Mathematics Knowledge for Teaching English Learners

Mark Driscoll, Education Development CenterKristen Malzahn, Horizon Research, Inc.

TDG Leadership SeminarFebruary 2011

“For ELLs to succeed in learning mathematics, they need to be more productive in mathematics classrooms—reasoning more, speaking more, writing more, drawing more.”

Maria SantosFormer Director, NYC OELL

Critical Question

What knowledge do (middle grades) teachers of mathematics need in order to support English Language Learners in becoming more productive and successful in mathematics classrooms?

Needed:

Knowledge new to many mathematics teachers—e.g., about policy, language development and cultural influences—is necessary

This new knowledge is necessary, but not sufficient

Also needed is a better marshaling of knowledge that drives good mathematics pedagogy

Session Goals

Explore a mathematics problem together

Discuss 3 instructional principles as framework for planning, implementing, and reflecting on lessons involving ELLs

View classroom video

Discuss instructional tools related to 3 principles

Reflect on relevance of the information and tools to your own practice

Projects

ELL-Focused Mathematics Coaching (EDC and Lawrence Hall of Science: NYC Office of English Language Learners)

Fostering Mathematics Success of ELLs (EDC and Horizon Research: National Science Foundation: DRL -0821950)

Investigating Area Problem(30 minutes)

At your tables, work on the Investigating Area problem.

Use any of the materials in the center of your table.

Discuss questions; prepare a response to assigned question for share out

Investigating Area: Discussion

1. If you were going to use this task with ELL students in your classroom, what are some challenges you may encounter when implementing the task?

2. What are some instructional decisions you might consider when planning and implementing this task that would help support ELLs in their mathematical thinking and academic language development?

3. What about this task invites productive thinking/reasoning in ELLs?

Guiding Principles for Shaping Pedagogy

1. Challenging Mathematical Tasks Principle

2. Multimodal Representation Principle

3. Academic Language Principle

Challenging Mathematical Tasks Principle

Silver, E.A. and Stein, M.K. (1996). The QUASAR project: The "revolution of the possible" in mathematics instructional reform in urban middle schools. Urban Education, 30, 476-522.

Brenner, M.E. (1998). Development of mathematical communication in problem solving groups by language minority students. Bilingual Research Journal 22( 2, 3, & 4), 103-128

Multimodal Representation Principle

Ng, S.F. & Lee, K. (2009). The model method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education. 40 (3), 282-313.

Chval, K.B, & Khisty, L. (2009). Latino students, writing, and mathematics: A case study of successful teaching and learning. In R. Barwell (Ed.) Multilingualism in mathematics classrooms:  Global perspectives. (pp. 128-144). Clevedon, UK: Multilingual Matters.

Academic Language Principle

Snow, C., Lawrence, J., & White, C. (2009). Generating knowledge of academic language among urban middle school students. Journal of Research on Educational Effectiveness, 2, 325-344. Also see www.serpinstitute.org/tools-and-resources/word-generation.php

Schleppegrell, M.J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23, 139-159.

Principles have a role in 3 stages

Lesson planning

Lesson implementation

Post-lesson reflection

Examples for Challenging Mathematical Tasks Principle

Planning: How will I introduce the mathematical ideas and challenges in the lesson without lowering the demand?

Implementing: Teacher might question students to extend their thinking and promote sense-making. Student might provide counterexamples and non-examples

Reflecting: What moves uncovered or advanced student mathematical understanding?

Examples for Multimodal Representation Principle

Planning: What opportunities are here for students to use mathematical diagrams, physical models, or technology? What kind of diagrams?

Implementing: Teacher might prompt students to represent reasoning using gestures, written/drawing, technology, concrete objects, mathematical symbols. Student might translate visual representation into verbal description

Reflecting: What evidence of student understanding or misunderstanding appeared in their writing and talking?

Examples for Academic Language Principle

Planning: What academic language will I model? How/when will I model it?

Implementation: Teacher might provide students ample opportunity to read, write and speak about mathematics. Student might self-correct from OE to ME.

Reflecting: What teaching moves promoted/advanced students’ academic language development?

Advantages of ELLs Working on Challenging Mathematics

For the ELL, a chance to show mathematical competence

For the teacher, the student’s efforts can produce much for the student to talk about or write about

Research shows a diet of ‘high demand’ mathematics tasks works for vast majority of students

Common Core Standards of Mathematical Practice

1. 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.

 

Looking for evidence: Video

7th Grade groups working on area task

Teacher goals included: students extending beyond mere formulas to reasoning about area, and more active participation by ELLs

Each student in each group has a card with a shape on it—different from what others in the group have

Small group of four ELLs, all of whom have Mandarin as first language

The Task

Determine 3 different ways tocalculate the area of this [figure].

Guiding Questions

1. What evidence of the three guiding principles can you find in the video?

2. What kind of design decisions, instructional moves, or student actions attributed to/led to this evidence?

3. Did you see any missed opportunities?

Chart the evidence

Document on chart paper evidence (from lesson set-up and video)

you saw for your assigned guiding principle

any missed opportunities related to your assigned principle

Be ready to share 1-2 pieces of evidence and what attributed to that evidence (design decisions/instructional moves)

Julie’s Reflection

Goals/Purposes of lesson students extending beyond mere

formulas to reasoning about area

more active participation by ELLs

Julie’s Reflection

Student evidence of understanding & communication Ivan and Jia Min were both using a good

strategy of enclosing their shape, but then erased their work

Jia Min showed some understanding of area when she said it meant “the boxes inside the triangle”

Jia Min seems more able and comfortable writing the academic language than speaking it

Julie’s Reflection

Aspects of lesson that supported ELLs Used a challenging problem that

elicited productive thinking Allowed for writing, drawing, gesturing

as a prelude to speaking Asked multiple questions of Jia Min to

push on her thinking and use of academic language

Julie’s Reflection

Implications for future lessons How do I continue to create a comfortable

environment in which the ELL students will speak? Perhaps have them write first, then speak.

In what other ways can I support ELLs in understanding the mathematics, developing the academic language to communicate that understanding in writing or orally?

Instructional Tools to Activate Three Guiding Principles

Lesson planning tool

Implementation tool

Reflection tool

Connection to Practice(15 minutes)

Think about and discuss:

What is currently being done in your school/district to support ELLs learn mathematics?

How might these instructional tools be used individually, with a colleague/coach, or in a professional learning community back at your own school/district?

Final Thoughts…

Knowledge of effective mathematics teaching must be tapped

3 key principles Challenging mathematics Multimodal representation Academic language

Principles should guide cycle of instruction