In this article, we present a coding framework based on simultaneity and connections. The coding focuses on microlevel attention to three aspects of simultaneity and connections: between representations, within examples, and between examples. Criteria for coding that we viewed as mathematically important within part-whole additive relations…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

The editors of Mathematics Teacher appreciate the interest of readers and value the views of those who write in with comments. The editors ask that name and affiliation including email address be provided at the end of their letters. This September 2016 Reader Reflections, provides reader comments on the following articles: (1) "Innocent…

According to the latest news about declining standards in mathematics learning in Australia, boys, and girls, in particular, need to be more engaged in mathematics learning. Only 30% of mathematics students at university level in Australia are female. Proofs are made up of words and mathematical symbols. One can assume the words would assist…

A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was…

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…

Despite reports of mathematical talent in autism spectrum disorders (ASD), little is known about basic number processing abilities in affected children. We investigated number sense, the ability to rapidly assess quantity information, in 36 children with ASD and 61 typically developing controls. Numerical acuity was assessed using symbolic (Arabic…

Teachers come across errors not only in tests but also in their mathematics classrooms virtually every day. When they respond to learners' errors in their classrooms, during or after teaching, teachers are actively carrying out formative assessment. In South Africa the Annual National Assessment, a written test under the auspices of the Department…

The "Building a System of Tens Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific mathematical…

This study investigated the differences in conceptions of variable among the groups of students identified as having a mathematics learning disability (MLD), other low mathematics achievement (LMA) students and typical mathematics achievement (TMA) students. This was done by analyzing the responses of these students on items involving the…

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in…

This study begins by connecting semantic elaboration with conceptual understanding and syntactic elaboration with procedural understanding in the context of fractions. Through case studies and discourse analysis, the work and communication of students in fourth through sixth grade is analyzed to determine the extent of their semantic and syntactic…

This article explores the curriculum integration of two learning areas: mathematics and music. We review the literature around effective integration and describe what integration might look like within a primary classroom. Integrating learning areas provide students with the opportunity to encounter key ideas/concepts in a variety of contexts.…

Several studies have investigated children's engagement with repeating pattern tasks, but few have related to patterns with ABA as the minimal unit of repeat. This study focuses on identifying intuitive characteristics of children's work as they engage with repeating pattern tasks of different structures, focusing on the differences between ABA…