Just Say the Word! (Part 1)

Creating School-Wide Agreements for Common Math Vocabulary

I recently witnessed a captivating first-grade lesson. As students interacted in small groups, using various visuals and models to capture their ideas of two-digit addition, the teacher moved around the room, asking them to justify their chosen visuals, to represent the visuals with numbers, and to explain the connections between the two. Both the engagement and rigor exceeded typical expectations for first-graders.

And then it happened…the teacher brought the students back together to share their discoveries. In the midst of their eloquent descriptions and uncharacteristically sophisticated explanations, the teacher asked, “Can anyone tell us how they used the flip-flop facts as part of the process?”

Flip-flop facts? Did I hear that correctly? Did she really use “flip-flop facts” in place of “commutative property?”

We’ve all done it – we’ve lost the battle for precision by using descriptive words in place of the proper language of mathematics. We think we are being helpful. However, we are ultimately doing damage in the long run. If our young children can say “tyrannosaurus rex” and compare him to “triceratops” with great precision, why shouldn’t they be expected to use frequently-encountered academic vocabulary at all grades?

Well-Intended Mistakes: Using Imprecise Language May Lead to Misconceptions

Here are a few more examples of teacher-prompted imprecision I’ve recently witnessed:

• Using the word “point” rather than “and” when reading a number with a decimal point
• Using “reducing” rather than “simplifying” for equivalent fractions
• Using “plugging in” rather than “substituting” when evaluating expressions or equations
• Using “equals” to describe the action of finding an answer rather than as a statement of equality
• Using “borrowing” and “carrying” rather than “grouping” and “ungrouping” for all four operations
• Using “moving the decimal” to describe unit conversion – it’s not the decimal point that moves but, rather, the digits that move to the left or right
• Using the word “decimal” to refer to “decimal point”
• Using “top and bottom number” to describe “numerator and denominator” (a fraction is one number – one value, not two)
• Using “keep-flip-change” to describe a rule for dividing fractions rather than actually developing the concept
• Using “rounding” as a synonym for “estimating” – rounding is but one strategy for finding an estimate

School-Wide Agreements: Establishing a Common Vocabulary Across Your Campus

Well-meaning teachers across the country tend to use descriptive language in place of mathematical precision. Don’t get me wrong – using descriptions when developing the vocabulary is a great strategy. However, we must also ensure that our students internalize and use the correct terminology with increasing frequency.

One way to ensure that teachers and students alike move toward a common mathematical language is to establish school-wide agreements around vocabulary usage. One way to achieve this is to follow these steps:

• Create grade-level lists: Using your standards or board-adopted curriculum, list the mathematical vocabulary for each grade level.
• Select words/concepts used across grade levels: Next, look for math language that appears across grade levels and select specific words that tend to be replaced with more common vernacular, such as the terms listed above. Select between 10 and 20 words to begin with.
• Discuss within grade levels: Ask each grade level to map out words and phrases they tend to use in place of the actual terminology. Discuss how this language might create misconceptions or misuses over time.
• Discuss across grade levels: Share out the mapped vocabulary across grade levels and discuss why some of the non-precise terminology may become problematic later on. This may be achieved in a school-wide meeting or through a shared bulletin board where comments may be left.
• Create an agreed-upon list of terms and definitions…and check in with one another! Once a list of agreed-upon math terms is created, post it where everyone can see it, and revisit it on occasion to ensure everyone continues to adhere to it.

Vocabulary Development in the Classroom

Tune in next week to learn classroom strategies for introducing and reinforcing school-wide agreed-upon math vocabulary. You won’t want to miss it!

For now, please join the conversation. Share your stories about math vocabulary uses and misuses in the comments section below. What have you noticed in the classroom, either from the teacher or the student perspective? How might we do better by our students? We look forward to hearing from you!

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

One more thing: Check out Peggy’s journal entry comparing  KP Ten-Frame Tiles with Base Ten Blocks. This week, she addresses the grouping nature of KP Ten-Frame Tiles while illuminating how base-ten blocks may do more damage than good when used to help children understand place value.