There have been many efforts to measure pedagogical content knowledge with multiple-choice survey instruments, but little is known about how different types of items contribute. In this study, we examined interviews with 9 Grade 4 teachers to develop a deeper understanding of how teachers select pedagogical representations in the context of a…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

Although cooperative learning is an effective instructional method, it cannot be taken for granted that students will gain new knowledge when engaging in a cooperative activity. Even if cooperative learning is effectively designed, problems might arise regarding cognitive, behavioral and motivational aspects of learning. For students to gain…

In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the…

Educators and several national standards highlight the role that problem solving should play in students' mathematics education: problem solving is recognized as one of the most significant activities of doing mathematics. From the research point of view, nowadays, it is well established that cognitive and affective factors come into play in…

Literature that investigates the factors underlying arithmetic problem-solving achievement extensively evaluates the cognitive components, such as working memory (WM) and processing speed, at the basis of this acquisition. Recently, studies have shown that also the emotional factors, such as math anxiety (MA), could play a crucial role in the…

The "Next Generation Science Standards" framework outlines scientific and engineering practices as a key element of student development. Educators are just beginning to discover effective and meaningful ways to teach science content to students with intellectual disability; however, the literature on teaching science practices is still…

Owing to the popularity of tablet computers and smart phones, e-books have become an important medium for both formal and informal learning. However, conventional e-books are mainly designed to provide information in the form of multimedia, implying that students spend most of their time memorizing and comprehending what they read from e-books,…

In this exploratory study, we documented teachers' knowledge of children's mathematical thinking as they engaged in the task of anticipating children's strategies for an equal sharing fraction problem. To elicit an array of knowledge, 18 teachers were deliberately selected with a variety of numbers of years participating in professional…

This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer…

Little to no information exists explaining the nature of conceptual gaps in understanding fractions for students with learning disabilities (LD); such information is vital to practitioners seeking to develop instruction or interventions. Many researchers argue such knowledge can be revealed through student's problem-solving strategies. Despite…

Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school…

The objectives of this research were to study and analyze the characteristics of computational thinking about the estimation of the students in mathematics classroom applying lesson study and open approach. Members of target group included 4th grade students of 2011 academic year of Choomchon Banchonnabot School. The Lesson plan used for data…

Over the course of her teaching career, this author learned to create environments in which both the teacher and learners embrace understanding. She introduced new concepts with a general question or word problem and encouraged students to find solutions with a strategy of their choice. By using this instructional method, she allowed her students…