English Language Learners and Algebra:

Teaming Rigorous Content and Accessible Pedagogy

English Language Learners and Algebra:

Teaming Rigorous Content and Accessible Pedagogy

Patricia Swanson, Ph.D.

Department of Elementary Education

Trisha Bergthold, Ph.D.

Department of Mathematics

San José State University

Patricia Swanson, Ph.D.

Department of Elementary Education

Trisha Bergthold, Ph.D.

Department of Mathematics

San José State University

English Language Development Institute for Algebra Readiness Through the Instruction

and Support of Educators (ELDI-ARISE)

English Language Development Institute for Algebra Readiness Through the Instruction

and Support of Educators (ELDI-ARISE)

Partners: Santa Clara Unified, Campbell Union, and San Jose State University

Participants: 44 teachers, grades 5-9 (Year 3)

Structure Intensive: 32 hours Jul-Aug, 28 hours Sep-May Coaching: 20 hours per teacher Aug-June

Partners: Santa Clara Unified, Campbell Union, and San Jose State University

Participants: 44 teachers, grades 5-9 (Year 3)

Structure Intensive: 32 hours Jul-Aug, 28 hours Sep-May Coaching: 20 hours per teacher Aug-June

LEARN ING GOAL: MATHEMAT ICAL PROFICIENCY

(Adding it Up: Helping [P- 8] Children Learn Mathematics, 2001)

COMPLEMENTARY INSTRUCTIONAL METHOD:

CONCRETE REPRESENTATIONAL ABSTRACT

Institute Activities - RatesInstitute Activities - Rates

Activity: Wind-up Toy Races Group Report: Rates and Lines Rates in Different Representations Rate Problems in Different Contexts Story Line Matching

Activity: Wind-up Toy Races Group Report: Rates and Lines Rates in Different Representations Rate Problems in Different Contexts Story Line Matching

COMPREHENSIBLE I NPUT makes grade level content accessible and increases students’ ability to think, solve problems,

and engage in mathematics through... •understandable delivery of ideas and information

•purposeful development of both conversational and academic language

Conceptual Understanding, Procedural Competence, and Representational Fluency of Important Ideas

Use of Real Life Paired or Group work Conte xts Use of Concrete Materials Graphic Organizers Use of N ative L anguage Visual Learning Questioning Teaching Vocabulary Scaffolding in Context

Multiple Representations Concrete to Abstract

ADOLESCENT LEARNERS

Thrive in environments that are intellectually and emotionally safe, allow social needs to be met, support abstract ideas with concrete representations, and promote motivation through

relevance, choice and flexibility

Swanson, Whittaker, & Riv era (2007)

Comprehensible Input:Understandable delivery of ideas and information… rate = distance over time

Comprehensible Input:Purposeful development of conversational and academic language…

Develop academic language in context.• rate• time• distance• unit rate• average distance

Practice computation inmeaningful settings.

The race!

Young adolescent learners thrive in environments that are intellectually and emotionally safe, allow social needs to be met, support abstract ideas with concrete representations,and promote motivation through relevance, choice, and flexibility.

Challenging Courses and Curriculum…..From races, to unit rates, to speed as expressed by the slope of the line…Which toy would you choose? Why?

COMPREHENSIBLE I NPUT makes grade level content accessible and increases students’ ability to think, solve problems,

and engage in mathematics through... •understandable delivery of ideas and information

•purposeful development of both conversational and academic language

Conceptual Understanding, Procedural Competence, and Representational Fluency of Important Ideas

Use of Real Life Paired or Group work Conte xts Use of Concrete Materials Graphic Organizers Use of N ative L anguage Visual Learning Questioning Teaching Vocabulary Scaffolding in Context

Multiple Representations Concrete to Abstract

ADOLESCENT LEARNERS

Thrive in environments that are intellectually and emotionally safe, allow social needs to be met, support abstract ideas with concrete representations, and promote motivation through

relevance, choice and flexibility

Swanson, Whittaker, & Riv era (2007)

March 2009 Math Resource Assessment Service (MARS) Performance by Treatment and Control

Status and by English Learner Status

March 2009 Math Resource Assessment Service (MARS) Performance by Treatment and Control

Status and by English Learner Status