What I’m Reading this Week

When I think of the word “language” I think of a community of people communicating with one another using a specific vocabulary of symbols and words. I currently teach in one of the most diverse cities in the state of Michigan, with a robust international community and culture. There are approximately eighty-three different languages spoken amongst our students in our school district. In addition, in any classroom you will find a variety of needs and abilities for each individual student. With all these differences in languages, background and abilities, I cannot help but question what role does vocabulary play in learning mathematics? How can I best teach my students the “language” of mathematics?

grandma foreign language

We are all curious about new words we may hear in everyday life situations and often we want to find out their meaning. For many of my students, when they come across a word they don’t know they either skip it or create their own meaning for the word. “Rich development and understanding of mathematics vocabulary is essential for students to become actively engaged in mathematics past mundane computational requirements to thorough understanding and meaning making.” (Riccomini et. al 2015). As teachers, parents and students we need to be aware of the critical role that vocabulary plays in mathematics, other content areas, and in real-world situations. Interestingly enough, it begins even before students step foot into a classroom.

David Barner, director of the Language and Development Lab at UC San Diego conducted research on the importance of using numbers when you talk to toddles. Rather than relying on the memorization or sing-a-longs for 1-2-3 counting rituals, “number talk” can help with the comprehension of what numbers really mean. Barner says his study provides “the strongest evidence to date that the language a child speaks affects the rate at which they learn number words, and also that hearing number words in naturalistic speech – not just in counting routines and procedures – is a critical part of number word learning.” For some of my students with specific learning disabilities I see their reliance on songs they they have memorized for how to skip count or complete an equation. However, this does not indicate they know the true meaning of how or why they are performing the task, let alone the vocabulary and language being used. On the flip side, learning this insightful information gets me thinking….perhaps some of my students who come from a variety of backgrounds with different language origins have an advantage in the classroom that I have yet to explore and find a way to open up.


This videos below explain the many challenges of the language of math

So what can we do? How can we teach the language of mathematics? Let’s count the ways by reviewing a few articles that will provide helpful insight into ways in which we can incorporate different strategies to learn the language of mathematics.

#1 Graphic Organizers:

Graphic organizers have the potential to support the development of conceptual knowledge in content areas by efficiently displaying key ideas and the relationships among them (Hughes, Maccini, & Gagnon, 2003). In the article, Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

by Allan Zollman, he demonstrates how many of the reading and writing strategies we use with various graphic organizers can have a positive influence in mathematics as well. With the four corners and a diamond graphic organizer, students answer the following five important questions:

  1. What do you need to find? ~ state the problem
  2. What do you already know? ~ list the given information
  3. Brainstorm possible ways to solve the problem. ~ explain the methods for solving
  4. Try your ways. ~ identify math procedures in your work
  5. What things do you need to include in your response? What mathematics did you learn by working this problem? ~specify the final answer and conclusions

The key here is that students can work around the problem even if they are unsure of the final answer. Working through a story problem with this method would be a great way for teacher to identify quickly where their students are struggling and “see” their thinking process.


# 2 Using Representations

Another way to teach many mathematical concepts and operations is through a concrete-representational-abstract (C-R-A) sequence.

  1. Each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, beans and bean sticks, pattern blocks).
  2. Then, math concept/skill is modeled at the representational (semi-concrete) level which involves drawing pictures that represent the concrete objects (e.g. tallies, dots, circles, stamps that imprint pictures for counting)
  3. Finally, the math concept/skill is modeled at the abstract level (using only numbers and mathematical symbols)

Dr. Okolo from Michigan State University says “Representations are particularly advantageous for students with weaker reading and/or language skills, as visual representations may provide access to knowledge that is not possible through text”. In the article The Role of Representation(s) in Developing Mathematical Understanding Pape and Tchoshanov address some of the important practices that should be used in the classroom when using C-R-A. The four key ideas include:

  • Students need opportunities to practice representation
  • Representation is a “social activity” and should be performed with students interacting with one another
  • Instruction should be both analytic and geometric
  • Representation should be used as thinking, explaining and justifying tools

CRA example  new_tools.jpg

Image Source

# 3 Explicit instruction

Whether using you are using graphic organizer or manipulative it imperative that you use them in conjunction with explicit instruction. “Common elements of explicit instruction include logically sequencing key skills, reviewing prior skills and knowledge, providing step-by-step teacher models of new skills along with opportunities for guided and independent practice, and assisting students with connections between new and existing knowledge” (Archer & Hughes, 2011). Explicit instruction could be in the form of preteaching vocabulary before a lesson to ensure the students are aware and understand the important terms that are going to be used. Making sure you are using appropriate labels clearly and consistently. In addition, it is beneficial to integrate vocabulary knowledge in assessments to ensure mastery or the need for reteaching. In the following article by Hughes, Powell, and Stevens they describe several common error that teachers often make that may cause disturbances in learning math vocabulary. They strongly believe that in order to support students and promote the understanding of mathematics, there must be a consistency, precision and accuracy of the language embedded into teach strategies.

# 4 Word Walls

word wall closeup

The use of word walls in classrooms no longer only applies to language arts classrooms. Using word walls to reinforce unit vocabulary is a great way to support long-term retention. As mentioned above, once words are explicitly taught in the context of the given unit, you can then add definitions, examples and visuals to the word wall. In the article Vocabulary beyond the Definitions from the National Council of Teachers of Mathematics they describe many unique and creative ideas for using word walls in your math classroom.  A helpful suggestion included displaying all the vocabulary for the unit as an anticipation guide, or a start to preteaching to stimulate interest in a topic and give students a preview of what is to come. Then from there you can make a pre-assessment by asking students to find the words that don’t belong or even group words of similar meaning.

From the various readings above it is clear that there are many ways to teach mathematics vocabulary. In addition, I think it would be beneficial to weave these strategies into your instruction to allow for students who learn in different ways.

While co-teaching math this coming school year I think I will try out a few of these skills!

References :

Archer, A. L., & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. New York, NY: Guilford Press

De Garcia, L. (2008, November 24). Concrete-Representational-Abstract Instructional Approach. In Strategies for Teaching Elementary Mathematics A resource to improve the teaching and understanding of elementary mathematics. . Retrieved June 30, 2017.

*Hughes, E. M., Powell, S. R., & Stevens, E. A. (2016). Supporting Clear and Concise Mathematics Language: Instead of That, Say This. TEACHING Exceptional Children, 49, 7-17. doi:10.1177/0040059916654901

*Kiderra, I. (2013, October 23). One, Two, Buckle My Shoe: International Study Documents Importance of Language to Learning Math. In UC San Diego UC San Diego News Center. Retrieved from http://ucsdnews.ucsd.edu/pressrelease/one_two_buckle_my_shoe_international_study_documents_importance_of_language

Moschkovich, Judit N. 2002. “Supporting the Participation of English Language Learners in Mathematical Discussions.” For the Learning of Mathematics 19 (1): 11–19.

Okolo, C. (2017, June). Teaching Math Concepts through Representation. Retrieved July 2, 2017 from: https://d2l.msu.edu/d2l/le/content/576255/viewContent/4999516/View

*Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary. Reading & Writing Quarterly, 235-252. doi:10.1080/10573569.2015.1030995

*Zollman, A. (2009, November). Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications. In Association for Middle Level Education. Retrieved from http://www.amle.org/BrowsebyTopic/WhatsNew/WNDet/TabId/270/ArtMID/888/ArticleID/130/Graphic-Organizers-Improve-Mathematical-Problem-Solving-Communications.aspx?_cldee=Ym5vbGFuZG96YnVybkBob3RtYWlsLmNvb