1

ELLs and Secondary Mathematics

Examining the Convergence of Mathematics and

Language

2

Connecting Mathematics and Language

In one word, state what comes to mind for most people when you say

“mathematics.”

3

Connecting Mathematics and Language

Imagine you are a sophomore taking the TAKS and you come upon problem number 14. Solve it and discuss with others at your table.

14) Find the ugloft of a bipkad if the rexnuza is 20.

4

Find the ugloft of a bipkad if the rexnuza is 20.

You look on the information sheet of the TAKS test and see the following:

• ugloft = area

• bipkad = circle

• rexnuza = diameter

Now solve the problem. What made the difference?

5

Kiplinger, Haug, & Abedi (2000)

1) The Kiplinger study investigated and evaluated mathematics ability rather than reading ability on a mathematics test at the 5th grade level.

2) Researchers gave 3 versions of a mathematics test:

– Original English, no changes

– Simplified English version, with changes to linguistic structure and non-math vocabulary

– Original test, with glossary of non-math vocabulary

6

Kiplinger, Haug, & Abedi (2000)

• Students performed at the lowest level on the original English test.

• Students performed better on both the simplified English version and the test with a glossary.

• Conclusion: Academic achievement for ELL students on a mathematics test is directly related to proficiency in reading English.

7

Mathematics and Language

What does the research say?

• You should each have a handout titled Six Key Discoveries in the Research.

• Read the contents of your table’s assigned research summary, then discuss with colleagues at your table, and note one or two key points.

8

Mathematics and Language

Research Summary

• Total isolation of mathematics and language arts

• Learning of vocabulary is part of the learning

• The difficulty of the English language itself

• Mathematical terms are rarely used outside of the mathematics classroom

• Abstract nature of many mathematical terms

• Ambiguity

9

Mathematics and Language

Mathematics and Language

It is not an ELL problem. (ELL students)

It is an ALL problem. (ALL students!)

10

Ambiguity

1) Which is larger?

35 4

11

Ambiguity

2) Which number is larger?

35 4

12

Ambiguity

3) Which numeral is larger?

35 4

13

Ambiguity

• Which is larger?• Which number is larger?• Which numeral is larger?

An example of– how language details are important and – there is ambiguity within mathematics.

14

Difficulties in Addressing Problems in Mathematical Language

• What is a cognate and how is that used as an ELL strategy?

• How could that be used to address teaching the concept of number?

• Based on what you learned previously, would that strategy be enough to address the concept of number for ELL students?

15

Difficulties in Addressing Problems in Mathematical Language

Most dictionaries and texts will not do a good job of clarifying the meaning for teachers.

http://www.teachers.ash.org.au/jeather/maths/dictionary.html

– Defines “numeral” as a symbol used to represent a number

– Defines “digit” as a symbol used to show a number

16

Difficulties in Addressing Problems in Mathematical Language

• Mathematical language is usually slighted in state standards.

http://www.tea.state.tx.us/rules/tac/chapter111/index.html

• A search (using the “find” feature) in the on-line TEKS for “numeral” yielded no occurrences.