through the material. Another important feature was that whole-class discussions followed the reading of these texts in order for students to share and discuss their interpretations of the material together.

These researchers found that the use of protocols combined with opportunities for students to share and discuss their interpretations of the texts did in fact provide students with effective strategies for understanding the mathematics content addressed in texts and also contributed to the development of new mathematical insights about that mathematics content. These findings suggest that sense-making protocols, while very useful tools for helping students read and make sense of mathematics materials, may be even more powerful when supported by small-group and whole-class discussion.

### THE IMPORTANCE OF SMALL-GROUP AND WHOLE-CLASS DISCUSSIONS

In *Classroom Discussions in Math: A Teacher’s Guide for Using Talk Moves to Support the Common Core and More*, Chapin, O’Connor, and Anderson (2013) describe a set of “talk moves” that teachers can use to (1) help individual students clarify and share their own thoughts; (2) help students orient themselves to the thinking of others; (3) help students deepen their own reasoning; and (4) help students engage in the reasoning of others. These kinds of talk moves provide useful tools for supporting student reading and sense making in mathematics, including when students are called upon to read and make sense of the mathematical work of their classmates.

Talk moves that help students clarify and share their own thinking include using wait time, turn and talk, “So, are you saying. . .?” (revoicing), and “Say more.” A talk move that helps orient students to the thinking of others includes “Who can repeat?” A talk move that helps students deepen their own reasoning is pressing for reasoning (“Why do you think that?”). Finally, talk moves that help students engage in the reasoning of others include “What do you think about that?” or “Do you agree or disagree . . . and why?,” and “Who can add on?” All of these contribute to rich small-group and whole-class discussions that support student sense making of mathematics texts.

Together, sense-making protocols, student collaboration in small groups as they use these sense-making protocols, and classroom discussions that are supported by these kinds of “talk moves” can help students successfully read and make sense of a wide range of mathematics texts. Importantly, small-group and whole-class discussions also provide teachers with opportunities to hear and think about how their students are making sense of these materials, thus providing important information that can then be used to shape instruction.

**Apply: **Think back to the videos that show students reading and making sense of mathematics materials. How did the teachers in these videos support small-group and whole-class discussions that helped students make sense of mathematics materials? How did these small-group and whole-class discussions provide teachers with information that could be used to shape their instruction? What teaching practices did you see in these videos that you would like to try in your own classroom?

### RECONNECTING WITH OUR MATHEMATICIANS

In the classroom videos you have seen, the students are making sense of mathematics in ways that reflect the authentic work of mathematicians. Mathematicians are regularly called upon to read and make sense of a range of mathematical problems that they often are seeing for this first time. They need to be able to determine what those problems are asking, identify what mathematics they might draw on as they explore possible solutions, and consider whether the solution they identify is justifiable and indeed does make sense. They need to be able to do this work collaboratively, with colleagues who are pursing similar mathematical questions, as well as independently. This is true for applied mathematicians who are using mathematics to find solutions for problems in the real world, often as part of a team, where a variety of perspectives are shared and discussed as the problem is addressed. This is also true for theoretical mathematicians who are working on rich mathematical problems that advance the field, sometimes working alone, but also talking with colleagues interested in similar mathematical questions or drawing on the published mathematical work addressing related problems.

An important question is how teachers might provide structured opportunities for students to read and make sense of a range of mathematical problems that they too may be seeing for the first time. How do the teachers in these videos organize and engage students in these structured opportunities? How do the protocols that are designed to offer support for reading and sense making do so? As you contemplate this question, it is important to keep in mind that there are times when students may need to read and make sense of mathematical text on their own as well as in collaboration with classmates and teachers. How do these strategies and protocols help students develop the expertise to also be able to do this work independently?

As you consider what you have seen in these videos, and as you reflect on your own experiences with the interactive protocols provided, consider how you can use what you are exploring here to support the engagement of your own students in the disciplinary literacy practice of reading and making sense of mathematical texts on an ongoing basis.