Mathematics Teachers Teaching English Language Learners: What Knowledge Do They Need?

1. Mathematics Teachers Teaching English Language Learners: What Knowledge Do They Need? Mark Driscoll, EDC, Inc. Daniel Heck, Horizon Research, Inc. Kathryn Chval, University of Missouri

2. The Challenge • Mathematics teachers of English Language Learners (ELLs) are increasingly expected to help ELLs learn academic language while learning mathematics. • Many are understandingly challenged by this expectation, possibly viewing it as something beyond supporting student learning of mathematics content.

3. Teacher Knowledge • Teachers must develop and draw from numerous knowledge bases to effectively teach mathematics to all their students. • Shulman, 1986; Grossman, 1990; Magnusson, Krajcik, and Borko, 1999; Hill, Ball, and Schilling, 2008 have conceptualized teacher knowledge and developed frameworks for consideration.

4. Outline of Session • Introduction of our work and guiding principles • Analysis of a mathematical task • Discussion of relevant teacher knowledge

5. Kathryn’s CAREER Grant • CAREER: A Study of Strategies and Social Processes that Facilitate the Participation of Latino English Language Learners in Elementary Mathematics Classroom Communities

6. Research Question In what ways and under what contexts do the identified research-based strategies facilitate Latino ELLs’ participation in elementary mathematics classrooms? Influence expectations and norms?

7. Fostering Mathematics Success of English Language Learners (FMSELL) A Collaboration of EDC and Horizon Research, Inc.

8. What led us to link geometry to ELLs: Fostering Geometric Thinking Fostering Geometric Thinking Toolkit Published by Heinemann, Inc.

9. FMSELL Research Questions • Does participation in FGTT increase teachers’ geometric content knowledge? • What effects does teachers’ participation in FGTT have on their attention to students’ thinking and mathematical communication when teachers analyze student work? • What effects does teachers’ participation in FGTT have on instructional practices, especially those known to benefit ELLs? • What impact on ELLs’ problem-solving strategies is evident when teachers participate in FGTT?

10. 3 Guiding Principles • The Challenging Mathematical Tasks Principle • The Multimodal Communication Principle • The Academic Language Principle

11. Principle 1: The Challenging Mathematical Tasks Principle No matter what category ELLs fit into—from students newly arrived in the country and just beginning to learn English, to those who have advanced to “Former Limited English Proficient”—it is both possible and important to engage all these students in regular mathematical work that challenges them to reason, solve problems, conjecture, and convince.

12. Principle 2: The Multimodal Communication Principle Classroom environments that make ample use of multimodal communication—pictures, diagrams, presentations, oral explanations, written explanations, and gestures—afford ELLs the means to express the thinking behind their reasoning and problem solving.

13. Principle 3: The Academic Language Principle In the mathematics classroom, ELLs can learn to express their mathematical thinking and reasoning in precise academic language, provided mathematics teachers work to understand and apply the ways in which language is implicated in the learning of mathematics. In brief, mathematics teachers of ELLs need to recognize that they also are language teachers.

15. The Dissections Problem Fostering Geometric Thinking Toolkit (Published by Heinemann, 2008)

16. The Dissections Problem – Purpose • Explore your own and your colleagues’ geometric thinking • See the principles in action • in particular, we’ll unpack the use of multi-modal communication • Prepare to analyze students’ language and geometric thinking on this problem

17. The Dissections Problem – Plan • (5 min) Begin Exploring Problem 1 Individually. • (15 min) Explore Problem 1 in Small Groups. • If you finish you can move on to Problem 2. • (10 min) Prepare to share convincing mathematical explanations. • Each group will be given instructions about how to share. • (10 min) Share thinking with full group. • (5 min) Debrief use of multi-modal communication and academic language.

18. The Dissections Problem – Sharing • Purpose: • Share and explore geometric thinking • Develop language around convincing mathematical explanations • Consider the affordances of different modes of communication • Directions: • Listen to or watch five different types of geometric thinking presentations • Take notes on the Presentation Notes handout

19. What helped you understand presenters’ geometric thinking?

20. Group Discussion What knowledge do teachers of mathematics need in order to support the learning of ELLs? How do we help preservice and practicing teachers develop this knowledge?

21. What Knowledge is Needed? • Strategies for engaging ELLs in oral and written production in the classroom • Strategies for scaffolding and structuring mathematics tasks to heighten access for ELLs, without watering down the cognitive challenges in the tasks • Strategies for facilitating productive peer interactions • Strategies for negotiating meanings

22. What Knowledge is Needed? • Knowledge of at least some basic ways in which language is implicated in the learning of mathematics—e.g., awareness that words like ‘same’ and ‘any’ underscore the importance of precision in mathematical language, as well as the privileged meaning of some words and phrases in mathematics • Knowledge of how to interpret gestures and other non-verbal modes of expressing mathematical thinking

23. What Knowledge is Needed? • How to assess and interpret oral and written mathematical work by ELLs, to see both evidence of mathematical thinking and evidence related to academic language development. • Mathematical tools—e.g., technology, manipulatives, symbolic representations—for supporting ELLs in mathematical investigations and communication of their thinking