ABN (Abierto Basado en Números--Open Calculation Based on Numbers) is a method for teaching basic arithmetic operations in primary education that has become popular in recent years and that is based on the decomposition of numbers through manipulative materials that encourage mental calculation. Currently there is limited number of tools that can…

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…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

According to the views of social constructivism, learning takes place when individuals engage socially to talk about and act on shared problems or interests. In recent years, this approach has been very popular for the teaching and learning of mathematics in primary and secondary education. On the contrary, in tertiary education, it seems that…

The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

Error analysis performed on data sets revealed that seventh grade students used a variety of rules of operation for solving the signed-number arithmetic problems. The data sets were obtained from an experimental study in which students were randomly assigned to study either of two lessons written on a computer based education system. The two…

This study investigated the effect on teachers of observing or implementing an alternative form of instruction in a primary-grade arithmetic class. Under consideration were the relationships between the beliefs teachers held about mathematics and about teaching mathematics, and their recognition and internalization of the principles of the…

This practicum investigated the effectiveness of using music activities to reinforce basic money skills with 10 students, ages 12 to 21, with mental retardation in the trainable range. The program used a combination of music and visual aids as strategies for reinforcing basic money skills and improving student on-task behaviors in the classroom.…

The Calculators and Mathematics Project, Los Angeles (CAMP-LA), funded by the National Science Foundation for developing use of technology in the classroom, developed curriculum materials focused solely on the use of calculators in three stages. The first stage studied the mathematics curricula from different states and identified topics that are…