# Visual Representations And English Learners

Language is deeply involved in learning mathematics as students both communicate and think about their mathematical ideas. For all students—and English learners in particular—access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics.

In today’s clip, Johannah Nikula, one of the authors of Mathematical Thinking and Communication, discusses the role of visual representations in supporting English learners, including how visual representations provide a support for developing language and the potential visual representations have to unearth student thinking for teachers to see.

# The Importance Of Rich Mathematical Tasks

Language is deeply involved in learning mathematics as students both communicate and think about their mathematical ideas. For all students—and English learners in particular—access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics.

# Video | Opportunities for Engaging English Learners in Math

Language is deeply involved in learning mathematics as students both communicate and think about their mathematical ideas. For all students—and English learners in particular—access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics.

# SMP #5: Use Appropriate Tools Strategically

By John SanGiovanni (@JohnSanGiovanni), coauthor of the Mastering the Basic Math Facts series

Stop me if you’ve heard this one before. Three students walk into a math classroom. They confront 709 – 340. Krista uses a number line to count back with three jumps of 100, a jump of 50, and another jump of 19. She then adds her jumps. Damian solves with paper and pencil. Oscar counts up mentally from 340 to 640 (300) and then 640 to 709 (69 more) to compose a difference of 369. So which student selected and used tools strategically?

# SMP #4: Model with Mathematics

By Nancy Butler Wolf (@drnanbut), author of Modeling with Mathematics

Mathematical modeling is not just a type of word problem—it is a mathemati­cal practice. Modeling can be infused throughout the math curriculum, and can be used in conjunction with many content areas or standards. Modeling represents a shift from learning math to doing math. The inclusion of model­ing in the math classroom can increase student engagement, increase students’ depth of understanding, and provide opportunities for investigation, contribu­tion, and success for all learners.

# SMP #3: Construct Viable Arguments and Critique the Reasoning of Others

## Arguably the Nine Most Important Words in the Math Common Core

By Steve Leinwand (@steve_leinwand), American Institutes for Research, author of Accessible Mathematics.

I am increasingly convinced that “construct viable arguments and critique the reasoning of others” (Standard for Mathematical Practice 3) may be the nine most important words in the entire Common Core. Far more than an equal among eight practices, SMP 3 is a principle that encompasses the entire Common Core.