Sometimes what we say or what we intend to say is not understood by those with whom we are speaking. In classrooms where a specialized vocabulary and structure of communication are necessary for academic success, teachers must be aware of any factors that might impede students' success. In mathematics, for example, language is the primary medium for constructing, sharing, and expanding ideas. Being both proficient with and understanding mathematical language in the form of vocabulary, symbols, expressions, definitions, and so on, are important. Therefore, it is critical for mathematics teachers to consider problems that students might be having with the language of mathematics.

### Beth A. Herbel-Eisenmann

A way to introduce and use mathematical language in mathematics classrooms that draws on multiple representations and student language.

### Diana F. Steele

The past decade has been a time for much discussion about the influence of social interaction on the development of mathematical understanding. The roots of this discussion can be traced back to the ideas of Lev Vygotsky, a Russian psychologist who conducted research during the 1920s and 1930s. He was interested in how children conceptualize the meanings of words. He concluded that social interaction and communication are essential components in this conceptualization process. To show how children learn mathematical language, this article examines a classroom vignette and demonstrates how Vygotsky's ideas can be put in action in the mathematics classroom. The NCTM's Standards documents (1989, 1991) emphasize the importance of social interaction and communication in learning mathematics. Mathematics as communication is a common thread woven throughout all levels of these documents.

### Kristen Lew and Juan Pablo Mejía-Ramos

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.

### Rusty Bresser, Kathy Melanese and Christine Sphar

Learn how to focus mathematical language on concepts to accommodate the needs of the 10 percent of U.S. students whose first language is not English.

### Karen M. Higgins

Teachers use “studio” time to review videotaped classroom episodes, learn about students' developmental levels in geometry, and increase students' use of mathematical language and vocabulary.

### Marvel Hess

Number sentences interest and aid second- grade children in solving problems. A sequence of developmental stages enables children to acquire skills in translating problem situations into mathematical language. A brief description of activities in problem-solving follows.

### Louis S. Cohen

Open number sentences are useful in finding solutions of verbal problems. To write open sentences for problems, one must be able to translate verbal phrases and sentences into mathematical language. Mathematical sentences, much like English sentences, are made up of phrases and verbs. It is the combination of these phrases and verbs that will make the mathematical sentence complete.

### Edited by Marcy Cook

Ideas for this month focuses on forming numbers to meet specific requirements. Careful reading of information and understanding of mathematical language are important to finding appropriate solutions. Using the problem-solving strategies of looking for patterns and establishing an organized list will aid students in finding all the possible solution sets.

### Bradley r. Jones, peggy F. hopper and dana pomykal Franz

[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.