In NCTM Teaching Children Mathematics (2022), Rheta Rubenstein and Denisse Thompson have written a "classic" which helps explain challenges in learning mathematics language and vocabulary. Article is access also here. A classic" which helps explain challenges in learning mathematics language and vocabulary.
This 2009 article from Teaching Children Mathematics by Jennifer M. Bay-Williams and Stefanie Livers looks at when and how to best introduce and teach vocabulary. While the examples are often from the early grades, the message translates to grades 6-12. BONUS: The article appendix has 7 games that can be played to reinforce mathematical vocabulary and concepts. (This article has been archived by NCTM. Members have access online through the archived "Teaching Children Mathematics" journal, 2009, Volume 16, Issue 4. Members have access online.)
This 2014 article from Mathematics Teaching in the Middle School by Stefanie D. Livers and Jennifer M. Bay-Williams advocates for intentionality in the timing of introducing or going deeper into mathematical vocabulary. Such intentionality can support both deeper mathematical understanding as well as much-improved abilities to read, hear, speak, and write about that mathematics. (NCTM members may have access online.)
This Beth A. Herbel-Eisenmann article from Mathematics Teaching in the Middle School discusses how to assist students in developing mathematics vocabulary using multiple representations and student thinking.
Academic Word Finder is a digital tool from Achieve.org that helps educators identify Tier II vocabulary terms in any text.
This Research Gage article describes commonly-used vocabulary terms in each discipline and focuses on morphology.
Teachers can make decks of mathematical terms (words, brief phrases) pertinent to content in units or time-periods (quarter, semester) of study. Teams of students can play whole-class or small groups against each other. You may need to develop "house rules" about what the picturer (drawer) is and isn't allowed to include (can they just draw || for "parallel"?) and how precise the identification needs to be.
From Chapter 4 of the book More Than Just Talk, this activity has teachers create decks of cards with geometric figures. Two players sit back to back. One sees the card and describes how to draw what they see to their partner (who cannot see the card). The partner draws what they hear described. This activity highlights precision in mathematical language.
This document outlines four design principles and eight mathematical language routines provide support for promoting mathematical language use and development through curriculum and instruction. A design goal is to make language development and integral part of planning and delivering instruction.
Practice 6 deals with "attending to precision." This includes precise language communication - vocabulary included. Making and using definitions, formulating expressions, and more are addressed.