Essentiality of math languageSchool Math, at the general education level can also

be viewed as a language – a simpler but more consistent than the language used in schools as medium of instruction and subject area.

Math as a language is essential for acquiring strong numeracy skills but often ignored by the school system and teachers.

Algorithm and rule method is often used by a large number of teachers

What is a language?Language is…a systematic means of communicating by the use of

sounds, visual or conventional abstract codes or symbols for thinking, reading and writing

a system of words or vocabulary and symbols used in a particular discipline

a grammar consisting of rules and structures of using these symbols

(Each of these components is also found in the language of mathematics)

Special features of math languageMathematical language is rich in symbols, notations,

visual representations which are central to its learning and communication of mathematics as a knowledge area.

Notational expressions, formulas and equations requiring written or spoken explanation

Scope for reading aloud fluently with understanding or information is lost in the translation to words

Vocabulary of mathematics

Like any other study and work area and profession, mathematics has… Technical terminologyWords in general usage having a different and specific

meaning within the subject area, e.g., group, ring, field, category, term, factor, etc.

Notations and symbolsVisual symbols and diagrams or constructionsTypical phrases and expressions

Gap In schools, all written work is done through use of

formulas, symbols and operations but teaching needs to be done with emphasis on the spoken nature of language of mathematics.

However, due to lack of proper training, math teachers and hence students are poor at language of mathematics

Development of mathematics related linguistic capabilities are missing.

Maths teaching seems to involve a form of thinking that has something in common with art and music. - Ford & Peat (1988)

Caution for teachersChildren difficulties in understanding written math

often lie in mathematical language dysfunction. The way mathematics as a language is

communicated in the classroom, students may have poor decoding (reading) skills or expressive or receptive mathematical language difficulties.

Math grammar Numbers represent nouns, while operational signs (+, -, x, / ,=, <, >, etc.) serve as

verbs or verbal phrases.Both components are governed by rules of syntax like

common language as a medium of instruction

Wrong way of teaching early mathTeacher: What is 2X3? …(not even how much)Student: 6

When a student responds with an unconnected single noun answer like “six” it is not stored with its entire fact sentence and has little meaning beyond its discrete value.

No ground is gained toward mental association and automatizing of 2 x 3 = 6 as a meaningful and logically vocalized sentence

In grades one and two: synonymous math sentences Math facts, such as 2 x 4 = 8, may be thought of as math

sentences. Students should be encouraged to speak in complete sentences,

to convey an entire thought, and to develop a consistent rehearsal pattern for the math fact.

4+4=8 ….four plus four equals eight…Two fours are eightAs generalization it is read as: first addend plus second addend

is the sum of two given addends2X4= 8…Two times four equals eightAs a generalization it is read as: multiplicand times multiplier is

the product of two given numbers.Here the the statements use the technical vocabulary of

mathematics

Reading of mathTeacher: Read the mathematical sentence 2X3=6Student: two times three equals six If teacher provides the stimulus and allows the student

to speak the entire sentence, proper ground is gained toward automatizing 2 x 3 = 6 mentally with a stimulus-response pairing.

Avoid parrot mathClearly, the intended meaning of each mathematical

sentence is governed by the same components that affect the accuracy of English sentences.

Is it any wonder why children develop mathematics learning disabilities have some associated difficulty when asked to learn math facts?

If any grammatical element is corrupt, the sentence is not valid and learning is mechanical.

Teacher is teaching ‘parrot mathematics’

Emphasize nouns and verbs of technical language of mathematicsAll human languages have grammatical structures

that distinguish between nouns and verbsthese structures express the distinction between the

objects themselves and the actions carried out by or on the objects or operations.

According to Schwartz (1996), dividing the elements of mathematics into objects (numbers and terms or concept labels) and actions (operations) has significant implications for effectiveness of teaching and learning of mathematics.

Age grade appropriate technical terms and vocabulary10 ones=1 ten= is read as verb : make, equalOne & ten as nouns with tens and ones as plural

Ten ones make one ten (Active voice for forward reading)

One ten is made of 10 ones (Passive voice for backward reading of a symbolic mathematical sentence)

Sudden increase in new technical vocabulary of mathematics after grade 3Revision and revisiting along with moving forward12 X 5=6012 times 5 equals 60 (repeated addition of 5)Twelve of fives equal 60 (direct multiplication, or

use of multiplication table as ‘twelve fives are sixty’)12 into 5 (distributive property of multiplication over

addition..12 is distributed equally into addition facts of five)

Introducing new vocabularymultiplicand X multiplier = product

So…Mathematics is not just about learning to 'get the right

answer‘ rule method. It is also about being able to think and read

mathematically, and then being able to show how you develop students’ abilities reading and thinking mathematics.

Adopting the approach of reading mathematics involves vocalising and interpreting technical text or language, mathematical expressions and diagrams, etc..

Start doing…learn by doing and apply rigour…persist..you will gain better insights in the language of mathematics