Abstract:  A student’s ability to explain concepts in writing is related to the ability to comprehend and apply them. Writing supports mathematical reasoning and problem solving and helps students adopt the characteristics of effective communication by helping strengthen their thinking while requiring them to reflect on their work and clarify their thoughts about the ideas. This paper illustrates how writing in mathematics give the instructor a window into the students’ thoughts that are normally not apparent when they are just asked to compute problems and barriers giving instructors ways aid in their comprehension.

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Teaching students to write well must be a part of any comprehensive mathematics program. Strategies that require students to demonstrate their knowledge of mathematics also provide opportunities to practice writing for real audiences. For writing in mathematics to impact student learning, it must be more than just copying the notes given in class. Information must be personalized in some way. Students must be expected to include reflections and questions when they write. By making these personal connections, students will begin to develop a conceptual understanding of the mathematics they are exploring in their studies (Burn, 2004). Many mathematics educators feel that students should already know how to write effectively when they come to their classrooms. This is not usually the case, however. Students have learned to, but they usually do not know how to apply these skills to mathematics. Mathematics teachers will find that they may have to explicitly teach and provide scaffolding for each of these strategies before their students will be able to implement writing in mathematics.

Learning mathematics is much more complex than memorizing sets of facts and examples. In order to develop new and/or improved conceptual frameworks, students must be given the opportunity to process their ideas before, during, and after new learning takes place. This can be done orally, mentally, or in writing. Writing in mathematics classrooms can take many forms and serve a variety of purposes. One form is the use of contextualization as a strategy for sense-making. As teachers try to build students’ conceptual understanding of abstract ideas, they can encourage students to create contexts that help them visualize elements like the relationships between values or the actions of operations (Urquhart, 2009). Creating real-life scenarios of abstract concepts can make the mathematics feel more intuitive and natural when done correctly. What’s most important is that writing in math class feels meaningful to students. If students only write so that we can evaluate their learning, they will not see writing as something that has personal meaning to them. However, if students are involved in engaging tasks, they are more eager to write about their ideas, because that thinking is important to them. Student should be encouraged to access the math to be learned and connect key representations.  Instructors need to open a window into their students’ thinking and current understandings; while having them engage in the mathematical practices of constructing viable arguments, critiquing the reasoning of others, and clarifying their own thinking.

Teachers can encourage students to write contexts to describe the mathematical concepts they are exploring to help them deepen their understanding of abstract ideas. When students contextualize the mathematics, they provide a familiar frame of reference from which they can make sense these ideas. This form of writing can be very powerful in math class and can make a big difference in students’ understanding.

Writing is thinking, but that thinking doesn’t always look the same. In math, students must organize and clarify information while planning for, reflecting on, and revisiting possible solutions to problems. Interestingly, these skills are exactly the ones required in writing. Often, the very process of writing clarifies thinking to such an extent that students experience a mathematical epiphany that brings everything together. Writing can become a critical tool for teachers to use in helping students unlock understandings.

There are several tools that can be used in writing for mathematical reasoning.  Using journals can help students on reflection on their learning or confusion with the content.  Essays about how to use math in real world situations or where students defend their process or answers to questions.  Another strategy for adding writing into the math classroom is having students write their own math word problems. This is effective for evaluating a student’s level of understanding about an operation. This writing strategy can reveal important math tactical issues, for example, if a student’s division word problem has a larger divisor than dividend. Effective writing also clarifies and organizes a student’s thoughts, and the slow pace of writing is beneficial to student learning because it allows them to reason carefully to make sure they’re correct before they state their thoughts. A student’s ability to explain concepts in writing is related to the ability to comprehend and apply them.

Writing in mathematics can also help students strengthen their thinking because it requires them to reflect on their work and clarify their thoughts about the ideas (Countryman, 2012). It also can reveal a student misconception.  Students may be able to execute an algorithm or select a correct multiple-choice answer, but do they truly understand the mathematical concepts? 

Writing, and communicating, about math is a skill used in everyday life. In our day-to-day lives, most of us communicate about math more than we do math. A letter to dispute the phone bill; the sales pitch to a client; the baseball statistics debated with a friend; math happens in a world of words. Students need to be able to clearly communicate and write about the math they encounter in their lives. The writing about mathematics and mathematical ideas can become a powerful component of the learning process which leads to a journey of discovery.

References

Burns, M. (2004). “Writing in Math.”  Educational Leadership, 62:30-33.

Burns, M. (2005) Writing in Math Class. Math Solutions Publications.

Countryman, J. (2012).  Writing to Learn Mathematics: Strategies That Work. Portsmouth, NH: Heinemann.

Urquhart, Vicki. “Using Writing in Mathematics to Deepen Students Learning.”  McREL, 2009.