Why Attention to Vocabulary in Math is Important

Learning math is like learning a second language (Kenny et al., 2005). When learning any second language, it is essential for students to talk, write, and read in that language. Talking, writing, and reading are important types of communication for learning mathematical concepts, procedures, and applications (National Research Council, 2001; NCTM, 2014; CCSSM, 2010; Hattie, Fischer & Fry, 2017). Language plays an important role in mathematics just as language is critical in learning other school subjects (Schleppegrell, 2010). Not only is “depth of word knowledge the most reliable predictor of English learner academic achievement across grade levels and curriculum . . . [but] mounting research has highlighted the benefits of planned, intentional vocabulary instruction to support literacy and content learning for all students” (Kinsella, 2017). Communicating about math requires facility with mathematics vocabulary, which makes teaching math vocabulary a priority (Fogelberg et al., 2008).

Challenges with Mathematical Vocabulary

Schleppegrell described mathematics as a multifaceted language that is “conceptually dense.”  Students must constantly learn new mathematical ideas in large part through the integration of several aspects of mathematical language that includes specialized words and academic language along with “the language of mathematics symbolism” – the meaning constructed through visual representations such as graphs, charts and diagrams (2010). Additionally, math-specific terms, words with multiple meanings, and small words are causes of confusion for students (Fogelberg et al., 2008).

The chart above provides examples of words and word types that add to the challenges with mathematical language. Schleppegrell also identified several semantic challenges with mathematics (2007, pp. 143-144).

• Long dense noun phrases, such as,

The volume of a rectangular prism with sides 8, 10, and 12 cm

• Classifying adjectives that precede the noun, such as,

prime number, rectangular prism

• Qualifiers that come after the noun, such as,

A number which can be divided by one and itself

• Conjunctions, such as, If, when, therefore, given, assume, etc.

Reading in math is a necessary skill. Math textbooks, which serve as a primary resource, are one important part of students’ mathematical education. Word problems, application problems, and challenging tasks are also a vital part of learning, understanding and applying mathematics (Hattie et al., 2017; NCTM, 2014; National Governors Association, 2010; Smith & Stein, 2005). However, struggles with math vocabulary can greatly inhibit students’ ability to decipher what they read. The greater the vocabulary knowledge the greater is one’s ability to read with comprehension (Brummer & Kartchner Clark, 2014; Honig, Diamond & Gutlohn, 2013). In order to understand mathematics, students need to understand the language of mathematics.

To define fraction a student must demonstrate understanding of the mathematical idea of a fraction. An example of a vocabulary activity for the term fraction is the use of a Frayer Model (Frayer, Frederick, & Klausmeier, 1969). The Frayer Model diagram shown to the right illustrates how the understanding of fraction is deepened, reinforced and/or developed as a student creates and completes this chart.

Students should also be required to use specific math vocabulary both orally and in writing beyond vocabulary-specific activities. The California Department of Education finds that teaching math vocabulary in context is “essential for instruction” and goes on to provide an excellent set of recommendations (2015, p. 685).

• Explicitly teach academic vocabulary for mathematics, and structure activities in which students regularly employ key mathematical terms. Be aware of words that have multiple meanings (such as root, plane, table, and so forth).
• Provide communication guides, sometimes called sentence frames, as a temporary scaffold to help students express themselves not just in complete sentences but articulately within the MP standards.
• Use graphic organizers and visuals to help students understand mathematical processes and vocabulary.

Mathematical Language Routines (MLRs) (Zwiers et al., 2017) are an excellent set of evidence-based techniques to assist students with math discourse and with understanding and solving math word problems. The eight MLRs are designed for high levels of student engagement with mathematics texts and discussions. Teachers need to implement techniques that are explicitly designed to assist students in understanding the language of mathematics.

Conclusion

Attention to math vocabulary is an essential part of math instruction. Attention must be given to the variety of challenges students face when learning and using the language of mathematics, such as, math specific words, words with multiple meanings, small words, and semantic challenges (for example, long dense noun phrases). Teachers must explicitly draw attention to mathematical terms as they arise throughout instruction by illustrating the meaning of the terms, helping students associate images with terms (Marzano et al., 2001) and providing constant reinforcement. Teachers can further improve learning by implementing other evidence-based techniques, such as the eight Mathematical Language Routines. Teachers need to keep in mind that math vocabulary goes hand-in-hand with math concepts. Learning math vocabulary in meaningful ways increases students’ learning of mathematics.

Bibliography

Braselton, S., & Decker, B. (1994, November). Using graphic organizers to improve the reading of mathematics. The Reading Teacher, 48(3), 276-281.

Brummer, T., & Kartchner Clark, S. (2014). Writing Strategies for Mathematics. Huntington Beach, CA: Shell Education Publishing Inc.

California Department of Education. (2015). Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve (pp. 661-697). Sacramento, CA: Author. Retrieved from http://www.cde.ca.gov/ci/ma/cf/mathfwchapters.asp

Fogelberg, E., Skalinder, C., Satz, P., Hiller, B., Bernstein, L., & Vitantonio, S. (2008). Integrating Literacy and Math Strategies for Kñ6 Teachers. New York, NY: The Guilford Press.

Frayer, D. A., Frederick, W. C., & Klausmeier, H. G. (1969, April). A schema for testing the level of concept mastery [Editorial]. Working Paper No. 16.

Hattie, J., Fisher, D., & Frey, N. (2017). Visible Learning for Mathematics. Thousand Oaks, CA: Corwin.

Honig, B., Diamond, L., & Gutlohn, L. (2013). Teaching Reading Sourcebook (2nd ed.). Novato, CA: Arena Press.

Kenney, J. M., Hancewicz, E., Heuer, L., Metsisto, D., & Tuttle, C. L. (2005). Literacy Strategies for Improving Mathematics Instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

Kinsella, K. (2017, March). Helping Academic English Learners Develop Productive Word Knowledge. Language Magazine, 16(7), 24-29.

Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom Instruction that Works(pp. 74-83). Upper Saddle River, NJ: Pearson Education Inc.

National Council of Teachers of Mathematics. (2014). Principles to Actions Ensuring Mathematical Success for All. Reston, VA: Author.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.

National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.

Schleppegrell, M. J. (2007, February 24). The Linguistic Challenges of Mathematics Teaching and Learning: A Research Review. Reading & Writing Quarterly, 23(2), 139-159.

Schleppegrell, M. J. (2010). Language in Mathematics Teaching and Learning: A Research Review. In J. N. Moschkovich (Ed.), Language and Mathematics Education (pp. 73-112). Charlotte, NC: Information Age Publishing, Inc.

Smith, M. S., & Stein, M. K. (2011). Five Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics.

Zwiers, J., Dieckmann, J., Rutherford-Quach, S., Daro, V., Skarin, R., Weiss, S., & Malamut, J. (2017) Principles for the Design of Mathematics Curricula: Promoting Language and Content Development, Stanford, CA: Understanding Language/Stanford Center for Assessment, Learning, and Equity. Retrieved from https://ell.stanford.edu/sites/default/files/u6232/ULSCALE_ToA_Principles_MLRs__Final_v2.0_030217.pdf