Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity…

This article is dedicated to the topic of discovering effective ways of developing students' programming abilities with the means of non-programming disciplines and activities. The authors argue that the process of educating students in programming becomes effective if students participates not only in programming lessons themselves, but also…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

We investigated the effects of proximal grouping of numbers, problem-solving goals to make 100, and prior knowledge on students' solution strategies in an online mathematics game. Logistic regression on 857 problem-level data points from 227 middle-school students showed that students were more likely to use productive solution strategies on…

As a self described lesson collector, author Charles Lovett enjoys gathering "interesting" lessons and teasing them apart to find out what makes them "tick", particularly the pedagogy. He often wonders what decisions the teacher made that generated such an interesting and successful learning environment. Here he describes a…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…

The research examined the calculation methods used by pupils in Grades 3-6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in…

Background: The poor performance of learners in mathematics has long been a matter of concern in South Africa. The Annual National Assessment (ANA) results reveal that the problem starts in the foundation phase with number concepts. Aim: This research sought to ascertain how foundation phase teachers used mathematical resources to teach number…

Problem Statement: Throughout history, many changes have occurred in the field of mathematics education. These changes have also occurred concerning special topics that mathematics educators have constantly been searching. The significance of problem posing in mathematics teaching has increased recently with respect to its contributions to the…

How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve…

Strategies such as reinforcement and stimulus fading have been shown to be effective in the acquisition of skills, particularly for individuals with developmental disabilities. Teleconsultation is a promising service delivery modality to support teachers and staff in the implementation of effective strategies to address the needs of underserved…

This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…