RTI - The Importance of Mathematical Vocabulary

Chapter 9 of Response Intervention in Mathematics is focused on the importance of teaching mathematical vocabulary. This is what I feel to be an unnecessarily long chapter. Therefore, I will try to briefly summarize this chapter and some include good takeaways.

The authors make a sound argument that the lower a students understand of mathematical language, the less proficient they will be in mathematics. Students with a low level of mathematical vocabulary (that is, they have mathematical terminology, understand the terminology and the contexts in which it is applied, and are proficient in using/applying it) have difficulties learning whatever it is being taught. I learned this last year, where most of my students were very deficient in mathematical language. It made it hard to teach new concepts and it was difficult for them to understand new things. This chapter includes seven recommendations for teaching vocabulary in math class. The following four resonated with me the most:

A) Establish a list of essential vocabulary words for each chapter or grade level

B) Evaluate student comprehension of mathematical vocabulary on a periodic basis

C) Develop an environment where mathematical vocabulary is a normal part of mathematics class.

D) Probe students' previous knowledge and usage of important terms before they are introduced during instruction.

Incorporating even a few of these recommendations will allow students to view mathematical vocabulary as important and not just a sidekick to what is being taught. Instead, they go hand in hand.
The book argues that teachers should devote instructional time to developing students' mathematical vocabulary. I certainly agree, but there is such little time to begin with. As such, one of the wonderful ideas that I found in this chapter included creating a list of mathematical words for students and sending it home (kind of like what is done for language arts). Here is an example of a vocabulary sheet taken from the book:

Let's face it: There's simply not enough time in a 45 minute period to teach concepts, procedures and vocabulary, all heavily dependent on the students in your classroom and the range of their abilities. However this is a great tool that can be used for students to study on their own time, and you can evaluate how useful it has been.

Another great tool that was presented in this chapter is an online math dictionary for kids. It can be found here: Children's Math Dictionary
It is an online interactive dictionary that  students can use to learn new mathematical terms, along with a visual representation or interactive way to learn its meaning.

Another idea that resonated with me in this chapter is the use of graphic organizers. Graphic organizers are a great way for all students to organize information and help them see the connections between concepts and their application.

Another interesting one that I found (and is inspiring me to make one for my students as I type this):

Lastly, to evaluate students knowledge (and the usefulness of explicit vocabulary instruction), teachers can put vocabulary questions on quizzes/tests, or timed assessments in which teachers pick a few random words from their created list of words students should know (by the end of the year). The idea is that as the year progresses, students vocabulary will also progress, therefore, students should score higher on these types of progress-monitored assessments over time. Using the book again as a resource, the following photo is an example of the "progress-monitoring probe" discussed in the textbook:

To summarize, many students do not learn fundamental mathematical vocabulary, and therefore, have difficulties become strong students in math. Strong students in math have excellent mathematical vocabulary and understand the meaning of many different math terms and know when they are applied. This chapter went over many different ways to help students gain the vocabulary fluency in math.

Edit: Here is a prime example of why mathematical vocabulary is important. I went over some home work with a student. While he was able to get the correct answer, his articulation of his reasoning is low (due to a low level of mathematical vocabulary).