teaching)mathema-cs)to)ells: goingbeyondgoodteaching )...teaching)mathema-cs)to)ells:...
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Teaching Mathema-cs to ELLs: Going Beyond Good Teaching
Nora G. Ramirez
2013 NCTM Annual Mee<ng
Denver, CO
Thoughts, Stories and Consejos from ELLs
What ELLs Observe
Teachers think they are saving us an embarrassment by not calling on us.
Teachers think they are doing us a favor by always grouping us together.
Teachers avoid conflicts by ignoring students who tease us.
How ELLs Respond
But not calling on us makes us feel invisible.
We like to work together, BUT WE NEED to work with all of our classmates.
I can’t ignore teasing. Address it.
Senior ELLs from Rebecca Merkel’s class, Iroquois High School, Jefferson County Public Schools, Louisville, KY
Celédon-‐PaZchis and Ramirez. (2011) NCTM
Thoughts, Stories and Consejos from ELLs
What ELLs Observe How ELLs Respond
Teachers give us idenGcal assignments instead of accommodaGons for our needs.
Teachers assume that when we don’t raise our hands this means we don’t need help. They also presume that help means translaGon.
We need accommodaGons to help us meet YOUR targets.
We need your help-‐which can mean giving an example, explaining the quesGon, defining the word, etc.
Senior ELLs from Rebecca Merkel’s class, Iroquois High School, Jefferson County Public Schools, Louisville, KY
Celédon-‐PaZchis and Ramirez. (2011) NCTM
Guiding Principles for Teaching Mathema<cs to ELLs
• Challenging Mathema<cal Tasks
• Linguis<cally Sensi<ve Social Environment
• Learning English while Learning Mathema<cs
• Mathema<cal Tools and Models as Resources
• Cultural and Linguis<c Differences as Intellectual Resources
Celédon-‐PaZchis and Ramirez. 2011
Essen<al Strategies for Teaching ELLs at Any Stage of Language Development
Beginning Stage
Intermediate Stage
Advanced Stage
Essen<al Strategies for Teaching Mathema<cs to ELLs (1)
• Use and provide access to challenging tasks. • Make group decisions based on the cogni<ve demand of the task.
• Sequence ac<vi<es and tasks to develop language and mathema<cs simultaneously.
• Facilitate par<cipa<on in a Mathema<cs Discourse Community.
• Allow and vary processing <me dependent on the complexity of the linguis<c demands of the task (i.e., speaking, reading, wri<ng, listening).
Essen<al Strategies for Teaching Mathema<cs to ELLs (2)
• Facilitate the use of tools to enhance mathema<cal discourse and understanding.
• Make visual references to mathema<cal models in the environment.
• Explicitly refer to terms and their meanings oaen and make dis<nc<on between terms in mathema<cs and everyday life (i.e., being mean and mean as in average).
• Develop awareness of the student’s language, culture, dialects, ways of knowing and communica<ng.
The Tor<lla Factory Lesson
Middle School Classroom 100% ELL Students Phoenix Metropolitan Area
Teacher: Bob McDonald My ability to ask probing ques<ons of the students who were stuck was oaen “lost in transla<on”. I compensated for this by leZng one person from the group be a “spy” to visit other groups if they were not making progress.
• Nora owns a tor<lla factory. In this factory there was a machine that made the tor<llas, placed them in packages, and put the packages in boxes.
• One day, there were 5 completed boxes that were unsold in the factory. Nora started the machine and kept track of how many boxes there were aaer each hour.
• Aaer one hour there were 8 boxes in the factory, aaer two hours there were 11 boxes in the factory, and aaer three hours there were 14 boxes. • How many boxes will there be at the end of a twelve hour day?
The Tor<lla Factory
The Tor<lla Factory The tor<lla factory now has two machines and each machine performs at the rate shown in the tables below.
hours boxes hours boxes 1 8 1 5 2 12 3 11 4 20 5 17
machine 1 machine 2
The tor<lla factory needs to fill an order for 48 boxes. How long will BOTH machines need to operate to fill the order?
Group Presenta<on on Day 1
Students Communica<ng Through Wri<ng
WRITING STRATEGIES
from Researchers at
Wisconsin Center for Educa<on Research
Rosalie Grant [email protected]
Rita MacDonald [email protected]
Wri<ng to support habits of mind
Standards for Mathema<cal Prac<ce, Standard 6:
A8end to precision
• describing en<<es (Which line, exactly?)
• describing procedures (Which step?)
• describing circumstances or qualifica<ons (When does it occur and when does it not occur?)
Grant and McDonald (2013) WIDA
A8end to precision-‐-‐Which line, exactly?
Exit Ticket wri-ng Pick one of the bold lines in this drawing, and write a sentence telling someone to draw a circle around it. Tell him or her, in one sentence, exactly which line you mean
Grant and McDonald (2013) WIDA
Precision in naming circumstances
Exit Ticket wri-ng
“A four-‐sided figure is a square.” What would make this true? What would make it false?
Complete these sentences: A four-‐sided figure is a square if………….. A four-‐sided figure is not a square if……….
Grant and McDonald (2013) WIDA
Common Student Ac<ons at the Beginning Stage
• Is a silent observer.
• Learns object words first.
• Con<nually par<cipates in an internal dialogue.
• Primarily uses first language to keep record of mathema<cal concepts using graphic organizers and journals.
• May or may not already know the mathema<cal concepts and/or related terminology in their first language.
Common Student Ac<ons at the Beginning Stage
• May use different procedures and nota<ons.
• Responds to gestures, pictures and visuals.
• May appear engaged in classroom ac<vi<es or display body language to pretend to understand.
• Interacts with peers by observing, gesturing, and responding with few words. Oaen requires teacher support for interac<ons.
Appropriate Teacher Ac<ons at the Beginning Stage
• Models pronuncia<on and usage of conversa<onal and mathema<cal language, enunciates clearly and avoids
the use of slang or idioms.
• Is aware that the absence of student ques<ons does not indicate understanding thus con<nually observes students’ ac<ons and gestures.
• Facilitates students’ use of models and drawings to
– assess what students know; and – communicate mathema<cally with the students.
Appropriate Teacher Ac<ons at the Beginning Stage
• Recognizes a need for and uses various resources (e.g., school family liaisons, cultural centers, consulates, etc.)
to gain understanding and to validate what the students bring to the classroom in terms of the following: language; home culture and prior school culture; and
mathema<cal experiences.
Common Student Ac<ons at the Intermediate Stage
• Reads and writes simple sentences that use high-‐frequency vocabulary and familiar mathema<cal terminology. Requires
support for wri<ng about abstract ideas.
• Uses simple sentences to express mathema<cal ideas with
support of tools for wripen and oral explana<ons.
• S<ll needs extended processing <me to respond to ques<ons
and engage in different mathema<cs tasks.
• Responds to and responds with mul<modal communica<on (gestures, pictures and models) to demonstrate
understanding of mathema<cs concepts.
Video Clip of Triangles Lesson with ELLs
• 4th grade class in the Southwest with 50% of students being ELL; Title I school
• Two students had IEPs.
• There are various stages of language acquisi<on.
• The teacher groups students so that each group has a strong English role model.
Video Clip of Triangles Lesson with ELLs (1 of 2)
• The task is to describe what they know about triangles.
• As you watch the video clip, no<ce the following:
– How does the teacher help students develop mathema<cal discourse?
– How does the teacher structure classroom interac<ons?
Video Clip of Triangles Lesson with ELLs (1 of 2)
Triangles Lesson with ELLs • The task: inves<gate the lengths of the sides of a triangle. The teacher asks students to mark off a strip of 4 cm, 4 cm, and 4 cm, then they cut it to experiment.
• Students conjecture whether any 3 lengths will make a triangle.
• Students work in groups to inves<gate.
Common Student Ac<ons at the Advanced Stage
• Requires extra <me to process unfamiliar topics, concepts, and vocabulary.
• Con<nues the use of both first language and English. • Interacts with other peers to construct mathema<cal knowledge and to plan and prepare for presenta<ons.
• Ac<vely par<cipates in group work by listening, responding, verbally agreeing (disagreeing), and offering alterna<ves.
• Records mathema<cal terminology and concepts using more complex language, non-‐verbal representa<ons and examples.
Aligning with the
Mathema<cal Prac<ces
Planning Lessons with ELLs in Mind • Apending to students understanding of the context to have
access to the mathema<cs
• Making connec<ons to students’ lives, culture and language
• Considering specific language that may need apen<on
• Planning for gestures • Recording terminology with clues
• Planning for opportuni<es for students to prac<ce using this terminology
• Grouping students with a purpose • Apending to students ac<vely par<cipa<ng, listening to each
other, being respecrul and inclusive of each other, and using each other as resources
Planning Lessons with ELLs in Mind
• Planning for language objec<ves (listening, speaking, reading and wri<ng) as well as content objec<ves
• Considering the planned trajectory for specific students
• Planning for student rehearsal of responses or presenta<ons
• Planning ahead for different strategies, tools and/or representa<ons
• Ensuring processing <me (how and when)
• Orchestra<ng opportuni<es for communica<on between students throughout the various stages of the lesson
Resources Celedón-‐PaZchis, S. and Ramirez, N . Beyond Good Teaching: Advancing Mathema<cs Educa<on for ELLs. NCTM (2012)
Understanding Language Project, Stanford University ell.stanford.edu/
TODOS: Mathema<cs for ALL todos-‐math.org