The problems posed and models employed by primary school teachers in subtraction with fractions

Abstract

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.

Students' Hypothetical Learning Trajectory (HLT) in Learning Fraction Division Calculation Operations

“…Fractions are one of the most complex and important mathematics materials in elementary school [1], [2]. Learning mathematics on fraction material is still considered difficult [3], [4], [5], [6]. The difficulty in learning the concept of fractions is because the ability to understand fractions as part of a whole expressed in symbols requires special understanding.…”