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Title of the Experience

Fractional Inequalities

Name of the teacher

Renzi Alessandra

Country where it took place

Italy

School typology

High Secondary School

Thematic Area

Maths

Experience typology

Teaching in class

Type of contact

Direct

Description of the Experience

I want to explain the difficulties I found when I was teaching fractional inequalities! The difficulty that I always find is the following: when the inequality is fractional and the exercise asks to answer when that ratio is minor than zero, some students make the mistake to solve the numerator and the denominator less than zero and in the final graph of the signs they put a positive sign in the chart instead of minus! For example if they have to solve (x-2)/(x-1)<0 some student does this x-2<0 and so x<2, then x-1<0 and so x<1. The second step is to do a chart of signs and they write the opposite signs:

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I think that this thing happens because when the teacher discusses the sign of the numerator and of the denominator, he always asks which is major than zero independently by the sign of the exercise. The teacher does not highlight the fact that, if you want to make the chart of the signs, you must study the sign of expression, you must ask for which value of the variable x the numerator is positive and for which value of the variable the denominator is minor than zero. Usually the teacher asks about the numerator when it is positive and he/she implies to ask when the numerator is minor than zero (x-2>0 and x-1>0). The students are used to do it without thinking to the meaning of what they are doing. So, in my opinion, the first thing that has to be done to overcome this problem is to pay attention to say to pupils that when I begin to solve the inequality I have to ask the sign (whether the positive or the negative one) to the numerator and to the denominator and so I write

x-2 >/< O and so when they will make a chart, they will put the right signs.

1 2

| |

+++++++++++|-----------|----------

+++++++++++|+++++++++++|----------

| |

I think that this thing happens because when the teacher discusses the sign of the numerator and of the denominator, he always asks which is major than zero independently by the sign of the exercise. The teacher does not highlight the fact that, if you want to make the chart of the signs, you must study the sign of expression, you must ask for which value of the variable x the numerator is positive and for which value of the variable the denominator is minor than zero. Usually the teacher asks about the numerator when it is positive and he/she implies to ask when the numerator is minor than zero (x-2>0 and x-1>0). The students are used to do it without thinking to the meaning of what they are doing. So, in my opinion, the first thing that has to be done to overcome this problem is to pay attention to say to pupils that when I begin to solve the inequality I have to ask the sign (whether the positive or the negative one) to the numerator and to the denominator and so I write

x-2 >/< O and so when they will make a chart, they will put the right signs.

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