What do ELLs Need Differently in Math Timothy Sims June 15, 2008

Myths Math is a universal language. Math is easy for ELLS. Math is culture free.

Math as a Language Math has its own grammar, syntax, writing system, etc. Consider the different ways in which we view language: Oral, Written, Pictorial, Symbolic Additionally, we use common words differently in math. i.e. root, function, right (angle), product

Analyze the Problem What context clues are needed to understand the problem? What math concepts are key to understanding the problem? Who may not have the background experiences to understand the problem?

Problem 1: The Laundry Problem Sandy’s family does its laundry at a coin-operated Laundromat. It costs $1.25 per load to use the washing machines and 25¢ per load to use the dryers for 10 minutes. Sandy’s family has 5 loads of laundry to do and each load will need to be in a dryer for 30 minutes. Which expression will give Sandy’s family the total cost of doing these loads of laundry? A. ($1.25 + $0.25) × 3 × 5 B. [$1.25 + (3 × $0.25)] × 5 C. [(3 × $1.25) + $0.25] × 5 D. 3 × ($1.25 + $0.25) × 5

In order for ELLs to be successful in math they need competence in: The Grammar of Math Discourse of Math Cultural Context of the Problems Strategic Competence

Think of a biker bar…. Is it enough to know the parts of a motorcycle to fit in?

Grammatical Competence Vocabulary Everyday words with new specific meanings Transference, table, mesa, tabla Multiple ways to convey one concept Syntax Reading may be required in all directions Comma vs decimal point

Discourse Competence Language Functions Juan bought 20 marbles and gave Tom 5 and Mary 10. How many marbles does Juan have? Directive vs Representative Function

Sociolinguistic Competence Having the cultural experience that goes with the linguistic expression to enable comprehension. The Laundromat

Strategic Competence Ability to decode the mathematical message. L1 to L2 transfer?

Mathematical Knowledge and Behaviors for Success Cognitive Resources (facts, concepts algorithms) Heuristics (General strategies used in problem solving) Control Process (moniter and regulate—metacognition) Belief System

Cognitive Resources Recommendations Allow use of native-language to make sense of communicaiton. Cooperative learning Use second language learning techniques Provide practice/rehearsal Semantic organizers/concept maps Cloze exercises Personal bilingual dictionaries

Heuristics Recommendations Promote multiple sources and forms of the same message. Manipulatives, Pictures and Kinesthetic tools Body language, picture and objects used to present the problem.

Control Process Develop metacognitive learning strategies Three step process Develop a plan Evaluate the plan Describe the strategy and evaluate the process Think Alouds Passing Strategic Expertise

Belief System Recommendations Develop Oral, Reading and Writing skills in English. Questioning—main idea, supporting detail Design activities that require interpretation of reading (small chunks). Ask students to read and interpret pictures, graphs, other text. Provide opportunities for oral practice in reading formulas etc. Engage in language activities (i.e. create word problems.)

6 Suggestions to Adapt Word Problems While Keeping the Rigor of the Concept

Suggestion 1 Familiarity or frequency of non-math vocabulary—change unfamiliar or infrequent words. For example change “a certain reference file” To “Mack’s Company”

Suggestion 2 Voice or verb phrase—Change passive verbs to active For example change “If a marble is taken from the bag” To “If you take a marble from the bag”

Suggestion 3 Replace conditional clauses with separate sentences For example change “If two batteries in the sample were found to be dead” To “He found three skateboards in the sample”

Suggestion 4 Remove or reword relative clauses For example change “The total number of newspaper that delivers in 5 days” To “How many newspapers does he deliver in 5 days?”

Suggestion 5 Change complex questions to simple ones. For example change “Which is the best approximation of the number” To “Approximately how many”

Suggestion 6 Make abstract or impersonal presentations more concrete. For example change “2,675 ratios sold” To “2,675 ratios that Mrs. Jones sold”

Interactive Lessons The 5 E’s Engage Explore Explain Elaborate Evaluate Source: http://txcc.sedl.org/resources/mell/files/interactive-lessons.html

Engage Begin with a demonstration that activates prior knowledge.

Explore Provide concrete experience before moving to the abstract.

Explain Students explain connections orally Provide Graphic Organizer with key concepts and vocabulary. Create opportunities for speaking and writing

Elaborate Cooperative groups to develop oral language and academic language Explicit and intensive concept/skill instruction Model and provide guided practice Independent practice and paired work to deepen understanding

Evaluate Evaluate responses for content Don’t all Frequent informal comprehension checks Modify Assessments for proficiency

References