SUBTRACTION OF FRACTIONS

Educational Research and Reviews, 2017

Students have difficulties in solving problems of fractions in almost all levels, and in problem posing. Problem posing skills influence the process of development of the behaviors observed at the level of comprehension. That is why it is very crucial for teachers to develop activities for student to have conceptual comprehension of fractions and operations involving fractions. The achievement of such conceptual comprehension can be accelerated through the use of mathematical models. For this, the aim of the study is to identify the errors in the problems posed by primary school teachers with respect to subtractions with fractions, and the models they employ to solve these problems. The present study employs both quantitative and qualitative methods together. This study was carried out with 31 primary school teachers. The teachers involved in the study were selected through random sampling. The study employs the "Problem Posing Test" comprising four items of subtractions with fractions. The test drawn up with reference to the operation of subtraction with fractions includes one item for each: subtracting a proper fraction from another proper fraction, and subtracting a mixed fraction from another mixed fraction. First of all, the answers provided by the teachers were categorized as problem, not-a-problem, or blank. Following such a classification is an analysis of the errors observed in the responses provided in the problem category. At the end, the study reveals that the rate of correct responses offered in the problem category falls as one progresses from item, one where both the minuend and the subtrahend are proper fractions, towards item four where a mixed fraction is subtracted from another mixed fraction. The fact that nine distinct types of errors were observed in the study reveals that the teachers have significant shortcomings when posing problems regarding subtraction with fractions.

Adaptive Reuse: Theoretical Reuse and Design Labs, 2024

Subtraction in architecture seems to be an antinomian entity with respect to a discipline conventionally conceived through its proliferative and additive contribution in the built environment, both in quantitative and qualitative terms. However, every addition is nourished and manifested by its opposite, and it is thanks to the subtractive processes, whether these are designed or derive from endogenous effects, that ultimately allow for the emergence of new disciplinary paradigm.

Human, 2016

Fractions represent the manner of writing parts of whole numbers (integers). Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered, which are essentially related to visualizing operations with fractions.

Procedia - Social and Behavioral Sciences, 2010

Subtraction of fractions involving mixed numbers confuses many pupils because of the many forms of the questions and the many alternative methods of performing the algorithm. The researcher created three formulae to do subtraction of mixed numbers. This study is a priori study to determine the effectiveness of using the three formulae which is called the "Formula Method" in doing subtraction of mixed numbers. The study involved five Year 5 Malaysian Primary school pupils in an urban primary school who were selected from 20 students who sat for a test on subtraction of mixed numbers. The participants for the study were pupils who demonstrated difficulties doing subtraction of mixed numbers. .

2013

Most assessments conducted across the country indicate that the first stumbling block for many children is the subtraction operation, followed by division. On looking more closely we see that the difficulties often arise in subtraction contexts involving double digit or larger numbers. This difficulty is largely caused by three factors: (i) improper understanding of place values (ii) lack of understanding of the rationale behind the formal subtraction procedure, (iii) not seeing the connection between addition facts and subtraction fact

Procedia - Social and Behavioral Sciences, 2010

This paper describes an action research that aimed at improving pupils' performance in doing subtraction with regrouping of 1-digit numbers from 2-digit numbers and 2-digit numbers from 2-digit numbers. This study involved six Year 4 Malaysian Primary school pupils who were selected from 22 pupils who had sat for a test consisting of questions on subtraction without and with regrouping. The six pupils were found to be able to do subtraction without regrouping problems but had difficulties doing subtraction with regrouping problems. The study examines the effectiveness of the method called "Shortcut for Subtraction" in improving pupils' skills in doing subtraction with regrouping problems. The "Shortcut for Subtraction" method was the method used to replace the traditional "borrowing" method which was used initially to teach the pupils to do subtraction with regrouping.

Majority teachers who explore students' understanding and operations with fractions agree that, "…many students understanding of fractions is characterized by a knowledge of rote procedures which are often incorrect, rather than by the concepts underlying the procedures." Students in my study who could memorize these 'magical procedures' in fact could produce brilliant answers but could not reason out even a very simple fraction problem or sometimes gave answers that contradicted with each other. This kind of understanding is not only present amongst the young students but also amongst the older students. Specifically this study focuses on the understanding of fraction concepts. The sample is made up of three groups of students: 66 primary school students, 67 secondary school students and 57 undergraduate students. This study employed quantitative as well as qualitative research methods. The quantitative data was collected from an administered short test consisting of 20 open-ended questions. The data was then analysed and issues that emerged were probed through a semi-structured clinical interview with selected subjects. This paper compares the work done by students age 12, 16 and 20 years old on the same problems designed to reveal the richness of their understandings.