Helping English Language Learners Show What They Know Mathematically Cristina Sanchez-Lopez Illinois Resource Center

Gradual Release of Responsibility Research- based model to teach skills. Enhance literacy for English language learners (Kong & Pearson, 2003). First developed by Pearson & Gallagher (1993)

Principles for teaching ELLs in the Mathematics Classroom 1)Developing Conversational Language: connecting students’ informal language to the mathematics register. (ELLs can take about 2-3 years to develop conversational second language.) Example “sorting shapes”: the formal term right triangle can be learned after students understand the properties through classroom experiences. These activities allow students to use their conversational language to then bridge to more formal mathematical language. Problem- solving approaches give students a reason to communicate about math in their home languages and English. Adapted from English Language Learners in the Mathematics Classroom. (2007) Coggins, Kravin, Davila Coates& Dreux Carroll. Corwin Press

Concept Attainment yesno

Concept Attainment yesno

Concept Attainment 1212

Rectangular arrays

Use Think-pair-share Example from Khan Academy On Lattice MultiplicationLattice Multiplication

Teach to Standards Common Core: Mathematical Practices K Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Vocabulary Development: appropriate formal mathematical vocabulary must be layered on top of experiences not presented abstractly Content Area Word Banks Topic: radius diameter surface area circumference Plane geometry Perimeter Geometry

Vocabulary and Concept Development: Vocabulary instruction is most effective when it is used to label experiences or concepts or constructs that have grown out of experiences. (P. 170, Schifini) Webbing p. 147 Farnan, Flood, & Lapp

Thematic word banks Vocabulary word RepresentationHome language slope Y- intercept Linear equations: (math concepts translated into various languages)

The stages of learning English socially and academically in the four domains: listening, speaking, reading and writing ELP Level 1 Entering ELP Level 2 Emerging ELP Level 3 Developing ELP Level 4 Expanding ELP Level 5 Bridging ELP Level 6 Reaching

Principles for teaching ELLs in the Mathematics Classroom 2) Developing Academic Language: mathematics is made up of concepts that are most effectively discussed with proficiency in academic language. (ELLs can take from 5-7 yrs or more to develop their academic second language.) There are specialized words and phrases related to content, procedures, the activity of learning and expression of complex thinking processes (Barnett-Clarke and Ramirez, 2004) Students benefit from multiple exposures to new terms in the course of meaningful activities (Bielenberg & Wong-Fillmore, 2005), and from multiple support systems, including activities with visual and tactile scaffolding Students must also become proficient in explaining and justifying mathematical ideas. Repeating mathematical terms/definitions DOES NOT necessarily indicate understanding of a concept. Adapted from English Language Learners in the Mathematics Classroom. (2007) Coggins, Kravin, Davila Coates& Dreux Carroll. Corwin Press

English Language Proficiency (ELP) Standards (

Standard 3: English language learners communicate information, ideas, and concepts necessary for academic success in the content area of mathematics. Domain Level 1 Entering Level 2 Emerging Level 3 Developing Level 4 Expanding Level 5 Bridging Listening · identify properties of quadrilaterals based on visual representations and oral descriptions · visualize, draw, or construct geometric figures described orally · compare two and three dimensional figures (including circles and spheres) based on oral descriptions · locate intersections of geometric figures described orally (such as points, lines, or planes) · follow oral directions from grade level material to transform figures (such as rotations, reflections or enlargements) Speaking · identify steps in problem solving using realia or visual support · sequence steps in problem solving using technology or visual support (such as calculators) · sequence steps in problem solving relying on mental math or think- alouds · describe two or more approaches to solving the same math problems · describe and give examples of strategies for solving grade level math problems Reading · organize graphically displayed data from a set of written directions and models (such as rank players or teams based on statistics from sports) · collect and organize graphically displayed data from newspapers or magazines (such as stock market trends) · collect, organize, and display data in charts, tables, or graphs · collect, organize, display, and interpret data · collect, organize, display, and interpret data; generalize and apply findings to other data sets Writing · produce information related to data presented in graphs, tables, or charts depicting practical situations (e.g., “This shows rain in summer.”) · make generalizations related to data presented in graphs, tables, or charts depicting practical situations (e.g., “It rains more in June than July.”) · summarize information related to data from graphs, tables, or charts taken from everyday sources (such as newspapers and magazines) · draw conclusions related to data from graphs, tables, or charts from everyday sources · provide a rationale and explain use of data presented in graphs, tables, or charts

Developing: ELP Stage 3

Express the following in terms of spoken and written language

1.) 2.) 3.) 4.)

Examples of academic language at the sentence level 9 x 6= 54 Math problem Sentence frame to practice Nine times six equals fifty-four ______times_______equals_______. Nine multiplied by six is fifty-four. ______multiplied by_____is_______. Nine and six are factors of fifty-four. ____and ______are factors of______ Fifty-four is a product of multiplying ______is a product of multiplying nine and six. _______and _______.

Examples of academic language at the sentence level ____________ is half of ________. __________is twice as much as ____________. __________is equivalent to______________. _________is between _____and __________. Twelve is four more than eight. (Four more than eight is twelve.) __________is larger than_____________. ___________is smaller than______________. ___________is less than__________________. ___________is greater than________________.

Three Features of Academic Language: Academic language analysis Discourse The big idea of what type of text it is (genre); how the text is organized/structure/skeleton; how ideas are linked together (e.g. analogy/compare; justification; use of transitional phrases) Sentence How words and phrases are put/strung together to make meaning; rules of grammar and syntax (e.g. is like; just as/just like) Word/Phrase What words / phrases are used to express meaning WIDA Consortium

Why Are We Doing This?  Anticipating what might be difficult or easy for the children  Making language visible  Developing criteria for choosing texts, materials  Highlighting patterns in the language of different content area materials  Making instructional decisions more intentional  Tying into Common Core with regard to text complexity

Discourse Sentence / Grammar Word / phrases Seeing the Academic Language

Discourse Sentence / Grammar Word / phrases Seeing the Academic Language

Principles for teaching ELLs in the Mathematics Classroom 3) Scaffolding is necessary to support both mathematics and language Teachers can ensure that students learn at a deeper level by incorporating visual learning strategies, demonstrations, questioning and other methods (Echevarria, Vogt & Short, 2004) Examples: visible graphic organizers, cue lists, classroom routines, multiple representations, predictable lesson patterns, teacher guiding/coaching, social interactions during problem-solving.

Lesson Cycle Framework Preview Phase Instructional Phase Application Phase Big Idea/ Enduring Understandings/Essential Questions Present Key concepts experientially/ concretely/brainstorm Engage in oral language practice/ establish collaborative tasks Build schema/ build on linguistic and cultural experiences Encourage mathematical conversations Use a variety of reading materials (in home languages & English); Language Experience Approach as first text Use graphic organizers that reflect text structure Begin project/research/ Engage in questioning/inquiry Use during reading strategies and graphics for writing Prepare small group presentations/ museum displays,etc. Engage in discussions, debates and real-world projects Adapted from Jeanette Gordon by Cristina Sanchez-Lopez

Graphic organizers (graphic organizers in English and Spanish)

Principles for teaching ELLs in the Mathematics Classroom 4) The role of concrete materials and visual learning Use multiple representations to develop mathematical understanding for ELLs and help them build mental models and solid understanding. Students may need concrete materials to build meaning initially, but then must reflect on their actions with the manipulatives to gain deeper understanding of the concepts (Clements & McMillen, 1996; NCTM, 2000) Do not rely so much on linguistic input as a teacher (all ELLs are visual learners until they become proficient in the 2nd language.) Allow students to show what they know through visual representation.

Equivalent Expressions:

Rectangular arrays

Quadratic relationships x x x x 2 1

Meaning-Making in the problem- solving classroom: Students speak, listen, read and write to: solve real- world problems research answers to interesting questions express themselves communicate with others complete a project think and contemplate

Average performance of native-English speakers making one year’s progress in each consecutive grade GRADE Program 1: Two-way developmental bilingual education (BE) Program 2: Late-exit bilingual education and ESL taught through academic content Program 3: Early-exit bilingual education and ESL taught through academic content Program 4: Early-exit bilingual education and ESL taught traditionally Program 5: ESL taught through academic content using current approaches Program 6: ESL Pullout-taught traditionally Data aggregated form a series of 3-7 year longitudinal studies from well-implemented, mature programs in five school districts © Wayne P. Thomas and Virginia P. Collier, 1997, 2002 General Pattern of K-12 Language Minority Student Achievement on Standardized Tests in English Reading Student Achievement on Standardized English Reading Tests

Writing in home language and English Good writers become better readers, read more frequently and improve comprehension and retention of information. Graphic Organizers- use graphic organizers during reading as a springboard for writing, brainstorming and think alouds Language Experience Approach- capitalize on students’ oral language/ model writing for students / shared writing to help students bridge to academic language Process Writing- allow students to work on a variety of writing projects at once/ students should show their writing at different stages of the writing process / connect reading, writing and discussion (notes, reports, summaries, lab reports, reflections, problems: writing specific to math and to science) Learning Logs- students should write everyday/ reflect on what they are learning/ use dated entries/ students can use diagrams, illustrations, drawings as part of their daily entries

Authentic Assessment Standard Measures do not tell us anything about the processes that students are undergoing while reading or writing. As teachers, we need to know how students are: APPROACHING, INTERPRETING and ENGAGING IN authentic learning tasks, AND we need to know how students are using their two languages Adapted from Spangenberg-Urbschat and Pritchard

Authentic Assessment Authentic Assessments – Do not interrupt instruction as they are embedded in the strategies and activities we use daily Establish clear criteria Give us immediate feedback that informs and shapes our instruction Let students see the practical applications of what they are learning Allow students, teachers, parents to see growth over time Allow students to show what they know

Authentic Assessments that are embedded in home language and English instruction Classroom observations Skill checklists clipboard charts Anecdotal notes group interactions rubrics types of utterances academic language use use of questions

Poster walks Writing in home language and English Oral retellings and explanations Problem of the week Illustrated explanations Physical models learning logs tape- recordings of student explanations in home language and English Performance & Products Authentic Assessments that are embedded in home language and English instruction

Language, Literacy and Content How do we make certain that students are understanding the academic content, concepts and skills independently of their language proficiency? What strategies do we use to promote social & academic listening, speaking, reading and writing? In what ways do we help ELLs show what they know separate from their language proficiency?

Setting Goals What is something you already do that supports ELLs’ learning of academic content? What is something new that you didn’t know about ELL students? What is something new that you would like to try to help ELLs show what they know in your content area?

Contact Information Cristina Sanchez-Lopez Illinois Resource Center