School District of Philadelphia, Office of Multilingual Curriculum and Programs (OMCP) Language of Mathematics Index Index ......................................................................................................................................................... 1 Course Description .............................................................................................................................. 2 Core Materials ....................................................................................................................................... 3 Language Central for Math: ......................................................................................................................... 3 Student texts: .................................................................................................................................................................... 3 Optional Materials for September / October .............................................................................. 3 Option 1 .............................................................................................................................................................. 3 Option 2 .............................................................................................................................................................. 5 Additional Resources .......................................................................................................................... 5 Mathematics and the English Language .................................................................................................. 7 Mathematics Operations Terminology .................................................................................................... 9 Mathematics Syntax (Word Order) ......................................................................................................... 10 Sample Unit Curriculum Map for Language Central for Math ............................................. 11 Lesson Planning Resources ............................................................................................................ 12 QTEL Principles ............................................................................................................................................. 13 QTEL Unit / Lesson Planning: Three Moments (components) in a Lesson and Sample Tasks ................................................................................................................................................................. 16 WIDA ....................................................................................................................................................... 16 Scaffolds Supports (WIDA) ........................................................................................................................ 17 Placement Test .................................................................................................................................... 18 Answer Key ..................................................................................................................................................... 18 2 Course Description Language of Mathematics is an mathematics credit bearing course. The class MUST be taught by a teacher with 7-12 mathematics certification. In addition, the teacher should have either ESL certification or have participate in Quality Teaching for English Learner (QTEL) professional development. The course is designed for newcomer high school students who either have limited and/or interrupted formal schooling or will benefit from a mathematics course to prepare them for Algebra I. In addition to learning and/or reviewing mathematical concepts and skills, students will expand their knowledge of the English academic language of mathematics. An assessment is at the end of this document to determine if students should be rostered in the course. Goals of the course include (1) building on students’ “funds of knowledge” / prior knowledge and experiences in mathematics, (2) engaging students in meaningful mathematical language practices (reading, writing, speaking, listening) with appropriate scaffolds, (3) learning in context the disciplinary vocabulary of mathematics, and (4) supporting students’ understanding, application and appreciation of mathematical concepts and skills, and (5) preparing students for advanced high school mathematics courses. When working with English Learners: 1. Focus on students’ mathematical reasoning, not accuracy in using language. 2. Focus on ALL students participating in mathematical discussions on important mathematical concepts and reasoning rather than pronunciation, vocabulary or low-level linguistic skills. 3. Recognize and support students to engage with the complexity of language in math classrooms. Student learn content / concepts and language simultaneously. Students learn to describe patterns, make generalization and use representation to support their claims. 4. Treat everyday language and experiences as resources, not as obstacles. 5. Uncover the mathematics in what students say and do. 6. Draw on multiple resources available in classrooms such as objects, drawings, graphs and gestures as well as home languages and experiences outside of school. (Judith Moschkovich in Mathematics, the Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the Common Core) 3 Core Materials Language Central for Math: Student texts: o 6th: Number and Operations, Algebra, Geometry and Measurement, Data Analysis and Probability (24 lessons) o 7th: Number and Operations, Algebra, Geometry and Measurement, Data Analysis and Probability (24 lessons) o 8th: Number and Operations, Algebra, Geometry and Measurement, Data Analysis and Probability (24 lessons) Teacher’s Edition: (Grades 6 – 8) o Language Proficiency Chart (pgs. T12 – T13) o Building Lesson Plans (T14 – T23) o Strategies for Teaching English Learners (T24 – T35) o Scope and Sequence (pgs. T38 – T39) Students may need additional preparation BEFORE using Language Central for Math. Optional Materials for September / October Option 1 Bridges to Academic Success Mathematics Unit 1 http://bridges-sifeproject.com/classes/math-unit-1/ Essential Question: How do we use math to describe the world around us? 6 sets or units with 5 lessons each (30 lessons) • Structure of the number system • Place value • Symbolic notation 4 • Four central operations (addition, subtraction, multiplication, division) • Solving simple world problems with whole numbers • Concrete measurement (area, perimeter) • Final performance task: Designing the Farm (apply knowledge of area, perimeter and operations with whole numbers) Materials: • Unit Map • Performance Task • Unit Guide • Lesson Plans • Glossaries • Flash Cards • Bilingual Translations (Bengla, Haitian Creole, Karen, Spanish, Somali) Mathematics Unit 2 http://bridges-sifeproject.com/classes/math-unit-2/ Essential Questions: How do we represent parts of a whole using words, numbers and symbols? What strategies and we use to solve problems with parts of a whole? 7 sets or units with 3 to nine lessons in each (35 lessons) • Concepts behind rational numbers • Fractions • Decimals • Percents • Construct number line, area models, ratio tables • Ratio and proportion Materials: • Unit Map • Performance Task • Unit Guide • Lesson Plans • Glossaries • Flash Cards • Bilingual Translations and Bilingual Unit Previews (Bengla, Haitian Creole, Karen, Spanish, Somali) 5 Option 2 Longman Mathematics (Out of print) Text is out of print. Each school will receive 1 – 2 copies. Materials will have to be photocopied. Content in Longman Mathematics that may be used before using Language of Mathematics includes: Unit 1: Reading and Saying Cardinal Numbers (pgs. 3 – 12) Reading and Saying Ordinal Numbers (pgs. 13 – 24) Rounding Off Numbers (pgs. 25 – 36) Unit 2: Addition (pgs. 39 – 50) Subtraction (pgs. 51 – 66) Multiplication (pgs. 67 – 86) Division (pgs. 87-110) Additional Resources A Framework for Re-envisioning Mathematics Instruction with English Language Learners (Council of Great City Schools, Dec. 2016) https://tinyurl.com/y77qevsu Bilingual Mathematics Word-to-Word Dictionaries http://steinhardt.nyu.edu/metrocenter/resources/glossaries • By course (e.g. middle school math, Algebra, Geometry, etc.) • By language (Albanian, Arabic, Bengali, Burmese, Chinese (traditional), Dutch, French, Greek, Haitian, Hindi, Japanese, Karen, Korean, Nepali, Portuguese, Punjabi, Romanian, Russian, Spanish, Tagalog, Tibetan, Ukrainian, Urdu, Uzbek, Vietnamese) Mathematical Notation Comparisons Between U.S. and Latin American Countries https://tinyurl.com/y7qytav7 Mathematics, the Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the Common Core Judith Moschkovich https://tinyurl.com/hf2cebm https://www.youtube.com/watch?v=gUfpnIbq4TA 6 Principles for Mathematics Instruction for ELs Understanding Language, Literacy and Learning in the Content Areas Judith Moschkovich https://tinyurl.com/hbxnw2g Supporting Language and Content Learning in Math (newcomers) https://www.teachingchannel.org/videos/math-for-newcomers-ousd Tasks (strategies) to Support Reading Math Problems https://tinyurl.com/llkzk8w Additional Task Teaching Resources: http://ell.stanford.edu/teaching_resources/math Teaching Mathematics to English Language Learners National Council of Teachers of Mathematics Position Statement https://tinyurl.com/ybfu6zvx