A Co-Teaching Partnership:Creating a Math Universal

Renee Abramson – ESL Teacher

Co-Teaching Partnership Incorporates:

Willing to try new methods of instruction. Open-minded and optimistic. Resourceful, flexible, and able and willing to

communicate effectively. Not offended by constructive criticism. A true partnership with no subordinate role.

When team teaching is organized and carried out effectively, positive effects are felt by students,

parents and school faculty.

Responsibilities

Joint responsibility for course content, presentations, and grading.

Interaction in front of the class; discussing specific topics from divergent perspectives. Includes planned and spontaneous role play.

The Math teacher focuses on the language of math and the ELL teacher focuses on the difficulties foreseen such as ambiguity that language presents in mathematics.

Research shows that students taught using a team teaching approach have higher levels of

achievement.

Results for English Language Learners

Total classroom integration of ELLs and Native Speakers of English with think/pair/share coupling and mentoring has shown:

The ‘affective filter’ lowered and ELLs take more risks in speaking.

Shortened ‘silent period’ for the ELL.

Acquisition of academic language for the beginning ELL with application to social language. Ex: Putting on a shirt “inverse” rather than ‘reverse’.

Instant friendships within the classroom that extend to outside the classroom- in the halls, cafeteria and outside of school.

MCAS scores across the spectrum for all ELLs appear the same as Native Speakers of English.

MYTH: “The ELLs are holding us back!”

With a co-teaching partnership quite often we observed the opposite.

The Native Speakers of English realize that ELLs are quite capable of success. Integration fosters friendships within and outside of school.

Standardized testing reveals that there is no difference between ELL and Native Speaker regardless of English proficiency as the shift toward fluency is fostered within the integrated classroom.

The scores achieved by the ELL students reflect their ability to pass Math MCAS.

SURPRISE TO US! First year LEP students are passing Math MCAS. First year

LEP students are learning the mathematical technical vocabulary and applying it to social language.

Math symbols and numerals in other languages

Arabic numerals . . . . . . . . .٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ Chinese numerals

Urdu and other languages used by Muslims in India and Pakistan follows the Hindu-Arabic

numeral system

Gurumukhi numerals Used in Punjabi (੦, ੧, ੨, ੩, ੪, ੫, ੬, ੭, ੮, ੯) Bengali numerals used in Bengali and Assamese (০, ১, ২, ৩, ৪, ৫, ৬, ৭, ৮, ৯) Oriya numerals used in Oriya (୦, ୧, ୨, ୩, ୪, ୫, ୬, ୭, ୮, ୯) Tamil numerals used in Tamil (௦, ௧, ௨, ௩, ௪, ௫, ௬, ௭, ௮, ௯) Kannada numerals used in Kannada (೦, ೧, ೨, ೩, ೪, ೫, ೬, ೭, ೮, ೯) Malayalam numerals used in Malayalam (൦, ൧, ൨, ൩, ൪, ൫, ൬, ൭, ൮, ൯) Thai numerals used in Thai (๐, ๑, ๒, ๓, ๔, ๕, ๖, ๗, ๘, ๙)

Also… Beware of Word to Word Dictionary flaws

Word Concept Confusion

Directionality

Figurative Language Behind Math

A ‘Math Universal’ will teach students to participate in their own learning, creating new thinking that will become their new “background information”. They will succeed during testing, real life situations and the rest of their academic education.

In short? Teach students to THINK in Math- a new language!

Respect Think Time

Number calculations occur in L1.

Remember: The Ellis Model of Second Language Acquisition.

INPUT TRANSFERENCE OUTPUT

Students need to receive input, transfer it from L1 to L2- think time- before it processes into output. This takes time.

Not all ELL students are created equal

=

Some read and write above grade level in their own language

Some have had limited schooling Some enter school highly motivated to learn Some have that innate drive to succeed Some have had negative school experiences that

squelched their motivation Some come from middle-class families with high levels of

literacy Some live in poverty without books in their homes Some ELL’s native language is Latin-based and can

recognize English words with the same Latin derivations Some have different language backgrounds with or

without a Romanized alphabet

LanguageAs part of culture, human language has many functions…The most important is communication. 

Language is used for more than communication.  People use language in many ways other than for sharing ideas.

The way people speak can express politeness and respect as well as social position.

People also identify themselves a part of a social group by what language they speak. 

Language can be used to create art, record activities, and guide thinking. 

Mathematics: It all adds upMathematics uses written and spoken symbols

in a way somewhat similar to human language. 

Mathematical symbols do not:

Cover the enormous spectrum of meaning that words do. 

Have the psychological impact that words do. 

HOWEVER…

The language of mathematics is different from that of language. 

Language is used for emotional communication. When you speak, you ultimately want to affect another person's mind.

Mathematics is used mostly for thought and reasoning. 

In other words…

Mathematics affects your own mind.

Myth: English Language Learners can do Math easily because Math is "nonverbal”.

Nothing could be further from the truth.

The lack of proficiency in the academic language of mathematics is one of the reasons that students who appear to be fluent in English still have difficulty in mathematics. Therefore Math is very verbal.

What makes academic language difficult and the last to acquire is the decreased contextual and experimental support or showing how math is used in real life.

Math Grammar: Prepositions6 divided by 12 is 1/2 (or 0.5).

6 divided into 12 is 2.

Why doesn't 6 divided into 12 mean the same thing as 6 divided by 12?

If you divide 6 into 12 equal groups, you get 1/2 in each group.

CLUE WORD CONFUSION …

6 multiplied by 12 is 72. I multiplied.

6 exceeds 12 by 6. I subtracted.

This is one reason why we try not to teach ELLs to use "clue words" to decide what operation to use.

Students benefit from drawing pictures to visualize new concepts.

Lack of correspondence between symbols and the words they represent In a dictation, students are asked to write the

division problem 648 divided by 8. If they write it 648 ÷ 8, they will have no

problems. But when dictated to confusion sets in.

Again, prepositions (that are difficult to acquire, especially languages that have no prepositions) may leave a child at risk to see ‘divides’ rather than ‘divided by’.

It takes ELLs a long time and a lot of practice to learn that they can't write the symbols in the same order in which they hear them.

VocabularyVocabulary is the first thing many people think of when theyfocus on language difficulties that ELLs have in Math class. Suppose an ELL needs to learn least common

multiple. She might come up with something like smallest

frequent multiplication. That won’t help much even if she knows the meaning of the words.

Math must be taught with concrete examples:Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54 It may not help her define the words least common

multiple but will help her conceptualize it.

Background Knowledge Here’s a problem:

A submarine is 285 feet under the surface of the ocean. A helicopter is flying at 4,500 feet above sea level. Given that the helicopter is directly above the submarine, how far apart are they?

Most students can learn submarine and helicopter easily as they quite often are cognates in other languages.

There is no technical math or vocabulary in this…BUT CONSIDER ………

Sea and ocean are used as synonyms; sea level and surface of the ocean refer to the same level.

The term sea level is an abstraction; it can apply to places that are nowhere near the ocean, and places that are below sea level are not literally under water.

The phrase how far apart does not specify horizontal distance or vertical distance; students must interpret the information in under the surface of the ocean and above sea level in order to determine this.

Sea Level (Where’s the sea?) BELOW SEA LEVEL

What do we do about the academic language of Math?

Teach it! Don’t wait for it to be picked up.

Compare it to how it is used in other situations:

Ex: In Math translations mean something different than “translation” in the world of ELL.

Teach how the word is used in different ways. Anticipate.