This study investigated children's knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was…

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate…

This study explored the relationships between task beliefs about the empty number line (ENL), mathematical ability, gender, and voluntary ENL use in multi-digit subtraction and addition. One hundred twenty-three Dutch third-grade students and nine teachers from six schools participated in this study. The multilevel path analysis showed that task…

Pre-service mathematics teachers' content knowledge is an important issue. Therefore, detailed studies are needed to be conducted on mathematical topics. The study examines preservice elementary mathematics teachers' (PEMTs) special content knowledge (SCK) of integer addition and subtraction in the context of using multiple representations,…

Whereas some evidence exists that math anxiety may interfere with math performance from the very beginning of primary school, no study to date has attempted to investigate whether math anxiety may also interfere with early math learning (i.e., the encoding of new math knowledge) and not only with recalling already mastered contents in test…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…

The aim of this qualitative case study is to investigate prospective mathematics teachers' subject matter knowledge of the underlying concepts of standard and nonstandard algorithms used to solve the problems with whole numbers. Twenty three prospective mathematics teachers enrolled in the Elementary Mathematics Education Program of one of the…

The longitudinal progress of 42 Grade 1 students who participated in a 10-20 week Extending Mathematical Understanding (EMU) intervention program was examined to evaluate the effectiveness of the program for enhancing and accelerating mathematics learning. Overall the students made accelerated progress during Grade 1 and their learning was…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously…

The "Extending Mathematical Understanding" (EMU) Program is a specialised mathematics program that aims to accelerate the learning of Grade 1 students who struggle with learning school mathematics. Forty-two students participated in an EMU Program in 2010 as part of the "Bridging the Numeracy Gap" (BTNG) project. Analysis of…