The Language Behind Mathematics Focusing on the English Learner

Quick Write Skim Levels of English Language Proficiency Write down the names of 2 students in your class that fit one of the profiles What are some of the challenges you face in supporting those students in learning mathematical concepts. Whole group share

Building a Language Rich Interactive Classroom  Teach students language and strategies when they don’t know what to say.  Encourage students to speak in complete sentences.  Randomize and rotate who is called on so students of all language levels can participate.  Use response signals for students to monitor their own comprehension.  Use visuals and a focus on vocabulary to build background.  Have students participate in structured conversation and writing activities.

Language of Math – enVision Math  Vocabulary Cards  Connections to Everyday Vocabulary  Vocabulary Activities

Explicitly teach vocabulary  When? Pre-teach? Pre-teach? During the lesson? During the lesson? Following the lesson? Following the lesson? It depends… Do they need to know the word to be successful? Would exposure to the concept help them understand the word?

Research on Vocabulary Acquisition  Read brief summary of article by Marzano on Vocabulary Acquisition  Share with partners any experience you have with using all of or parts of this routine to introduce vocabulary with your students. A rule of thumb is to provide 6 exposures to a new word during the initial lesson and at least 30 additional exposures during the ensuing month. Vocabulary should be repeated often in meaningful settings before students will retain and actually use it to construct mathematical concepts.

5 Broad Categories of Vocabulary Problems 1. Words with more than one meaning 2. Words with Special Emphasis in Mathematics 3. Technical Vocabulary 4. Varied Forms 5. Abbreviations and Specialized Symbols

Words with more than one meaning  Square Geometric figureOutdated  Mathematical Operation 2

Technical Vocabulary  Chord  Cored  Cord

Varied forms, abbreviations and specialized symbols  ½  2 1 one divided by 2  cm mm in ft sq.  = > < +

Words with Special Emphasis in Mathematics  Function If y = x + 5 Then f (x) = x + 5

Frayer Model DefinitionCharacteristics Examples Non-examples Word

Equation Definition A math statement showing that two things are equal. (Same thing as an equality.) Characteristics Needs an = Both sides need to equal the same number Is balanced if put on a balance scale Has a mathematical expression on each side of the equal sign examples 4 = = = 8 6 = 6 X + 3 = 8 Non-examples X 2x Equation

Expression Symbols that represent numbers or operations. A way of writing something that uses numbers and symbols. Cannot have an = sign or an inequality sign > or < Examples 4 3 – 2 X + 12 Y Non-examples = 5 3(7) = 21 X + 9 < 17 Expression

Word Walls  Show examples.  List any other words or expressions that have the same meaning.  List the word in the native language of any of your students.  List the word or phrase. Commutative Property Propiedad conmutativa = ab = ba

Vocabulary Bingo  Write the numbers 1-24 randomly on your bingo card.  What does randomly mean? What does it tell you about this situation?  “Math Vocabulary Bingo” is available at NCTM Illuminations.com under - lessons

Interactive Learning – enVision Math  Engage  Pose the Problem  Expand Student Responses  Academic Vocabulary  Small-Group Interaction  Extend

Supporting Mathematical Conversations  Read handout from Implementing Investigations, using A/B Each Teach. With your A/B partner discuss successes you have had with mathematical discussions or the roadblocks you have encountered while trying to conduct mathematical conversations.

What to say instead of “I don’t know” May I have some time to think? Would you please repeat the question? I have a question about… I don’t understand this about the question… I don’t know what the word ____ means.

20 Language Functions Functions are the purposes for communicating orally and in writing.

Dominant Language Functions  Language functions commonly found in content standards, include: Identification and explanation (includes description, definition) Cause and effect relationships Compare and contrast attributes or actions Prediction and inference Express sequence and time relationships Summary and generalization

Connection : Language Function Signal Words B/EI – is going to, will, I think I – think, believe, probably, predict, might EA/A – most likely, certainly, doubt, based on, Predict/HypothesizeSequence B/EI – first, second, next, then, last, I – To get started, from there, continue to, to finish EA/A – initially, eventually, to begin/conclude the process, Explain through classification B/EI – have, are, are called, is used to I – described as, is part of, is related to, is used for EA/A – characterized by, utilized for, identified by, employed as, features,

Sentence Frames 1. I think the answer is _____ because … 2. First I _____ then I _______ I agree with [name's] answer because… 4. I don't agree with [name's] answer because… 5. I started the problem like [name] but then I...

Thinking Mathematically Video  What is the teacher or students’ language purpose (function) throughout this conversation?  What are the signal words or phrases that you heard, which helped identify the function?  Considering this function or functions, what might the teacher have done to further support the participation and success of her English Learners?

Applying New Learnings Take some time now to work with your team around planning a lesson in enVision where you are able to incorporate something that you have learned today.

Share Out and Conclusion  What our you already doing?? Toot your own horns. Use the Talking Stick to allow some participants and resident experts to share some of the things they are already doing with Math Vocabulary and Math Talks.

Evaluation  Please tell us what you think by completing the short evaluation at your table. THANKS FOR HAVING US!