Opportunities for communication—in particular classroom discourse—are foundational to the problem-based structure of the IM curriculum. The National Council of Teachers of Mathematics’s Principles and Standards for School Mathematics (NCTM, 2000) states, “Students, who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes, reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically.” Opportunities for each action are intentionally embedded directly into the curriculum materials through the student-task structures and supported by the accompanying teacher directions.

One highly visible form of discourse is students’ discussion during the lesson. Another, less visible form of discourse is writing. While this often is seen only as the written responses in a student workbook, journal writing provides an additional opportunity to support each student in their learning of mathematics.

Writing is a useful catalyst in learning mathematics because not only does it supply students with an opportunity to describe their feelings, thinking, and ideas clearly, but also it serves as a means of communicating with other people (Baxter, Woodward, Olson, & Robyns, 2002; Liedtke & Sales, 2001; NCTM, 2000). The NCTM (1989) suggests that writing about mathematics helps students clarify their ideas and develop a deeper understanding of the mathematics at hand.

To encourage journal writing in math class, use the list of journal prompts at any point in time during a unit and across the year. These prompts are divided into two overarching categories: Reflecting on Content and Practices and Reflecting on Learning and Feelings about Math.

Prompts for the first category  focus on students’ learning, or on specific learning objectives in each lesson. Students reflect on the mathematical content because the act of writing generally entails careful analysis, encouraging the explicit connection between what is known and new knowledge, which becomes incorporated into a consciously constructed network of meaning (Vygotsky, 1987). For example, when students write about ways in which the math they learned in class that day is connected to something they know from an earlier unit or grade, they explicitly connect their prior and new understandings.

Prompts for the second category are more metacognitive and focus on students’ feelings, mindset, and thinking around using mathematics. Writing about these subjects promotes metacognitive frameworks that extend students’ reflection and analysis (Pugalee, 2001, 2004). For example, as students describe an aspect of a lesson they found challenging during a lesson, they have the chance to reflect on the factors that made it a challenge.

John Dewey (1933) asserted that students make sense of the world through metacognition, making connections between their lived experiences and their knowledge base, and argued that education should offer students opportunities to make connections between school and their lived experiences in the world. Ladson-Billings encourages the idea that teachers must help students effectively connect their culturally- and community-based knowledge to the learning experiences taking place in the classroom. These beliefs support the need for students to reflect continually not only on the mathematics, but on their own beliefs and experiences as well. 

Use the prompts given here at any point during the year, regardless of category. Use them as discussion prompts between partners, or students can establish a math journal at the beginning of the year and record their reflections at the beginning, in the middle, or at the end of lesson, depending on the prompt. For schools or districts that require homework, the prompts serve as a nice way for students to reflect on the learning of the day, or to ask questions they may not have asked during the class period. As noted, some prompts may lead students to consider aspects of the Standards for Mathematical Practice (MP). 

Journal writing not only encourages explicit connections between current and new knowledge and promotes metacognitive frameworks to extend ideas, but also offers opportunities to learn more about each student’s identity and math experiences. Writing in mathematics offers a means for teachers to forge connections with students who typically drift—or run rapidly—away from mathematics and offers students the opportunity to continually relate mathematical ideas to their own lives (Baxter, Woodward, and Olson, 2005). Writing prompts and journaling work well because students who may not advocate for themselves when they are struggling, get their voices heard in a different way, and thus their needs met (Miller, 1991).

Use these questions and prompts with the intention that students communicate to learn mathematics and  learn to communicate mathematically.

Reflecting on Content and Practices

• What math did you learn and do today that connected to something you knew from an earlier unit or grade?
• Describe a time you used math outside of school. 
• How did your thinking change about something in math today?
• How did any predictions you made in class today work out? Why do you think that happened? 
• What questions do you still have about the math today? What new questions do you have? 
• Describe the way you solved a problem in class today that makes you proud.
• Where do you see the math you did in class today outside of school? (MP4)
• What math tool did you find most helpful today? Why? (MP5)
• What patterns did you notice in the mathematics today? Why did that pattern happen? (MP7, MP8)
• Starter prompts:
  • The most important thing I learned today is . . .Today, I struggled and worked through a problem when . . . (MP1)
  • I could use the math that I learned today outside of school when I . . .
  • At the end of this unit, I want to know how to . . .
  • I knew my answer was right today when . . .
  • Another strategy I could have used to solve a problem today is . . .
  • The most important point to remember about the strategy we used today is . . .

Reflecting on Learning and Feelings about Math

• Describe something you understand well after today’s lesson, or describe something that was confusing or challenging.
• In math class, it’s important to explain your thinking. Describe a time when you explained your ideas to other people in your class. (MP3)
• In math class, it’s important to listen to other people’s ideas. Describe a time when you learned something by listening carefully to someone in your class. (MP3)
• What does it mean to be “good at math”?
• Describe a time when you asked a question about the math that you were doing. How did asking a question help you?
• If you could change anything about math class, what would you change? Why?
• Starter prompts:
  • I learned from a mistake today in math when . . .
  • When it comes to math, I find it difficult to . . .
  • I love math because . . .
  • I felt heard during class today when . . .
  • I felt my ideas were valued during class today when . . .
  • The most helpful thing that happened today was . . .