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

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

3. 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

4. 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?

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

6. 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

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

8. 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

9. 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

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

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

12. 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

13. 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

14. 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.

15. 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

16. 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.)

17. 6 Suggestions to Adapt Word Problems While Keeping the Rigor of the Concept

18. 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”

19. 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”

20. 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”

21. 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?”

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

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

24. Interactive Lessons The 5 E’s Engage Explore Explain Elaborate
Evaluate
Source:

25. Engage
Begin with a demonstration that activates prior knowledge.

26. Explore
Provide concrete experience before moving to the abstract.

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

28. 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

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

30. References