key issues in teaching fraction, decimal and

8/12/2019 Key Issues in Teaching Fraction, Decimal And

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Key Issues In Teaching

Fraction, Decimal andPercentages


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Key issues in teaching of fractions,

decimals and percentage :

Student related

Teacher related

Environmentally related (Social-economic demands)


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Student related

students should build their understanding of fractions asparts of a whole and as division.

They will need to see and explore a variety of models offractions, focusing primarily on familiar fractions such as

halves, thirds, fourths, fifths, sixths, eights, and tenths. By using an area model in which part of a region is

shaded, students can see how fractions are related to aunit whole, compare fractional parts of a whole, and findequivalent fractions.

They should develop strategies for ordering andcomparing fractions, often using benchmarks such as and 1.


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Student related


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Not seeing decimals as representing part

of a unit quantity

Some children see the decimal point as

separating two whole numbers.

At one extreme, they might see two quiteseparate numbers in one decimal number.

More commonly, children who have not

completely made the decimal-fraction link will

think of two different types of whole numbersmaking up a decimal such as 4.63, (perhaps as

4 whole numbers and 63 of another unit)


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These children will tend to select longer

decimal numbers as larger.

For example, they would pick 4.63 as

larger than 4.8.

*Many of them will be categorised as

whole number thinkers*
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Some students simply consider howmany parts there are in the decimal anddo not consider the size of the parts.

They conclude that 0.621 with 621 partsmust be larger than 0.7, which has only7 parts.

They do not think about what theseparts, or extra bits or remainders etcmight be


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Cognitive difficulties common to

understanding both decimals

and fractions

(i) Coordinating number of parts and sizeof parts of a fraction

Because decimals and fractions are both used todescribe parts of a unit quantity, some of thedifficulties that students show in understanding

fractions are evident in understanding decimals.


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To understand the size of a fraction, thenumerator and the denominator must beconsidered simultaneously. The denominatorindicates the size of the parts into which the

referent whole has been divided and thenumerator indicates how many parts thereare. Not being able to coordinate these twofactors is a major developmental difficulty inunderstanding both fractions and decimals.


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(ii) Partitioning, unitising andreunitising

Partitioning, unitising and reunitising are three cognitiveprocesses that are required for dealing with commonfractions and they also affect students' understanding ofdecimals.

There is general agreement (Behr et al, 1992) that manystudents' difficulties relate to changes in the nature of theunit that they have to deal with.

For example, to find three quarters of 24 counters, thecounters are first thought of as individual units, then the24 counters need to be perceived as a whole so that onequarter can be taken.
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Then three of these new composite unitsneed to be taken to make three quarters.

Decimals present problems especially withre-unitising between tenths andhundredths etc.

For example to see 2 strips of a 100square as representing

20 hundredths of one unit OR

2 tenths of one unit OR 0.2 or 0.20 of one unit

requires several cognitive steps.


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The initial counting unitsare the small squares

Two different composite unitsare created fromthese - a tenth is a new composite unit made

from a strip of ten small squares and the whole

square is a new composite unit, made of the 100

small squares.

Seeing the square as being composed of 10

strips (each a tenth) requires the idea of a unit-

of-units. Finally to talk about 0.2 of the squaremeans that the square itself is a measure unit.

(Baturo and Cooper, 1997)
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Many young children and some

throughout secondary school do not make

the decimal-fraction link correctly.

Others exhibit the same cognitive

difficulties that are encountered with

fractions in their thinking about decimals.

Fundamental understanding of fractions,

such as dealing with equivalent fractions,is critical to decimals as well.


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Understanding The Relationship

Among Fractions, Decimals,

Percents:

All represent a part of a whole

A fraction is based on the number into which

the whole is divided(the denominator). Thenumerator (the top) is the PART, thedenominator (the bottom) is the WHOLE.

A decimal is based on the number in terms oftenths, hundredths, thousandths, etc.

A percent is based on the number in terms of100.


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TEACHER RELATED

To help students understand decimals, a teacher must first teach them theconcept of the place values.

The concept of place value is the key to our whole number system. Thenumber zero was invented as a symbol to represent nothing, and its role inour number system is to hold place for a value. For example, the number'1000' has three zero place holders. It has no hundreds, no tens, and noones, so 1000 needs three zeros to keep the place.

Moving the decimal increases or decreases the value by a power of 10,meaning each place to the left of the decimal is 10 times the value of theone directly to its right. The order is ones, tens, hundreds, thousands, andso forth.

Our decimal system gives us the flexibility to write numbers as large orsmall as we like. The key to the decimal system is the decimal point.

Anything on the left of the decimal point represents a whole number,anything on the right of the decimal represents less than one (similar to afraction). Going from left to right, the value of each place on the right of thedecimal point is 1/10 the value of the place on the left.


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(A) To ensure that students understand decimal numbers,we should teach

them the meaning of place value by using the language

of tenths, hundredths, thousandths, etc.

(B) The usual way of comparing, for example, 0.45 and 0.6through the routine of add a zero so numbers are thesame size does not require a

knowledge of the size of decimal numbers nor developan understanding of number size and should thereforebe avoided.

(C) The comparison of 0.45 < 0.6 can be understoodthrough the use of verbal descriptions such as: six-

tenths is more than 45 hundredths because45 hundredths has only 4 tenths and whats left is lessthan another tenth.


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Most of the blame on students non-learning of decimalscan be placed squarely on the following two facts:

(i) decimals are mostly taught as a topic independent of

the subject of fractions, and

(ii) no clear and precise definition of a decimal is evergiven.

For example, the preceding commentary implies that tounderstand decimals, it sufffices to concentrate ontenths, hundredths,

thousandths, etc,. of the unit 1, but nowhere does it saywhat a decimal really is. In the learners mind, a decimal

becomes something elusive and ineffable: it issomething one can talk about indirectly, but notsomething one can say outright what it is.


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If teacher cannot say explictly what a

decimal is, then it is not a concept teacher

can expect students to understand.


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General observation that when

mathematical difficulties are not removed

from lessons, discussions of pedagogicalimprovements are meaningless.

Great pedagogy lavished on incorrect

mathematics makes bad education.Students do not learn mathematics when

they are taught incorrect mathematics.

Teachers, content knowledge dictatespedagogy in mathematics education.


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The key issues in teaching fractions is always related topupils inability to master the concepts of fraction.

seeing fraction comprising of two numbers Cannot understand the concept of equality in fraction

Inability to state relationship between numerator anddenominator

Inability to state the conceptual meaning of denominator

and numerator

Students non-learning of decimals may be caused by

There are no clear and precise definition of a decimalnumber given.

Place value and rounding off the decimal numbers arenot emphasized.

Decimals are mostly taught as a topic independent of thesubject of fractions.

key issues in teaching fraction, decimal and

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