Mathematics and ESL – Common Ground and Uncommon Solutions By Prabha Betne (from Math) & Carolyn Henner Stanchina (from ESL) LaGuardia Community College, NY 5/7/2005

We are presenting what we have learned from our collaboration on a series of workshops for teachers of mathematics struggling to help English language learners who are, in turn, struggling to pass the Mathematics A Regents examination. Background

Objective We will discuss The parallels between second language and mathematics acquisition and methodology The roles of teachers and the immense challenges facing an education system dealing with approximately 150,000 students who are classified as English Language Learners (15-17% of total enrollment) speaking some 140 languages.

MATH Standards The 1990 revised academic standards for high school graduation requires all students, including English Language Learners, to pass five Regents examinations, including Mathematics, with a score of 65 or above. Simultaneously, the Mathematics Regents has shifted focus from de-contextualized manipulation skills to contextualized problem-solving strategies.

Our Pre-Workshop Questionnaire Results Analysis indicated  Lack of collaboration between ESL and math teachers  Some teachers had developed strategies for addressing the students’ overwhelming linguistic and cultural barriers to learning  Others blamed the students for a lack of critical thinking skills, lack of practice in math, and their “unwillingness to catch up in English reading abilities.”

The Language of Math  Contextualizing math has resulted in the use of culturally-bound concepts which may not be part of the ELL students’ schema knowledge.  Language of math lacks redundancy, therefore, there are few clues to meaning and guessing.

Language of Math (Continued)  In addition to specialized vocabulary, there are long noun phrases, complex collocations, confusing prepositions and cultural differences in the symbolic denotations of mathematical processes.  While certain words designate specific math operations, (“less than” indicates subtraction), the opposite may seem true (as in: Jerry has 8 CD’s. He has 4 less than Mike. How many does Mike have?) (Mike has 8+4)

Language of Math (Continued)  Students map the surface syntax of the problem statements onto their equations. Given the problem, “There are 5 times as many students as professors in the math department. Write an equation that represents this statement,” students typically write 5S=P because they follow the literal word order of the natural language sentence. This brief description of the challenges inherent in solving mathematical word problems mirrors the learning process itself.

Parallels between Second Language and Math Learning Language and mathematics learning are both cognitive processes. They can be understood through a constructivist model in which meaning is derived through a combination of one’s own background knowledge and experience (top- down processing) and one’s ability to process the given task or decode text (bottom-up processing).

Parallels between Second Language and Math Learning (Continued) These two modes are complementary: one can be used to compensate for weakness in the other, but each alone is insufficient in terms of learning and performance. They benefit from the activation of cognitive, meta-cognitive and affective learning strategies. They develop through feedback on top- down and bottom-up processing.

Parallels between Second Language and Math Learning (Continued) Bottom-up processing refers to lower level skills that must be practiced in order to achieve automaticity. In mathematics as in language learning, this is associated with memorizing facts and formulas, focusing on discrete elements often without the benefit of comprehension, doing mechanical, de- contextualized arithmetic or grammar drills.

Parallels between Second Language and Math Learning (Continued) Top-down processing refers to higher- order thinking skills. In math, this is revealed in conceptual understanding of structures and patterns, appropriate application of basic arithmetic and algebraic operations and concepts.

Parallels between Second Language and Math Learning (Continued) Similarly, in language learning, Top-down processing translates as the activation and application of appropriate background knowledge to the processing of meaning. Both models imply learning strategy use, self-monitoring, and learning transfer.

Implications for Learning If the students’ initial understandings or preconceptions are not engaged, they may fail to grasp new information and concepts. It is incumbent, then, on the teacher to elicit and interact with students’ prior understandings, to mediate their difficulties so that a restructuring of students’ knowledge may take place.

Uncommon Solutions Trends toward task-based methodology in ESL, as well as a statement in 2000 in the Principles and Standards document published by the National Council of Teachers of Mathematics that “Solving problems is not only a goal of learning mathematics but also a major means of doing so,” represent a call for change.

Uncommon Solutions (Continue) The inductive, problem-based approaches provide a more authentic context for learning which is not separated from doing.  They are more learner-centered and engaging because they provide the window into students’ math and language hypotheses which teachers need in order to skillfully determine the sources of student error and provide feedback at that crucial moment when a meaningful revision of hypotheses is apt to occur.

Uncommon Solutions (Continue)  This approach also lends itself to a focus on writing to learn. Paraphrasing to check one’s comprehension of a word problem, writing to define, explain a concept or demonstrate a procedure for problem-solving, to create word problems, or writing to record learning experiences and insights in a journal, are only some of the ways we can systematically integrate language development and mathematics and enhance the learning of both.

Conclusions We plan to pursue our conversation about the relationship between language and mathematics learning. In particular, we would like to focus on the level of preparedness of mathematics teachers working with ELL students.

Conclusions (Continue) Within this group, there are some teachers who are themselves non-native speakers of English, some who may have limited mathematical knowledge or pedagogical repertoires, and some whose underlying assumptions and beliefs about teaching and student failure may not promote learning. We hope, as well, to be able to continue our conversation with them, to seek further uncommon solutions to the very difficult problems we share.

Thank You