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Why Teach Vocabulary in Math?

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Wendy Ward Hoffer

According to the Global Language Monitor, this is how many words are in the English language as of January 1, 2014. (Now I am not sure how a language can include four-fifths of a word, but let’s leave that aside for now.) Consider the vastness of this number, and then the number of words you yourself may know as a fraction of those over one million words. Then, consider the growth rate of our language: A new word is created every ninety minutes, adding nearly fifteen words a day to the English lexicon. Word learning, therefore, is a critical part of life as an English speaker.


Vocabulary development can start to lag in preschool

Students come to us with various levels of vocabulary development and a variety of experiences learning new words. In fact, according to Beck, McKeown, & Kucan (2002), high knowledge 3rd graders have vocabularies about equivalent to our lowest-performing high school seniors. How can this be? Researchers Hart and Risley estimate that by age three, less advantaged students have heard thirty million fewer words than their more advantaged peers; the same authors estimate those less advantaged students’ vocabularies to be half the size of their more advantaged counterparts’. Upon entering preschool, therefore, some students are already lagging in their vocabulary development.

How to catch up on vocabulary development?
To catch up is difficult: A synthesis of the research on vocabulary acquisition tells us that a typical student learns roughly 3,000 words per school year. Suppose that students with average vocabularies come to school knowing 6,000 words, while their less advantaged contemporaries know 3,000. One year later, that first group of students’ total vocabularies has grown to 9,000 words (6,000 + 3,000), or a growth rate of y = 3000x + 6,000. Without intervention, students entering school with smaller vocabularies continue to lag behind, gaining new words at a rate half that of their peers: year one of school, 3,000 + 1,500 = 4,500 words, and their vocabulary growth rate would be described by the equation y = 1,500x + 3,000. If we graph those two lines, we will see that they will never intersect.

Without intervention, those students who began school with smaller vocabularies will continue to lag behind; by the time they reach middle and high school, this deficit poses a significant risk factor for school achievement and high school graduation. Slow vocabulary development puts English language learners, in particular, at risk. Without the necessary academic language development opportunities, these students struggle to comprehend text at their grade level, and they are also at a higher risk of being misdiagnosed as learning disabled (August, Carlo, Dressler, & Snow 2005).

Change the historical disparity
Radical intervention is required in order to change the historical disparity in word learning and put the low vocabulary students on an exponential learning curve. Authors Beck, McKeown, and Kucan write that “a large vocabulary repertoire facilitates becoming an educated person to the extent that vocabulary knowledge is strongly related to reading proficiency in particular and school achievement in general” (2002, 1).

Even in mathematics, academic vocabulary development facilitates understanding.


In Developing Literate Mathematicians, we will explore the nature of mathematical texts and how we can support learners in understanding these texts deeply as a means to understanding mathematics.

developing-literate-mathematicians-coverExcerpt from
Hoffer, Wendy Ward. Developing Literate Mathematicians: A Guide for Integrating Language and Literacy Instruction into Secondary Mathematics. Reston: The National Council of Teachers of Mathematics, Inc., 2016. (57-58)

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August, Diane, Marie Carlo, Cheryl Dressler, and Catherine Snow. “The Critical Role of Vocabulary Development for English Language Learners.” Learning Disabilities Research and Practice 20, no. 1 (2005): 50-57

Beck, Isabel L., Margaret McKeown, and Linda Kucan. Bringing Words to Life: Robust Vocabulary Instruction. New York: Guilford, 2002.

Wendy Ward Hoffer, MA is the author of Developing Literate Mathematicians: A Guide for Integrating Language and Literacy Instruction into Secondary Mathematics, Minds on Mathematics: Using Math Workshop to Develop Understanding in Grades 4-8 and Science as Thinking: The Constants and Variable of Inquiry Work. Wendy works with teachers, schools and districts locally and nationally to promote deep thinking in math and science.
She is the creator and facilitator of several PEBC professional development institutes including, Minds on Math Institute, Science Institute, and STEM Identity Institute. Wendy received an MA in Science Education from Stanford University and earned National Board Certification while teaching middle school math and science.

See Wendy Ward Hoffer in person at a PEBC event

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