The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

Background: Internationally, the teaching of division has noted that the use of sharing situations with sharing actions (one-by-one distribution) is the predominant division model at the beginning of schooling. In South Africa, research suggests a sharing situation with sharing actions is also preferred in the early grades. Aim: This paper aims to…

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional…

Nat Banting, argues that the "invert and multiply" algorithm for division of fractions is, in fact, not an algorithm. He suggests that Liping Ma's (1999) algorithm, which involves writing the fractions with a common denominator and then dividing the numerator of the first fraction by the numerator of the second fraction, is better as it…

Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students' understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related…

There is evidence that student attitudes towards mathematics become more negative as students move through their schooling. However, less is known about the different factors that shape student attitudes at various stages. This qualitative study sought to shed light on this issue and consider how stage of schooling influenced self-perceived…

Students' difficulties understanding the meaning of logarithms could stem in part from differences between teachers' and students' views of them. The purpose of this article is to unpack some specialized content knowledge for teaching logarithms. The author discusses the history of logarithms to show why they can be understood as repeated…

Recently a team of third- and fourth-grade teachers tested instructional ideas on the topic of division with remainders (DWR) using lesson study. The Common Core State Standards for Mathematics give little attention to the concept of the remainder, specifying only that students are to solve problems for which remainders must be interpreted (NGA…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

The purpose of this study is to explore preservice teachers' (PTs') ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher…

Mathematics is still viewed as a culture-free subject. This forms a negative perception for students on mathematics. Most students assume that mathematics and culture are not related. This may occur because mathematics taught in school is not contextual and far from the reality of everyday life. Historically, mathematics has become a part of daily…

Mathematics is a particularly notable domain in which to understand the role of body movement for improving reasoning, instruction, and learning. One reason is that mathematics ideas are often expressed and taught through disembodied formalisms--diagrams and symbols that are culturally designed to be abstract, amodal, and arbitrary (Glenberg et…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…